Document1

Solutions Guide: Please reword the answers to essay type parts so as to guarantee that your answer is an original. Do not submit as is

1.Gruner Company produces golf discs which it normally sells to retailers for $7 each. The cost of manufacturing 20,000 golf discs is:

Materials $ 10,000 Labor 30,000 Variables overhead 20,000 Fixed overhead 40,000

Total 100,000

Gruner also incurs 5% sales commission ($0.35) on each disc sold. Travis Corporation offers Guner $4.75 per disc for 5,000 discs. Travis would sell the discs under its own brand name in foreign market not yet serves by Gruner. If Gruner accepts the offer, its fixed overhead will increase from $40,000 to $45,000 due to the purchase of a new imprinting machine. No sales commission will result from the special order.

a. Prepare an incremental analysis for the special order.b. Should Gruner accept the special order? Why or Why not?c. What assumptions underlie the decision made in part (b)

(a) RejectOrder

AcceptOrder Net Income Effect

RevenuesMaterials ($0.50)Labor ($1.50)Variable overhead ($1.00)Fixed overheadSales commissionsNet income

$ -0- -0- -0- -0- -0- -0-$ -0-

$23,750 (2,500) (7,500) (5,000) (5,000) -0- $ 3,750

$23,750 (2,500) (7,500) (5,000) (5,000)

-0- $ 3,750

(b) As shown in the incremental analysis, Gruner should accept the special order because incremental revenue exceeds incremental expenses by $3,750.

(c) It is assumed that sales of the golf discs in other markets would not be affected by this special order. If other sales were affected. Gruner would have to consider the lost sales in

Harcourt, Inc. Learning Objectives: 6 - 1

making the decision. Second, if Gruner is operating at full capacity, it is likely that the special order would be rejected.

2. Selleck has recently started the manufacture of RecRobo, a three-wheeled robot that can scan a home for fires and gas leaks and then transmit this information to a mobile phone. The cost structure to manufacture 20,000 RecRobo's is as follows.

Cost Direct materials ($40 per robot) $ 800.00 Direct Labor ($30 per robot) 600,00 Variables overhead ($6 per robot) 120,000 Allocated fixed overhead ($25 per robot) 500,000

Total 2,020,000

Selleck is approached by Padong Inc. , which offer to make RecRobo for $90 per unit or $1,800,000.

a. Using incremental analysis, dertemine whether Selleck should accept this offer under each of the following independent assumptions.(1). Assume that $300.000 of the fixed overhead cost can be reduced (avoided).(2). Assume that none of the fixed overhead can be reduced (avoided). However, if the robots are purchased from Padong Inc., Selleck can use the released productive resources to generate additional income of $300,000.

b. Describe the qualitative factors that might affect the decision to purchase the robot from an outside supplier.

(a) (1)

Make Buy

Net Income Increase

(Decrease) Direct materials $ 800,000 $ -0- $ 800,000Direct labor 600,000 -0- 600,000Variable overhead 120,000 -0- 120,000Fixed overhead 500,000 200,000 300,000

Purchase price 0 1,800,000 (1,800,000)Total annual cost $2,020,000 $2,000,000 $ 20,000

Yes. The offer should be accepted as net income will increase by $20,000.(2)

Make Buy

Net Income Increase

(Decrease) Direct materials $ 800,000 $ 0 $ 800,000Direct labor 600,000 0 600,000Variable overhead 120,000 0 120,000Fixed overhead 500,000 500,000 0Opportunity cost 300,000 0 300,000Purchase price 0 1,800,000 (1,800,000 )

Totals $2,320,000 $2,300,000 $ 20,000

Yes. The offer should be accepted as net income would be $20,000 more.

(b) Qualitative factors include the possibility of laying off those employees that produced the robot and the resulting poor morale of the remaining employees, maintaining quality standards, and controlling the purchase price in the future.

3. Nichols Company makes three models of phasers. Information on the three products is given below.

Stunner Double-Set Mega-Power Sales 300,000 $500,000 $200,000 Variables exp 150,000 200,000 140,000

Contribution marg 150,000 300,000 60,000 Fixed expen 120,000 225,000 90,000 Net income $ 30,000 $ 75,000 $(30,000)

Fixed expenses consist of $300,000 of common costs allocated to the three products based on relative sales, and additional fixed expenses of $30,000 (Stunner), $75,000 (Double-Set), and $30,000 (Mega-Power). The common costs will be incurred regardless of how many models are produced. The other fixed expenses would be eliminated if a model is phased out.

Ralph Port, an executive with the company, feels the Mega-Power line should be discontinued to increase the company's net income.

a. Compute current not income for Nichols Company.b. Compute net income by product line and in total Nichols Company if the company discontinues the Mega-Power product line.( Hint: Allocate the $300,000 common cist to the two remaining product lines based in their relative sales).c. Should Nichols eliminate the Mega-Power product line? Why or Why not?

(a) $30,000 + $75,000 – $30,000 = $75,000

Stunner Double-Set TotalSales $300,000 $500,000 $800,000Variable expenses $150,000 $200,000 $350,000Contribution margin $150,000 $300,000 $450,000Fixed expenses $142,500* $262,500** $405,000Net income $7,500 $37,500 $45,000

*$30,000 + [($300,000 ÷ $800,000) × $300,000]**$75,000 + [($500,000 ÷ $800,000) × $300,000]

(c) As shown in the analysis above, Nichols should not eliminate the Mega-Power product line. Elimination of the line would cause net income to drop from $75,000 to $45,000. The reason for this decrease in net income is that elimination of the product line would result in the loss of $60,000 of contribution margin while saving only $30,000 of fixed expenses.

Accounting problem- Depreciation? On March 31, 2013, the Herzog Company purchased a factory complete with machinery and equipment. The allocation of the total purchase price of $1,020,000 to the various types of assets along with estimated useful lives and residual values are as follows:

Asset Cost Estimated Residual Value Estimated Useful Life in Years Land $ 110,000 N/A N/A Building 520,000 none 25 Machinery 220,000 12% of cost 10

Equipment 170,000 $ 14,000 5

Total $ 1,020,000

On June 29, 2014, machinery included in the March 31, 2013, purchase that cost $102,000 was sold for $82,000. Herzog uses the straight-line depreciation method for buildings and machinery and the sum-of-the-years'-digits method for equipment. Partial-year depreciation is calculated based on the number of months an asset is in service.

On March 31, 2013, the Herzog Company purchased a factory complete with machinery and equipment. The allocation of the total purchase price of $1,080,000 to the various types of assets along with estimated useful lives and residual values are as follows:

Asset CostEstimated Residual

ValueEstimated Useful

Life in Years Land $ 140,000 N/A N/A Building 580,000 none 25 Machinery 160,000 10% of cost 8 Equipment 200,000 $ 14,000 5

Total $ 1,080,000

On June 29, 2014, machinery included in the March 31, 2013, purchase that cost $108,000 was sold for $88,000. Herzog uses the straight-line depreciation method for buildings and machinery and the sum-of-the-years'-digits method for equipment. Partial-year depreciation is calculated based on the number of months an asset is in service.

Required: 1. Compute depreciation expense on the building, machinery, and equipment for 2013. (Do not round intermediate calculations.) Building: $520,000 / 25 years x 9/12 = $15,600 Machinery: [$160,000 - ($160,000 x 10%)] / 8 = $18,000 Equipment:

($200,000 - $14,000) x 5/15* = $62,000 $62,000 x 9/12 = $46,500

*Sum of the digits: [5 x (5 + 1)] / 2 = 15

2. Prepare the journal entry to record the depreciation on the machinery sold on June 29, 2014, and the sale of machinery. (If no entry is required for a transaction, select "No journal entry required" in the first account field.)

Depreciation on the machinery sold on June 29, 2014 Dr Depreciation expense 4,488 Cr Accumulated depreciation--Machinery 4,488

**[$108,000 - ($108,000 x 10%)] / 8 years = $12,150 $12,150 x 6/12 = $6,075

The sale of machinery on June 29, 2014 Dr Cash 88,000 Dr Accumulated depreciation--Machinery 11,220*** Dr Loss on sale of machinery 8,780 Cr Machinery 108,000

***$6,075 x 9/12 = $4,556 $12,15 x 6/12 = $6,075 Total $10,631

3. Compute depreciation expense on the building, remaining machinery, and equipment for 2014. (Do not round intermediate calculations.) Building: $520,000 / 25 years = $20,800

Machinery: [$52,000 - ($52,000 x 10%)] / 10 = $4,680

($160,000 - 108,000 = $52,000)

Equipment: ($200,000 - 14,000) x 5/15 x 3/12 = $15,500 ($200,000 - 14,000) x 4/15 x 9/12 = $37,200 Total $52,700

CHAPTER 11

DECISION MAKING AND RELEVANT INFORMATION

11-16 (20 min.) Disposal of assets.

1. This is an unfortunate situation, yet the $75,000 costs are irrelevant regarding the decision to remachine or scrap. The only relevant factors are the future revenues and future costs. By ignoring the accumulated costs and deciding on the basis of expected future costs, operating income will be maximized (or losses minimized). The difference in favor of remachining is $2,000:

(a) (b)Remachine Scrap

Future revenues $30,000 $3,000Deduct future costs 25,000 – Operating income $ 5,000 $3,000

Difference in favor of remachining $2,000

2. This, too, is an unfortunate situation. But the $100,000 original cost is irrelevant to this decision. The difference in relevant costs in favor of rebuilding is $5,000 as follows:

(a) (b)Replace Rebuild

New truck $105,000 –Deduct current disposal price of existing truck 15,000 –Rebuild existing truck – $85,000

$ 90,000 $85,000

Difference in favor of rebuilding $5,000

Note, here, that the current disposal price of $15,000 is relevant, but the original cost (or book value, if the truck were not brand new) is irrelevant.

11-17 (20 min.) Relevant and irrelevant costs.

1. Make Buy

Relevant costs Variable costs $180 Avoidable fixed costs 20 Purchase price ____ $210 Unit relevant cost $200 $210

Dalton Computers should reject Peach’s offer. The $30 of fixed costs are irrelevant because they will be incurred regardless of this decision. When comparing relevant costs between the choices, Peach’s offer price is higher than the cost to continue to produce.

2.Keep Replace Difference

Cash operating costs (4 years) $80,000 $48,000 $32,000Current disposal value of old machine (2,500) 2,500Cost of new machine ______ 8,000 (8,000) Total relevant costs $80,000 $53,500 $26,500

AP Manufacturing should replace the old machine. The cost savings are far greater than the cost to purchase the new machine.

11-18 (15 min.) Multiple choice.

1. (b) Special order price per unit $6.00Variable manufacturing cost per unit 4.50Contribution margin per unit $1.50

Effect on operating income = $1.50 20,000 units = $30,000 increase

2. (b) Costs of purchases, 20,000 units $60 $1,200,000Total relevant costs of making: Variable manufacturing costs, $64 – $16 $48 Fixed costs eliminated 9 Costs saved by not making $57 Multiply by 20,000 units, so total costs saved are $57 20,000 1,140,000Extra costs of purchasing outside 60,000Minimum overall savings for Reno 25,000Necessary relevant costs that would have to be saved in manufacturing Part No. 575 $ 85,000

11-19 (30 min.) Special order, activity-based costing.

1. Award Plus’ operating income under the alternatives of accepting/rejecting the special order are:

Without One-Time Only

Special Order7,500 Units

With One-Time Only

Special Order10,000 Units

Difference 2,500 Units

Revenues $1,125,000 $1,375,000 $250,000Variable costs:

Direct materials 262,500 350,0001 87,500Direct manufacturing labor 300,000 400,0002 100,000Batch manufacturing costs 75,000 87,5003 12,500

Fixed costs:Fixed manufacturing costs 275,000 275,000 ––Fixed marketing costs 175,000 175,000 ––

Total costs 1,087,500 1,287,500 200,000Operating income $ 37,500 $ 87,500 $ 50,000

1 10,000 2 10,000 3$75,000 + (25 $500)

Alternatively, we could calculate the incremental revenue and the incremental costs of the additional 2,500 units as follows:

Incremental revenue $100 2,500 $250,000

Incremental direct manufacturing costs 2,500 87,500

Incremental direct manufacturing costs 2,500 100,000

Incremental batch manufacturing costs $500 25 12,500Total incremental costs 200,000Total incremental operating income from accepting the special order $ 50,000

Award Plus should accept the one-time-only special order if it has no long-term implications because accepting the order increases Award Plus’ operating income by $50,000.

If, however, accepting the special order would cause the regular customers to be dissatisfied or to demand lower prices, then Award Plus will have to trade off the $50,000 gain from accepting the special order against the operating income it might lose from regular customers.

2. Award Plus has a capacity of 9,000 medals. Therefore, if it accepts the special one-time order of 2,500 medals, it can sell only 6,500 medals instead of the 7,500 medals that it currently sells to existing customers. That is, by accepting the special order, Award Plus must forgo sales of 1,000 medals to its regular customers. Alternatively, Award Plus can reject the special order and continue to sell 7,500 medals to its regular customers.

Award Plus’ operating income from selling 6,500 medals to regular customers and 2,500 medals under one-time special order follow:

Revenues (6,500 $150) + (2,500 $100) $1,225,000Direct materials (6,500 $351) + (2,500 $351) 315,000Direct manufacturing labor (6,500 $402) +(2,500 $402) 360,000Batch manufacturing costs (1303 $500) + (25 $500) 77,500Fixed manufacturing costs 275,000Fixed marketing costs 175,000Total costs 1,202,500Operating income $ 22,500

1$35 = 2$40 =

3Award Plus makes regular medals in batch sizes of 50. To produce 6,500 medals requires 130 (6,500 ÷ 50) batches.

Accepting the special order will result in a decrease in operating income of $15,000 ($37,500 – $22,500). The special order should, therefore, be rejected.

A more direct approach would be to focus on the incremental effects––the benefits of accepting the special order of 2,500 units versus the costs of selling 1,000 fewer units to regular customers. Increase in operating income from the 2,500-unit special order equals $50,000 (requirement 1). The loss in operating income from selling 1,000 fewer units to regular customers equals:

Lost revenue, $150 1,000 $(150,000)Savings in direct materials costs, $35 1,000 35,000Savings in direct manufacturing labor costs, $40 1,000 40,000Savings in batch manufacturing costs, $500 20 10,000Operating income lost $ (65,000)

Accepting the special order will result in a decrease in operating income of $15,000 ($50,000 – $65,000). The special order should, therefore, be rejected.

3. Award Plus should not accept the special order.

Increase in operating income by selling 2,500 units under the special order (requirement 1) $ 50,000Operating income lost from existing customers ($10 7,500) (75,000 ) Net effect on operating income of accepting special order $(25,000)

The special order should, therefore, be rejected.

11-20 (30 min.) Make versus buy, activity-based costing.

1. The expected manufacturing cost per unit of CMCBs in 2009 is as follows:

Total Manufacturing Costs of CMCB

Manufacturing Cost per Unit

(2) = (1) ÷ 10,000Direct materials, $170 10,000Direct manufacturing labor, $45 10,000Variable batch manufacturing costs, $1,500 80Fixed manufacturing costs

Avoidable fixed manufacturing costsUnavoidable fixed manufacturing costs

Total manufacturing costs

$1,700,000450,000120,000

320,000 800,000 $3,390,000

$1704512

32 80 $339

2. The following table identifies the incremental costs in 2009 if Svenson (a) made CMCBs and (b) purchased CMCBs from Minton.

TotalIncremental Costs

Per-UnitIncremental Costs

Incremental Items Make Buy Make BuyCost of purchasing CMCBs from MintonDirect materialsDirect manufacturing laborVariable batch manufacturing costsAvoidable fixed manufacturing costsTotal incremental costs

$1,700,000450,000120,000

320,000 $2,590,000

$3,000,000

$1704512

32 $259

Difference in favor of making $410,000 $41

Note that the opportunity cost of using capacity to make CMCBs is zero since Svenson would keep this capacity idle if it purchases CMCBs from Minton.

Svenson should continue to manufacture the CMCBs internally since the incremental costs to manufacture are $259 per unit compared to the $300 per unit that Minton has quoted. Note that the unavoidable fixed manufacturing costs of $800,000 ($80 per unit) will continue to be incurred whether Svenson makes or buys CMCBs. These are not incremental costs under either the make or the buy alternative and hence, are irrelevant.

3. Svenson should continue to make CMCBs. The simplest way to analyze this problem is to recognize that Svenson would prefer to keep any excess capacity idle rather than use it to make CB3s. Why? Because expected incremental future revenues from CB3s, $2,000,000, are less than expected incremental future costs, $2,150,000. If Svenson keeps its capacity idle, we know from requirement 2 that it should make CMCBs rather than buy them.

An important point to note is that, because Svenson forgoes no contribution by not being able to make and sell CB3s, the opportunity cost of using its facilities to make CMCBs is zero. It is, therefore, not forgoing any profits by using the capacity to manufacture CMCBs. If it does not manufacture CMCBs, rather than lose money on CB3s, Svenson will keep capacity idle.

A longer and more detailed approach is to use the total alternatives or opportunity cost analyses shown in Exhibit 11-7 of the chapter.

Choices for Svenson

Relevant Items

Make CMCBs and Do Not Make CB3s

Buy CMCBs and Do Not Make CB3s

Buy CMCBs and Make

CB3sTOTAL-ALTERNATIVES APPROACH TO MAKE-OR-BUY DECISIONS

Total incremental costs of making/buying CMCBs (from requirement 2)

Excess of future costs over future revenues from CB3s

Total relevant costs

$2,590,000

$3,000,000

150,000

$3,150,000

Svenson will minimize manufacturing costs by making CMCBs.

OPPORTUNITY-COST APPROACH TO MAKE-OR-BUY DECISIONSTotal incremental costs of

making/buying CMCBs (from requirement 2) $2,590,000 $3,000,000 $3,000,000

Opportunity cost: profit contribution forgone because capacity will not be used to make CB3s 0 * 0 * 0

Total relevant costs $2,590,000 $3,000,000 $3,000,000

*Opportunity cost is 0 because Svenson does not give up anything by not making CB3s. Svenson is best off leaving the capacity idle (rather than manufacturing and selling CB3s).

11-21 (10 min.) Inventory decision, opportunity costs.

1. Unit cost, orders of 20,000 $9.00Unit cost, order of 240,000 (0.96 $9.00) $8.64

Alternatives under consideration:(a) Buy 240,000 units at start of year.(b) Buy 20,000 units at start of each month.

Average investment in inventory:(a) (240,000 $8.64) ÷ 2 $1, 036,800(b) ( 20,000 $9.00) ÷ 2 90,000Difference in average investment $ 946,800

Opportunity cost of interest forgone from 240,000-unit purchase at start of year= $946,800 0.10 = $94,680

2. No. The $94,680 is an opportunity cost rather than an incremental or outlay cost. No actual transaction records the $94,680 as an entry in the accounting system.

3. The following table presents the two alternatives:

Alternative A:Purchase 240,000

spark plugs at beginning of

year(1)

Alternative B:Purchase

20,000 spark plugsat beginning

of each month(2)

Difference(3) = (1) – (2)

Annual purchase-order costs(1 $200; 12 $200)

Annual purchase (incremental) costs(240,000 $8.64; 240,000 $9)

Annual interest income that could be earned if investment in inventory were invested (opportunity cost)(10% $1,036,800; 10% $90,000)

Relevant costs

$ 2002,073,600

103,680 $2,177,480

$ 2,4002,160,000

9,000 $2,171,400

$ (2,200)(86,400)

94,680 $ 6,080

Column (3) indicates that purchasing 20,000 spark plugs at the beginning of each month is preferred relative to purchasing 240,000 spark plugs at the beginning of the year because the opportunity cost of holding larger inventory exceeds the lower purchasing and ordering costs. If other incremental benefits of holding lower inventory such as lower insurance, materials handling, storage, obsolescence, and breakage costs were considered, the costs under Alternative A would have been higher, and Alternative B would be preferred even more.

11-22 (20–25 min.) Relevant costs, contribution margin, product emphasis.

Cola Lemonade Punch

NaturalOrangeJuice

Selling price $18.80 $20.00 $27.10 $39.20Deduct variable cost per case 14.20 16.10 20.70 30.20Contribution margin per case $ 4.60 $ 3.90 $ 6.40 $ 9.00

2. The argument fails to recognize that shelf space is the constraining factor. There are only 12 feet of front shelf space to be devoted to drinks. Sexton should aim to get the highest daily contribution margin per foot of front shelf space:

Cola Lemonade Punch

NaturalOrangeJuice

Contribution margin per case $ 4.60 $ 3.90 $ 6.40 $ 9.00Sales (number of cases) per foot

of shelf space per day 25 24 4 5 Daily contribution per foot

of front shelf space $115.00 $93.60 $25.60 $45.00

3. The allocation that maximizes the daily contribution from soft drink sales is:

Daily ContributionFeet of per Foot of Total Contribution

Shelf Space Front Shelf Space Margin per DayCola 6 $115.00 $ 690.00Lemonade 4 93.60 374.40Natural Orange Juice 1 45.00 45.00Punch 1 25.60 25 .60

$1,135 .00

The maximum of six feet of front shelf space will be devoted to Cola because it has the highest contribution margin per unit of the constraining factor. Four feet of front shelf space will be devoted to Lemonade, which has the second highest contribution margin per unit of the constraining factor. No more shelf space can be devoted to Lemonade since each of the remaining two products, Natural Orange Juice and Punch (that have the second lowest and lowest contribution margins per unit of the constraining factor) must each be given at least one foot of front shelf space.

11-23 (10 min.) Selection of most profitable product.

Only Model 14 should be produced. The key to this problem is the relationship of manufacturing overhead to each product. Note that it takes twice as long to produce Model 9; machine-hours for Model 9 are twice that for Model 14. Management should choose the product mix that maximizes operating income for a given production capacity (the scarce resource in this situation). In this case, Model 14 will yield a $9.50 contribution to fixed costs per machine hour, and Model 9 will yield $9.00:

Model 9 Model 14

Selling price Variable costs per unit (total cost – FMOH)Contribution margin per unitRelative use of machine-hours per unit of productContribution margin per machine hour

$100.00 82.00$ 18.00÷ 2$ 9.00

$70.00 60.50$ 9.50÷ 1$ 9.50

11-24 (20 min.) Which base to close, relevant-cost analysis, opportunity costs.

The future outlay operating costs will be $400 million regardless of which base is closed, given the additional $100 million in costs at Everett if Alameda is closed. Further, one of the bases will permanently remain open while the other will be shut down. The only relevant revenue and cost comparisons are

a. $500 million from sale of the Alameda base. Note that the historical cost of building the Alameda base ($100 million) is irrelevant. Note also that future increases in the value of the land at the Alameda base is also irrelevant. One of the bases must be kept open, so if it is decided to keep the Alameda base open, the Defense Department will not be able to sell this land at a future date.

b. $60 million in savings in fixed income note if the Everett base is closed. Again, the historical cost of building the Everett base ($150 million) is irrelevant.

The relevant costs and benefits analysis favors closing the Alameda base despite the objections raised by the California delegation in Congress. The net benefit equals $440 ($500 – $60) million.

11-25 (2530 min.) Closing and opening stores.

1. Solution Exhibit 11-25, Column 1, presents the relevant loss in revenues and the relevant savings in costs from closing the Rhode Island store. Lopez is correct that Sanchez Corporation’s operating income would increase by $7,000 if it closes down the Rhode Island store. Closing down the Rhode Island store results in a loss of revenues of $860,000 but cost savings of $867,000 (from cost of goods sold, rent, labor, utilities, and corporate costs). Note that by closing down the Rhode Island store, Sanchez Corporation will save none of the equipment-related costs because this is a past cost. Also note that the relevant corporate overhead costs are the actual corporate overhead costs $44,000 that Sanchez expects to save by closing the Rhode Island store. The corporate overhead of $40,000 allocated to the Rhode Island store is irrelevant to the analysis.

2. Solution Exhibit 11-25, Column 2, presents the relevant revenues and relevant costs of opening another store like the Rhode Island store. Lopez is correct that opening such a store would increase Sanchez Corporation’s operating income by $11,000. Incremental revenues of $860,000 exceed the incremental costs of $849,000 (from higher cost of goods sold, rent, labor, utilities, and some additional corporate costs). Note that the cost of equipment written off as depreciation is relevant because it is an expected future cost that Sanchez will incur only if it opens the new store. Also note that the relevant corporate overhead costs are the $4,000 of actual corporate overhead costs that Sanchez expects to incur as a result of opening the new store. Sanchez may, in fact, allocate more than $4,000 of corporate overhead to the new store but this allocation is irrelevant to the analysis.

The key reason that Sanchez’s operating income increases either if it closes down the Rhode Island store or if it opens another store like it is the behavior of corporate overhead costs. By closing down the Rhode Island store, Sanchez can significantly reduce corporate overhead costs presumably by reducing the corporate staff that oversees the Rhode Island operation. On the other hand, adding another store like Rhode Island does not increase actual corporate costs by much, presumably because the existing corporate staff will be able to oversee the new store as well.

SOLUTION EXHIBIT 11-25Relevant-Revenue and Relevant-Cost Analysis of Closing Rhode Island Store and Opening Another Store Like It.

Incremental(Loss in Revenues) Revenues and

and Savings in (Incremental Costs)Costs from Closing of Opening New StoreRhode Island Store Like Rhode Island Store

(1) (2)

Revenues $(860,000) $ 860,000Cost of goods sold 660,000 (660,000)Lease rent 75,000 (75,000)Labor costs 42,000 (42,000)Depreciation of equipment 0 (22,000)Utilities (electricity, heating) 46,000 (46,000)

Corporate overhead costs 44,000 (4,000)Total costs 867,000 (849,000 ) Effect on operating income (loss) $ 7,000 $ 11,000

11-26 (20 min.) Choosing customers.

If Broadway accepts the additional business from Kelly, it would take an additional 500 machine-hours. If Broadway accepts all of Kelly’s and Taylor’s business for February, it would require 2,500 machine-hours (1,500 hours for Taylor and 1,000 hours for Kelly). Broadway has only 2,000 hours of machine capacity. It must, therefore, choose how much of the Taylor or Kelly business to accept.

To maximize operating income, Broadway should maximize contribution margin per unit of the constrained resource. (Fixed costs will remain unchanged at $100,000 regardless of the business Broadway chooses to accept in February, and is, therefore, irrelevant.) The contribution margin per unit of the constrained resource for each customer in January is:

Taylor Kelly Corporation Corporation

Contribution margin per machine-hour = $52 = $64

Since the $80,000 of additional Kelly business in February is identical to jobs done in January, it will also have a contribution margin of $64 per machine-hour, which is greater than the contribution margin of $52 per machine-hour from Taylor. To maximize operating income, Broadway should first allocate all the capacity needed to take the Kelly Corporation business (1,000 machine-hours) and then allocate the remaining 1,000 (2,000 – 1,000) machine-hours to Taylor.

Taylor Kelly Corporation Corporation Total Contribution margin per machine-hour $52 $64Machine-hours to be worked 1,000 1,000 Contribution margin $52,000 $64,000 $116,000Fixed costs 100,000Operating income $ 16,000

11-27 (30–40 min.) Relevance of equipment costs.

1a. Statements of Cash Receipts and Disbursements

Keep Buy New Machine

Year 1

EachYear2, 3, 4

FourYears

Together Year 1

EachYear2, 3, 4

Four Years

TogetherReceipts from operations:RevenuesDeduct disbursements:

Other operating costsOperation of machinePurchase of “old” machinePurchase of “new” equipment

Cash inflow from sale of old equipment

Net cash inflow

$150,000

(110,000)

(15,000)(20,000)

$ 5,000

$150,000

(110,000)

(15,000)

25,000

$600,000

(440,000) (60,000) (20,000)

$ 80,000

$150,000

(110,000)

(9,000)(20,000)(24,000)

8,000 $

(5,000 )

$150,000

(110,000)

(9,000)

31,000

$600,000

(440,000) (36,000) (20,000) (24,000)

8,000 $ 88,000

*Some students ignore this item because it is the same for each alternative. However, note that a statement for the entire year has been requested. Obviously, the $20,000 would affect Year 1 only under both the “keep” and “buy” alternatives.

The difference is $8,000 for four years taken together. In particular, note that the $20,000 book value can be omitted from the comparison. Merely cross out the entire line; although the column totals are affected, the net difference is still $8,000.

1b. Again, the difference is $8,000:Income Statements

Keep Buy New MachineEachYear

1, 2, 3, 4

FourYears

Together Year 1

EachYear2, 3, 4

Four Years Together

Revenues Costs (excluding disposal): Other operating costs Depreciation Operating costs of machine Total costs (excluding disposal)Loss on disposal:

Book value (“cost”)Proceeds (“revenue”) Loss on disposal

Total costsOperating income

$150,000

110,000 5,000 15,000 130,000

130,000 $ 20,000

$600,000

440,000 20,000 60,000 520,000

520,000 $ 80,000

$150,000

110,000 6,000 9,000 125,000

20,000 (8,000 ) 12,000 137,000 $ 13,000

$150,000

110,000 6,000 9,000 125,000

125,000 $ 25,000

$600,000

440,000 24,000 36,00 0 500,000

20,000*

(8,000 ) 12,000 512,000 $ 88,000

*As in part (1), the $20,000 book value may be omitted from the comparison without changing the $8,000 difference. This adjustment would mean excluding the depreciation item of $5,000 per year (a cumulative effect of $20,000) under the “keep” alternative and excluding the book value item of $20,000 in the loss on disposal computation under the “buy” alternative.

1c. The $20,000 purchase cost of the old equipment, the revenues, and the other operating costs are irrelevant because their amounts are common to both alternatives.

2. The net difference would be unaffected. Any number may be substituted for the original $20,000 figure without changing the final answer. Of course, the net cash outflows under both alternatives would be high. The Auto Wash manager really blundered. However, keeping the old equipment will increase the cost of the blunder to the cumulative tune of $8,000 over the next four years.

3. Book value is irrelevant in decisions about the replacement of equipment, because it is a past (historical) cost. All past costs are down the drain. Nothing can change what has already been spent or what has already happened. The $20,000 has been spent. How it is subsequently accounted for is irrelevant. The analysis in requirement (1) clearly shows that we may completely ignore the $20,000 and still have a correct analysis. The only relevant items are those expected future items that will differ among alternatives.

Despite the economic analysis shown here, many managers would keep the old machine rather than replace it. Why? Because, in many organizations, the income statements of part (2) would be a principal means of evaluating performance. Note that the first-year operating income would be higher under the “keep” alternative. The conventional accrual accounting model might motivate managers toward maximizing their first-year reported operating income at the expense of long-run cumulative betterment for the organization as a whole. This criticism is often made of the accrual accounting model. That is, the action favored by the “correct” or “best” economic decision model may not be taken because the performance-evaluation model is either inconsistent with the decision model or because the focus is on only the short-run part of the performance-evaluation model.

There is yet another potential conflict between the decision model and the performance evaluation model. Replacing the machine so soon after it is purchased may reflect badly on the

manager’s capabilities and performance. Why didn’t the manager search and find the new machine before buying the old machine? Replacing the old machine one day later at a loss may make the manager appear incompetent to his or her superiors. If the manager’s bosses have no knowledge of the better machine, the manager may prefer to keep the existing machine rather than alert his or her bosses about the better machine.

11-28 (30 min.) Equipment upgrade versus replacement.

1. Based on the analysis in the table below, TechMech will be better off by $180,000 over three years if it replaces the current equipment.

Over 3 years Difference Comparing Relevant Costs of Upgrade and Upgrade Replace in favor of Replace Replace Alternatives (1) (2) (3) = (1) – (2)Cash operating costs $140; $80 per desk 6,000 desks per yr. 3 yrs. $2,520,000 $1,440,000 $1,080,000Current disposal price (600,000) 600,000One time capital costs, written off periodically as depreciation 2,700,000 4,200,000 (1,500,000 )Total relevant costs $5,220,000 $5,040,000 $ 180,000

Note that the book value of the current machine ($900,000) would either be written off as depreciation over three years under the upgrade option, or, all at once in the current year under the replace option. Its net effect would be the same in both alternatives: to increase costs by $900,000 over three years, hence it is irrelevant in this analysis.

2. Suppose the capital expenditure to replace the equipment is $X. From requirement 1, column (2), substituting for the one-time capital cost of replacement, the relevant cost of replacing is $1,440,000 – $600,000 + $X. From column (1), the relevant cost of upgrading is $5,220,000. We want to find X such that

$1,440,000 – $600,000 + $X < $5,220,000 (i.e., TechMech will favor replacing)Solving the above inequality gives us X < $5,220,000 – $840,000 = $4,380,000.

TechMech would prefer to replace, rather than upgrade, if the replacement cost of the new equipment does not exceed $4,380,000. Note that this result can also be obtained by taking the original replacement cost of $4,200,000 and adding to it the $180,000 difference in favor of replacement calculated in requirement 1.

3. Suppose the units produced and sold over 3 years equal y. Using data from requirement 1, column (1), the relevant cost of upgrade would be $140y + $2,700,000, and from column (2), the relevant cost of replacing the equipment would be $80y – $600,000 + $4,200,000. TechMech would want to upgrade if

$140y + $2,700,000 < $80y – $600,000 + $4,200,000$60y < $900,000

y < $900,000 $60 = 15,000 units

or upgrade when y < 15,000 units (or 5,000 per year for 3 years) and replace when y > 15,000 units over 3 years.

When production and sales volume is low (less than 5,000 per year), the higher operating costs under the upgrade option are more than offset by the savings in capital costs from

upgrading. When production and sales volume is high, the higher capital costs of replacement are more than offset by the savings in operating costs in the replace option.

4. Operating income for the first year under the upgrade and replace alternatives are shown below:

Year 1 Upgrade Replace (1) (2)Revenues (6,000 $500) $3,000,000 $3,000,000Cash operating costs $140; $80 per desk 6,000 desks per year 840,000 480,000Depreciation ($900,000a + $2,700,000) 3; $4,200,000 3 1,200,000 1,400,000Loss on disposal of old equipment (0; $900,000 – $600,000) 0 300,000 Total costs 2,040,000 2,180,000 Operating Income $ 960,000 $ 820,000

aThe book value of the current production equipment is $1,500,000 3 5 = $900,000; it has a remaining useful life of 3 years.

First-year operating income is higher by $140,000 under the upgrade alternative, and Dan Doria, with his one-year horizon and operating income-based bonus, will choose the upgrade alternative, even though, as seen in requirement 1, the replace alternative is better in the long run for TechMech. This exercise illustrates the possible conflict between the decision model and the performance evaluation model.

11-29 (20 min.) Special Order.

1. Revenues from special order ($25 10,000 bats) $250,000Variable manufacturing costs ($161 10,000 bats) (160,000)Increase in operating income if Ripkin order accepted $ 90,000

Louisville should accept Ripkin’s special order because it increases operating income by $90,000. Since no variable selling costs will be incurred on this order, this cost is irrelevant. Similarly, fixed costs are irrelevant because they will be incurred regardless of the decision.

2a. Revenues from special order ($25 10,000 bats) $250,000 Variable manufacturing costs ($16 10,000 bats) (160,000) Contribution margin foregone ([$32─$181] 10,000 bats) (140,000) Decrease in operating income if Ripkin order accepted $ (50,000)1

Based strictly on financial considerations, Louisville should reject Ripkin’s special order because it results in a $50,000 reduction in operating income.

2b. Louisville will be indifferent between the special order and continuing to sell to regular customers if the special order price is $30. At this price, Louisville recoups the variable manufacturing costs of $160,000 and the contribution margin given up from regular customers of $140,000 ([$160,000 + $140,000] ÷ 10,000 units = $30). Looked at a different way, Louisville expects the full price of $32 less the $2 saved on variable selling costs.

2c. Louisville may be willing to accept a loss on this special order if the possibility of future long-term sales seem likely. However, Louisville should also consider the effect on customer relationships by refusing sales from existing customers. Also, Louisville cannot afford to adopt the special order price long-term or with other customers who may ask for price concessions.

11-30 (30 min.) Contribution approach, relevant costs.

1. Average one-way fare per passenger $ 500Commission at 8% of $500 (40)Net cash to Air Frisco per ticket $ 460Average number of passengers per flight × 200Revenues per flight ($460 × 200) $ 92,000Food and beverage cost per flight ($20 × 200) 4,000Total contribution margin from passengers per flight $ 88,000

2. If fare is $ 480.00Commission at 8% of $480 (38.40)Net cash per ticket 441.60Food and beverage cost per ticket 20.00Contribution margin per passenger $ 421.60Total contribution margin from passengers per flight

($421.60 × 212) $89,379.20All other costs are irrelevant.

On the basis of quantitative factors alone, Air Frisco should decrease its fare to $480 because reducing the fare gives Air Frisco a higher contribution margin from passengers ($89,379.20 versus $88,000).

3. In evaluating whether Air Frisco should charter its plane to Travel International, we compare the charter alternative to the solution in requirement 2 because requirement 2 is preferred to requirement 1.

Under requirement 2, contribution from passengers $89,379.20Deduct fuel costs 14,000.00Total contribution per flight $75,379.20

Air Frisco gets $74,500 per flight from chartering the plane to Travel International. On the basis of quantitative financial factors, Air Frisco is better off not chartering the plane and, instead, lowering its own fares.

Other qualitative factors that Air Frisco should consider in coming to a decision area. The lower risk from chartering its plane relative to the uncertainties regarding the

number of passengers it might get on its scheduled flights.b. The stability of the relationship between Air Frisco and Travel International. If this is

not a long-term arrangement, Air Frisco may lose current market share and not benefit from sustained charter revenues.

11-31 (30 min.) Relevant costs, opportunity costs.

1. Easyspread 2.0 has a higher relevant operating income than Easyspread 1.0. Based on this analysis, Easyspread 2.0 should be introduced immediately:

Easyspread 1.0 Easyspread 2.0 Relevant revenues $160 $195Relevant costs:

Manuals, diskettes, compact discs $ 0 $30Total relevant costs 0 30

Relevant operating income $160 $165

Reasons for other cost items being irrelevant are

Easyspread 1.0 Manuals, diskettes—already incurred Development costs—already incurred Marketing and administrative—fixed costs of period

Easyspread 2.0 Development costs—already incurred Marketing and administration—fixed costs of period

Note that total marketing and administration costs will not change whether Easyspread 2.0 is introduced on July 1, 2009, or on October 1, 2009.

2. Other factors to be considered:a. Customer satisfaction. If 2.0 is significantly better than 1.0 for its customers, a

customer driven organization would immediately introduce it unless other factors offset this bias towards “do what is best for the customer.”

b. Quality level of Easyspread 2.0. It is critical for new software products to be fully debugged. Easyspread 2.0 must be error-free. Consider an immediate release only if 2.0 passes all quality tests and can be fully supported by the salesforce.

c. Importance of being perceived to be a market leader. Being first in the market with a new product can give Basil Software a “first-mover advantage,” e.g., capturing an initial large share of the market that, in itself, causes future potential customers to lean towards purchasing Easyspread 2.0. Moreover, by introducing 2.0 earlier, Basil can get quick feedback from users about ways to further refine the software while its competitors are still working on their own first versions. Moreover, by locking in early customers, Basil may increase the likelihood of these customers also buying future upgrades of Easyspread 2.0.

d. Morale of developers. These are key people at Basil Software. Delaying introduction of a new product can hurt their morale, especially if a competitor then preempts Basil from being viewed as a market leader.

11-32 (20 min.) Opportunity costs.

1. The opportunity cost to Wolverine of producing the 2,000 units of Orangebo is the contribution margin lost on the 2,000 units of Rosebo that would have to be forgone, as computed below:

Selling priceVariable costs per unit: Direct materials Direct manufacturing labor Variable manufacturing overhead Variable marketing costsContribution margin per unit

Contribution margin for 2,000 units

4 11$ 9

$ 18,000

The opportunity cost is $18,000. Opportunity cost is the maximum contribution to operating income that is forgone (rejected) by not using a limited resource in its next-best alternative use.

2. Contribution margin from manufacturing 2,000 units of Orangebo and purchasing 2,000 units of Rosebo from Buckeye is $16,000, as follows:

ManufactureOrangebo

PurchaseRosebo Total

Selling priceVariable costs per unit:

Purchase costsDirect materialsDirect manufacturing laborVariable manufacturing costsVariable marketing overhead

Variable costs per unitContribution margin per unitContribution margin from selling 2,000 units

of Orangebo and 2,000 units of Rosebo

–232

2 9 $ 6

$12,000

4 18 $ 2

$4,000 $16,000

As calculated in requirement 1, Wolverine’s contribution margin from continuing to manufacture 2,000 units of Rosebo is $18,000. Accepting the Miami Company and Buckeye offer will cost Wolverine $2,000 ($16,000 – $18,000). Hence, Wolverine should refuse the Miami Company and Buckeye Corporation’s offers.

3. The minimum price would be $9, the sum of the incremental costs as computed in requirement 2. This follows because, if Wolverine has surplus capacity, the opportunity cost =

$0. For the short-run decision of whether to accept Orangebo’s offer, fixed costs of Wolverine are irrelevant. Only the incremental costs need to be covered for it to be worthwhile for Wolverine to accept the Orangebo offer.11-33 (30–40 min.) Product mix, relevant costs.

R3 HP6Selling price $100 $150Variable manufacturing cost per unit 60 100Variable marketing cost per unit 15 35Total variable costs per unit 75 135Contribution margin per unit $ 25 $ 15

= $25 = $30

Total contribution margin from selling only R3 or only HP6R3: $25 50,000; HP6: $30 50,000 $1,250,000 $1,500,000

Less Lease costs of high-precision machine to produce and sell HP6 300,000Net relevant benefit $1,250,000 $1,200,000

Even though HP6 has the higher contribution margin per unit of the constrained resource, the fact that Pendleton must incur additional costs of $300,000 to achieve this higher contribution margin means that Pendleton is better off using its entire 50,000-hour capacity on the regular machine to produce and sell 50,000 units (50,000 hours 1 hour per unit) of R3. The additional contribution from selling HP6 rather than R3 is $250,000 ($1,500,000 $1,250,000), which is not enough to cover the additional costs of leasing the high-precision machine. Note that, because all other overhead costs are fixed and cannot be changed, they are irrelevant for the decision.

2. If capacity of the regular machines is increased by 15,000 machine-hours to 65,000 machine-hours (50,000 originally + 15,000 new), the net relevant benefit from producing R3 and HP6 is as follows:

R3 HP6

Total contribution margin from selling only R3 or only HP6R3: $25 65,000; HP6: $30 65,000 $1,625,000 $1,950,000Less Lease costs of high-precision machine that would be incurred if HP6 is produced and sold 300,000Less Cost of increasing capacity by 15,000 hours on regular machine 150,000 150,000Net relevant benefit $1,475,000 $1,500,000

Investing in the additional capacity increases Pendleton’s operating income by $250,000 ($1,500,000 calculated in requirement 2 minus $1,250,000 calculated in requirement 1), so Pendleton should add 15,000 hours to the regular machine. With the extra capacity available to it, Pendleton should use its entire capacity to produce HP6. Using all 65,000 hours of capacity to produce HP6 rather than to produce R3 generates additional contribution margin of $325,000 ($1,950,000 $1,625,000) which is more than the additional cost of $300,000 to lease the high-precision machine. Pendleton should therefore produce and sell 130,000 units of HP6 (65,000 hours 0.5 hours per unit of HP6) and zero units of R3.

3.R3 HP6 S3

Selling price $100 $150 $120Variable manufacturing costs per unit 60 100 70Variable marketing costs per unit 15 35 15Total variable costs per unit 75 135 85Contribution margin per unit $ 25 $ 15 $ 35

= $25 = $30 = $35

The first step is to compare the operating profits that Pendleton could earn if it accepted the Carter Corporation offer for 20,000 units with the operating profits Pendleton is currently earning. S3 has the highest contribution margin per hour on the regular machine and requires no additional investment such as leasing a high-precision machine. To produce the 20,000 units of S3 requested by Carter Corporation, Pendleton would require 20,000 hours on the regular machine resulting in contribution margin of $35 20,000 = $700,000.

Pendleton now has 45,000 hours available on the regular machine to produce R3 or HP6.

R3 HP6

Total contribution margin from selling only R3 or only HP6 R3: $25 45,000; HP6: $30 45,000 $1,125,000 $1,350,000Less Lease costs of high-precision machine to produce and sell HP 6 300,000Net relevant benefit $1,125,000 $1,050,000

Pendleton should use all the 45,000 hours of available capacity to produce 45,000 units of R3. Thus, the product mix that maximizes operating income is 20,000 units of S3, 45,000 units of R3, and zero units of HP6. This optimal mix results in a contribution margin of $1,825,000 ($700,000 from S3 and $1,125,000 from R3). Relative to requirement 2, operating income increases by $325,000 ($1,825,000 minus $1,500,000 calculated in requirement 2). Hence, Pendleton should accept the Carter Corporation business and supply 20,000 units of S3.

11-34 (35–40 min.) Dropping a product line, selling more units.

1. The incremental revenue losses and incremental savings in cost by discontinuing the Tables product line follows:

Difference:Incremental

(Loss in Revenues)and Savings in Costs

from DroppingTables Line

RevenuesDirect materials and direct manufacturing laborDepreciation on equipmentMarketing and distributionGeneral administration Corporate office costsTotal costsOperating income (loss)

$(500,000 )300,000

070,000

0 0 370,000 $(130,000 )

Dropping the Tables product line results in revenue losses of $500,000 and cost savings of $370,000. Hence, Grossman Corporation’s operating income will be $130,000 lower if it drops the Tables line.

Note that, by dropping the Tables product line, Home Furnishings will save none of the depreciation on equipment, general administration costs, and corporate office costs, but it will save variable manufacturing costs and all marketing and distribution costs on the Tables product line.

2. Grossman’s will generate incremental operating income of $128,000 from selling 4,000 additional tables and, hence, should try to increase table sales. The calculations follow:

Incremental Revenues (Costs) and Operating Income Revenues $500,000Direct materials and direct manufacturing labor (300,000)Cost of equipment written off as depreciation (42,000)*

Marketing and distribution costs (30,000)†

General administration costs 0**

Corporate office costs 0**

Operating income $128,000*Note that the additional costs of equipment are relevant future costs for the “selling more tables decision” because they represent incremental future costs that differ between the alternatives of selling and not selling additional tables.†Current marketing and distribution costs which varies with number of shipments = $70,000 – $40,000 = $30,000. As the sales of tables double, the number of shipments will double, resulting in incremental marketing and distribution costs of (2 $30,000) – $30,000 = $30,000.

**General administration and corporate office costs will be unaffected if Grossman decides to sell more tables. Hence, these costs are irrelevant for the decision.

3.Solution Exhibit 11-34, Column 1, presents the relevant loss of revenues and the relevant savings in costs from closing the Northern Division. As the calculations show, Grossman’s operating income would decrease by $140,000 if it shut down the Northern Division (loss in revenues of $1,500,000 versus savings in costs of $1,360,000).Grossman will save variable manufacturing costs, marketing and distribution costs, and division general administration costs by closing the Northern Division but equipment-related depreciation and corporate office allocations are irrelevant to the decision. Equipment-related costs are irrelevant because they are past costs (and the equipment has zero disposal price). Corporate office costs are irrelevant because Grossman will not save any actual corporate office costs by closing the Northern Division. The corporate office costs that used to be allocated to the Northern Division will be allocated to other divisions.

4. Solution Exhibit 11-34, Column 2, presents the relevant revenues and relevant costs of opening the Southern Division (a division whose revenues and costs are expected to be identical to the revenues and costs of the Northern Division). Grossman should open the Southern Division because it would increase operating income by $40,000 (increase in relevant revenues of $1,500,000 and increase in relevant costs of $1,460,000). The relevant costs include direct materials, direct manufacturing labor, marketing and distribution, equipment, and division general administration costs but not corporate office costs. Note, in particular, that the cost of equipment written off as depreciation is relevant because it is an expected future cost that Grossman will incur only if it opens the Southern Division. Corporate office costs are irrelevant because actual corporate office costs will not change if Grossman opens the Southern Division. The current corporate staff will be able to oversee the Southern Division’s operations. Grossman will allocate some corporate office costs to the Southern Division but this allocation represents corporate office costs that are already currently being allocated to some other division. Because actual total corporate office costs do not change, they are irrelevant to the division.

SOLUTION EXHIBIT 11-34Relevant-Revenue and Relevant-Cost Analysis for Closing Northern Division and Opening Southern Division

(Loss in Revenues) and Savings in

Costs from Closing Northern Division

Incremental Revenues and

(Incremental Costs) from Opening

Southern Division(2)

Revenues $(1,500,000 ) $1,500,000 Variable direct materials and direct

manufacturing labor costs 825,000 (825,000)Equipment cost written off as depreciation 0 (100,000)Marketing and distribution costs 205,000 (205,000)

Division general administration costs 330,000 (330,000)Corporate office costs 0 0 Total costs 1,360,000 (1,460,000 )Effect on operating income (loss) $ (140,000 ) $ 40,000

11-35 (30–40 min.) Make or buy, unknown level of volume.

1. The variable costs required to manufacture 150,000 starter assemblies are

Direct materials $200,000Direct manufacturing labor 150,000Variable manufacturing overhead 100,000Total variable costs $450,000

The variable costs per unit are $450,000 ÷ 150,000 = $3.00 per unit.

Let X = number of starter assemblies required in the next 12 months.

The data can be presented in both “all data” and “relevant data” formats:

All Data Relevant DataAlternative

1:Make

Alternative 2:

Alternative 1:

Alternative 2: Buy

Variable manufacturing costsFixed general manufacturing overheadFixed overhead, avoidableDivision 2 manager’s salaryDivision 3 manager’s salaryPurchase cost, if bought from Tidnish ElectronicsTotal

$ 3X 150,000

100,00040,00050,000

– $340,000+ $ 3X

–$150,000

–50,000

4X $200,000+ $ 4X

$ 3X–

100,00040,00050,000

– $190,000+ $ 3X

– ––

$50,000–

4X $50,000+ $ 4X

The number of units at which the costs of make and buy are equivalent is

All data analysis: $340,000 + $3X = $200,000 + $4XX = 140,000

orRelevant data analysis: $190,000 + $3X = $50,000 + $4X

X = 140,000

Assuming cost minimization is the objective, then• If production is expected to be less than 140,000 units, it is preferable to buy units

from Tidnish.

• If production is expected to exceed 140,000 units, it is preferable to manufacture internally (make) the units.

• If production is expected to be 140,000 units, Oxford should be indifferent between buying units from Tidnish and manufacturing (making) the units internally.

2. The information on the storage cost, which is avoidable if self-manufacture is discontinued, is relevant; these storage charges represent current outlays that are avoidable if self-manufacture is discontinued. Assume these $50,000 charges are represented as an opportunity cost of the make alternative. The costs of internal manufacture that incorporate this $50,000 opportunity cost are

All data analysis: $390,000 + $3XRelevant data analysis: $240,000 + $3X

The number of units at which the costs of make and buy are equivalent is

All data analysis: $390,000 + $3X = $200,000 + $4XX = 190,000

Relevant data analysis: $240,000 + $3X = $50,000 + $4XX = 190,000

If production is expected to be less than 190,000, it is preferable to buy units from Tidnish. If production is expected to exceed 190,000, it is preferable to manufacture the units internally.

11-36 (30 min.) Make versus buy, activity-based costing, opportunity costs.

1. Relevant costs under buy alternative: Purchases, 10,000 $8.20 $82,000

Relevant costs under make alternative: Direct materials $40,000 Direct manufacturing labor 20,000 Variable manufacturing overhead 15,000 Inspection, setup, materials handling 2,000 Machine rent 3,000

Total relevant costs under make alternative $80,000

The allocated fixed plant administration, taxes, and insurance will not change if Ace makes or buys the chains. Hence, these costs are irrelevant to the make-or-buy decision. The analysis indicates that Ace should make and not buy the chains from the outside supplier.

2. Relevant costs under the make alternative: Relevant costs (as computed in requirement 1) $80,000

Relevant costs under the buy alternative: Costs of purchases (10,000 $8.20) $82,000 Additional fixed costs 16,000 Additional contribution margin from using the space

where the chains were made to upgrade the bicycles by adding mud flaps and reflector bars, 10,000 ($20 – $18) (20,000)Total relevant costs under the buy alternative $78,000

Ace should now buy the chains from an outside vendor and use its own capacity to upgrade its own bicycles.

3. In this requirement, the decision on mud flaps and reflectors is irrelevant to the analysis.

Cost of manufacturing chains:Variable costs, ($4 + $2 + $1.50 = $7.50) 6,200 $46,500Batch costs, $200/batcha 8 batches 1,600Machine rent 3,000

$51,100

Cost of buying chains, $8.20 6,200 $50,840

a$2,000 10 batches

In this case, Ace should buy the chains from the outside vendor.

11-37 (60 min.) Multiple choice, comprehensive problem on relevant costs.

You may wish to assign only some of the parts.

Per Unit Manufacturing costs: Total Fixed Variable

Direct materials $1.00Direct manufacturing labor 1.20Variable manufac. indirect costs 0.80Fixed manufac. indirect costs 0.50 $3.50 $0.50 $3.00

Marketing costs:Variable $1.50Fixed 0.90 2.40 0.90 1.50

$5.90 $1.40 $4.50

1. (b) $3.50 Manufacturing Costs Variable $3.00Fixed 0.50Total $3.50

2. (e) None of the above. Decrease in operating income is $16,800.

Old Differential NewRevenues 240,000 $6.00 $1,440,000+ $ 91,200* 264,000 $5.80

$1,531,200Variable costs

Manufacturing 240,000 $3.00 720,000 + 72,000 264,000 $3.00792,000Marketing and other 240,000 $1.50 360,000 + 36,000 264,000 $1.50

396,000 Variable costs 1,080,000 + 108,000 1,188,000

Contribution margin 360,000 – 16,800 343,200Fixed costs

Manufacturing $0.50 20,000 12 mos. =120,000 –– 120,000Marketing and other$0.90 240,000 216,000 –– 216,000 Fixed costs 336,000 –– 336,000

Operating income $ 24,000 – $ 16,800 $ 7,200

*Incremental revenue:$5.80 24,000 $139,200Deduct price reduction$0.20 240,000 48,000

$ 91,200

3. (c) $3,500

If this order were not landed, fixed manufacturing overhead would be underallocated by $2,500, $0.50 per unit 5,000 units. Therefore, taking the order increases operating income by $1,000 plus $2,500, or $3,500.

Another way to present the same idea follows:

Revenues will increase by (5,000 $3.50 = $17,500) + $1,000 $18,500Costs will increase by 5,000 $3.00 (15,000)Fixed overhead will not change – Change in operating income $ 3,500

Note that this answer to (3) assumes that variable marketing costs are not influenced by this contract. These 5,000 units do not displace any regular sales.

4. (a) $4,000 less ($7,500 – $3,500)

Government Contract Regular ChannelsAs above $3,500 Sales, 5,000 $6.00 $30,000

Increase in costs: Variable costs only: Manufacturing, 5,000 $3.00 $15,000 Marketing,

5,000 $1.50 7,500 22,500Fixed costs are not affected

Change in operating income $ 7,500

5. (b) $4.15

Differential costs: Variable: Manufacturing $3.00

Shipping 0.75 $3.75 10,000 $37,500 Fixed: $4,000 ÷ 10,000 0 .40 10,000 4,000

$4 .15 10,000 $41,500

Selling price to break even is $4.15 per unit.

6. (e) $1.50, the variable marketing costs. The other costs are past costs and therefore, are irrelevant.

7. (e) None of these. The correct answer is $3.55. This part always gives students trouble. The short-cut solution below is followed by a longer solution that is helpful to students.

Short-cut solution:The highest price to be paid would be measured by those costs that could be avoided by

halting production and subcontracting:

Variable manufacturing costs $3.00Fixed manufacturing costs saved $60,000 ÷ 240,000 0.25Marketing costs (0.20 $1.50) 0.30Total costs $3.55

Longer but clearer solution:Comparative Annual Income Statement

Present Difference Proposed

RevenuesVariable costs:

Manufacturing, 240,000 $3.00Marketing and other, 240,000 $1.50

Variable costsContribution marginFixed costs:

ManufacturingMarketing and other

Total fixed costsOperating income

$1,440,000

720,000 360,000 1,080,000 360,000

120,000 216,000 336,000 $ 24,000

+132,000– 72,000

– 60,000

$1,440,000

852,000*

288,000 1,140,000 300,000

60,000 216,000 276,000 $ 24,000

*This solution is obtained by filling in the above schedule with all the known figures and working “from the bottom up” and “from the top down” to the unknown purchase figure. Maximum variable costs that can be incurred, $1,140,000 – $288,000 = maximum purchase costs, or $852,000. Divide $852,000 by 240,000 units, which yields a maximum purchase price of $3.55.

11-38 (25 min.) Closing down divisions.1.

Division A Division D

Sales $530,000 $450,000Variable costs of goods sold($450,000 0.90; $390,000 0.95) 405,000 370,500Variable S,G & A($100,000 0.60; $120,000 0.80) 60,000 96,000 Total variable costs 465,000 466,500

Contribution margin $ 65,000 $(16,500)

2.Division A Division D

Fixed costs of goods sold($450,000 ─ $405,000; $390,000 ─ $370,500) $45,000 $19,500Fixed S,G & A($100,000 ─ $60,000; $120,000 ─ $96,000) 40,000 24,000 Total fixed costs $85,000 $43,500Fixed costs savings if shutdown($85,000 0.60; $43,500 0.60) $51,000 $26,100

Division A’s contribution margin of $65,000 more than covers its avoidable fixed costs of $51,000. The difference of $14,000 helps cover the company’s unavoidable fixed costs. Since $51,000 of Division A’s fixed costs are avoidable, the remaining $34,000 is unavoidable and will be incurred regardless of whether Division A continues to operate. Division A’s $20,000 loss is the rest of the unavoidable fixed costs ($34,000 ─ $14,000). If Division A is closed, the remaining divisions will need to generate sufficient profits to cover the entire $34,000 unavoidable fixed cost. Consequently, Division A should not be closed since it helps defray $14,000 of this cost.

In contrast, Division D earns a negative contribution margin, which means its revenues are less than its variable costs. Division D also generates $26,100 of avoidable fixed costs. Based strictly on financial considerations, Division D should be closed because the company will save $42,600 ($26,100 + $16,500).

An alternative set of calculations is as follows:Division A Division D

Total variable costs $465,000 $466,500Avoidable fixed costs if shutdown 51,000 26,100 Total cost savings if shutdown 516,000 492,600Loss of revenues if shutdown 530,000 450,000

Cost savings minus loss of revenues $ (14,000) $ 42,600

Division A should not be shut down because loss of revenues if Division A is shut down exceeds cost savings. Division D should be shut down because cost savings from shutting down Division D exceeds loss of revenues.

3. Before deciding to close Division D, management should consider the role that the Division’s product line plays relative to other product lines. For instance, if the product manufactured by Division D attracts customers to the company, then dropping Division D may have a detrimental

effect on the revenues of the remaining divisions. Management may also want to consider the impact on the morale of the remaining employees if Division D is closed. Talented employees may become fearful of losing their jobs and seek employment elsewhere.

11-39 (25 min.) Product mix, constrained resource.

1. A110 B382 C657

Selling price $84 $ 56 $70Variable costs: Direct materials (DM) 24 15 9 Labor and other costs 28 27 40 Total variable costs 52 42 49 Contribution margin $32 $ 14 $21Pounds of DM per unit1 ÷8 lbs. ÷5 lbs. ÷ 3 lbs.Contribution margin per lb. $ 4 per lb. $2.80 per lb. $ 7 per lb.

1A110: = 8 lb. per unit

B382: = 5 lb. per unit

C657: = 3 lb. per unit

First, satisfy minimum requirements.A110 B382 C657 Total

Minimum units 200 200 200Times pounds per unit ×8 lb. per unit ×5 lb. per unit ×3 lb. per unitPounds needed to produce minimum units 1,600 lb. 1,000 lb. 600 lb. 3,200 lb.

The remaining 1,800 pounds (5,000 ─ 3,200) should be devoted to C657 because it has the highest contribution margin per pound of direct material. Since each unit of C657 requires 3 pounds of Bistide, the remaining 1,800 pounds can be used to produce another 600 units of C657. The following combination yields the highest contribution margin given the 5,000 pounds constraint on availability of Bistide.

A110: 200 unitsB382: 200 unitsC657: 800 units (200 minimum + 600 extra)

2. The demand for Westford’s products exceeds the materials available. Assuming that fixed costs are covered by the original product mix, Westford should be willing to pay upto an additional $7 per pound (the contribution margin per pound of C657) for another 1,000 pounds of Bistide. That is, Westford should be willing to pay $3 + $7 = $10 per pound of Bistide1. This cost assumes that sufficient demand exists to sell another 333 units (1000 pounds ÷ 3 pounds per unit) of C657. If not, then the maximum price falls to an additional $4 per pound (the contribution margin per pound of A110) so that Westford can produce up to 125 more units of A110 (1,000 pounds ÷ 8 pounds per unit). In this case, Westford would be willing to pay $3 + $4 = $7 per pound. If there is insufficient demand to sell another 125 units of A110, then the maximum price Westford would be willing to pay falls to an additional $2.80 per pound (the contribution margin per pound of B382). Westford would be willing to pay $2.80 + $3 = $5.80 per pound of Bistide.

1An alternative calculation focuses on column 3 for C657 of the table in requirement 1.Selling price $70Variable labor and other costs (excluding direct materials) 40 Contribution margin $30Divided by pounds of direct material per unit ÷3

lbs.Direct material cost per pound that Westford can pay

without contribution margin becoming negative $10

11-40 (30–40 min.) Optimal product mix.

1. Let D represent the batches of Della’s Delight made and sold. Let B represent the batches of Bonny’s Bourbon made and sold. The contribution margin per batch of Della’s Delight is $300.The contribution margin per batch of Bonny’s Bourbon is $250.

The LP formulation for the decision is:

Maximize $300D + $250 BSubject to 30D + 15B 660 (Mixing Department constraint)

15B 270 (Filling Department constraint)10D + 15B 300 (Baking Department constraint)

2. Solution Exhibit 11-40 presents a graphical summary of the relationships. The optimal corner is the point (18, 8) i.e., 18 batches of Della’s Delights and 8 of Bonny’s Bourbons.

SOLUTION EXHIBIT 11-40Graphic Solution to Find Optimal Mix, Della Simpson, Inc.

Della Simpson Production Model

0 5 10 15 20 25 30 35 40

D (batches of Della's Delight)

atches of B

y's Bou

Filling Dept. Constraint

Mixing Dept. Constraint

Baking Dept. Constraint

Equal Contribution Margin Lines

Optimal Corner (18,8)

Feasible Region

We next calculate the optimal production mix using the trial-and-error method.

The corner point where the Mixing Dept. and Baking Dept. constraints intersect can be calculated as (18, 8) by solving:

30D + 15B = 660 (1) Mixing Dept. constraint10D + 15B = 300 (2) Baking Dept. constraint

Subtracting (2) from (1), we have20D = 360or D = 18

Substituting in (2)(10 18) + 15B = 300

that is, 15B = 300 180 = 120or B = 8

The corner point where the Filling and Baking Department constraints intersect can be calculated as (3,18) by substituting B = 18 (Filling Department constraint) into the Baking Department constraint:

10 D + (15 18) = 30010 D = 300 270 = 30

The feasible region, defined by 5 corner points, is shaded in Solution Exhibit 11-40. We next use the trial-and-error method to check the contribution margins at each of the five corner points of the area of feasible solutions.

Trial Corner (D,B) Total Contribution Margin1 (0,0) ($300 0) + ($250 0) = $02 (22,0) ($300 22) + ($250 0) = $6,6003 (18,8) ($300 18) + ($250 8) = $7,4004 (3,18) ($300 3) + ($250 18) = $5,4005 (0,18) ($300 0) + ($250 18) = $4,500

The optimal solution that maximizes contribution margin and operating income is 18 batches of Della’s Delights and 8 batches of Bonny’s Bourbons.

11-41 (30 min.) Make versus buy, ethics.

1. Direct materials per unit = $195,000 30,000 = 6.50Direct manufacturing labor per unit = $120,000 30,000 = $4Variable manufacturing overhead for 30,000 units = 40% of $225,000 = $90,000Variable manufacturing overhead as a percentage of direct manufacturing labor = $90,000 $120,000 = 75%Fixed manufacturing overhead = 60% of $225,000 = $135,000

SOLUTION EXHIBIT 11-41A

Manufacturing

Costs for 30,000 Units

Manufacturing

Costs for 32,000 Units with Porter Estimates

Purchase Costs for

32,000 Units with Porter Estimates

(3)Purchasing costs ($17.30/unit 32,000 units) $553,600Direct materials ($6.50/unit 30,000; 32,000 units) $195,000 $208,000 Direct manufacturing labor ($4/unit 30,000; 32,000 units) 120,000 128,000 Plant space rental (or penalty to terminate) 84,000 84,000 10,000Equipment leasing (or penalty to terminate) 36,000 36,000 5,000Variable overhead (75% of direct manufacturing labor) 90,000 96,000 Fixed manufacturing overhead 135,000 135,000 135,000 Total manufacturing or purchasing costs $660,000 $687,000 $703,600

On the basis of Porter’s estimates, Solution Exhibit 11-41A suggests that in 2009, the cost to purchase 32,000 units of MTR-2000 will be $703,600, which is greater than the estimated $687,000 costs to manufacture MTR-2000 in-house. Based solely on these financial results, the 32,000 units of MTR-2000 for 2009 should be manufactured in-house.

2. SOLUTION EXHIBIT 11-41B

ManufacturingCosts for

32,000 Unitswith

Hart Estimates(4)

Purchase Costs for

32,000 Units with

Hart Estimates(5)

Purchasing costs ($17.30/unit 32,000 units) $553,600Direct materials ($208,000 1.08) $224,640 Direct manufacturing labor ($128,000 1.05) 134,400 Plant space rental (or penalty to terminate) 84,000 10,000Equipment leasing (or penalty to terminate) 36,000 3,000Variable overhead (75% of direct mfg. labor) 100,800 Fixed manufacturing overhead 135,000 135,000

Total manufacturing or purchasing costs $714,840 $701,600

Based solely on the financial results shown in Solution Exhibit 11-41B, Hart’s estimates suggest that the 32,000 units of MTR-2000 should be purchased from Marley. The total cost from Marley would be $701,600, or $13,240 less than if the units were made by Paibec.

3. At least four other factors that Paibec Corporation should consider before agreeing to purchase MTR-2000 from Marley Company include the following:

In future years, Paibec will not incur the rental and lease contract termination costs on its annual contacts that it will incur in 2009. This will make the purchase option even more attractive, in a financial sense. But then, Marley’s own longevity, its ability to provide the required units of MTR-2000, and its demanded price should be considered, since terminating the contracts may make the make-versus-buy decision a long-term one for Paibec.

The quality of the Marley component should be equal to, or better than, the quality of the internally made component. Otherwise, the quality of the final product might be compromised and Paibec’s reputation affected.

Marley’s reliability as an on-time supplier is important, since late deliveries could hamper Paibec’s production schedule and delivery dates for the final product.

Layoffs may result if the component is outsourced to Marley. This could impact Paibec’s other employees and cause labor problems or affect the company’s position in the community. In addition, there may be labor termination costs, which have not been factored into the analysis.

4. Referring to “Standards of Ethical Conduct for Management Accountants,” in Exhibit 1-7, Lynn Hart would consider the request of John Porter to be unethical for the following reasons.

Competence Prepare complete and clear reports and recommendations after appropriate analysis of

relevant and reliable information. Adjusting cost numbers violates the competence standard.

Integrity Refrain from either actively or passively subverting the attainment of the organization’s

legitimate and ethical objectives. Paibec has a legitimate objective of trying to obtain the component at the lowest cost possible, regardless of whether it is manufactured internally or outsourced to Marley.

Communicate unfavorable as well as favorable information and professional judgments or opinions. Hart needs to communicate the proper and accurate results of the analysis, regardless of whether or not it favors internal production.

Refrain from engaging in or supporting any activity that would discredit the profession. Falsifying the analysis would discredit Hart and the profession.

Credibility Communicate information fairly and objectively. Hart needs to perform an objective make-

versus-buy analysis and communicate the results fairly.

Disclose fully all relevant information that could reasonably be expected to influence an intended user’s understanding of the reports, comments, and recommendations presented. Hart needs to fully disclose the analysis and the expected cost increases.

Confidentiality Not affected by this decision.

Hart should indicate to Porter that the costs she has derived under the make alternative are correct. If Porter still insists on making the changes to lower the costs of making MTR-2000 internally, Hart should raise the matter with Porter’s superior, after informing Porter of her plans. If, after taking all these steps, there is a continued pressure to understate the costs, Hart should consider resigning from the company, rather than engage in unethical conduct.

11-42 (30 min.) Product mix, constrained resource.

Units(1)

Machine Hrs Per Unit(2) = Var. Mach. Cost/Unit ÷ $200/Hour

Machine Hrs Demanded

(3) = (1) × (2)Nealy 1,800 $600 ÷ $200 = 3 5,400 Tersa 4,500 $500 ÷ $200 = 2.5 11,250 Pelta 39,000 $200 ÷ $200 = 1 39,000 Total 55,650

2. Nealy Tersa Pelta

Selling price $3,000 $2,100 $800Variable costs: Direct materials 750 500 100 Variable machining 600 500 200 Sales commissions (5%, 5%, 10%) 150 105 80 Total variable costs 1,500 1,105 380 Contribution margin per unit $1,500 $ 995 $420

3. Total machine hours needed to satisfy demand exceed the machine hours available (55,650 needed > 50,000 available). Consequently Marion Taylor needs to evaluate these products based on the contribution margin per machine hour.

Nealy Tersa PeltaUnit contribution margin $1,500 $995 $420Machine-hours (MH) per unit ÷3 MH ÷2.5 MH ÷1 MHUnit contribution margin per MH $ 500 $398 $420

Based on this analysis, Marion Taylor should produce to meet the demand for products with the highest unit contribution margin per machine hour, first Nealy, then Pelta, and finally Tersa. The optimal product mix will be as follows:

Nealy 1,800 units = 5,400 MHPelta 39,000 units = 39,000 MHTersa 2,240 (5,600 MH ÷ 2.5 MH/unit) units = 5,600 MH (50,000 ─ 5,400 ─ 39,000)Total 50,000 MH

4. The optimal product mix in Part 3 satisfies the demand for Nealy and Pelta and leaves only 2,260 units (4,500 ─ 2,240) of Tersa unfilled. These remaining units of Tersa require 5,650 machine hours (2,260 units 2.5 MH per unit). The maximum price Marion Taylor is willing to pay for extra machine hours is $398, which is the unit contribution per machine hour for additional units of Tersa. That is, total cost per machine-hour for these units will be $398 + $200 (variable cost per machine-hour) = $598 per machine-hour.

CHAPTER 18Investment Decisions: Ratios

Test Questions1. Income multipliers:

a. are useful as a preliminary analysis tool to weed out obviously unacceptable investment opportunities.

2. The overall capitalization rate calculated on a potential acquisition:a. is the reciprocal of the net income multiplier.

3. The operating expense ratio:c. expresses operating expenses as a percent of effective gross income.

4. The equity dividend rate:b. expresses before-tax cash flow as a percent of the required equity capital investment.

5. Ratio analysis:d. serves as an initial evaluation of the adequacy of an investment’s expected cash flows.

6. Assume a retail shopping center can be purchased for $5.5 million. The center’s first year NOI is expected to be $489,500. A $4,000,000 loan has been requested. The loan carries a 9.25 percent fixed contract rate, amortized monthly over 25 years with a 7-year term. What will be the property’s (annual) debt coverage ratio in the first year of operations?b. 1.19

7. Which of the following is not an operating expense associated with income-producing (commercial) property? a. Debt service

Use the following information to answer questions 8-9. You are considering purchasing an office building for $2,500,000. You expect the potential gross income (PGI) in the first year to be $450,000; vacancy and collection losses to be 9 percent of PGI; and operating expenses and capital expenditures to be 38 percent and 4 percent, respectively, of effective gross income (EGI).

8. What is the implied first-year overall capitalization rate?a. 9.5 percent

9. What is the effective gross income multiplier?b. 6.11

10. Given the following information, what is the required equity down payment?• Acquisition price: $800,000• Loan-to-value ratio: 75%• Total up-front financing costs: 3%c. $218,000

Study Questions

Use the following information to answer questions 1 – 3:You are considering the purchase of an office building for $1.5 million today. Your expectations include the following: first-year potential gross income of $340,000; vacancy and collection losses equal to 15 percent of potential gross income; operating expenses equal to 40 percent of effective gross income and capital expenditures equal 5 percent of EGI. You expect to sell the property five years after it is purchased. You estimate that the market value of the property will increase four percent a year after it is purchased and you expect to incur selling expenses equal to 6 percent of the estimated future selling price.

1. What is estimated effective gross income (EGI) for the first year of operations?

Solution: Item AmountPotential gross income (PGI) $340,000less: V&C allowance (at 15% of PGI) 51,000Effective gross income (EGI) $289,000

2. What is estimated net operating income (NOI) for the first year of operations?

Solution:Item AmountEffective gross income (EGI) $289,000less: Operating expenses (OE) (115,600)less: Capital expenditures (CAPX) (14,450)Net operating income (NOI) $158,950

3. What is the estimated going-in cap rate (Ro) using NOI for the first year of operations?

Solution: The overall cap rate is 10.6 percent ($158,950 / $1,500,000)

4. An investment opportunity having a market price of $1,000,000 is available. You could obtain a $750,000, 25-year mortgage loan requiring equal monthly payments with interest at 7.0 percent. The following operating results are expected during the first year.

Effective gross income $200,000Less operating expenses and CAPX $100,000Net operating income $100,000

For the first year only, determine the:

a. Gross income multiplier

Solution: Market price / Effective gross income = $1,000,000 / $200,000 = 5.0

b. Operating expense ratio (including CAPX)

Solution: Operating expenses / Effective gross income = $100,000 / $200,000 = 0.50 or 50 percent.

c. Monthly and annual payment

Solution: Monthly payment is $5,300.84. Annual payment is $63,610.13

d. Debt coverage ratio

Solution: NOI / Annual debt service = $100,000 / $63,610 = 1.57

e. Overall capitalization rate

Solution: NOI / Market price = $100,000 / $1,000,000 = 10 percent

f. Equity dividend rate

Solution: Before-tax cash flow / Equity = $36,390 / $250,000 = 14.6 percent

Note: Equity investment = Acquisition price – loan amount = $1,000,000 - $750,000

5. You are considering the purchase of a quadruplex apartment. Effective gross income (EGI) during the first year of operations is expected to be $33,600 ($700 per month per unit). First-year operating expenses are expected to be $13,440 (at 40 percent of EGI). Ignore capital expenditures. The purchase price of the quadruplex is $200,000. The acquisition will be financed with $60,000 in equity and a $140,000 standard fixed-rate mortgage. The interest rate on the debt financing is eight percent and the loan term is 30

years. Assume, for simplicity, that payments will be made annually and that there are no up-front financing costs.

a. What is the overall capitalization rate?

Solution: NOI = EGI – operating expenses = $33,600 – $13,440

= $20,160

NOI / Market price = $20,160 / $200,000 = 10.08 percent

b. What is the effective gross income multiplier?

Solution: Market price / Effective gross income = $200,000 / $33,600 = 5.95

c. What is the equity dividend rate (the before-tax return on equity)?

Solution:

Debt service = $12,436, as calculated below

N = 30 I/YR = 8 PV = $140,000 PMT = ? FV = 0

Before-tax cash flow = NOI - Debt service = $20,160 - $12,436

= $7,724

Equity dividend rate = Before-tax cash flow / equity invested = $7,724 / $60,000 = 12.87 percent

d. What is the debt coverage ratio?

Solution: DCR= NOI / debt service = $20,160 / $12,436 = 1.62

e. Assume the lender requires a minimum debt coverage ratio of 1.2. What is the largest loan that you could obtain if you decide to borrow more than $140,000?

Solution: Debt service must be such that the following relationship holds:

But, debt service is equal to the loan amount times the mortgage constant (contract interest rate plus principal amortization). Thus, we can rewrite the above expression as

Rearranging,

For our problem,

The mortgage constant is the stated interest rate plus the first-year principal payment divided by the loan amount (1,236/140 000 = .0088), or .0888.

$189,130 = loan amount

6. Why do Class B properties generally sell at higher going-in cap rates than Class A properties?

Solution: Relative to class A properties, class B properties are more risky and/or are expected to produce smaller rental increases over time. Both effects reduce the amount a rational investor is willing to pay today per dollar of current income. When values/prices fall relative to current net rental income, cap rates increase.

7. Why might a commercial real estate investor borrow to help finance an investment even if she could afford to pay 100 percent cash?

Solution: Borrowing--i.e., the use of “other people’s money”—is also refereed to as the use of financial leverage. If the overall return on the property exceeds the cost of debt, the use of leverage can significantly increase the rate of return investors earn on their invested equity. This expected magnification of return often induces investors to partially debt finance even if they have the accumulated wealth to pay all cash for the property.

8. You are considering purchasing an office building for $2,500,000. You expect the potential gross income (PGI) in the first year to be $450,000; vacancy and collection losses to be 9 percent of PGI; and operating expenses and capital expenditures to be 42 percent of effective gross income (EGI). What is the estimated Net Operating Income? What is the implied first year overall capitalization rate? What is the effective gross income multiplier?

Item Amount Potential gross income (PGI) $450,000- Vacancy & collection loss (VC) 40,500= Effective gross income (EGI)

409,500

- Operating expenses (OE) 171,990= Net operating income (NOI) 237,510

What is the overall capitalization rate?

What is the effective gross income multiplier?

9. What distinguishes an operating expense from a capital expenditure?

Solution: An operating expense does not fundamentally alter the market value or remaining economic life of the asset; rather operating expenses simply keep the property operating and competitive in its local market. In contrast, a capital expenditure is defined as an expense that does increase the market value and/or remaining economic life of the asset.

10. Explain why income property cash flow is not the same as taxable income.

Solution: For several reasons, the actual net cash flow generated by a rental property investment is different than the amount of income the owner must report for federal income tax purposes. First and foremost, a deduction for depreciation is allowed in the calculation of taxable income from annual operations; however, the owner does not “write a check” for depreciation on an annual basis. This reduces taxable income relative to the actual cash flow. The same is true for amortized financing expenses. Conversely, the owner often does make mortgage payments that include both interest and principal amortization. However, only the interest portion of the mortgage payment is tax deductible. The principal portion is, therefore, a cash outflow that is not tax deductible.

11. What is the basic shortcoming of most ratios and rules of thumb used in commercial real estate investment decision making?

Solution: The major weakness of most ratios and rules of thumb is that they ignore cash inflows and outflows that are likely to occur beyond the first year of operations. Also, there are no clear decisions rules associated with rules of thumb. For example, how much higher does the going-in cap rate on a potential acquisition have to be relative to the cap rate on similar properties before the investor can conclude that acquiring the property will increase wealth?

CHAPTER 19Investment Decisions: NPV and IRR

Test Questions1. A real estate investment is available at an initial cash outlay of $10,000, and is expected

to yield cash flows of $3,343.81 per year for five years. The internal rate of return (IRR) is approximately:b. 20 percent.

2. The net present value of an acquisition is equal to:b. the present value of expected future cash flows, less the initial cash outlay.

3. Present value:b. is the value now of all net benefits that are expected to be received in the future.

d. is also correct.

4. The internal rate of return equation incorporates:d. initial cash outflow and inflow, and future cash outflow and inflow.

5. The purchase price that will yield an investor the lowest acceptable rate of return is:a. The property’s investment value to that investor.

6. What term best describes the maximum price a buyer is willing to pay for a property? a. Investment value

7. An income-producing property is priced at $600,000 and is expected to generate the following after-tax cash flows: Year 1: $42,000; Year 2: $44,000; Year 3: $45,000; Year 4: $50,000; and Year 5: $650,000. Would an investor with a required after-tax rate of return of 15 percent be wise to invest at the current price?b. No, the NPV is -$148,867.

8. As a general rule, using financial leverage:

b. increases risk to the equity investor.

9. What is the IRR, assuming an industrial building can be purchased for $250,000 and is expected to yield cash flows of $18,000 for each of the next five years and be sold at the end of the fifth year for $280,000?c. 9.20 percent

10. Which of the following is the least true?

d. After-tax discount rates are greater than discount rates used to value before-tax cash flows.

Study Questions

1. List three important ways in which DCF valuation models differ from direct capitalization models.

Solution: Direct capitalization models require an estimate of stabilized income for one year. DCF models require estimates of net cash flows over the entire expected holding period. In addition, the cash flow forecast must include the net cash flow expected to be produced by the sale of the property at the end of the expected holding period. Finally, the appraiser must select the appropriate yield (required IRR) at which to discount all future cash flows or to use as the hurdle rate in an IRR analysis.

2. Why might a commercial real estate investor borrow to help finance an investment even if she could afford to pay 100 percent cash?

Solution: Borrowing--i.e., the use of “other people’s money”—is also refereed to as the use of financial leverage. If the overall return on the property exceeds the cost of debt, the use of leverage can significantly increase the rate of return investors earn on their invested equity. This expected magnification of return often induces investors to partially debt finance even if they have the accumulated wealth to pay all cash for the property. Other potential benefits of leverage include: the ability to break through equity capital constraint in order to acquire more + NPV projects; the ability to apply the owner/operator’s comparative advantage in acquisition and management to more projects; and increased portfolio diversification.

3. Using the “CFj” key of your financial calculator determine the IRR of the following series of annual cash flows: CF0= -$31,400; CF1 = $3,292; CF2 = $3,567; CF3 = $3,850; CF4 = $4,141; and CF5 = $50,659.

Solution: IRR = 18.51%

4. A retail shopping center is purchased for $2.1 million. During the next four years, the property appreciates at 4 percent per year. At the time of purchase, the property is financed with a 75 percent loan-to-value ratio for 30 years at 8 percent (annual) with monthly amortization. At the end of year 4, the property is sold with 8 percent selling expenses. What is the before-tax equity reversion?

Solution:Item AmountLoan amount = 0.75 x (2,100,000) $1,575,000Monthly payments 11,556.79Remaining mtg. balance 1,515,450

Selling price [2,100,000 x (1.04)4] 2,456,703less: Selling expenses (at 8% of SP) 196,536Net selling price 2,260,167less: Unpaid mtg. balance 1,515,450Before-tax equity reversion $ 744,717

5. State, in no more than one sentence, the condition for favorable financial leverage in the calculation of NPV.

Solution: Increasing the use of leverage will increase the calculated NPV if the discount rate exceeds the effective cost of mortgage debt.

6. State, in no more than one sentence, the condition for favorable financial leverage in the calculation of the IRR.

Solution: Increasing the use of leverage will increase the calculated IRR if the unlevered IRR exceeds the effective cost of mortgage debt.

7. An office building is purchased with the following projected cash flows:• NOI is expected to be $130,000 in year 1 with 5 percent annual increases.• The purchase price of the property is $720,000.• 100% equity financing is used to purchase the property• The property is sold at the end of year 4 for $860,000 with selling costs of 4

percent.• The required unlevered rate of return is 14 percent.

a. Calculate the unlevered internal rate of return (IRR).b. Calculate the unlevered net present value (NPV).

Solution:

YearPurchase

Net Operating Income

Net Sale Proceeds

Total Cash Flow

Present Value at

14%0 ($720,000) ($720,000) ($720,000)1 130,000 130,000 114,0352 136,500 136,500 105,0323 143,325 143,325 96,7404 150,491 825,600 $976,091 $577,924

a. IRR = 21.88 percentb. NPV = 173,732

8. With a purchase price of $350,000, a small warehouse provides for an initial before-tax cash flow of $30,000, which grows by 6 percent per year. If the before-tax equity reversion after four years equals $90,000, and an initial equity investment of $175,000 is required, what is the IRR on the project? If the required going-in levered rate of return on the project is 10 percent, should the warehouse be purchased?

Solution:

YearPurchase

PriceBefore-

Tax Cash Flow

Before-Tax Equity

Reversion

Total Cash Flow

Present Value at

10%0 ($175,000) ($175,000) ($175,000)1 30,000 30,000 27,2722 31,800 31,800 26,2813 33,708 33,708 25,3254 35,730 90,000 $125,730 $85,875

The IRR is 7.84 percent. Based on a going-in levered rate of return on the project of 10 percent, the NPV equals ($10,246) and the project should not be undertaken.

9. You are considering the acquisition of a small office building. The purchase price is $775,000. Seventy-five percent of the purchase price can be borrowed with a 30-year, 7.5 percent mortgage. Payments will be made annually. Up-front financing costs will total three percent of the loan amount. The expected before-tax cash flows from operations--assuming a 5-year holding period—are as follows:

Year BTCF1 $48,492

2 53,7683 59,2824 65,0435 $71,058

The before-tax cash flow from the sale of the property is expected to be $295,050. What is the net present value of this investment, assuming a 12 percent required rate of return on levered cash flows? What is the levered internal rate of return?

Solution: As solved below, the NPV is ($11,166) and the IRR is 10.75 percent

YearEquity

Investment NOIDebt

Service BTERTotal Cash

FlowPresent Value

at 12%0 ($211,188) ($211,188) ($211,188)1 $48,492 $49,215 (723) (646)2 53,768 49,215 4,553 3,6303 59,282 49,215 10,067 7,1654 65,043 49,215 15,828 10,0595 $71,058 $49,215 $295,050 $316,893 $179,814

10. You are considering the purchase of an apartment complex. The following assumptions are made:• The purchase price is $1,000,000.• Potential gross income (PGI) for the first year of operations is projected to be

$171,000.• PGI is expected to increase at 4 percent per year.• No vacancies are expected.• Operating expenses are estimated at 35 percent of effective gross income. Ignore

capital expenditures.• The market value of the investment is expected to increase 4 percent per year.• Selling expenses will be 4 percent.• The holding period is 4 years.• The appropriate unlevered rate of return to discount projected NOIs and the

projected NSP is 12 percent.• The required levered rate of return is 14 percent.• 70 percent of the acquisition price can be borrowed with a 30-year, monthly

payment mortgage.• The annual interest rate on the mortgage will be 8.0 percent.• Financing costs will equal 2 percent of the loan amount.

• There are no prepayment penalties.

a. Calculate net operating income (NOI) for each of the four years.

Solution:Item 1 2 3 4PGI $171,000 $177,840 $184,954 $192,352Less: V&C 0 0 0 0EGI 171,000 177,840 184,954 192,352Less: OE 59,850 62,244 64,734 67,323NOI $111,150 $115,596 $120,220 $125,029

b. Calculate the net sale proceeds from the sale of the property.

Solution:Item AmountSelling price [1,000,000 x (1.04)4] $1,169,859less: Selling expenses (at 4% of SP) 46,794Net Selling price $1,123,065

c. Calculate the net present value of this investment, assuming no mortgage debt. Should you purchase? Why?

Solution:

Item Cash Flow Present Value at 12%Initial Outflow Yr. 0 -$1,000,000 -$1,000,000NOI Yr.1 111,150 99,241NOI Yr.2 115,596 92,152NOI Yr.3 120,220 85,570NOI Yr.4 125,029 79,458Reversion Yr. 4 1,123,065 713,727Net Present Value $70,150

Yes, purchase the property because it is a positive NPV project.

d. Calculate the internal rate of return of this investment, assuming no debt. Should you purchase? Why?

Solution: IRR = 14.22 percent. Purchase because unlevered required rate of return is 12 percent

e. Calculate the monthly mortgage payment. What is the total per year?

Solution: Monthly payment = $5,136.35 as calculated below:

Annual payment = monthly payment x 12 = $61,636

f. Calculate the loan balance at the end of years 1, 2, 3, and 4. (Note: the unpaid mortgage balance at any time is equal to the present value of the remaining payments, discounted at the contract rate of interest.)

Solution:Unpaid mortgage balance in year 1 = $694,152Unpaid mortgage balance in year 2 = $687,820Unpaid mortgage balance in year 3 = $680,961Unpaid mortgage balance in year 4 = $673,533

g. Calculate the amount of principal reduction achieved during each of the four years.

Solution:Principal reduction in year 1 = $700,000 - $694,152 = $5,848Principal reduction in year 2 = $694,152 - $687,820 = $6,332Principal reduction in year 3 = $687,820 - $680,961 = $6,859Principal reduction in year 4 = $680,961 - $673,533 = $7,428

h. Calculate the total interest paid during each of the four years. (Note: Remember that debt service equals principal plus interest.)

Solution:Interest paid in year 1 = $61,636 - $5,848 = $55,788Interest paid in year 2 = $61,636 - $6,332 = $55,304Interest paid in year 3 = $61,636 - $6,859 = $54,777Interest paid in year 4 = $61,636 - $7,428 = $54,208

i. Calculate the levered required initial equity investment.

Solution: Loan amount (0.70 x $1,000,000) = $700,000Up-front financing costs (0.02 x $700,000) = $14,000Equity investment = $1,000,000 - $700,000 + $14,000 = $314,000

j. Calculate the before-tax cash flow (BTCF) for each of the four years.

Solution:Item 1 2 3 4NOI $111,150 $115,596 $120,220 $125,029

less: Debt Service 61,636 61,636 61,636 61,636BTCF $49,514 $53,960 $58,584 $63,393

k. Calculate the before-tax equity reversion (BTER) from the sale of the property.

Solution:Item AmountNet selling price $1,123,065less: Remaining mortgage balance in year 4 673,533Before-tax equity reversion $449,532

l. Calculate the levered net present value of this investment. Should you purchase? Why?

Solution:

Item Cash Flow

Present Value at

14%BTCF Yr.1 $49,514 $43,433BTCF Yr.2 53,960 41,520BTCF Yr.3 58,584 39,543BTCF Yr.4 63,392 37,534Reversion Yr. 4 449,532 266,159Total $428,189

NPV = Present value of the cash flows less the equity investment: $428,189 - $314,000 = $114,189.

Decision: Purchase the property because the NPV > 0; wealth will increase by $114,189.

m. Calculate the levered internal rate of return of this investment (assuming no debt and no taxes). Should you purchase? Why?

Solution: Levered IRR = 25.02 percent; Decision: Purchase the property because IRR > 14 percent, the required return.

n. Calculate, for the first year of operations, the: (1) overall (cap) rate of return, (2) equity dividend rate, (3) gross income multiplier, (4) debt coverage ratio.

Solution: (1) Overall cap rate = NOI / Market price = $111,150 / $1,000,000 =

11.12%

(2) Equity dividend rate = BTCF / equity = $49,514 / $314,000 = 15.8 percent

(3) Gross income multiplier = Market price / EGI = $1,000,000 / $171,000 = 5.85

(4) Debt coverage ratio = NOI / Debt service = $111,150 / $61,636 = 1.8

11. The expected before-tax IRR on a potential real estate investment is 14 percent. The expected after-tax IRR is 10.5 percent. What is the effective tax rate on this investment?

Solution: The effective tax rate is (1-(10.5/14)) = 0.25 or 25 percent.

12. An office building is purchased with the following projected cash flows:• NOI is expected to be $130,000 in year 1 with 5 percent annual increases.• The purchase price of the property is $720,000.• 100% equity financing is used to purchase the property• The property is sold at the end of year 4 for $860,000 with selling costs of 4 percent.• The required unlevered rate of return is 14 percent.

a. Calculate the unlevered internal rate of return (IRR).

Year 1 Year 2 Year 3 Year 4 Year 5NOI $130,000 $136,500 $143,325 $150,491 $158,016

Sale price $860,000Minus selling costs $ 34,400Net selling price $825,600

Total cash flows $130,000 $136,500 $143,325 $150,491 $983,616

With a cash outflow of $720,000 at time zero (CF0), and using the cash flow (“CF”) key of your calculator, the unlevered internal rate of return (IRR) = 21.50%

b. Calculate the unlevered net present value (NPV).

Again, with a cash outflow of $720,000 at time zero (CF0), a required unlevered rate of return of 14 percent, and using the cash flow (“CF”) key of your calculator, the unlevered net present value (NPV) = 195,769.78

Chapter 9Real Estate Finance: The Laws and Contracts

Test Problems

1. The element of an adjustable interest rate that is the “moving part” is the:

b. Index

2. Which of these aspects of a mortgage loan will be addressed in the note rather than in the mortgage?a. Prepayment penalty

3. A lender may reserve the right to require prepayment of a loan at any time they see fit through a(n):c. Demand clause

4. When a buyer of a property with an existing mortgage loan acquires the property without signing the note for an existing loan the buyer is acquiring the property:e. Subject to the mortgage

5. Which if these points in a mortgage loan would be addressed in the mortgage (possibly in the note as well)?d. Escrows

6. To finance property where either the borrower, the property, or both fail to qualify for the standard mortgage financing, a common nonmortgage solution is through the: d. Contract for deed.

7. Ways that a lender may respond to a defaulted loan without resorting to foreclosure include all of the following except:d. Accelerate the debt.

8. If the lender in a standard first mortgage wishes to foreclose cost effectively, it is crucial to have which clause in the mortgage:a. Acceleration clause

9. A common risk that frequently interferes with a lender’s efforts to work out a defaulted loan through either nonforeclosure means or foreclosure is:d. Bankruptcy.

10. The characteristics of a borrower than can be considered by a lender in a mortgage loan appreciation are limited by the:c. Equal Credit Opportunity Act.

11. The Real Estate Settlement Procedures Act does which of these:e. All of the above.

12. Foreclosure tends to be quickest in states that:d. Have power of sale.

13. From a home mortgage lender’s perspective, which statement is true about the effect of bankruptcy upon foreclosure?a. Chapter 7 bankruptcy is the most “lender friendly” form.

14. The most internationally oriented index rate for adjustable rate mortgages is:c. A LIBOR rate.

15. A type of loan that has grown in volume in recent years which has raised concerns about predatory lending practices is the: d. Subprime mortgage

16. A partially amortizing loan always will have c. A balloon payment.

17. Which of these statements is true about mortgage loans for income producing real estate?e. All of the above.

18. With what type of loan security arrangement is the deed held by a neutral party and returned upon payment of the mortgage in full?c. Deed of trust.

19. The Truth in Lending Act gives a home mortgage borrower how long to rescind a mortgage loan?c. Three days.

20. Which statement is correct about the right of prepayment of a home mortgage loan?b. Most home mortgage loans have the right of prepayment without charge, but not all, and the borrower should check the loan carefully.

Study Questions

1. Mortgage law is as clear, consistent, and enforceable in the United States as in any place in the world, and far more so than in many countries. Why is this a vital element of an efficient real estate finance system?

Solution: Clear, consistent, and enforceable mortgage law is critical to the real estate finance system for many reasons. Since debt financing is used in most real estate transactions, eliminating uncertainty is crucial for both parties in the transaction. Certainty reduces the cost of borrowing. The lender can be more certain of the rights and risks involved, which reduces the necessary risk premium required in the interest rate. The borrower benefits from the same certainty both due to a lower interest rate, and due to the greater predictability of outcome. For example, the borrower can understand, in case of delinquent payments, how much risk actually is involved. For most individuals, a debt-financed home purchase will be the largest financial transaction that they will undertake. The lender is more informed than is the borrower in mortgage transactions.

Therefore, it is necessary to establish clear laws to protect consumers and place them on equal footing. Mortgage financing is also a complicated process and requires unambiguous mortgage law to anticipate all possible issues that may arise. Standardized mortgage law is also important to financial markets, as mortgage markets have become national because this enhances trading liquidly and has served to reduce the cost of borrowing to potential homeowners.

2. The Congress has adopted changes in bankruptcy law that would make Chapter 7 bankruptcy more difficult for households, requiring greater use of Chapter 13, thus providing greater protection to unsecured credit card companies. As a mortgage lender, do you care about this? If so, what would be your position?

Solution: The mortgage lender is entitled to the value of the mortgage indebtedness under both Chapter 7 and Chapter 13 because their claim has priority. However, Chapter 13 is essentially a debt workout plan that will most likely delay the efforts by a lender to foreclose on the property. Delays may cost the lender opportunity costs through uncollected interest and legal expenses. Addtionally, the value of the property may deteriorate due to neglect during this process.

3. Residential mortgage terms (mortgage notes) have become increasingly uniform as the mortgage market has become more national and efficient. Is there any downside to this for the homeowner?

Solution: The increased uniformity of mortgage terms reduces the opportunity for customization of terms based on a homeowner’s unique situation and characteristics. However, the standardization of the mortgage process has allowed the borrower to reap the benefits of reduced costs associated with the lending process as well as reduced delays. Furthermore, the standardization of the mortgage process has been accompanied by the introduction of more laws to protect consumers’ rights.

4. Most lenders making adjustable rate mortgage loans offer a “teaser rate.” Is this a good policy or is it misrepresentation?

Solution: The primary concerns with “teaser rates” is that the terms of the mortgage be transparent, and that they clearly address the interaction of periodic caps with the “teaser rate.” The reduction from a teaser rate may be a percentage point or two below the sum of index plus margin, but this usually applies for a short time, perhaps one year. The consumer must be aware of the mechanics of the adjustable feature of the loan.

5. Home mortgage lending is heavily regulated by federal laws. Is this a result of Congressional pandering to consumer groups, or are there good reasons why home mortgage lending should be regulated more than, say, automobile financing?

Solution: The purchase of a home is typically the largest financial transaction undertaken by most individuals. Unlike a car, the purchase of a home typically cannot be readily

undone by quickly selling the property to another party. Mortgage financing is normally more complex than automobile financing. Mortgage financing requires some basic understanding of law, and, without consumer protection laws, the lender has a disproportionate advantage over the borrower in this transaction. From a public policy perspective, federal regulation prohibits discrimination and financially abusive practices.

6. For your own state, determine whether:

a. It is a judicial or non-judicial foreclosure state. b. The standard home loan is based on a deed of trust or a mortgage. c. There is a statutory right of redemption, and, if so, how long.d. Deficiency judgments are allowed against defaulted homeowners.

Based on this information can you judge your state is relatively debtor friendly or borrower friendly?

Solution: For the student to decide as answers to the above questions vary by state.

7. Download one mortgage and one deed of trust from the Freddie Mac website. Compare them to see what differences you can find in their clauses

Solution: Differences between a mortgage and a deed of trust include the following:

A deed of trust is not a mortgage contract; it is a special kind of deed that is recorded in public records.

The trustee holds your title in trust until the debt is paid but cannot take your property for any reason.

The deed of trust is cancelled when the debt is paid.

The primary differences between a mortgage and a deed of trust occur if the home is foreclosed. The trustee has power of sale. Therefore, if your loan becomes delinquent, the lender will give the trustee proof of the delinquency and ask the trustee to initiate foreclosure proceedings.

CHAPTER 10Residential Mortgage Types and Borrower Decisions

Test Problems

1. Private mortgage insurance (PMI) is usually required on _____ loans with loan-to-value ratios greater than _____ percent.d. Home, 80 percent.

2. The dominant loan type originated and kept by most depository institutions is the:b. Adjustable rate mortgage.

3. Which of the following mortgage types has the most default risk, assuming the initial loan-to-value ratio, contract interest rate, and all other loan terms are identical?a. Interest only loans.

4. A mortgage that is intended to enable older households to “liquify” the equity in their home is the:d. Reverse annuity mortgage.

5. A jumbo loan is:b. A conventional loan that is too large to be purchased by Fannie Mae or Freddie Mac.

6. The maximum loan-to-value ratio for an FHA loan over $50,000 is approximately:b. 97 percent.

7. The maximum loan-to-value ratio on a VA guaranteed loan is:d. 100 percent.

8. Conforming conventional loans are loans that:c. Are eligible for purchase by Fannie Mae and Freddie Mac.

9. Home equity loans typically: d. Have tax-deductible interest charges.

10. The best method of determining whether to refinance is to use:a. Net benefit analysis.

11. Probably the greatest contribution of FHA to home mortgage lending was to:a. Establish the use of the level-payment home mortgage.

Study Questions

1. On an adjustable mortgage, do borrowers always prefer smaller (i.e. tighter) rate caps that limit the amount the contract interest rate can increase in any given year or over the life if the loan? Explain why or why not.

Solution: Borrowers preferences are influenced by their expectations of future interest rates. For example, borrowers may prefer wider caps if they believe interest rates will not increase substantially. In this scenario, the loan interest rate will be lower because the borrower, not the lender, bears the risk of interest rates increasing.

2. Explain the potential tax advantages associated with home equity loans:

Solution: Unlike interest on consumer debt, interest paid on the first $100,000 of a home equity loan is fully deductible for federal and, in some cases, state income tax purposes. By including the interest paid on a home equity loan as an itemized deduction, taxpayers can effectively reduce the cost of this loan on an after-tax basis.

3. Distinguish between conforming and nonconforming residential mortgage loans and explain the importance of the difference.

Solution: Conforming residential loans meet the standards required for purchase in the secondary market by Fannie Mae or Freddie Mac. Conforming loans have significantly greater liquidity in the secondary market, and consequently require a lower interest rate.

4. Discuss the role and importance of private mortgage insurance in the residential mortgage market.

Solution: Private mortgage insurance protects a lender against losses due to default. Private mortgage insurance companies provide such insurance, which usually covers the top 20 percent of loans. In other words, if a borrower defaults and the property is foreclosed and sold for less than the amount of the loan, the PMI will reimburse the lender for a loss up to 20 percent of the loan amount. The net effect of the private mortgage insurance is to reduce default risk for lenders, which allows lenders to make loans to a larger pool of borrowers who are unable to place a 20% downpayment towards the purchase of a home.

5. Explain the maturity imbalance problem faced by savings and loan associations that hold fixed-payment mortgages as assets.

Solution: Savings and loan associations historically have used short-term savings deposits to fund long-term, fixed rate home loans. This mismatch in the maturity of assets and liabilities exposes them to severe interest rate risk. Consequently, the cost of funds from interest paid on short-term savings deposits may rise faster than the yield on their investments, or issued loans. A benefit of adjustable rate mortgages is that they closely track an institution’s cost of funds.

6. Suppose a homeowner has an existing mortgage loan with these terms: Remaining balance of $50,000, interest rate of 8%, and remaining term of 10 years (monthly payments). This loan can be replaced by a loan at an interest rate of 6 percent, at a cost of 8% of the outstanding loan amount. Should the homeowner refinance? What difference would it make if the homeowner expects to be in the home for only five more years?

Solution a, using net benefit analysis: The payment on the existing loan is $606.64 while the payment on a new loan for the remaining term of ten years would be $555.10. Thus, the new loan results in a monthly savings of $51.54. Over the ten years to maturity the

monthly savings sum to $6,184.80 (120 x $51.54). The cost of refinancing is 8 percent of the amount refinanced, or $4,000 (.08 x 50,000). Thus, to maturity, the estimated net benefit for refinancing would be $2,184.24 ($6,184.24 - $4,000). Over the expected holding period of five years the monthly savings sum to $3,092.12 (60 x $51.54). Thus the net benefit of refinancing would be negative $907.87 (3,092.12 – 4,000).

Solution b, using net present value (see online chapter appendix): The present value of the existing loan, with monthly payments of $606.64 discounted at 6%, is $54,641.98. The cost of refinancing is $4,000, which results in a NPV of $641.98 assuming the loan is held to maturity. If the loan is to be paid off anyway in five years, the benefit of refinancing is only $3,559.38 (n=60, I=.50, Pmt = 606.64, FV=29,918.43). Thus, NPV is negative ($3,559.38 - $4,000 = -440.62) if the homeowner expects to be in the home for only five more years.

7. Assume an elderly couple owns a $140,000 home that is free and clear of mortgage debt. A reverse annuity mortgage (RAM) lender has agreed to a $100,000 RAM. The loan term is 12 years, the contract is 9.25%, and payments will be made at the end of each month.

a. What is the monthly payment on this RAM?b. Fill in the following partial loan amortization table:

Month Beginning Balance Monthly Payment Interest Ending Balance12345

c. What will be the loan balance at the end of the 12-year term?d. What portion of the loan balance at the end of year 12 represents principal? What

portion represents interest?

Solution:

a. The monthly payment on the RAM is $381.32 (n=144, I=9.25, PV=0, FV=$100,000.)

b. The amortization is as follows:

Month Beginning Balance Monthly Payment Interest Ending Balance1 0 381.32 0 381.322 381.32 381.32 2.94 765.583 765.58 381.32 5.90 1,152.804 1,152.80 381.32 8.89 1,543.01

5 1,543.01 381.32 11.89 1,936.22

c. The balance at the end of 12 years is $100,000.d. Principal is 144 x 381.32, or $54,910. Interest is $45,090, or $100,000 -

$54,910.

8. Five years ago you borrowed $100,000 to finance the purchase of a $120,000 house. The interest rate on the old mortgage is 10%. Payment terms are being made monthly to amortize the loan over 30 years. You have found another lender who will refinance the current outstanding loan balance at 8% with monthly payments for 30 years. The new lender will charge two discount points on the loan. Other refinancing costs will equal $3,000. There are no prepayment penalties associated with either loan. You feel the appropriate opportunity cost to apply to this refinancing decision is 8%.

a. What is the payment on the old loan?b. What is the current loan balance on the old loan (five years after origination)?c. What should be the monthly payment on the new loan?d. Should you refinance today if the new loan is expected to be outstanding for five

years?

Solution:a. The payment on the old loan is $877.57.b. The current balance is $96,574.32.c. The payment on the new loan is $708.63.d. If the new loan is to be paid off in five years, the balance of the original loan after

year ten is $90,938.02, calculated with the following inputs: (N = 240, I = 0.8333, PMT = 877.57, and FV = 0.

Answer based on net benefit analysis:A new loan at 8 percent with the same term as remains on the original loan (25 years) would have a payment of $745.38. The savings in monthly payment by going to the new loan is $132.19 (877.57 – 745.38). This results in an accumulated savings of $7,931.40 (60 x 132.19) over the assumed holding period of five years. The cost of refinancing is $3,000 plus two percent of the balance, or $1,931.49 (.02 x 96,574.32), for a sum of $4,931.49. Thus, the net benefit is $2,999.91 (7,931.40 – 4,931.49), and refinancing is financially beneficial.

Answer based on net present value:The present value of the old loan, paid off 5 years from today is 104,318.93 (N = 60, I=0.6667, PMT=$877.57, FV= 90,938.02).

The PV of payment reductions is $7,744.61 (104,318.93 – 96,574.32).

The cost of refinancing is $3,000 plus 1,931.49 (0.02 x 96,574.32), or 4,931.49.

The NPV of refinancing the loan is $2,813.12 (7,744.61 – 4,931.49). Therefore, you should refinance today if the new loan is expected to be outstanding for five years.

CHAPTER 11

Sources of Funds for Residential Mortgages

Test Problems

1. Mortgage banking companies:a. Collect monthly payments and forward them to the mortgage investor.

2. In recent years, the mortgage banking industry has experienced:d. Rapid consolidation.

3. Currently, which type of financial institution in the primary mortgage market provides the most funds for the residential (owner-occupied) housing market?d. Commercial banks

4. For all except very high loan-to-value conventional home loans the standard payment ratios for underwriting are:a. 28 percent and 36 percent

5. The numerator of the standard housing expense (front-end) ratio in home loan underwriting includes:c. Monthly principal, interest, property taxes, and hazard insurance.

6. The most profitable activity of residential mortgage bankers is typicallyb. Loan servicing.

7. Potential justifiable subprime borrowers include persons who:d. All of these.

8. The normal securitization channel for jumbo conventional loans is:c. Private conduits.

9. The reduced importance of certain institutions in the primary mortgage market has been largely offset by an expanded role for others. Which has diminished and which has expanded?d. Savings and loan associations; mortgage bankers.

10. Warehousing in home mortgage lending refers tob. Short-term loans made by commercial banks to mortgage bankers.

Study Questions

1. What is the primary purpose of the risk-based capital requirements that Congress enacted as part of the Financial Institutions Reform, Recovery, and Enforcement Act (FIRREA)?

Solution: The goal of the Financial Institutions Reform, Recovery, and Enforcement Act is to charge banks and thrifts for risky lending practices and to reward safer practices. It supplanted the conventional regulatory approach of simply attempting to prohibit risky behavior even though banks and thrifts found the risk-taking profitable.

2. Explain what is meant by forward commitments and standby forward commitments. Which part of the mortgage banker’s pipeline is often hedged with forward commitments? With standby forward commitments? Why?

Solution: A forward commitment is a commitment now to sell/buy something in the future at a price set now. The commitment is mandatory; that is, the parties must complete the transaction. A standby forward commitment is the same arrangement except that one party, usually the seller, has the option of completing the transaction (delivering) or abandoning the contract.

Mortgage bankers use forward commitments to hedge against price changes on loans. This commitment obligates the secondary market investor to purchase, and the mortgage banker to sell, a pre-specified dollar amount of a certain type of loan. It is used for loans that are sure to be originated.

Standby forward commitments hedge price changes for loans that may or may not be originated. Standby forward commitments from secondary market investors give lenders the right, but not the obligation, to sell a certain dollar amount of a certain loan type to the issuer of the standby commitment.

3. Describe the basic activities of Fannie Mae in the secondary mortgage market. How are these activities financed?

Solution: Fannie Mae purchases both conventional and government-underwritten residential mortgages from mortgage companies, commercial banks, savings and loan associations, and other approved lenders. Part of these acquired mortgages are combined into packages or mortgage pools, mortgage-backed securities are written against the pools, and the MBSs are then sold to investors. Another part of the acquired mortgages are “held in portfolio.”

The agency only needs to fund securitized loans until they are sold as securities. For loans held in portfolio its obtains funds for the acquisition of mortgages by obtaining (forward) commitment fees from originating lenders for loan purchases, by earning

interest on its mortgage portfolio and other investments, and by selling notes and bonds to fixed-income investors.

4. Explain the importance of Fannie Mae and Freddie Mac to the housing finance system in the United States.

Solution: Fannie Mae and Freddie Mac have had a vast array of effects on the housing finance system of the U.S. Their first impact was to bring much-needed liquidity to housing finance. Probably their second effect was to standardize the documents and procedures in home mortgage lending. A third effect has been to encourage greater efficiency and flexibility in the process of home mortgage lending. Another effect has been to broaden the range of households able to obtain mortgage financing through more sophisticated and effective loan underwriting. Finally, they have had a great effect on the types of loans presently available to homeowners. Through all of this the GSEs have reduced the interest rates and costs of borrowing for homeowners.

5. What went wrong with mortgage brokerage? Is it being fixed?

Solution: There were at least three fundamental problems with residential mortgage brokerage as practiced in the years up to 2009. First, brokers were compensated at the beginning of a transaction and had no continuing responsibility or liability. Thus they could not be held financially accountable for errors or bad practices. Second, there were few, if any, qualification requirements enforced for a person to act as a broker. Third, brokers tended to be given larger fees for higher cost loans, encouraging them to lead borrowers toward high-cost loans. Some states, and the Congress, have passed legislation both to impose national broker qualification requirements and probably to prevent fees that increase with the cost of the loan. The effect of this legislation remains to be seen.

6. Describe the mechanics of warehouse financing in mortgage banking..

Solution: A warehouse loan is a credit line provided by large banks to mortgage bankers to fund loans. The originated mortgage serves as security to the lender and the lender is repaid when the loan is closed and sold in the secondary mortgage market. In this arrangement the mortgage banker places the escrow deposits for the loan (deposits for expected property tax and hazard insurance payments) with the warehouse lender, at no interest charge. In return, the mortgage banker receives a favorable interest rate on the warehouse credit line.

7. Explain how affordable housing loans differ from standard home loans.

Solution: Affordable housing loans include a low down payment requirement and allow for extensive flexibility in one of the "three Cs" of underwriting, while maintaining the other two at more normal standards. Therefore, three factors involved in qualifying for a loan may be relaxed: the loan-to-value ratio, credit qualifications, and payment capacity.

8. List three “clienteles” for subprime home mortgage loans.

Solution: Three clienteles for subprime loans are borrowers with inadequate income documentation, borrowers who want 100 percent or greater financing, and borrowers who have a poor credit record.

9. You have just signed a contract to purchase your dream house. The price is $120,000 and you have applied for a $100,000, 30-year, 5.5 percent loan. Annual property taxes are expected to be $2,000. Hazard insurance will cost $400 per year. Your car payment is $400, with 36 months left. Your monthly gross income is $5,000. Calculate:

a. The monthly payment of principal and interest (PI).b. One-twelfth of annual property tax payments and hazard insurance payments.c. Monthly PITI (principal, interest, taxes, and insurance).d. The housing expense (front-end) ratio.e. The total obligations (back-end) ratio.

Solution:

a. $567.79b. 200c. 767.79d. 15.36% (767.79/5,000)e. 23.36% ((767.79 + 200 + 400)/5,000)

10. Contrast automated underwriting with the traditional “Three Cs” approach

Solution: In automated underwriting, the three Cs are used as factors with other criteria in a statistical evaluation that is designed to distinguish risky from safe borrower. A critical difference from the traditional approach is that credit evaluation is accomplished through a credit score. Two advantages of automated underwriting are that it is faster than traditional underwriting, and it enables lenders to more safely make “affordable housing” loans.

CHAPTER 16Commercial Mortgage Types and Decisions

Test Problems

1. Due-on-sales clauses are included in commercial mortgages primarily to protect lenders from:b. Default risk.

2. Consider a 30-year, 7 percent, fixed rate, fully amortizing mortgage with a yield maintenance provision. Relative to this mortgage, a 10-year balloon mortgage with the same interest rate and yield maintenance provisions will primarily reduce the lender’s:a. Interest rate risk.

3. Lockout provisions are primarily intended to reduce the lender’s :c. Reinvestment risk

4. The tax-benefits associated with installment sales are:b. Captured exclusively by the seller.

5. Which of the following statements is most accurate?b. Joint ventures usually decrease the amount of equity capital the developer/borrower must invest in the project.

6. Which of the following financing structures provides for 100 percent financing?d. Complete (land and building) sale-leaseback

7. Using financial leverage on a real estate investment can be for the purpose of all of the following except:d. Reduction of financial risk for the leveraged investment.

8. Which of these ratios is an indicator of the financial risk for an income property?d. Both a and b, but not c

9. If the property’s NOI is expected to be $22,560 operating expenses $12,250, and the debt service $19,987, the debt coverage ratio (DCR) is approximately equal to:b. 1.13.

10. With a mezzanine loanc. the borrower’s promise to pay is secured by the equity interest in the borrower’s limited partnership or limited liability company.

Study Questions

1. Discuss several differences between long-term commercial mortgages and their residential counterparts.

Solution: Commercial mortgages have shorter terms than residential mortgages; five to ten- year terms are common for commercial mortgages and residential mortgages can be payable for up to 30 years. Commercial loans are typically nonrecourse, while residential borrowers are personally responsible for the amount borrowed. Restrictions on

prepayment are commonly included with commercial mortgages but not residential mortgages. Residential mortgages are typically standardized; in contrast, most commercial mortgages do not conform to any specific standards or regulations, although this is changing rapidly as an increasing number of commercial real estate loans are being securitized.

2. Answer the following questions on financial leverage, value, and return:a. Define financial riskb. Should the investor select the origination LTV that maximizes the IRR on equity?

Explain why or why not.

Solution:

a. Financial risk refers to the risk that NOI will be less than debt service. A positive correlation exists between the amount of debt service and financial risk.

b. Higher expected returns are gained from additional leverage but the average return per unit of risk decreases as leverage increases. Leverage maximizes return when a property is performing well but amplifies the downside when a property is performing poorly. Therefore, the use of leverage may increase the investor’s going-in IRR on equity, but financial leverage also increases the riskiness of the equity because of the increased risk of default and the increased sensitivity of the realized return on equity to changes in rental rates and resale values. Thus, the increase in expected return from the use of debt may not be large enough to offset the corresponding increase in risk.

3. Distinguish between recourse and nonrecourse financing.

Solution: When a note is used and the borrower has personal liability, the arrangement is known as recourse financing. The borrower has personal responsibility for recourse debt, and, upon default and foreclosure, the borrower is liable for the difference between the proceeds generated from foreclosure sale and the amount owed to the lender. When a note is not used and the borrower does not have personal liability for the debt, the arrangement is known as nonrecourse financing. In these cases, the provisions of the debt are contained in the mortgage or a separate contract. The borrower is not personally liable for nonrecourse debt and the lender receives the property pledged as collateral in satisfaction of the loan deficiency.

4. Explain lockout provisions and yield-maintenance agreements. Does the inclusion of one or both of these provisions affect the borrower’s cost of debt financing? Explain.

Solution: A lockout provision prohibits prepayment of a commercial mortgage over a specified period after the origination of the mortgage. This provision reduces a lender’s reinvestment risk from prepayments in falling interest rate environments.

A yield-maintenance agreement is another mechanism for creating a prepayment penalty. If interest rates decline and borrowers could prepay at par, lenders would have to reinvest the remaining loan balance at current (lower) rates. The prepayment penalty paid by borrowers with a yield maintenance agreement is set equal to the present value of the lender’s loss resulting from reinvesting the remaining loan balance at the lower market rates. The yield-maintenance provision restores the lender’s position as if rates had never changed and no prepayment had occurred.

The borrower’s cost of debt financing is effectively increased because of these provisions. Unlike residential borrowers, who generally have the ability to prepay or refinance existing debt without charge, commercial borrowers are unable to reduce their cost of debt financing if market interest rates fall.

5. Assume the annual interest rate on a $500,000 7-year balloon mortgage is 6 percent. Payments will be made monthly based on a 30-year amortization schedule.

a. What will be the monthly payment?b. What will be the balance of the loan at the end of year 7?c. What will be the balance of the loan at the end of year 3?d. Assume that interest rates have fallen to 4.5% at the end of year 3. If the

remaining mortgage balance at the end of year 3 is refinanced at the 4.5 percent annual rate, what would be the new monthly payment assuming a 27-year amortization schedule?

e. What is the difference in the old 6 percent monthly payment and the new 4.5 percent payment?

f. What will be the remaining mortgage balance on the new 4.5 percent loan at the end of year 7 (four years after refinancing)?

g. What will be the difference in the remaining mortgage balances at the end of year 7 (four years after refinancing)?

h. At the end of year 3 (beginning of year 4), what will be the present value of the difference in monthly payments in years 4-7, discounting at an annual rate of 4.5 percent?

i. At the end of year 3 (beginning of year 4), what will be the present value of the difference in loan balances at the end of year 7, discounting at an annual rate of 4.5 percent?

j. At the end of year 3 (beginning of year 4), what will be the total present value of lost payments in years 4-7 from the lender’s perspective?

k. If the mortgage contains a yield maintenance agreement that requires the borrower to pay a lump sum prepayment penalty at the end of year 3 equal to the present value of the borrower’s lost payments in years 4-7, what should that lump sum penalty be?

Solution:a. Based on a 30-year amortization schedule, the monthly payment is $2,997.75

(n=360, I =6/12, PV=-500,000, and FV = 0).

b. The balance of the loan at the end of year 7 is $448,197 (solving for the present value of the remaining payments: N=276, I =6/12, PV= ?, PMT = 2,997.75, and FV=0).

c. The balance of the loan at the end of year 3 is $480,420 (solving for the present value of the remaining payments: N=324, I =6/12, PV= ?, PMT = 2,997.75, and FV=0).

d. The new monthly payment assuming a 27-year amortization schedule is $2,564.10 (n=324, I =4.5/12, PV = 480,420.35, and FV = 0).

e. The new loan payment on the new 4.5 percent loan is $433.65 less than the payment on the old 6 percent loan.

f. The remaining mortgage balance on the new 4.5 percent loan at the end of year 7 (four years after refinancing) is $440,400 (solving for the future value: n=48, I = 4.5/12, PV = 480,420 and PMT = 2,564.10.

g. The difference in the remaining mortgage balances at the end of year 7 (four years after refinancing) is as follows: The balance at year seven for the original loan at 7% is $448,197. The balance of the new loan fours years after refinancing is $440,400. The difference between the two is $7,797.

h. At the end of year 3 (beginning of year 4), the present value of the differences in monthly payments in years 4-7, discounting at an annual rate of 4.5 percent, is $19,017 (n = 48, I = 4.5/12, PMT= 433.65, and FV = 0).

i. At the end of year 3 (beginning of year 4), the present value of the differences in loan balances at the end of year 7, discounting at an annual rate of 4.5 percent, is $6,515 (n = 48, I = 4.5/12, PMT = 0, and FV = 7,797).

j. At the end of year 3 (beginning of year 4), the total present value of lost payments in years 4-7 from the lender’s perspective is $19,017 (n = 48, I = 4.5/12, PMT = 433.65, and FV = 0)

k. The lump sum payment should be 25,532 ($19,017 + $6,515).

6. Consider the stand-alone locations favored by Walgreens for locating their drugstores. In most cases, Walgreens does not own these properties. Instead, they lease the properties on a long-term basis from institutional owners. What does Walgreens gain by leasing instead of owning? What do they lose?

Solution: Walgreens obtains the use of a structure that is well suited to its needs. They gain the benefit of investing their funds in its core business operations rather than committing their money in real estate. They also benefit from tax benefits associated with sale-leasebacks. Conversely, Walgreens will not benefit from the appreciation of the property and the tax depreciation benefits that come with ownership.

7. Consider the following table of annual mortgage rates and yields on 10-year Treasury securities.

a. What is the average annual spread on mortgage rates relative to the 10-year Treasury securities?

b. What is the correlation between annual mortgage rates and Treasury yields over the 1990-2005 period?

Solution:a. The average annual spread on mortgage rates relative to the 10-year Treasury

securities is 1.71%b. The correlation between annual mortgage rates and yields over the 1990-2005

period is 96.9%.

8. List and briefly describe the typical items included in a commercial mortgage loan application package.

Solution: Loan application packages typically include the following: Loan application – the specific document that serves as a request for

funds. Property description – a detailed description, including maps, photos,

surveys, etc., of the property securing the loan. Legal aspects – precise description of the property and identification of

any easements or encroachments. Cash flow estimates – a copy of the property’s financial statements and

rent roll to future income producing ability of the property. Appraisal report – a third-party appraisal of the property’s fair market

value.

9. List at least six characteristics of a commercial loan application that the lender should carefully evaluate.

Solution: Characteristics of a commercial loan application that the lender should carefully evaluate include the property type, location, tenant quality, lease terms, property management, building quality, environmental concerns, and borrower quality.

10. What is the difference in the present value of these two loan alternatives? Assume the appropriate discount rate is 6 percent.

Solution: The difference in NPVs is $50,000: Option “A” is more expensive.

Present value of Option A is $1,050,000: initial equity ($300,000) + upfront financing fees ($50,000) + present value of interest payments ($578,123) + present value of loan principal upon repayment ($121,877).

Present value of Option B is $1,000,000: initial equity ($250,000) + present value of interest payments ($619,417) + present value of loan principal upon repayment ($130,583).

11. You are considering the purchase of an industrial warehouse. a. Calculate the overall rate of return (or “cap rate”)b. Calculate the debt coverage ratio.c. What is the largest loan that you can obtain (holding the others terms constant) if

the lender requires a debt service coverage ratio of at least 1.2?

Solution:

a. The overall rate of return (or “going-in” cap rate) is 10.8% (NOI of 108,000/purchase price of 1,000,000)

b. The debt coverage ratio is computed below:

DCR = NOI/DS = 108,000/42,000 = 2.57

c. The maximum amount of interest that you can afford to pay based on the lender’s requirements is $90,000 (108,000/1.2). Therefore, the largest loan you can obtain is $90,000/.06, or $1,500,000.

12. Distinguish among land acquisitions loans, land development loans, and construction loans. How would you rank these three with respect to lender risk?

Solution: Land acquisition loans finance the purchase of raw land. Land development loans finance the installation of the onsite and offsite improvements to land that are necessary to prepare the land for construction. Construction loans are used to finance the costs associated with erecting the building(s).

13. Discuss the potential advantages of a miniperm loan from the prospective of the developer/investor, relative to the separate financing of each stage of the development.

Solution: The existence of a single lender and a single application process simplifies the financing process. Miniperm loans enable developers to proceed with construction without long-term financing. A miniperm loan is an attractive financing option if the developer expects to sell the project or refinance into a permanent loan before the term of the miniperm expires.

14. You are considering purchasing an office building for $2,500,000.a. What is the implied first-year overall capitalization rate?b. What is the expected debt coverage ratio in year 1 of operations?c. If the lender requires DCR to be 1.25 or greater, what is the maximum loan

amount?d. What is the break-even ratio?

Solution: a. PGI $450,000

Vacancy and collections (40,500)EGI 409,500Op Expenses and CAPX (171,990)NOI 237,510DS (138,170)BTCF $ 99,340

the implied first-year overall capitalization rate is $237,510/$2,500,000 or 0.095b. The expected debt coverage ratio in year 1 of operations is 1.72

($237,510/$138,170)c. If the lender requires DCR to be 1.25 or greater, the maximum loan amount is

determined by first calculating the maximum debt service amount: $190,008 ($237,510/1.25). The maximum loan amount implied by this debt service amount is $2,578,460 (N = 300, I = 5.5/12, PMT = 190,008/12, and FV = 0)

d. The break-even ratio is 68.9% ($171,990 + $138,170)/ ($450,000).

CHAPTER 17SOURCES OF COMERCIAL DEBT AND EQUITY CAPITAL

Test Problems

1. Double taxation is most likely to occur if the commercial properties are held in the form of a(n):c. C Corporation

2. With regard to double taxation, distributions, and the treatment of the losses, general partnerships are most like:c. Limited partnerships

3. Special allocations of income or loss are available if the form of ownership is a(n):c. Limited partnership

4. Real estate syndicates traditionally have been legally organized most frequently as: c. Limited partnerships

5. A real estate investment trust generally:d. None of the above

6. Which of the following forms of ownership involve both limited and unlimited liability?a. limited partnerships

7. Which statement is false concerning the limited partnership of ownership?c. The limited partners cannot enjoy tax deduction benefits but the general partners can.

8. Which of these lenders is most likely to provide a construction loan?c. Commercial bank

9. Which of these loans is a life insurance company most likely to invest in?c. Large office building loan (nonconstruction)

10. Which of these financial firms is the least likely to invest in a large, long-term mortgage loan on a shopping center?d. Mortgage broker

Study Questions

1. For what debt in a general partnership is each of the general partners liable?

Solution: General partners have unlimited liability and are liable for all debts of the partnership. This includes contractual debts and debts resulting from tort actions against the partnership. General partners are also jointly and severally liable for wrongful acts committed by other partners in the course of the partnership’s business. Therefore, the personal assets of the general partners are subject to the claims of the partnership’s creditors.

2. Why are many pension funds reluctant to invest in commercial real estate?

Solution: Pension funds have historically viewed real estate as too risky, difficult to manage, and illiquid. Addtionally, the lack of available information for performing quantitative investment analysis has also contributed to the reluctance of pension funds to invest in real estate.

3. Discuss the role life insurance companies play in financing commercial real estate.

Solution: Given the long-term nature of their liabilities, life insurance companies prefer to invest in assets on a long-term basis. They are a major source of commercial real estate capital and are heavily involved in the long-term commercial mortgage market.

4. Approximately 88 percent of investable commercial real estate (on a value- weighted basis) is owned by “noninstitutional” investors. Who are these investors?

Solution: These “noninstitutional” investors include both individual investors and groups of private investors who pool their capital via several types of ownership structures, including C corporations, S corporations, general partnerships, limited partnerships, and limited liability companies, to purchase real estate assets. Pooled investments comprise the bulk of the market value of real estate held by “noninstitutional” investors. Individual investors, or investors who

own property jointly with other family members, comprise a small fraction of these “noninstitutional” investors.

5. Briefly explain a commingled fund. Who are the investors in these funds and why do these investors use commingled funds for their purchases?

Solution: A commingled fund is a means for pension funds that do not possess sufficient in-house real estate expertise to invest in real estate. Pension funds contribute funds to a real estate fund manager who pools, or commingles, these funds with finds from other pension funds to purchase real estate assets.

6. There are two primary considerations that affect the form in which investors choose to hold commercial real estate. List each and explain how they affect the choice of ownership form.

Solution: Federal income taxation rules, and the avoidance of personal liability for debts and obligations affect the form in which investors choose to hold commercial real estate.

Federal income taxation is a critical factor in the determination of which ownership form to use in real estate investment. The income produced by properties owned by C corporations is potentially subject to double taxation because tax is assessed at both the corporate and investor level. S corporations, limited liability companies, general partnerships, and limited partnerships are pass-through entities and avoid double taxation. A limited partnership has the added benefit of permitting special allocations of cash distributions and taxable income.

Investors prefer ownership structures that provide limited liability. C corporations, S corporations, limited partnerships, and limited liability companies shield investors from any personal liability; liability is restricted to the amount of capital invested. General partnerships require at least one general partner who has unlimited liability for the debts of the partnership.

7. Explain what is meant by the double taxation of income.

Solution: Double taxation refers to the taxation of income at both the entity and investor level. For example, a C corporation pays tax on its income, which reduces the amount available to be distributed to shareholders by the amount of the entity-level tax. Shareholders are then taxed on the income distributed to them in the form of dividends, resulting in the double taxation of the income generated by the corporation.

8. What are the major restrictions that a REIT must meet on an ongoing basis in order to avoid taxation at the entity level?

Solution: A REIT must have at least 100 shareholders and 50 percent or more of the REIT’s shares cannot be owned by five or fewer investors. A REIT is required to distribute at least 90 percent of its taxable income to shareholders in the form of dividends. A REIT is required to have at least 75 percent of its assets invested in real estate assets, cash, and government

securities. Additionally, 75 percent of a REIT’s gross income must be derived from real estate assets.

9. Compare the tax advantages and disadvantages of holding income-producing property in the form of a REIT to the tax advantaged and disadvantages of holding property in the form of a real estate limited partnership. Does either form dominate from a tax perspective?

Solution:

A REIT is a C corporation and but, unlike the standard C corporation, does not pay income tax at the entity level if it adheres to a set of conditions outlined in the Internal Revenue Code. A disadvantage of the REIT ownership form is that tax losses do not pass through to shareholders.

Real estate limited partnerships are not subject to double taxation because income tax is not assessed at the entity level. Limited partnerships may allocate tax losses to partners, but the ability of limited partners to use tax losses is potentially limited by passive activity loss restrictions.

In practice and from a tax perspective, pass through entities such as limited partnerships and limited liability companies are the dominant form of ownership structures used to invest in real estate assets. However, REITs are also able to avoid double taxation and are favored as a form of ownership by some investors.

10. Of the more than $3.6 trillion in outstanding commercial real estate debt, what percent is traded in public markets? What percent is traded in private markets? What institutions or entities are the long-term holders of private commercial real estate debt? What is the fastest growing source of long-term mortgage funds?

Solution: Approximately 29 percent of commercial real estate debt is traded in public markets and the remaining 71 percent is privately held by institutional and individual investors. Commercial banks, savings institutions, and life insurance companies are the long-term holders of private commercial real estate debt. At least until 2008, Commercial mortgage-backed securities (CMBSs) had been the fastest growing source of long-term mortgage funds.

11. Distinguish among equity REITs, mortgage REITs, and hybrid REITs.

Solution: Equity REITs invest in and operate commercial properties. Mortgage REITs purchase mortgage obligations (typically commercial) and thus become, effectively, real estate lenders. Hybrid REITs invest a significant percentage of their assets in both properties and mortgages.

12. Define funds from operations (FFO) and explain why this measure is often used instead of GAAP net income to quantify the income-producing ability of a real estate investment trust.

Solution: GAAP accounting includes non-cash deductions, such as deprecation and amortization of certain financial and fixed assets. Therefore, if a REIT has significant depreciable assets,

which result in non-cash expense deductions for depreciation, GAAP net income may not reflect the net cash flow available to distribute to investors. Funds from operations (FFO) is an alternative earnings measure that adds back deprecation and amortization expenses to GAP income. Additionally, FFO adjusts GAAP income for gains and losses from infrequent and unusual events. Formally, FFO is defined as:

FFO = Net income (GAAP) + Depreciation (real property) + Amortization of leasing expenses + Amortization of tenant improvements

- Gains/losses from infrequent and unusual events

13. How have equity REITs, measured in terms of total returns, performed in recent years relative to alternative stock investments?

Solution: As a sector, equity REITs produced an average annual return of 22.9 percent from 2000-2006. The corresponding average return on the S&P 500 and Russell 2000 were 2.5 percent and 9.6 percent, respectively. In 2007 and 2008, however, equity REITs provided returns of -15.7 percent and -37.7 percent, respectively. This two-year total return of -59 percent was even worse than the -34 percent two-year return produced by the S&P 500.

Chapter 15Mortgage Calculations and Decisions

Test Problems

1. The most typical adjustment interval on an adjustable rate mortgage (ARM) once the interest begins to change is:b. One year.

2. A characteristic of a partially amortized loan is:b. A balloon payment is required at the end of the loan term.

3. If a mortgage is to mature (i.e. become due) at a certain future time without any reduction in principal, this is called:d. An interest-only mortgage.

4. The dominant loan type originated by most financial institutions is the:a. Fixed-payment, fully amortized mortgage

5. Which of the following statements is true about 15-year and 30-year fixed-payment mortgages?

d. Assuming they can afford the payments on both mortgages, borrowers usually should choose a 30-year mortgage over an otherwise identical 15-year loan if their discount rate (opportunity cost) exceeds the mortgage rate.

6. Adjustable rate mortgages (ARMs) commonly have all the following except:e. An inflation index.

7. The annual percentage rate (APR) was created by:a. The Truth-in-Lending Act of 1968

8. On a level-payment loan with 12 years (144 payments) remaining, at an interest rate of 9 percent, and with a payment of $1,000, the balance is:c. $87,871.

9. On the following loan, what is the best estimate of the effective borrowing cost if the loan is prepaid in six years?

Loan: $100,000Interest rate: 7 percentTerm: 180 monthsUp-front costs: 7 percent of loan amount

d. 8.7 percent.

10. Lender’s yield differs from effective borrowing costs (EBC) because: c. EBC accounts for additional up-front expenses that lender’s yield does not.

Study Questions

1. Calculate the original loan size of a fixed-payment mortgage if the monthly payment is $1,146.78, the annual interest is 8.0%, and the original loan term is 15 years.

Solution: Rounding to the nearest whole dollar, the original size of the loan is $120,000. This problem is solved using the following keystrokes on a financial calculator:

N = 180 I = 8/12 PV = ? PMT =$1,146.78 FV = 0

2. For a loan of $100,000, at 7 percent interest for 30 years, find the balance at the end of 4 years and 15 years.

Solution: The loans balance at the end of 4 years and 15 years is $95,474.55, and $74,018.87, respectively, as solved below

First, the loan payment must be calculated. The loan payment is $665.30, as solved below:

N = 360 I = .5833 PV = -$100,000 PMT =? FV = 0

The balance at the end of four years is $95,474.55, which is calculated by entering the following data into a financial calculator.

N = 312 I = .5833 PV = ? PMT =$665.30 FV =0

The balance at the end of 15 years is $74,018.87, which is calculated by entering the following data into a financial calculator.

N = 180 I = .5833 PV = ? PMT =$665.30 FV = 0

3. On an adjustable rate mortgage, do borrowers always prefer smaller (tighter) rate caps that limit the amount the contract interest rate can increase in any given year or over the life of the loan?

Solution: Borrower preference is dependent, at elast in part, on their expectations of future interest rates. Borrowers choosing ARMs with price caps are charged a higher initial interest rate, a higher margin, more upfront costs, or a combination of the three. The borrower must consider these factors. For example, borrowers may prefer larger caps if they believe interest rates will not increase substantially. In this scenario, the loan interest rate will be lower because the borrower, not the lender, bears the risk of interest rates increasing.

4. Consider a $75,000 mortgage loan with an annual interest rate of 8%. The loan term is 7 years, but monthly payments will be based on a 30-year amortization schedule. What is the monthly payment? What will be the balloon payment at the end of the loan term?

Solution: The monthly payment is $550.32 and the balloon payment is $69,358.07.

The payment is calculated using the following calculator keystrokes:

N = 360 I = .667 PV = -$75,000 PMT =? FV = 0

The balloon payment at the end of year seven is $69,358.07, as calculated with the following calculator keystrokes:

N = 276 I = .667 PV = ? PMT =550.32 FV = 0

5. A mortgage banker is originating a level-payment mortgage with the following terms:

Annual interest rate: 9 percentLoan term: 15 yearsPayment frequency: monthlyLoan amount: $160,000Total up-front financing costs (including discount points): $4,000Discount points to lender: $2,000

a. Calculate the annual percentage rate (APR) for Truth-in-Lending purposes.b. Calculate the lender’s yield with no prepayment.c. Calculate the lender’s yield with prepayment is five years.d. Calculate the effective borrowing costs with prepayment in five years.

Solution:

The first step is to solve for the payment, which is $1,622.83, with the following calculator keystrokes:

N = 180 I = .75 PV = -$160,000 PMT =? FV = 0

a. The APR is approximately 9.43 percent as solved below:

N = 180 I = ? PV = -$156,000 PMT =$1,622.83 FV = 0

b. The lender’s yield to maturity is 9.22 percent

N = 180 I = ? PV = -$158,000 PMT =$1,622.83 FV = 0

c. In order to calculate the lender’s yield, the loan balance remaining at the end of year five must first be calculated”

N = 120 I = .75 PV = ? PMT =$1,622.83 FV = 0

The remaining balance is $128,108.67. With this information, the lender’s yield is 9.34 percent as calculated below:

N = 60 I = ? PV = -$158,000 PMT =$1,622.83 FV =$128,108.67

d. The effective borrowing cost with prepayment in five years is 9.69 percent.

N = 60 I = ? PV = -$156,000 PMT =$1,622.83 FV =$128,108.67

6. Give some examples of up-front financing costs associated with residential mortgages. What rule can one apply to determine if a settlement (closing) cost should be included in the calculation of the effective borrowing costs?

Solution: Examples of upfront costs include discount points, loan origination fee, loan application and documentation preparation fees, appraisal fees, credit check fees, title insurance, mortgage insurance, charges to transfer the deed and record the mortgage, pest inspection, survey costs, and attorney’s fees.

The effective borrowing cost calculation should not include expenses that would be incurred if no mortgage financing were obtained. Therefore, only upfront costs associated with obtaining the mortgage funds should be included.

7. A homeowner is attempting to decide between a 15-year mortgage loan at 5.5 percent and a 30-year loan at 5.90 percent. What would you advise? What would you advise if the borrower also has a large amount of credit card debt outstanding at a rate of 15 percent?

Solution: If the borrower does not have a significant amount of debt at a rate well above the rates on the loan, then the difference in mortgage rates should be viewed as a maturity premium difference, and the borrower can consider the loans as equivalent on a purely financial basis. If the borrower owes significant amounts of high interest consumer debt, then the longer-term loan is preferable. It will have a lower present value (present cost) discounted at the borrower’s opportunity cost. In other words, if the opportunity costs of the household are substantially greater than the mortgage interest rate, the household will be better off with the longer-term mortgage.

8. Suppose a one-year ARM loan has a margin of 2.75, an initial index of 3.00 percent, a teaser rate for the first year of 4.00 percent, and a cap of 1.00 percent. If the index rate is 3.00 percent at the end of the first year, what will be the interest rate on the loan in year two? If there is more than one possible answer, what does the outcome depend on?

Solution: If the periodic cap applies to the teaser rate, the interest rate in year two will be constrained to 5.00 percent. If the cap applies only to index plus margin, the rate in year two would be 5.75 percent.

9. Assume the following for a one-year rate adjustable rate mortgage loan that is tied to the one-year Treasury rate:

Loan amount: $150,000Annual rate cap: 2%Life-of-loan cap: 5%Margin: 2.75%First-year contract rate: 5.50%One-year Treasury rate at end of year 1: 5.25%One-year Treasury rate at end of year 2: 5.50%

Loan term in years: 30

Given these assumptions, calculate the following:

a. Initial monthly paymentb. Loan balance end of year 1c. Year 2 contract rated. Year 2 monthly paymente. Loan balance end of year 2f. Year 3 contract rateg. Year 3 payment

Solution:a. The first year payment, based on an interest rate of 5.5 percent, is $851.68, as

calculated below:

N = 360 I = .4583 PV = -$150,000 PMT =? FV =0

b. The loan balance at the end of year one is $147,979, as shown below:

N = 348 I = .4583 PV = ? PMT =$851.68 FV =0

c. Assuming the annual cap applies to the teaser rate, the interest rate in year two is 5.50 plus 2.00, or 7.50 percent.

d. With a remaining term of 29 years, interest rate of 7.5 percent and a balance of $147,979.41, the new payment in year 2 is $1,044.32, calculated on a financial calculator with the following keystrokes.

N = 348 I = .6250 PV = -$147,979 PMT =? FV =0

e. The loan balance at the end of year two is $146,496:

N = 336 I = .6250 PV = ? PMT =$1,044.32 FV =0

f. The year three contract interest rate is index plus margin, or 8.25 percent.

g. The year three payment, based on a balance of $146,496, remaining term of 28 years and an interest rate of 8.25 percent, is $1,119.

10. Assume the following:

Loan Amount: $100,000Interest rate: 10 percent annually

Term: 15 years, monthly payments

a. What is the monthly payment?b. What will be the loan balance at the end of nine years?c. What is the effective borrowing cost on the loan if the lender charges 3 points at

origination and the loan goes to maturity?d. What is the effective borrowing cost on the loan if the lender charges 3 points at

origination and the loan is prepaid at the end of year 9?

Solution:a. The monthly payment is $1,074.61.

N = 180 I = .8333 PV = -$100,000 PMT =? FV =0

b. The loan balance at the end of 9 years is $58,006.

N = 252 I = .8333 PV = ? PMT =$1,074.61 FV =0

c. The effective borrowing cost of the loan, with financing costs of 3 discount points, that is held to maturity and is 10.54 percent:

N = 180 I = ? PV = -$97,000 PMT =$1,074.61 FV =0

d. The effective borrowing cost of the loan, with financing costs of 3 points, that is prepaid at the end of year nine and is 10.61 percent:

N = 108 I = ? PV = -$97,000 PMT =$1,074.61 FV =58,004.90

CHAPTER 21Enhancing Value through Ongoing Management

Test Problems

1. The Institute of Real Estate Management (IREM) awards which of the following designations?b. CPM.

2. A contractual relationship in which an individual must act in the best interests of a principal when dealing with a third party is termed:a. An agency relationship.

3. The requirement of a real estate property manager to act in the best interests of the landlord when dealing with a tenant is termed:

c. A fiduciary responsibility

4. Which of these is not typically a responsibility of a property manager?d. Income tax analysis.

5. Remodeling and rehabilitation:c. Are expected to add value to the property if undertaken.

6. Both the owner and the manager may be better off if property management compensation were based on a percentage of the property’s:c. Net operating income.

7. The following are necessary for a lease to be valid, except:c. Tenant’s contact phone number, or address, in the event of an emergency.

8. The asset manager is generally NOT responsible for: c. Making maintenance decisions.

9. Demolition of an existing property on an urban site will likely occur:c. When the site value, assuming a new use, exceeds the value of the site under its existing use, plus the cost of demolition.

10. For non-real estate corporations, which of the following is not a potential advantage of a real estate sale-leaseback?c. The firm benefits from property appreciation that occurs after the sale-leaseback.

Study Questions

1. An investor purchased a property with an equity investment of $100,000 and an $800,000 mortgage. She has held the property for five years, and the mortgage now has a balance of $750,000. The market value of her property is estimated to be $950,000. What is her present equity investment?

Solution: Her current equity investment in the property is $200,000, which is equal to the current market value of the property ($950,000) minus the current loan balance ($750,000).

2. What should be included as costs to be matched by value added after rehabilitation?

Solution: An improvement, such as rehabilitation, should be undertaken only if the value added to the property exceeds the cost of improvements, which include material, labor, the contractor’s profit, architect’s fees, and an allowance for contingencies. If the rehab work prevented the owner from renting all or part of the structure for some period of time, the present value of the lost net rental income should be included as a cost.

3. In what ways are the maintenance and repair decision and the rehabilitation decision similar? How do they differ?

Solution: Maintenance and repair costs include expenditures for custodial, corrective, and preventive costs. Sometimes, costs related to the performance of ordinary maintenance are not undertaken; they are deferred. The deferment of such costs may increase the short-term NOI of the property but may result in the accelerated deterioration of the building and reduced cash flows in the future.

Rehabilitation costs include painting, roof replacement, or the replacement of other deteriorated portions of the building. The need to perform rehabilitation costs may be the result of deferred maintenance. Therefore, unlike maintenance and repair costs, rehabilitation costs are not recurring costs related to maintaining the property for ordinary use; rehabilitation costs add value to a property.

The decisions to undertake either maintenance and repair costs or rehabilitation costs are investment decisions. The decision to perform or forego maintenance costs must be evaluated from an economic perspective, as are rehabilitation costs. Neither category of costs results in modifications to the property structure.

4. What factors can change after rehabilitation of a property to produce a higher “after” value than “before” value?

Solution: The rehabilitation of a property can result in a larger net operating income, an extension of the building’s remaining economic life, or a reduction in discount rate used to calculate the present value of future income.

5. What does the property management agreement accomplish?

Solution: The management agreement is the basis of the relationship between the property owner and property manager. This management agreement establishes the manager’s duties, authority, and compensation. The management agreement creates an agency relationship and establishes the fiduciary responsibility of the manager to act in the best interest of the property owner.

6. How does routine maintenance and repair affect a property’s performance?

Solution: Routine maintenance and repair expenditures maintain the condition and economic performance of a property. These costs do not increase the value or economic performance of a property but merely maintain the property’s level of performance. Ideally, the present value of money spent on maintenance and repairs will be equal to or less than the present value of the loss in net operating income and sale proceeds that is averted by undertaking the expenditures. The deferment of routine maintenance and repair expenditures may increase the short-term NOI of the property, but this may result in the accelerated deterioration of the building, which, in turn, will reduce net rental income and the property’s market value.

7. Define deferred maintenance and list some examples.

Solution: Deferred maintenance describes costs related to ordinary maintenance that is not performed at the time a problem is detected. Examples of deferred maintenance include needed roof repairs, HVAC & control systems that are not functioning efficiently, floor repairs, old paint, and broken windows.

8. How is the financial compensation for property managers usually determined? What “agency” problem does this seem to create?

Solution: The typical property management fee is based on a percentage of gross rental income. An agency problem is created by this arrangement because the property manager may be motivated to overly maintain the property or pursue other strategies to promote and maximize the property’s gross income. This may occur because the contract rewards the maximization of gross income with no explicit incentive to minimize operating costs. Therefore, the property manager may be more concerned about the top line and not the bottom line.

9. Why is the tenant mix critically important to the performance of shopping center investments?

Solution: The correct mix of tenants in a shipping center can maximize each individual tenant’s sales and the property’s total rent potential. Synergies are created from the complimentary relationship of the property’s tenants. For example, customers shopping at a large anchor store may shop at a smaller business located next to a larger anchor store.

10. In the real estate asset management/investment advisory business, why has performance-based management replaced, or at least supplemented, the “traditional” scheme for compensating some asset managers?

Solution: The practice of compensating asset managers based on the value of net assets managed creates an agency problem because managers have the incentive to acquire and hold assets--rather than maximizing the investor’s rate of return. Establishing management compensation based on maximizing the investor’s rate of return better aligns the interests of the manager and investor/principal.

11. In the context of asset management agreements in the private commercial real estate industry, what is a benchmark index? What is the most typical benchmark index?

Solution: A benchmark index is a reference point that can be used as a standard to measure the relative performance of an asset manager. The typical benchmark index for evaluating the performance of a manager/adviser hired to acquire and manage a portfolio of publicly traded REITS is produced by NAREIT and Wilshire Associates. The most frequently used index to evaluate the performance of privately held and traded commercial properties is produced by NCREIF.

12. With respect to complying with applicable landlord-tenant laws, would you rather be managing an apartment complex or an office building? Explain.

Solution: In general, managing a commercial property, such as an office building, is less problematic than managing an apartment complex for various reasons. State law governs landlord-tenant relationships in the commercial arena, and state courts strictly interpret the language of commercial lease agreements. It is assumed that the parties entering into a commercial lease are competent businesspersons. Although, residential rental properties are also governed by state law, state legislators have passed detailed legislation to protect the rights and interests of households in order to level the playing field between landlords and tenants. Residential tenants are also given certain rights under state laws and landlord actions are restricted under state law.

CHAPTER 23

DEVELOPMENT: THE DYNAMICS OF CREATING VALUE

Test Problems

1. The first step in the process of development is to:a. Establishing site control.

2. To gain control of a site, a developer may use:e. All of the above

3. Which of these stages of the development process comes first?a. Feasibility analysis, refinement, and testing

4. All of the following are valuable in facilitating the development permitting process except: d. Establishing the strength of your legal position early in the process.

5. A method of construction where the actual construction begins before the design is finished is known as:d. Fast-track.

6. In a land-development, the primary design professional is a :c. Land planner.

7. Soft costs include all except: e. Land improvement costs.

8. Which statement is incorrect concerning the typical construction loan?d. The loan extends a few years after a certificate of occupancy is issued.

9. The professional responsible for determining adequate specifications for building footings and foundation is a:d. Soils engineer.

10. When construction costs exceed the amount of the construction loan, a developer frequently will seek to cover the “gap” with:c. Mezzanine financing.

Study Questions

1. Why is the permitting stage of development often the riskiest stage of the process?

Solution: The process of obtaining permitting entails a commitment of significant time and cost. However, the ultimate outcome is uncertain as to whether the project will go

forward. Public hearings, for example, are especially treacherous for developers because the local land use authorities may effectively kill a project. Furthermore, community opposition to the developer’s plans may result in costly delays or force the developer to terminate the project.

2. List at least five ways that a developer may attempt to reduce the risks of the permitting process.

Solution: A developer may attempt to reduce the risks associated with the permitting process in many ways. The developer may offer provisions for buffering the surrounding land from the proposed project. The developer may provide an improvement, such as a park, that will benefit the local neighborhood. The developer should be prepared to negotiate with the land use authorities and neighborhood owners groups. The developer should establish a positive relationship with the local regulatory authorities and keep them informed throughout the development process.

3. Explain what a construction manager is, and why the role could be important in development.

Solution: A construction manager serves as the developer’s liaison and representative on the project site. This is an especially important role because the developer is responsible for monitoring and addressing any problems that occur during the construction process. The construction manager also may stand in for the developer in meetings between the general contractor and architect.

4. In selecting an architect, what must a developer consider about the architect besides design credentials and relevant experience?

Solution: The selection of an architect is a critical decision for the developer. It is important that the architect have values and goals that are comparable to those of the developer. Another selection factor is the architect’s communication skills and rapport with the developer. Addtionally, the presentation skills of the architect are important because architects play a vital role in representing the developer in public meetings with land authorities, particularly during the permitting stage.

5. Why, in some cases, must a developer begin leasing efforts even before the design is complete?

Solution: Depending on the property type, leasing efforts should begin before the completion of the design stage. For example, leasing efforts for office buildings and other facilities with long-term tenants should typically begin well before the tenant actually requires space. Presales are also frequently required for obtaining financing for condominium projects. Retail and office projects may not be viable without securing anchor tenants. Take-out commitments for construction loan financing frequently require preleasing to be in process.

6. Compare the advantages of competitive bidding for a general contractor with negotiated cost plus fee. What is the argument for using a maximum cost with sharing of overruns or savings between developer and general contractor?

Solution: The advantage of competitive bidding for a general contractor is that the selection criterion is based purely on the lowest cost contract price. It places a premium on delivering the proposed project at the lowest possible price. A critical assumption in competitive bidding is that the bidders will offer bids based on acceptable quality standards, and will execute construction at those standards. Unfortunately, this is sometimes difficult to assure. Assuming an owner has confidence in the professionalism of all the bidders, a competitive bidding situation can be a good solution to a situation where the primary need is to maximize the value of every dollar committed to the project.Also, most government projects are based on competitive bidding for a general contractor.

On the other hand, a negotiated cost and fee contract reduces the incentive to “cut costs” while including a maximum cost provision. Therefore, if the cost exceeds the maximum contract amount, the developer and general contractor split the overrun. Conversely, if the cost is less than the maximum amount, the savings are shared by both parties.

7. Explain the possible advantages of miniperm financing as opposed to traditional construction financing followed by “permanent” financing.

Solution: A miniperm loan serves as a construction loan for a few years after the property is completed. The typical term for a minperm loan is five years.As a rental property becomes fully occupied and establishes a performance record, it tends to reduce the property’s risk and increase its value. Therefore, a year or two after initial occupancy, lower cost financing may be available. A mini-perm loan can enable the owner to reach that point before needing to pay off the construction financing.

8. Why is property development more vulnerable to business cycle risk than investment in existing property of similar type?

Solution: New development projects typically possess the highest cost structure in the real estate market and, consequently, have the highest break-even cost points. Therefore, a downturn in the business cycle will adversely affect a new project more severely.

After reading this chapter, students should be able to:

Define dollar return and rate of return.

Define risk and calculate the expected rate of return, standard deviation, and coefficient of variation for a probability distribution.

Specify how risk aversion influences required rates of return.

Graph diversifiable risk and market risk; explain which of these is relevant to a well-diversified investor.

State the basic proposition of the Capital Asset Pricing Model (CAPM) and explain how and why a portfolio’s risk may be reduced.

Explain the significance of a stock’s beta coefficient, and use the Security Market Line to calculate a stock’s required rate of return.

List changes in the market or within a firm that would cause the required rate of return on the firm’s stock to change.

Identify concerns about beta and the CAPM.

Explain how stock price volatility is more likely to imply risk than earnings volatility.

Chapter 6Risk and Rates of Return

LEARNING OBJECTIVES

Risk analysis is an important topic, but it is difficult to teach at the introductory level. We just try to give students an intuitive overview of how risk can be defined and measured, and leave a technical treatment to advanced courses. Our primary goals are to be sure students understand (1) that investment risk is the uncertainty about returns on an asset, (2) the concept of portfolio risk, and (3) the effects of risk on required rates of return.

What we cover, and the way we cover it, can be seen by scanning Blueprints, Chapter 6. For other suggestions about the lecture, please see the “Lecture Suggestions” in Chapter 2, where we describe how we conduct our classes.

DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods)

Harcourt Brace & Company Lecture Suggestions: 5 - 105

LECTURE SUGGESTIONS

6-1 a. The probability distribution for complete certainty is a vertical line.

b. The probability distribution for total uncertainty is the X-axis from - to +.

6-2 Security A is less risky if held in a diversified portfolio because of its negative correlation with other stocks. In a single-asset portfolio, Security A would be more risky because A > B and CVA > CVB.

6-3 a. No, it is not riskless. The portfolio would be free of default risk and liquidity risk, but inflation could erode the portfolio’s purchasing power. If the actual inflation rate is greater than that expected, interest rates in general will rise to incorporate a larger inflation premium (IP) and--as we shall see in Chapter 8--the value of the portfolio would decline.

b. No, you would be subject to reinvestment rate risk. You might expect to “roll over” the Treasury bills at a constant (or even increasing) rate of interest, but if interest rates fall, your investment income will decrease.

c. A U.S. government-backed bond that provided interest with constant purchasing power (that is, an indexed bond) would be close to riskless. The U.S. Treasury currently issues indexed bonds.

6-4 a. The expected return on a life insurance policy is calculated just as for a common stock. Each outcome is multiplied by its probability of occurrence, and then these products are summed. For example, suppose a 1-year term policy pays $10,000 at death, and the probability of the policyholder’s death in that year is 2 percent. Then, there is a 98 percent probability of zero return and a 2 percent probability of $10,000:

Expected return = 0.98($0) + 0.02($10,000) = $200.

This expected return could be compared to the premium paid. Generally, the premium will be larger because of sales and administrative costs, and insurance company profits, indicating a negative expected rate of return on the investment in the policy.

b. There is a perfect negative correlation between the returns on the life insurance policy and the returns on the policyholder’s human capital. In fact, these events (death and future lifetime earnings capacity) are mutually exclusive.

c. People are generally risk averse. Therefore, they are willing to pay a premium to decrease the uncertainty of their future cash flows. A life insurance policy guarantees an income (the face value of the policy) to the policyholder’s beneficiaries when the policyholder’s future earnings capacity drops to zero.

6-5 The risk premium on a high-beta stock would increase more.

RPj = Risk Premium for Stock j = (kM - kRF)bj.

If risk aversion increases, the slope of the SML will increase, and so will the market risk premium (kM - kRF). The product is the risk premium of the jth stock. If b j is low (say, 0.5), then the

Harcourt, Inc. Answers and Solutions: 6 - 106

ANSWERS TO END-OF-CHAPTER QUESTIONS

product will be small; RPj will increase by only half the increase in . However, if bj is large (say, 2.0), then its risk premium will rise by twice the increase in RPM.

6-6 According to the Security Market Line (SML) equation, an increase in beta will increase a company’s expected return by an amount equal to the market risk premium times the change in beta. For example, assume that the risk-free rate is 6 percent, and the market risk premium is 5 percent. If the company’s beta doubles from 0.8 to 1.6 its expected return increases from 10 percent to 14 percent. Therefore, in general, a company’s expected return will not double when its beta doubles.

6-7 Yes, if the portfolio’s beta is equal to zero. In practice, however, it may be impossible to find individual stocks that have a nonpositive beta. In this case it would also be impossible to have a stock portfolio with a zero beta. Even if such a portfolio could be constructed, investors would probably be better off just purchasing Treasury bills, or other zero beta investments.

6-8 No. For a stock to have a negative beta, its returns would have to logically be expected to go up in the future when other stocks’ returns were falling. Just because in one year the stock’s return increases when the market declined doesn’t mean the stock has a negative beta. A stock in a given year may move counter to the overall market, even though the stock’s beta is positive.

6-1 = (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)= 11.40%.

2 = (-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4) + (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1)

2 = 712.44; = 26.69%.

CV = = 2.34.

6-2 Investment Beta $35,000 0.8 40,000 1.4Total $75,000

bp = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.

6-3 kRF = 5%; RPM = 6%; kM = ?

kM = 5% + (6%)1 = 11%.

ks when b = 1.2 = ?

ks = 5% + 6%(1.2) = 12.2%.

6-4 kRF = 6%; kM = 13%; b = 0.7; ks = ?

ks = kRF + (kM - kRF)b= 6% + (13% - 6%)0.7= 10.9%.

6-5 a. k = 11%; kRF = 7%; RPM = 4%.

k = kRF + (kM – kRF)b11% = 7% + 4%b 4% = 4%b b = 1.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

b. kRF = 7%; RPM = 6%; b = 1.

k = kRF + (kM – kRF)bk = 7% + (6%)1

k = 13%.

6-6 a. = (0.3)(15%) + (0.4)(9%) + (0.3)(18%) = 13.5%.

= (0.3)(20%) + (0.4)(5%) + (0.3)(12%) = 11.6%.

b. M = [(0.3)(15% - 13.5%)2 + (0.4)(9% - 13.5%)2 + (0.3)(18% - 13.5%)2]1/2

= = 3.85%.

J = [(0.3)(20% - 11.6%)2 + (0.4)(5% - 11.6%)2 + (0.3)(12% - 11.6%)2]1/2

= = 6.22%.

c. CVM = = 0.29.

CVJ = = 0.54.

6-7 a. .

= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)

= 14% versus 12% for X.

b. = .

= (-10% - 12%)2(0.1) + (2% - 12%)2(0.2) + (12% - 12%)2(0.4)

+ (20% - 12%)2(0.2) + (38% - 12%)2(0.1) = 148.8%.

X = 12.20% versus 20.35% for Y.

CVX = X/ X = 12.20%/12% = 1.02, while

CVY = 20.35%/14% = 1.45.

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

6-8 a. kA = kRF + (kM - kRF)bA

12% = 5% + (10% - 5%)bA

12% = 5% + 5%(bA) 7% = 5%(bA)1.4 = bA.

b. kA = 5% + 5%(bA)kA = 5% + 5%(2)kA = 15%.

6-9 a. ki = kRF + (kM - kRF)bi = 9% + (14% - 9%)1.3 = 15.5%.

b. 1. kRF increases to 10%:

kM increases by 1 percentage point, from 14% to 15%.

ki = kRF + (kM - kRF)bi = 10% + (15% - 10%)1.3 = 16.5%.

2. kRF decreases to 8%:

kM decreases by 1%, from 14% to 13%.

ki = kRF + (kM - kRF)bi = 8% + (13% - 8%)1.3 = 14.5%.

c. 1. kM increases to 16%:

ki = kRF + (kM - kRF)bi = 9% + (16% - 9%)1.3 = 18.1%.

2. kM decreases to 13%:

ki = kRF + (kM - kRF)bi = 9% + (13% - 9%)1.3 = 14.2%.

6-10 Old portfolio beta = (b) + (1.00)

1.12 = 0.95b + 0.05 1.07 = 0.95b 1.1263 = b.

New portfolio beta = 0.95(1.1263) + 0.05(1.75) = 1.1575 1.16.

Alternative Solutions:

1. Old portfolio beta = 1.12 = (0.05)b1 + (0.05)b2 + ... + (0.05)b20

1.12 = (0.05)

= 1.12/0.05 = 22.4.

New portfolio beta = (22.4 - 1.0 + 1.75)(0.05) = 1.1575 1.16.

2. excluding the stock with the beta equal to 1.0 is 22.4 - 1.0 =

21.4, so the beta of the portfolio excluding this stock is b = 21.4/19 = 1.1263. The beta of the new portfolio is:

1.1263(0.95) + 1.75(0.05) = 1.1575 1.16.

6-11 Portfolio beta = (1.50) + (-0.50)

+ (1.25) + (0.75)

= (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75) = 0.15 - 0.075 + 0.3125 + 0.375 = 0.7625.

kp = kRF + (kM - kRF)(bp) = 6% + (14% - 6%)(0.7625) = 12.1%.

Alternative solution: First, calculate the return for each stock using the CAPM equation [k RF + (kM - kRF)b], and then calculate the weighted average of these returns.

kRF = 6% and kM - kRF = 8%.

Stock Investment Beta k = kRF + (kM - kRF)b Weight A $ 400,000 1.50 18% 0.10 B 600,000 (0.50) 2 0.15 C 1,000,000 1.25 16 0.25 D 2,000,000 0.75 12 0.50Total $4,000,000 1.00

kp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.

6-12 First, calculate the beta of what remains after selling the stock:

bp = 1.1 = ($100,000/$2,000,000)0.9 + ($1,900,000/$2,000,000)bR

1.1 = 0.045 + (0.95)bR

bR = 1.1105.

bN = (0.95)1.1105 + (0.05)1.4 = 1.125.

6-13 We know that bR = 1.50, bS = 0.75, kM = 13%, kRF = 7%.

ki = kRF + (kM - kRF)bi = 7% + (13% - 7%)bi.

kR = 7% + 6%(1.50) = 16.0%kS = 7% + 6%(0.75) = 11.5 4.5 %

6-14 kX = 10%; bX = 0.9; X = 35%.

kY = 12.5%; bY = 1.2; Y = 25%.kRF = 6%; RPM = 5%.

a. CVX = 35%/10% = 3.5. CVY = 25%/12.5% = 2.0.

b. For diversified investors the relevant risk is measured by beta. There-fore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.

c. kX = 6% + 5%(0.9)kX = 10.5%.

kY = 6% + 5%(1.2)kY = 12%.

d. kX = 10.5%; = 10%.

kY = 12%; = 12.5%.

Stock Y would be most attractive to a diversified investor since its expected return of 12.5% is greater than its required return of 12%.

e. bp = ($7,500/$10,000)0.9 + ($2,500/$10,000)1.2 = 0.6750 + 0.30 = 0.9750.

kp = 6% + 5%(0.975)kp = 10.875%.

f. If RPM increases from 5% to 6%, the stock with the highest beta will have the largest increase in its required return. Therefore, Stock Y will have the greatest increase.

Check:kX = 6% + 6%(0.9) = 11.4%. Increase 10.5% to 11.4%.

kY = 6% + 6%(1.2) = 13.2%. Increase 12% to 13.2%.

6-15 a. ($1 million)(0.5) + ($0)(0.5) = $0.5 million.

b. You would probably take the sure $0.5 million.

c. Risk averter.

d. 1. ($1.15 million)(0.5) + ($0)(0.5) = $575,000, or an expected profit of $75,000.

2. $75,000/$500,000 = 15%.

3. This depends on the individual’s degree of risk aversion.

4. Again, this depends on the individual.

5. The situation would be unchanged if the stocks’ returns were perfectly positively correlated. Otherwise, the stock portfolio would have the same expected return as the single stock (15 percent) but a lower standard deviation. If the correlation coefficient between each pair of stocks was a negative one, the portfolio would be virtually riskless. Since r for stocks is generally in the range of +0.6 to +0.7, investing in a portfolio of stocks would definitely be an improvement over investing in the single stock.

6-16 a. M = 0.1(7%) + 0.2(9%) + 0.4(11%) + 0.2(13%) + 0.1(15%) = 11%.

kRF = 6%. (given)

Therefore, the SML equation is

ki = kRF + (kM - kRF)bi = 6% + (11% - 6%)bi = 6% + (5%)bi.

b. First, determine the fund’s beta, bF. The weights are the percentage of funds invested in each stock.

A = $160/$500 = 0.32B = $120/$500 = 0.24C = $80/$500 = 0.16D = $80/$500 = 0.16E = $60/$500 = 0.12

bF = 0.32(0.5) + 0.24(2.0) + 0.16(4.0) + 0.16(1.0) + 0.12(3.0)= 0.16 + 0.48 + 0.64 + 0.16 + 0.36 = 1.8.

Next, use bF = 1.8 in the SML determined in Part a:

F = 6% + (11% - 6%)1.8 = 6% + 9% = 15%.

c. kN = Required rate of return on new stock = 6% + (5%)2.0 = 16%.

An expected return of 15 percent on the new stock is below the 16 percent required rate of return on an investment with a risk of b = 2.0. Since kN = 16% > N = 15%, the new stock should not be purchased. The expected rate of return that would make the fund indifferent to purchasing the stock is 16 percent.

6-17 The answers to a, b, c, and d are given below:

kA kB Portfolio1997 (18.00%) (14.50%) (16.25%)1998 33.00 21.80 27.401999 15.00 30.50 22.752000 (0.50) (7.60) (4.05)2001 27.00 26.30 26.65

Mean 11.30 11.30 11.30Std. Dev. 20.79 20.78 20.13Coef. Var. 1.84 1.84 1.78

e. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated (rAB = 0.88).

6-18 a. bX = 1.3471; bY = 0.6508.

b. kX = 6% + (5%)1.3471 = 12.7355%.kY = 6% + (5%)0.6508 = 9.2540%.

c. bp = 0.8(1.3471) + 0.2(0.6508) = 1.2078.

kp = 6% + (5%)1.2078 = 12.04%.

Alternatively,kp = 0.8(12.7355%) + 0.2(9.254%) = 12.04%.

d. Stock X is undervalued, because its expected return exceeds its required rate of return.

SPREADSHEET PROBLEM

6-19 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of the Harcourt College Publishers’ web site: http://www.harcourtcollege.com/finance/concise3e.

6-20 The detailed solution for the cyberproblem is available on the instructor’s side of the Harcourt College Publishers’ web site: http://www.harcourtcollege.com/finance/concise3e.

Harcourt, Inc. Computer/Internet Applications: 6 - 115

CYBERPROBLEM

INTEGRATED CASE

Merrill Finch Inc.Risk and Return

6-21 ASSUME THAT YOU RECENTLY GRADUATED WITH A MAJOR IN FINANCE, AND YOU JUST LANDED A JOB AS A FINANCIAL PLANNER WITH MERRILL FINCH INC., A LARGE FINANCIAL SERVICES CORPORATION. YOUR FIRST ASSIGNMENT IS TO INVEST $100,000 FOR A CLIENT. BECAUSE THE FUNDS ARE TO BE INVESTED IN A BUSINESS AT THE END OF ONE YEAR, YOU HAVE BEEN INSTRUCTED TO PLAN FOR A ONE-YEAR HOLDING PERIOD. FURTHER, YOUR BOSS HAS RESTRICTED YOU TO THE FOLLOWING INVESTMENT ALTERNATIVES, SHOWN WITH THEIR PROBABILITIES AND ASSOCIATED OUTCOMES. (DISREGARD FOR NOW THE ITEMS AT THE BOTTOM OF THE DATA; YOU WILL FILL IN THE BLANKS LATER.)

RETURNS ON ALTERNATIVE INVESTMENTS ESTIMATED RATE OF RETURN STATE OF THE T- HIGH COLLEC- U.S. MARKET 2-STOCK ECONOMY PROB. BILLS TECH TIONS RUBBER PORTFOLIO PORTFOLIORECESSION 0.1 8.0% -22.0% 28.0% 10.0%* -13.0% 3.0%BELOW AVG 0.2 8.0 -2.0 14.7 -10.0 1.0AVERAGE 0.4 8.0 20.0 0.0 7.0 15.0 10.0ABOVE AVG 0.2 8.0 35.0 -10.0 45.0 29.0BOOM 0.1 8.0 50.0 -20.0 30.0 43.0 15.0

k-HAT ( ) 1.7% 13.8% 15.0%STD DEV () 0.0 13.4 18.8 15.3 3.3COEF OF VAR (CV) 7.9 1.4 1.0 0.3BETA (b) -0.87 0.89

*NOTE THAT THE ESTIMATED RETURNS OF U.S. RUBBER DO NOT ALWAYS MOVE

IN THE SAME DIRECTION AS THE OVERALL ECONOMY. FOR EXAMPLE, WHEN

THE ECONOMY IS BELOW AVERAGE, CONSUMERS PURCHASE FEWER TIRES THAN

THEY WOULD IF THE ECONOMY WAS STRONGER. HOWEVER, IF THE ECONOMY IS

IN A FLAT-OUT RECESSION, A LARGE NUMBER OF CONSUMERS WHO WERE

PLANNING TO PURCHASE A NEW CAR MAY CHOOSE TO WAIT AND INSTEAD

PURCHASE NEW TIRES FOR THE CAR THEY CURRENTLY OWN. UNDER THESE

CIRCUMSTANCES, WE WOULD EXPECT U.S. RUBBER’S STOCK PRICE TO BE

HIGHER IF THERE IS A RECESSION THAN IF THE ECONOMY WAS JUST BELOW

AVERAGE.

Harcourt, Inc. Integrated Case: 6 - 116

MERRILL FINCH’S ECONOMIC FORECASTING STAFF HAS DEVELOPED

PROBABILITY ESTIMATES FOR THE STATE OF THE ECONOMY, AND ITS SECURITY

ANALYSTS HAVE DEVELOPED A SOPHISTICATED COMPUTER PROGRAM, WHICH

WAS USED TO ESTIMATE THE RATE OF RETURN ON EACH ALTERNATIVE UNDER

EACH STATE OF THE ECONOMY. HIGH TECH INC. IS AN ELECTRONICS FIRM;

COLLECTIONS INC. COLLECTS PAST-DUE DEBTS; AND U.S. RUBBER

MANUFACTURES TIRES AND VARIOUS OTHER RUBBER AND PLASTICS PRODUCTS.

MERRILL FINCH ALSO MAINTAINS A “MARKET PORTFOLIO” THAT OWNS A

MARKET-WEIGHTED FRACTION OF ALL PUBLICLY TRADED STOCKS; YOU CAN

INVEST IN THAT PORTFOLIO, AND THUS OBTAIN AVERAGE STOCK MARKET

RESULTS. GIVEN THE SITUATION AS DESCRIBED, ANSWER THE FOLLOWING

QUESTIONS.

A. 1. WHY IS THE T-BILL’S RETURN INDEPENDENT OF THE STATE OF THE ECONOMY?

DO T-BILLS PROMISE A COMPLETELY RISK-FREE RETURN?

ANSWER: [SHOW S6-1 THROUGH S6-7 HERE.] THE 8 PERCENT T-BILL RETURN DOES NOT DEPEND

ON THE STATE OF THE ECONOMY BECAUSE THE TREASURY MUST (AND WILL)

REDEEM THE BILLS AT PAR REGARDLESS OF THE STATE OF THE ECONOMY.

THE T-BILLS ARE RISK-FREE IN THE DEFAULT RISK SENSE BECAUSE THE

8 PERCENT RETURN WILL BE REALIZED IN ALL POSSIBLE ECONOMIC STATES.

HOWEVER, REMEMBER THAT THIS RETURN IS COMPOSED OF THE REAL RISK-FREE

RATE, SAY 3 PERCENT, PLUS AN INFLATION PREMIUM, SAY 5 PERCENT. SINCE THERE

IS UNCERTAINTY ABOUT INFLATION, IT IS UNLIKELY THAT THE REALIZED REAL RATE

OF RETURN WOULD EQUAL THE EXPECTED 3 PERCENT. FOR EXAMPLE, IF INFLATION

AVERAGED 6 PERCENT OVER THE YEAR, THEN THE REALIZED REAL RETURN WOULD

ONLY BE 8% - 6% = 2%, NOT THE EXPECTED 3 PERCENT. THUS, IN TERMS OF

PURCHASING POWER, T-BILLS ARE NOT RISKLESS.

ALSO, IF YOU INVESTED IN A PORTFOLIO OF T-BILLS, AND RATES THEN DECLINED,

YOUR NOMINAL INCOME WOULD FALL; THAT IS, T-BILLS ARE EXPOSED TO

REINVESTMENT RATE RISK. SO, WE CONCLUDE THAT THERE ARE NO TRULY RISK-

FREE SECURITIES IN THE UNITED STATES. IF THE TREASURY SOLD INFLATION-

INDEXED, TAX-EXEMPT BONDS, THEY WOULD BE TRULY RISKLESS, BUT ALL ACTUAL

SECURITIES ARE EXPOSED TO SOME TYPE OF RISK.

A. 2. WHY ARE HIGH TECH’S RETURNS EXPECTED TO MOVE WITH THE ECONOMY

WHEREAS COLLECTIONS’ ARE EXPECTED TO MOVE COUNTER TO THE

ECONOMY?

ANSWER: [SHOW S6-8 HERE.] HIGH TECH’S RETURNS MOVE WITH, HENCE ARE POSITIVELY

CORRELATED WITH, THE ECONOMY, BECAUSE THE FIRM’S SALES, AND HENCE

PROFITS, WILL GENERALLY EXPERIENCE THE SAME TYPE OF UPS AND DOWNS AS THE

ECONOMY. IF THE ECONOMY IS BOOMING, SO WILL HIGH TECH. ON THE OTHER

HAND, COLLECTIONS IS CONSIDERED BY MANY INVESTORS TO BE A HEDGE AGAINST

BOTH BAD TIMES AND HIGH INFLATION, SO IF THE STOCK MARKET CRASHES,

INVESTORS IN THIS STOCK SHOULD DO RELATIVELY WELL. STOCKS SUCH AS

COLLECTIONS ARE THUS NEGATIVELY CORRELATED WITH (MOVE COUNTER TO) THE

ECONOMY. (NOTE: IN ACTUALITY, IT IS ALMOST IMPOSSIBLE TO FIND STOCKS THAT

ARE EXPECTED TO MOVE COUNTER TO THE ECONOMY. EVEN COLLECTIONS SHARES

HAVE POSITIVE (BUT LOW) CORRELATION WITH THE MARKET.)

B. CALCULATE THE EXPECTED RATE OF RETURN ON EACH ALTERNATIVE AND FILL

IN THE BLANKS ON THE ROW FOR IN THE TABLE ABOVE.

ANSWER: [SHOW S6-9 AND S6-10 HERE.] THE EXPECTED RATE OF RETURN, , IS EXPRESSED AS

FOLLOWS:

HERE Pi IS THE PROBABILITY OF OCCURRENCE OF THE iTH STATE, k i IS THE

ESTIMATED RATE OF RETURN FOR THAT STATE, AND n IS THE NUMBER OF STATES.

HERE IS THE CALCULATION FOR HIGH TECH:

HIGH TECH = 0.1(-22.0%) + 0.2(-2.0%) + 0.4(20.0%) + 0.2(35.0%) + 0.1(50.0%)

= 17.4%.

WE USE THE SAME FORMULA TO CALCULATE k’S FOR THE OTHER ALTERNATIVES:

T-BILLS = 8.0%.

COLLECTIONS = 1.7%.

U.S.RUBBER = 13.8%.

M = 15.0%.

C. YOU SHOULD RECOGNIZE THAT BASING A DECISION SOLELY ON EXPECTED

RETURNS IS ONLY APPROPRIATE FOR RISK-NEUTRAL INDIVIDUALS. SINCE YOUR

CLIENT, LIKE VIRTUALLY EVERYONE, IS RISK AVERSE, THE RISKINESS OF EACH

ALTERNATIVE IS AN IMPORTANT ASPECT OF THE DECISION. ONE POSSIBLE

MEASURE OF RISK IS THE STANDARD DEVIATION OF RETURNS.

1. CALCULATE THIS VALUE FOR EACH ALTERNATIVE, AND FILL IN THE BLANK ON

THE ROW FOR IN THE TABLE ABOVE.

ANSWER: [SHOW S6-11 AND S6-12 HERE.] THE STANDARD DEVIATION IS CALCULATED AS

FOLLOWS:

HIGH TECH = [(-22.0 - 17.4)2(0.1) + (-2.0 - 17.4)2(0.2) + (20.0 - 17.4)2(0.4) + (35.0 - 17.4)2(0.2) + (50.0 - 17.4)2(0.1)]½

= = 20.0%.

HERE ARE THE STANDARD DEVIATIONS FOR THE OTHER ALTERNATIVES:

T-BILLS = 0.0%.

COLLECTIONS = 13.4%.

U.S. RUBBER = 18.8%.

M = 15.3%.

C. 2. WHAT TYPE OF RISK IS MEASURED BY THE STANDARD DEVIATION?

ANSWER: [SHOW S6-13 THROUGH S6-15 HERE.] THE STANDARD DEVIATION IS A MEASURE OF A

SECURITY’S (OR A PORTFOLIO’S) STAND-ALONE RISK. THE LARGER THE STANDARD

DEVIATION, THE HIGHER THE PROBABILITY THAT ACTUAL REALIZED RETURNS WILL

FALL FAR BELOW THE EXPECTED RETURN, AND THAT LOSSES RATHER THAN PROFITS

WILL BE INCURRED.

C. 3. DRAW A GRAPH THAT SHOWS ROUGHLY THE SHAPE OF THE PROBABILITY

DISTRIBUTIONS FOR HIGH TECH, U.S. RUBBER, AND T-BILLS.

ANSWER:

ON THE BASIS OF THESE DATA, HIGH TECH IS THE MOST RISKY INVESTMENT, T-BILLS

THE LEAST RISKY.

D. SUPPOSE YOU SUDDENLY REMEMBERED THAT THE COEFFICIENT OF VARIATION

(CV) IS GENERALLY REGARDED AS BEING A BETTER MEASURE OF STAND-ALONE

RISK THAN THE STANDARD DEVIATION WHEN THE ALTERNATIVES BEING

CONSIDERED HAVE WIDELY DIFFERING EXPECTED RETURNS. CALCULATE THE

MISSING CVs, AND FILL IN THE BLANKS ON THE ROW FOR CV IN THE TABLE

ABOVE. DOES THE CV PRODUCE THE SAME RISK RANKINGS AS THE STANDARD

DEVIATION?

ANSWER: [SHOW S6-16 AND S6-17 HERE.] THE COEFFICIENT OF VARIATION (CV) IS A

STANDARDIZED MEASURE OF DISPERSION ABOUT THE EXPECTED VALUE; IT SHOWS

THE AMOUNT OF RISK PER UNIT OF RETURN.

CV = .

CVT-BILLS = 0.0%/8.0% = 0.0.

CVHIGH TECH = 20.0%/17.4% = 1.1.

CVCOLLECTIONS = 13.4%/1.7% = 7.9.

CVU.S. RUBBER = 18.8%/13.8% = 1.4.

CVM = 15.3%/15.0% = 1.0.

WHEN WE MEASURE RISK PER UNIT OF RETURN, COLLECTIONS, WITH ITS LOW

EXPECTED RETURN, BECOMES THE MOST RISKY STOCK. THE CV IS A BETTER

MEASURE OF AN ASSET’S STAND-ALONE RISK THAN BECAUSE CV CONSIDERS BOTH

THE EXPECTED VALUE AND THE DISPERSION OF A DISTRIBUTION--A SECURITY WITH

A LOW EXPECTED RETURN AND A LOW STANDARD DEVIATION COULD HAVE A

HIGHER CHANCE OF A LOSS THAN ONE WITH A HIGH BUT A HIGH .

E. SUPPOSE YOU CREATED A 2-STOCK PORTFOLIO BY INVESTING $50,000 IN HIGH

TECH AND $50,000 IN COLLECTIONS.

1. CALCULATE THE EXPECTED RETURN ( ), THE STANDARD DEVIATION (p), AND

THE COEFFICIENT OF VARIATION (CVp) FOR THIS PORTFOLIO AND FILL IN THE

APPROPRIATE BLANKS IN THE TABLE ABOVE.

ANSWER: [SHOW S6-18 THROUGH S6-21 HERE.] TO FIND THE EXPECTED RATE OF RETURN ON

THE TWO-STOCK PORTFOLIO, WE FIRST CALCULATE THE RATE OF RETURN ON THE

PORTFOLIO IN EACH STATE OF THE ECONOMY. SINCE WE HAVE HALF OF OUR MONEY

IN EACH STOCK, THE PORTFOLIO’S RETURN WILL BE A WEIGHTED AVERAGE IN EACH

TYPE OF ECONOMY. FOR A RECESSION, WE HAVE: kp = 0.5(-22%) + 0.5(28%) = 3%. WE

WOULD DO SIMILAR CALCULATIONS FOR THE OTHER STATES OF THE ECONOMY, AND

GET THESE RESULTS:

STATE PORTFOLIORECESSION 3.0%BELOW AVERAGE 6.4AVERAGE 10.0ABOVE AVERAGE 12.5BOOM 15.0

NOW WE CAN MULTIPLY PROBABILITIES TIMES OUTCOMES IN EACH STATE TO

GET THE EXPECTED RETURN ON THIS TWO-STOCK PORTFOLIO, 9.6 PERCENT.

ALTERNATIVELY, WE COULD APPLY THIS FORMULA,

k = wi ki = 0.5(17.4%) + 0.5(1.7%) = 9.6%,

WHICH FINDS k AS THE WEIGHTED AVERAGE OF THE EXPECTED RETURNS OF THE

INDIVIDUAL SECURITIES IN THE PORTFOLIO.

IT IS TEMPTING TO FIND THE STANDARD DEVIATION OF THE PORTFOLIO AS THE

WEIGHTED AVERAGE OF THE STANDARD DEVIATIONS OF THE INDIVIDUAL

SECURITIES, AS FOLLOWS:

p wi(i) + wj(j) = 0.5(20%) + 0.5(13.4%) = 16.7%.

HOWEVER, THIS IS NOT CORRECT--IT IS NECESSARY TO USE A DIFFERENT FORMULA,

THE ONE FOR THAT WE USED EARLIER, APPLIED TO THE TWO-STOCK PORTFOLIO’S

RETURNS.

THE PORTFOLIO’S DEPENDS JOINTLY ON (1) EACH SECURITY’S AND

(2) THE CORRELATION BETWEEN THE SECURITIES’ RETURNS. THE BEST WAY TO

APPROACH THE PROBLEM IS TO ESTIMATE THE PORTFOLIO’S RISK AND RETURN IN

EACH STATE OF THE ECONOMY, AND THEN TO ESTIMATE p WITH THE FORMULA.

GIVEN THE DISTRIBUTION OF RETURNS FOR THE PORTFOLIO, WE CAN CALCULATE

THE PORTFOLIO’S AND CV AS SHOWN BELOW:

p = [(3.0 - 9.6)2(0.1) + (6.4 - 9.6)2(0.2) + (10.0 - 9.6)2(0.4) + (12.5 - 9.6)2(0.2) + (15.0 - 9.6)2(0.1)]½ = 3.3%.

CVp = 3.3%/9.6% = 0.34.

E. 2. HOW DOES THE RISKINESS OF THIS 2-STOCK PORTFOLIO COMPARE WITH THE

RISKINESS OF THE INDIVIDUAL STOCKS IF THEY WERE HELD IN ISOLATION?

ANSWER: [SHOW S6-22 THROUGH S6-25 HERE.] USING EITHER OR CV AS OUR STAND-ALONE

RISK MEASURE, THE STAND-ALONE RISK OF THE PORTFOLIO IS SIGNIFICANTLY LESS

THAN THE STAND-ALONE RISK OF THE INDIVIDUAL STOCKS. THIS IS BECAUSE THE

TWO STOCKS ARE NEGATIVELY CORRELATED--WHEN HIGH TECH IS DOING POORLY,

COLLECTIONS IS DOING WELL, AND VICE VERSA. COMBINING THE TWO STOCKS

DIVERSIFIES AWAY SOME OF THE RISK INHERENT IN EACH STOCK IF IT WERE HELD IN

ISOLATION, i.e., IN A 1-STOCK PORTFOLIO.

OPTIONAL QUESTION

DOES THE EXPECTED RATE OF RETURN ON THE PORTFOLIO DEPEND ON THE PERCENTAGE OF THE PORTFOLIO INVESTED IN EACH STOCK? WHAT ABOUT THE RISKINESS OF THE PORTFOLIO?

ANSWER: USING A SPREADSHEET MODEL, IT’S EASY TO VARY THE COMPOSITION OF THE

PORTFOLIO TO SHOW THE EFFECT ON THE PORTFOLIO’S EXPECTED RATE OF RETURN

AND STANDARD DEVIATION:

HIGH TECH PLUS COLLECTIONS % IN HIGH TECH p p

0% 1.7% 13.4% 10 3.3 10.0 20 4.9 6.7 30 6.4 3.3 40 8.0 0.0 50 9.6 3.3 60 11.1 6.7 70 12.7 10.0 80 14.3 13.4 90 15.8 16.7 100 17.4 20.0

THE EXPECTED RATE OF RETURN ON THE PORTFOLIO IS MERELY A LINEAR

COMBINATION OF THE TWO STOCK’S EXPECTED RATES OF RETURN. HOWEVER,

PORTFOLIO RISK IS ANOTHER MATTER. p BEGINS TO FALL AS HIGH TECH AND

COLLECTIONS ARE COMBINED; IT REACHES ZERO AT 40 PERCENT HIGH TECH; AND

THEN IT BEGINS TO RISE. HIGH TECH AND COLLECTIONS CAN BE COMBINED TO

FORM A NEAR ZERO RISK PORTFOLIO BECAUSE THEY ARE VERY CLOSE TO BEING

PERFECTLY NEGATIVELY CORRELATED; THEIR CORRELATION COEFFICIENT IS

-0.9998. (NOTE: UNFORTUNATELY, WE CANNOT FIND ANY ACTUAL STOCKS WITH r = -

F. SUPPOSE AN INVESTOR STARTS WITH A PORTFOLIO CONSISTING OF ONE

RANDOMLY SELECTED STOCK. WHAT WOULD HAPPEN (1) TO THE RISKINESS AND

(2) TO THE EXPECTED RETURN OF THE PORTFOLIO AS MORE AND MORE

RANDOMLY SELECTED STOCKS WERE ADDED TO THE PORTFOLIO? WHAT IS THE

IMPLICATION FOR INVESTORS? DRAW A GRAPH OF THE TWO PORTFOLIOS TO

ILLUSTRATE YOUR ANSWER.

ANSWER: [SHOW S6-26 AND S6-27 HERE.]

THE STANDARD DEVIATION GETS SMALLER AS MORE STOCKS ARE COMBINED IN THE

PORTFOLIO, WHILE kp (THE PORTFOLIO’S RETURN) REMAINS CONSTANT. THUS, BY

ADDING STOCKS TO YOUR PORTFOLIO, WHICH INITIALLY STARTED AS A

1-STOCK PORTFOLIO, RISK HAS BEEN REDUCED.

IN THE REAL WORLD, STOCKS ARE POSITIVELY CORRELATED WITH ONE

ANOTHER--IF THE ECONOMY DOES WELL, SO DO STOCKS IN GENERAL, AND VICE

VERSA. CORRELATION COEFFICIENTS BETWEEN STOCKS GENERALLY RANGE FROM

+0.5 TO +0.7. A SINGLE STOCK SELECTED AT RANDOM WOULD ON AVERAGE HAVE A

STANDARD DEVIATION OF ABOUT 35 PERCENT. AS ADDITIONAL STOCKS ARE ADDED

TO THE PORTFOLIO, THE PORTFOLIO’S STANDARD DEVIATION DECREASES BECAUSE

THE ADDED STOCKS ARE NOT PERFECTLY POSITIVELY CORRELATED. HOWEVER, AS

MORE AND MORE STOCKS ARE ADDED, EACH NEW STOCK HAS LESS OF A RISK-

REDUCING IMPACT, AND EVENTUALLY ADDING ADDITIONAL STOCKS HAS

VIRTUALLY NO EFFECT ON THE PORTFOLIO’S RISK AS MEASURED BY . IN FACT,

STABILIZES AT ABOUT 20.4 PERCENT WHEN 40 OR MORE RANDOMLY SELECTED

STOCKS ARE ADDED. THUS, BY COMBINING STOCKS INTO WELL-DIVERSIFIED

PORTFOLIOS, INVESTORS CAN ELIMINATE ALMOST ONE-HALF THE RISKINESS OF

HOLDING INDIVIDUAL STOCKS. (NOTE: IT IS NOT COMPLETELY COSTLESS TO

DIVERSIFY, SO EVEN THE LARGEST INSTITUTIONAL INVESTORS HOLD LESS THAN ALL

STOCKS. EVEN INDEX FUNDS GENERALLY HOLD A SMALLER PORTFOLIO THAT IS

HIGHLY CORRELATED WITH AN INDEX SUCH AS THE S&P 500 RATHER THAN HOLD

ALL THE STOCKS IN THE INDEX.)

THE IMPLICATION IS CLEAR: INVESTORS SHOULD HOLD WELL-DIVERSIFIED

PORTFOLIOS OF STOCKS RATHER THAN INDIVIDUAL STOCKS. (IN FACT, INDIVIDUALS

CAN HOLD DIVERSIFIED PORTFOLIOS THROUGH MUTUAL FUND INVESTMENTS.) BY

DOING SO, THEY CAN ELIMINATE ABOUT HALF OF THE RISKINESS INHERENT IN

INDIVIDUAL STOCKS.

G. 1. SHOULD PORTFOLIO EFFECTS IMPACT THE WAY INVESTORS THINK ABOUT THE

RISKINESS OF INDIVIDUAL STOCKS?

ANSWER: [SHOW S6-28 THROUGH S6-31 HERE.] PORTFOLIO DIVERSIFICATION DOES AFFECT

INVESTORS’ VIEWS OF RISK. A STOCK’S STAND-ALONE RISK AS MEASURED BY ITS

OR CV, MAY BE IMPORTANT TO AN UNDIVERSIFIED INVESTOR, BUT IT IS NOT

RELEVANT TO A WELL-DIVERSIFIED INVESTOR. A RATIONAL, RISK-AVERSE

INVESTOR IS MORE INTERESTED IN THE IMPACT THAT THE STOCK HAS ON THE

RISKINESS OF HIS OR HER PORTFOLIO THAN ON THE STOCK’S STAND-ALONE RISK.

STAND-ALONE RISK IS COMPOSED OF DIVERSIFIABLE RISK, WHICH CAN BE

ELIMINATED BY HOLDING THE STOCK IN A WELL-DIVERSIFIED PORTFOLIO, AND THE

RISK THAT REMAINS IS CALLED MARKET RISK BECAUSE IT IS PRESENT EVEN WHEN

THE ENTIRE MARKET PORTFOLIO IS HELD.

G. 2. IF YOU DECIDED TO HOLD A 1-STOCK PORTFOLIO, AND CONSEQUENTLY WERE

EXPOSED TO MORE RISK THAN DIVERSIFIED INVESTORS, COULD YOU EXPECT TO

BE COMPENSATED FOR ALL OF YOUR RISK; THAT IS, COULD YOU EARN A RISK

PREMIUM ON THAT PART OF YOUR RISK THAT YOU COULD HAVE ELIMINATED BY

DIVERSIFYING?

ANSWER: [SHOW S6-32 THROUGH S6-34 HERE.] IF YOU HOLD A ONE-STOCK PORTFOLIO, YOU

WILL BE EXPOSED TO A HIGH DEGREE OF RISK, BUT YOU WON’T BE COMPENSATED

FOR IT. IF THE RETURN WERE HIGH ENOUGH TO COMPENSATE YOU FOR YOUR HIGH

RISK, IT WOULD BE A BARGAIN FOR MORE RATIONAL, DIVERSIFIED INVESTORS. THEY

WOULD START BUYING IT, AND THESE BUY ORDERS WOULD DRIVE THE PRICE UP

AND THE RETURN DOWN. THUS, YOU SIMPLY COULD NOT FIND STOCKS IN THE

MARKET WITH RETURNS HIGH ENOUGH TO COMPENSATE YOU FOR THE STOCK’S

DIVERSIFIABLE RISK.

H. THE EXPECTED RATES OF RETURN AND THE BETA COEFFICIENTS OF THE

ALTERNATIVES AS SUPPLIED BY MERRILL FINCH’S COMPUTER PROGRAM ARE AS

FOLLOWS:

SECURITY RETURN ( ) RISK (BETA) HIGH TECH 17.4% 1.30 MARKET 15.0 1.00 U.S. RUBBER 13.8 0.89 T-BILLS 8.0 0.00 COLLECTIONS 1.7 (0.87)

(1) WHAT IS A BETA COEFFICIENT, AND HOW ARE BETAS USED IN RISK ANALYSIS?

(2) DO THE EXPECTED RETURNS APPEAR TO BE RELATED TO EACH

ALTERNATIVE’S MARKET RISK? (3) IS IT POSSIBLE TO CHOOSE AMONG THE

ALTERNATIVES ON THE BASIS OF THE INFORMATION DEVELOPED THUS FAR?

USE THE DATA GIVEN AT THE START OF THE PROBLEM TO CONSTRUCT A GRAPH

THAT SHOWS HOW THE T-BILL’S, HIGH TECH’S, AND COLLECTIONS’ BETA

COEFFICIENTS ARE CALCULATED. THEN DISCUSS WHAT BETAS MEASURE AND

HOW THEY ARE USED IN RISK ANALYSIS.

ANSWER: [SHOW S6-35 THROUGH S6-42 HERE.]

(DRAW THE FRAMEWORK OF THE GRAPH, PUT UP THE DATA, THEN PLOT THE POINTS

FOR THE MARKET (45 LINE) AND CONNECT THEM, AND THEN GET THE SLOPE AS

Y/X = 1.0.) STATE THAT AN AVERAGE STOCK, BY DEFINITION, MOVES WITH THE

High Tech(slope = beta = 1.30)

Market(slope = beta = 1.0)

U.S. Rubber(slope = beta = 0.89)

Return on Stock i(%)

Return on the Market(%)

-20 20 40

MARKET. THEN DO THE SAME WITH HIGH TECH AND U.S. RUBBER. BETA

COEFFICIENTS MEASURE THE RELATIVE VOLATILITY OF A GIVEN STOCK VIS-A-VIS

AN AVERAGE STOCK. THE AVERAGE STOCK’S BETA IS 1.0. MOST STOCKS HAVE

BETAS IN THE RANGE OF 0.5 TO 1.5. THEORETICALLY, BETAS CAN BE NEGATIVE, BUT

IN THE REAL WORLD THEY ARE GENERALLY POSITIVE.

BETAS ARE CALCULATED AS THE SLOPE OF THE “CHARACTERISTIC” LINE, WHICH

IS THE REGRESSION LINE SHOWING THE RELATIONSHIP BETWEEN A GIVEN STOCK

AND THE GENERAL STOCK MARKET.

AS EXPLAINED IN APPENDIX 6A, WE COULD ESTIMATE THE SLOPES, AND THEN

USE THE SLOPES AS THE BETAS. IN PRACTICE, 5 YEARS OF MONTHLY DATA, WITH 60

OBSERVATIONS, WOULD GENERALLY BE USED, AND A COMPUTER WOULD BE USED

TO OBTAIN A LEAST SQUARES REGRESSION LINE.

THE EXPECTED RETURNS ARE RELATED TO EACH ALTERNATIVE’S MARKET RISK--

THAT IS, THE HIGHER THE ALTERNATIVE’S RATE OF RETURN THE HIGHER ITS BETA.

ALSO, NOTE THAT T-BILLS HAVE ZERO RISK.

WE DO NOT YET HAVE ENOUGH INFORMATION TO CHOOSE AMONG THE VARIOUS

ALTERNATIVES. WE NEED TO KNOW THE REQUIRED RATES OF RETURN ON THESE

ALTERNATIVES AND COMPARE THEM WITH THEIR EXPECTED RETURNS.

I. THE YIELD CURVE IS CURRENTLY FLAT, THAT IS, LONG-TERM TREASURY BONDS

ALSO HAVE AN 8 PERCENT YIELD. CONSEQUENTLY, MERRILL FINCH ASSUMES

THAT THE RISK-FREE RATE IS 8 PERCENT.

1. WRITE OUT THE SECURITY MARKET LINE (SML) EQUATION, USE IT TO

CALCULATE THE REQUIRED RATE OF RETURN ON EACH ALTERNATIVE, AND

THEN GRAPH THE RELATIONSHIP BETWEEN THE EXPECTED AND REQUIRED

RATES OF RETURN.

ANSWER: [SHOW S6-43 THROUGH S6-46 HERE.] HERE IS THE SML EQUATION:

ki = kRF + (kM – kRF)bi.

IF WE USE THE T-BILL YIELD AS A PROXY FOR THE RISK-FREE RATE, THEN kRF =

8%. FURTHER, OUR ESTIMATE OF kM = M IS 15 PERCENT. THUS, THE REQUIRED RATES

OF RETURN FOR THE ALTERNATIVES ARE AS FOLLOWS:

HIGH TECH: 8% + (15% - 8%)1.30 = 17.10%.MARKET: 8% + (15% - 8%)1.00 = 15.0%.U.S. RUBBER: 8% + (15% - 8%)0.89 = 14.23%.

T-BILLS: 8% + (15% - 8%)0 = 8.0%.COLLECTIONS: 8% + (15% - 8%)-0.87 = 1.91%.

I. 2. HOW DO THE EXPECTED RATES OF RETURN COMPARE WITH THE REQUIRED

RATES OF RETURN?

ANSWER: WE HAVE THE FOLLOWING RELATIONSHIPS:

EXPECTED REQUIRED RETURN RETURN SECURITY ( ) (k) CONDITION HIGH TECH 17.4% 17.1% UNDERVALUED: > kMARKET 15.0 15.0 FAIRLY VALUED (MARKET EQUILIBRIUM)U.S. RUBBER 13.8 14.2 OVERVALUED: k > T-BILLS 8.0 8.0 FAIRLY VALUED COLLECTIONS 1.7 1.9 OVERVALUED: k >

(NOTE: THE PLOT LOOKS SOMEWHAT UNUSUAL IN THAT THE X-AXIS EXTENDS TO

THE LEFT OF ZERO. WE HAVE A NEGATIVE BETA STOCK, HENCE A REQUIRED RETURN

THAT IS LESS THAN THE RISK-FREE RATE.) THE T-BILLS AND MARKET PORTFOLIO

PLOT ON THE SML, HIGH TECH PLOTS ABOVE IT, AND COLLECTIONS AND U.S. RUBBER

PLOT BELOW IT. THUS, THE T-BILLS AND THE MARKET PORTFOLIO PROMISE A FAIR

RETURN, HIGH TECH IS A GOOD DEAL BECAUSE ITS EXPECTED RETURN IS ABOVE ITS

REQUIRED RETURN, AND COLLECTIONS AND U.S. RUBBER HAVE EXPECTED RETURNS

BELOW THEIR REQUIRED RETURNS.

I. 3. DOES THE FACT THAT COLLECTIONS HAS AN EXPECTED RETURN THAT IS LESS

THAN THE T-BILL RATE MAKE ANY SENSE?

ANSWER: COLLECTIONS IS AN INTERESTING STOCK. ITS NEGATIVE BETA INDICATES NEGATIVE

MARKET RISK--INCLUDING IT IN A PORTFOLIO OF “NORMAL” STOCKS WILL LOWER

THE PORTFOLIO’S RISK. THEREFORE, ITS REQUIRED RATE OF RETURN IS BELOW THE

RISK-FREE RATE. BASICALLY, THIS MEANS THAT COLLECTIONS IS A VALUABLE

SECURITY TO RATIONAL, WELL-DIVERSIFIED INVESTORS. TO SEE WHY, CONSIDER

THIS QUESTION: WOULD ANY RATIONAL INVESTOR EVER MAKE AN INVESTMENT

THAT HAS A NEGATIVE EXPECTED RETURN? THE ANSWER IS “YES”--JUST THINK OF

THE PURCHASE OF A LIFE OR FIRE INSURANCE POLICY. THE FIRE INSURANCE POLICY

HAS A NEGATIVE EXPECTED RETURN BECAUSE OF COMMISSIONS AND INSURANCE

COMPANY PROFITS, BUT BUSINESSES BUY FIRE INSURANCE BECAUSE THEY PAY OFF

AT A TIME WHEN NORMAL OPERATIONS ARE IN BAD SHAPE. LIFE INSURANCE IS

SIMILAR--IT HAS A HIGH RETURN WHEN WORK INCOME CEASES. A NEGATIVE BETA

STOCK IS CONCEPTUALLY SIMILAR TO AN INSURANCE POLICY.

I. 4. WHAT WOULD BE THE MARKET RISK AND THE REQUIRED RETURN OF A 50-50

PORTFOLIO OF HIGH TECH AND COLLECTIONS? OF HIGH TECH AND U.S.

RUBBER?

ANSWER: [SHOW S6-47 AND S6-48 HERE.] NOTE THAT THE BETA OF A PORTFOLIO IS SIMPLY THE

WEIGHTED AVERAGE OF THE BETAS OF THE STOCKS IN THE PORTFOLIO. THUS, THE

BETA OF A PORTFOLIO WITH 50 PERCENT HIGH TECH AND 50 PERCENT COLLECTIONS

bp = 0.5(bHIGH TECH) + 0.5(bCOLLECTIONS) = 0.5(1.30) + 0.5(–0.87)

= 0.215,

kp = kRF + (kM - kRF)bp = 8.0% + (15.0% - 8.0%)(0.215)

= 8.0% + 7%(0.215) = 9.51% 9.5%.

FOR A PORTFOLIO CONSISTING OF 50 PERCENT HIGH TECH PLUS 50 PERCENT

U.S. RUBBER, THE REQUIRED RETURN WOULD BE 15.7 PERCENT:

bp = 0.5(1.30) + 0.5(0.89) = 1.095.

kp = 8.0% + 7%(1.095) = 15.665% 15.7%.

J. 1. SUPPOSE INVESTORS RAISED THEIR INFLATION EXPECTATIONS BY 3

PERCENTAGE POINTS OVER CURRENT ESTIMATES AS REFLECTED IN THE 8

PERCENT RISK-FREE RATE. WHAT EFFECT WOULD HIGHER INFLATION HAVE ON

THE SML AND ON THE RETURNS REQUIRED ON HIGH- AND LOW-RISK

SECURITIES?

ANSWER: [SHOW S6-49 AND S6-50 HERE.]

HERE WE HAVE PLOTTED THE SML FOR BETAS RANGING FROM 0 TO 2.0. THE BASE

CASE SML IS BASED ON kRF = 8% AND = 15%. IF INFLATION EXPECTATIONS

INCREASE BY 3 PERCENTAGE POINTS, WITH NO CHANGE IN RISK AVERSION, THEN

THE ENTIRE SML IS SHIFTED UPWARD (PARALLEL TO THE BASE CASE SML) BY

3 PERCENTAGE POINTS. NOW, kRF = 11%, kM = 18%, AND ALL SECURITIES’ REQUIRED

RETURNS RISE BY 3 PERCENTAGE POINTS. NOTE THAT THE MARKET RISK PREMIUM,

kM - kRF, REMAINS AT 7 PERCENTAGE POINTS.

J. 2. SUPPOSE INSTEAD THAT INVESTORS’ RISK AVERSION INCREASED ENOUGH TO

CAUSE THE MARKET RISK PREMIUM TO INCREASE BY 3 PERCENTAGE POINTS.

(INFLATION REMAINS CONSTANT.) WHAT EFFECT WOULD THIS HAVE ON THE

SML AND ON RETURNS OF HIGH- AND LOW-RISK SECURITIES?

ANSWER: [SHOW S6-51 THROUGH S6-55 HERE.] WHEN INVESTORS’ RISK AVERSION INCREASES,

THE SML IS ROTATED UPWARD ABOUT THE Y-INTERCEPT (kRF). kRF REMAINS AT 8

PERCENT, BUT NOW kM INCREASES TO 18 PERCENT, SO THE MARKET RISK PREMIUM

INCREASES TO 10 PERCENT. THE REQUIRED RATE OF RETURN WILL RISE SHARPLY ON

HIGH-RISK (HIGH-BETA) STOCKS, BUT NOT MUCH ON LOW-BETA SECURITIES.

OPTIONAL QUESTION

FINANCIAL MANAGERS ARE MORE CONCERNED WITH INVESTMENT DECISIONS RELATING TO REAL ASSETS SUCH AS PLANT AND EQUIPMENT THAN WITH INVESTMENTS IN FINANCIAL ASSETS SUCH AS SECURITIES. HOW DOES THE ANALYSIS THAT WE HAVE GONE THROUGH RELATE TO REAL ASSET INVESTMENT DECISIONS, ESPECIALLY CORPORATE CAPITAL BUDGETING DECISIONS?

ANSWER: THERE IS A GREAT DEAL OF SIMILARITY BETWEEN YOUR FINANCIAL ASSET

DECISIONS AND A FIRM’S CAPITAL BUDGETING DECISIONS. HERE IS THE LINKAGE:

1. A COMPANY MAY BE THOUGHT OF AS A PORTFOLIO OF ASSETS. IF THE COMPANY

DIVERSIFIES ITS ASSETS, AND ESPECIALLY IF IT INVESTS IN SOME PROJECTS THAT

TEND TO DO WELL WHEN OTHERS ARE DOING BADLY, IT CAN LOWER THE

VARIABILITY OF ITS RETURNS.

2. COMPANIES OBTAIN THEIR INVESTMENT FUNDS FROM INVESTORS, WHO BUY THE

FIRM’S STOCKS AND BONDS. WHEN INVESTORS BUY THESE SECURITIES, THEY

REQUIRE A RISK PREMIUM THAT IS BASED ON THE COMPANY’S RISK AS THEY

(INVESTORS) SEE IT. FURTHER, SINCE INVESTORS IN GENERAL HOLD WELL-

DIVERSIFIED PORTFOLIOS OF STOCKS AND BONDS, THE RISK THAT IS RELEVANT

TO THEM IS THE SECURITY’S MARKET RISK, NOT ITS STAND-ALONE RISK. THUS,

INVESTORS VIEW THE FIRM’S RISK FROM A MARKET RISK PERSPECTIVE.

3. THEREFORE, WHEN A MANAGER MAKES A DECISION TO BUILD A NEW PLANT, THE

RISKINESS OF THE INVESTMENT IN THE PLANT THAT IS RELEVANT TO THE FIRM’S

INVESTORS (ITS OWNERS) IS ITS MARKET RISK, NOT ITS STAND-ALONE RISK.

ACCORDINGLY, MANAGERS NEED TO KNOW HOW PHYSICAL ASSET INVESTMENT

DECISIONS AFFECT THEIR FIRM’S BETA COEFFICIENT. A PARTICULAR ASSET MAY

LOOK QUITE RISKY WHEN VIEWED IN ISOLATION, BUT IF ITS RETURNS ARE

NEGATIVELY CORRELATED WITH RETURNS ON MOST OTHER STOCKS, THE ASSET

MAY REALLY HAVE LOW RISK. WE WILL DISCUSS ALL THIS IN MORE DETAIL IN

OUR CAPITAL BUDGETING DISCUSSIONS.

SOLUTIONS TO APPENDIX 6A PROBLEMS

6A-1 a.

b = Slope = 0.62. However, b will depend on students’ freehand line. Using a calculator, we find b = 0.62.

b. Because b = 0.62, Stock Y is about 62 percent as volatile as the market; thus, its relative risk is about 62 percent that of an average firm.

c. 1. Stand-alone risk as measured by would be greater, but beta and hence systematic (relevant) risk would remain unchanged. However, in a 1-stock portfolio, Stock Y would be riskier under the new conditions.

2. CAPM assumes that company-specific risk will be eliminated in a portfolio, so the risk premium under the CAPM would not be affected. However, if the scatter were wide, we would not have as much confidence in the beta, and this could increase the stock's riskiness and thus its risk premium.

d. 1. The stock's variance and would not change, but the risk of the stock to an investor holding a diversified portfolio would be greatly reduced, because it would now have a negative correlation with kM.

2. Because of a relative scarcity of such stocks and the beneficial net effect on portfolios that include it, its “risk premium” is likely to be very low or even negative. Theoretically, it should be negative.

e. The following figure shows a possible set of probability distributions. We can be reasonably sure that the 100-stock portfolio comprised of b = 0.62 stocks as described in Condition 2 will be less risky than the “market.” Hence, the distribution for Condition 2 will be more peaked than that of Condition 3.

Harcourt, Inc. Solutions to Appendix Problems: 6 - 135

We can also say on the basis of the available information that Y is smaller than M; Stock Y’s market risk is only 62 percent of the “market,” but it does have company-specific risk, while the market portfolio does not, because it has been diversified away. However, we know from the given data that Y = 13.8%, while M = 19.6%. Thus, we have drawn the distribution for the single stock portfolio more peaked than that of the market. The relative rates of return are not reasonable. The return for any stock should be

ki = kRF + (kM – kRF)bi.

Stock Y has b = 0.62, while the average stock (M) has b = 1.0; therefore,

ky = kRF + (kM – kRF)0.62 < kM = kRF + (kM – kRF)1.0.

A disequilibrium exists--Stock Y should be bid up to drive its yield down. More likely, however, the data simply reflect the fact that past returns are not an exact basis for expectations of future returns.

f. The expected return could not be predicted with the historical characteristic line because the increased risk should change the beta used in the characteristic line.

g. The beta would decline to 0.53. A decline indicates that the stock has become less risky; however, with the change in the debt ratio the stock has actually become more risky. In periods of transition, when the risk of the firm is changing, the beta can yield conclusions exactly opposite to the actual facts. Once the company's risk stabilizes, the calculated beta should rise and should again approximate the true beta.

6A-2 a.

The slope of the characteristic line is the stock’s beta coefficient.

Slope = .

SlopeA = BetaA = = 1.0.

SlopeB = BetaB = = 0.5.

b. = 0.1(-14%) + 0.2(0%) + 0.4(15%) + 0.2(25%) + 0.1(44%)

= -1.4% + 0% + 6% + 5% + 4.4% = 14%.

The graph of the SML is as follows:

The equation of the SML is thus:

ki = kRF + (kM – kRF)bi = 9% + (14% – 9%)bi = 9% + (5%)bi.

c. Required rate of return on Stock A:

kA = kRF + (kM - kRF)bA = 9% + (14% - 9%)1.0 = 14%.

Required rate of return on Stock B:

kB = 9% + (14% - 9%)0.5 = 11.50%.

d. Expected return on Stock C:

= 18%.

Return on Stock C if in equilibrium:

kC = kRF + (kM - kRF)bC = 9% + (14% - 9%)2 = 19% 18% = .

Therefore, Stock C is not in equilibrium. Equilibrium will be restored when the expected return on Stock C is driven up to 19 percent. With an expected return of 18 percent on Stock C, investors should sell it, driving its price down and its yield up.

HOMEWORK #2

1. Ben Collins plans to buy a house for $65,000. If that real estate property is expected to increase in value 5 percent each year, what would its approximate value be seven years from now?

$65,000 1.407 = $91,455

2. Using the rule of 72, approximate the following:

a. If land in an area is increasing six percent a year, how long will it take for property values to double?

About 12 years (72 / 6)

b. If you earn ten percent on your investments, how long would it take for your money to double?

About 7.2 years (72 / 10)

c. At an annual interest rate of five percent, how long would it take for your savings to double?

About 14.4 years (72 / 5)

3. What would be the yearly earnings for a person with $6,000 in savings at an annual interest rate of 5.5 percent?

$6,000 .055 = $330

4. Using time value of money tables, calculate the following:

a. The future value of $450 six years from now at 7 percent.

$450 1.501 = $675.45

b. The future value of $800 saved each year for 10 years at 8 percent.

$800 14.487 = $11,589.60

c. The amount that a person would have to deposit today (present value) at a 6 percent interest rate in order to have $1,000 five years from now.

$1,000 .747 = $747

d. The amount that a person would have to deposit today in order to be able to take out $500 a year for 10 years from an account earning 8 percent.

Harcourt College Publishers Answers and Solutions: 2 - 142

$500 6.710 = $3,355

5. If you desire to have $20,000 for a down payment for a house in five years, what amount would you need to deposit today? Assume that your money will earn 5 percent.

$20,000 x 0.784 (present value of single amount) = $15,680.

6. Pete Morton is planning to go to graduate school in a program of study that will take three years. Pete wants to have $10,000 available each year for various school and living expenses. If he earns 4 percent on his money, how much must he deposit at the start of his studies to be able to withdraw $10,000 a year for three years?

$10,000 x 2.775 (present value of a series) = $27,750.

7. Carla Lopez deposits $3,000 a year into her retirement account. If these funds have an average earning of 8 percent over the 40 years until her retirement, what will be the value of her retirement account?

$3,000 x 259.060 (future value of a series) = $777,180

8. If a person spends $10 a week on coffee (assume $500 a year), what would be the future value of that amount over 10 years if the funds were deposited in an account earning 4 percent?

$500 x 12.006 (future value of a series) = $6,003.

9. A financial company that advertises on television will pay you $60,000 now in exchange for annual payments of $10,000 that you are expected to receive for a legal settlement over the next 10 years. If you estimate the time value of money at 10 percent, would you accept this offer?

First, calculate the future value of the annual payment $10,000 X 15.937 = $159,370Next, calculate the present value of that future flow $159,370 X 0.386 = $61,516.82Finally, the $60,000 being offered now is less than the present value of the future flow.

10. A budget should have five attributes. It should be (fill in the blanks):

Specific

Measurable

Attainable

RealisticTimely

True / False Questions

1. (p. 2) Financial planning has specific techniques that will be effective for every individual FALSE

2. (p. 13) Inflation reduces the buying power of money. TRUE

3. (p. 9) Planning to buy a house is an example of an intangible goal. FALSE

4. (p. 16) Opportunity costs refer to what a person gives up when making a decision. TRUE

5. (p. 17) Time value of money refers to changes in consumer spending when inflation occurs. FALSE

6. (p. 16) Most decisions have only a few alternatives from which to choose. FALSE

Multiple Choice Questions

7. (p. 2) The main goal of personal financial planning is: A. saving and investing for future needs.B. reducing a person's tax liability.C. achieving personal economic satisfaction.D. spending to achieve financial objectives.E. saving, spending, and borrowing based on current needs.

8. (p. 13) With an inflation rate of 9 percent, prices would double in about ___________ years. A. 4B. 6C. 8D. 10E. 12

9. (p. 12) The stages that an individual goes through based on age, financial needs, and family situation is called the: A. financial planning process.B. budgeting procedure.C. personal economic cycle.D. adult life cycle.E. tax planning process.

10. (p. 22) The ability to convert financial resources into usable cash with ease is referred to as: A. bankruptcy.B. liquidity.C. investing.D. saving.E. opportunity cost.

11. (p. 22) A question associated with the saving component of financial planning is: A. Do you have an adequate emergency fund?B. Is your will current?C. Is your investment program appropriate to your income and tax situation?D. Do you have a realistic budget for your current financial situation?E. Are your transportation expenses minimized through careful planning?

12. (p. 8) As Jean Tyler plans to set aside funds for her young children's college education, she is setting a(n) ____________ goal. A. intermediateB. long-termC. short-termD. intangibleE. durable

13. (p. 9) Which of the following goals would be the easiest to implement and measure its accomplishment? A. "Reduce our debt payments."B. "Save funds for an annual vacation."C. "Save $100 a month to create a $4,000 emergency fund."D. "Invest $2,000 a year for retirement."E. "Increase our emergency fund."

14. (p. 17) The time value of money refers to: A. personal opportunity costs such as time lost on an activity.B. financial decisions that require borrowing funds from a financial institution.C. changes in interest rates due to changes in the supply and demand for money in our economy.D. increases in an amount of money as a result of interest.E. changing demographic trends in our society.

15. (p. 18) Which type of computation would a person use to determine current value of a desired amount for the future? A. simple interestB. future value of a single amountC. future value of a series of depositsD. present value of a single amount

16. (p. 13) If inflation is increasing at 3 percent per year, and your salary increases at the same rate, how long will it take your salary to double? A. 30 yearsB. 24 yearsC. 18 yearsD. 12 yearsE. 6 years

17. (p. 13) When prices are increasing at a rate of 6 percent, the cost of products would double in about how many years? A. 7.2 yearsB. 10 yearsC. 6 yearsD. 12 yearsE. 18 years

18. (p. 18) Future value calculations involve: A. discounting.B. add-on interest.C. compounding.D. simple interest.E. an annuity.

19. (p. 18) If you put $1,000 in a saving account and make no further deposits, what type of calculation would provide you with the value of the account in 20 years? A. future value of a single amountB. simple interestC. present value of a single amountD. present value of a series of depositsE. future value of a series of deposits

20. (p. 3) The first step of the financial planning process is to: A. develop financial goals.B. implement the financial plan.C. analyze your current personal and financial situation.D. evaluate and revise your actions.E. create a financial plan of action.

21. (p. 5) Which of the following is an example of opportunity cost? A. renting an apartment near schoolB. saving money instead of taking a vacationC. setting aside money for paying income taxD. purchasing automobile insuranceE. using a personal computer for financial planning

22. (p. 5) The uncertainty associated with decision making is referred to as: A. opportunity cost.B. selection of alternatives.C. financial goals.D. personal values.E. risk.

23. (p. 7) The financial planning process concludes with efforts to: A. develop financial goals.B. create a financial plan of action.C. analyze your current personal and financial situation.D. review the financial plan.E. review and revise your actions.

24. (p. 8) Which of the following is usually considered a long-term financial strategy? A. creating a budgetB. using savings to pay off a loan earlyC. renting an apartment to save for the purchase of a homeD. investing in a growth mutual fund to accumulate retirement fundsE. purchasing auto insurance to cover the needs of dependents

25. (p. 13) When prices are rising at a rate of 3 percent, the cost of products and services would double in ______ years. A. 3B. 6C. 12D. 24E. 36

26. (p. 14) The annual price increase for consumer goods and services measured by the Bureau of Labor Statistics is referred called ________. A. deflationB. inflationC. the consumer price indexD. the price calculatorE. goods and all of the above

27. (p. 42) A job tends to have less of a long-term commitment to a field than a career. TRUE

28. (p. 42) A possible opportunity cost associated with career advancement is a need to relocate your household. TRUE

29. (p. 44) An interest inventory measures a person's aptitudes. FALSE

30. (p. 50) Libraries usually have a variety of information sources for career planning and job exploration. TRUE

31. (p. 57) A tax-exempt employee benefit is usually more advantageous than a tax-deferred benefit. TRUE

32. (p. 42) Compared to a job, a career: A. is often less financially rewarding.B. requires minimum training.C. demands regular updating of knowledge.D. has limited opportunities for advancement.E. is one who engage in for your lifetime.

33. (p. 42) A (n) ____________ is an employment position that is obtained mainly to earn money. A. careerB. jobC. internshipD. apprenticeshipE. cooperative

34. (p. 43) Mathematical abilities, problem-solving skills, and physical dexterity are examples of: A. interests.B. survival skills.C. aptitudes.D. occupational attitudes.E. on-the-job training.

35. (p. 58) Barb Hotchkins is in the 28 percent tax bracket. A tax-exempt employee benefit with a value of $500 would have a tax-equivalent value of: A. $694.B. $528.C. $500.D. $360.E. $140.

36. (p. 57) Federal tax-deferred employee benefits are: A. not subject to federal income tax.B. not subject to state income tax.C. taxed at some future time.D. are taxed at a special rate.E. only available to union employees.

37. (p. 46) Caroline lives in City A and earns $50,000 per year. The cost of living index in City A is .8. She is considering a move to City B which has a cost of living index of .9. How large a salary will she require in City B to maintain her current standard of living? A. $44,444B. $40,000C. $56,250D. $45,000E. $50,000

38. (p. 58) Joseph is eligible for a nontaxable life insurance benefit with an annual premium of $400 paid entirely by his employer. Assuming Joseph is in a 25% bracket, how much would he have to earn to pay for this benefit with after-tax dollars? A. $425.00B. $533.33C. $433.33D. $500.00E. $400.00

39. (p. 78-79) Opportunity costs are only associated with money management decisions involving long-term financial security. FALSE

40. (p. 80) Financial records that are referred to on a regular basis should be kept in a safe-deposit box. FALSE

41. (p. 82) A personal balance sheet reports your income and expenses. FALSE

42. (p. 82) A person's net worth is the difference between the value of the items owned and the amounts owed to others. TRUE

43. (p. 83) Furniture, jewelry, and an automobile are examples of liquid assets. FALSE

44. (p. 86) Take-home pay is a person's earnings after deductions for taxes and other items. TRUE

45. (p. 78) Opportunity costs refer to: A. current spending habits.B. changing economic conditions that affect a person's cost of living.C. storage facilities to make financial documents easily available.D. trade-offs associated with financial decisions.E. avoiding the use of consumer credit.

46. (p. 81) A home file should be used for: A. storing all financial documents and records.B. financial records for current needs.C. documents that require maximum security.D. obsolete financial documents.E. records that are difficult to replace.

47. (p. 82) Which of the following are considered to be personal financial statements? A. budget and credit card statementsB. balance sheet and cash flow statementC. checkbook and budgetD. tax returnsE. bank statement and savings passbook

48. (p. 82) A personal balance sheet presents: A. amounts budgeted for spending.B. income and expenses for a period of time.C. earnings on savings and investments.D. items owned and amounts owed.E. family financial goals.

49. (p. 82) The current financial position (including net worth) of an individual or family is best presented with the use of a(n): A. budget.B. cash flow statement.C. balance sheet.D. bank statement.E. time value of money report.

50. (p. 82) Items that you own with a monetary worth are referred to as: A. liabilities.B. variable expenses.C. net worth.D. income.E. assets.

51. (p. 84) Liabilities are amounts representing: A. debts.B. items of value.C. living expenses.D. taxable income.E. current assets.

52. (p. 85) Which one of the following presents a summary of income and outflows for a period of time? A. balance sheetB. bank statementC. investment summaryD. cash flow statementE. asset report

53. (p. 86) Total earnings of a person minus the deductions for taxes and other items is called: A. budgeted income.B. gross pay.C. net worth.D. total revenue.E. take-home pay.

54. (p. 86) A common deduction from a person's paycheck is for: A. interest.B. taxes.C. rent.D. unemployment.E. current liabilities.

55. (p. 87-88) Payments that do not vary from month to month are ____________ expenses. A. fixedB. usageC. variableD. luxury

56. (p. 93) If a family planned to spend $370 for food during March but only spent $348, this difference would be referred to as a: A. variance.B. deficit.C. fixed living expense.D. budget reduction.E. contribution to net worth.

57. (p. 93) A budget deficit would result when a person's or family's: A. actual expenses are less than planned expenses.B. actual expenses are greater than planned expenses.C. actual expenses equal planned expenses.D. assets exceed liabilities.

58. (p. 82) Karen Price has created a financial statement for herself that lists all of the assets she owns as well as the debts she owes. This would be an example of: A. money management.B. opportunity cost analysis.C. a balance sheet.D. a liquidation exercise.E. a budget variance.

59. (p. 82) A family has a net worth of $156,000 and liabilities of $167,000, what is the amount of their assets? A. $11,000B. $156,000C. $167,000D. $323,000

60. (p. 83-84) Katherine Kocher has determined the following information about her own financial situation. Her checking account is worth $850 and her savings account is worth $1,200. She owns her own home that has a market value of $98,000. She has furniture and appliances worth $12,000 and a home computer and laptop worth $3,300. She has a car worth $12,500. She has recently purchased a 2-year certificate of deposit worth $5,500 and she has a retirement account worth $38,550. What is the total value of her assets? A. $127,850B. $98,000C. $168,600D. $159,900E. $171,900

61. (p. 85) This month, Ken Grossman has cash inflows of $3,100 and cash outflows of $2,950, resulting in a A. balanced budget.B. surplus of $150.C. deficit of $150.D. surplus of $3,100.E. deficit of $2,950.

62. (p. 87) A person has $1,250 in liabilities, monthly savings of $200, and monthly gross income of $2,500. What is the person's savings ratio? A. 0.52B. 0.08C. 2.35D. 0.16E. 12.58

63. (p. 93) The Hernandez family budgets $420 a month for food. Last month they spent $413, which creates a A. budget surplus of $7.B. budget deficit of $7.C. budget surplus of $420.D. budget deficit of $413.E. balanced budget.

64. (p. 123) Taxes are only considered as financial planning activities in April. FALSE

65. (p. 106) A state may impose a personal property tax. TRUE

66. (p. 106) A general sales tax is also referred to as an excise tax. FALSE

67. (p. 106) A tax on the value of automobiles, boats, or furniture is referred to as a personal property tax. TRUE

68. (p. 106) An estate tax is imposed on the value of an individual's property at the time of his or death. TRUE

69. (p. 109) An exclusion is earnings not included in taxable income. TRUE

70. (p. 109) Exemptions are deductions for yourself, your spouse, and qualified dependents that you can deduct from adjusted gross income. TRUE

72. (p. 113) A tax credit is an amount subtracted directly from the amount of taxes owed. TRUE

73. (p. 117) A person's filing status is affected by marital status and dependents. TRUE

74. (p. 106) The ______________ property tax is based on the value of land and buildings at some point in time. A. personalB. real estateC. directD. proportionalE. regressive

75. (p. 108) What type of tax is imposed on the value of an individual's property at the time of his or her death? A. inheritanceB. exciseC. giftD. personal propertyE. estate

76. (p. 113) Interest earnings of $1,600 from a taxable investment for a person in a 28 percent tax bracket would result in after-tax earnings of: A. $1,600B. $1,152C. $1,100D. $448E. $152

77. (p. 112) A taxpayer with a taxable income of $47,856 and a total tax bill of $5,889 would have an average tax rate of ____ percent. A. 8.6B. 10.3C. 12.3D. 14.2E. 16.7

78. (p. 109) A person has $4,000 in medical expenses and an adjusted gross income of $32,000. If taxpayers are allowed to deduct the amount of medical expenses that exceed 7.5 percent of adjusted gross income, what would be the amount of the deduction in this situation? A. $300B. $1,600C. $2,400D. $4,000E. $32,000

79. (p. 109) Which of the following would result in a reduction of taxable income? A. portfolio incomeB. tax creditsC. exclusionsD. passive incomeE. earned income

80. (p. 109) Which one of the following is not included in gross income? A. Tax credit.B. Exemption.C. Exclusion.D. Earned income.E. Portfolio income.

81. (p. 108) Which of the following would be deducted from gross income to obtain adjusted gross income? A. alimony paymentsB. mortgage interestC. medical expensesD. foreign income exclusionE. charitable contributions

82. (p. 111) A deduction from adjusted gross income for yourself, your spouse, and qualified dependents is: A. the standard deduction.B. a tax credit.C. an itemized deduction.D. an exclusion.E. an exemption.

83. (p. 113) A tax ____________ is an amount subtracted directly from the amount of taxes owed. A. creditB. exemptionC. deductionD. exclusionE. shelter

84. (p. 113) A tax credit of $50 for a person in a 28 percent tax bracket would reduce a person's taxes by: A. $10.B. $28.C. $14.D. $50.E. $35.

85. (p. 118) The Form 1040 is most helpful to a person who: A. is single with no other exemptions.B. makes less than $50,000 with no interest or dividends.C. itemizes deductions.D. has exempt income.E. has a simple tax situation.

86. (p. 121) Itemized deductions are recorded on: A. Form 1040A.B. Schedule A.C. Schedule B.D. Form 2106.E. Form 1040 B

87. (p. 113) An itemized deduction of $500 with a 36 percent tax rate would reduce a person's taxes by: A. $500.B. $36.C. $464.D. $280.E. $180.

88. (p. 106) The state of Oklahoma imposes a tax of $.17 per gallon on gasoline. What type of tax is this most likely to be? A. general sales taxB. excise taxC. personal property taxD. income taxE. estate tax

89. (p. 130) A allows a taxpayer to put pre-tax dollars into an employer-sponsored program to cover medical and child care costs. A. tax creditB. tax deductionC. flexible spending accountD. tax deferred investmentE. tax exempt investment

Chapter 2

Risk and Return: Part I

ANSWERS TO BEGINNING-OF-CHAPTER QUESTIONS

Our students have had an introductory finance course, and many have also taken a course on investments and/or capital markets. Therefore, they have seen the Chapter 2 material previously. However, we use the Beginning of Chapter (BOC) Questions to review it because our students need a refresher.

With some groups of students it is best to go through the chapter on a point-by-point basis, using the PowerPoint slides. With other groups, this would involve repeating too much of the intro course. In the latter situation, we tell our students that the chapter is a review and that we will call on them to discuss the BOC questions in class. We supplement their answers to make sure the key points are covered.

Our students have mainly taken multiple-choice exams, so they are uncomfortable with essay tests. Also, we cover the chapters quickly, so the assignments cover a lot of pages. We explain that much of the material is a review, and that if they can answer the BOC questions they will do OK on the exams. We also tell them, partly for motivation and partly to reduce anxiety, that our exams will consist of 5 slightly modified BOC questions, and they must answer 3. We also tell them that they can use a 4-page “cheat sheet,” two sheets of paper, front and back. They can put anything they want on it—formulas, definitions, outlines of answers to the questions, or complete answers. All this helps them focus and get better prepared. Writing out answers is a good way to study, and outlining answers to fit them on the cheat sheet (in really small font!) also helps them learn.

We try to get students to think in a more integrated manner, relating topics covered in different chapters to one another. Studying all of the BOC questions in a fairly compressed period before the exams helps in this regard.

We expected really excellent exams, given that they had the questions and could use cheat sheets. Some of the exams were indeed excellent, but we were surprised and disappointed at the poor quality of many of the papers. Part of the problem is that they were not used to taking essay exams. Also, they would have done better if they had taken the exam after we covered cases (in the second half of the semester), where we apply the text material to real-world cases. While both points are true, but it’s also true that some students are just better than others. Finally, since our students are all graduating seniors, we graded rather easily.

Answers

2-1 Stand-alone risk is the risk faced by an investor who holds just one asset, versus the risk inherent in a diversified portfolio.

Stand-alone risk is measured by the standard deviation (SD) of expected returns or the coefficient of variation (CV) of returns = SD/expected return.

A portfolio’s risk is measured by the SD of its returns, and the risk of the individual stocks in the portfolio is measured by their beta

coefficients. Note that unless returns on all stocks in a portfolio are perfectly positively correlated, the portfolio’s SD will be less than the average of the SD’s of the individual stocks. Diversification reduces risk.

In theory, investors should be concerned only with portfolio risk, but in practice many investors are not well diversified, hence are concerned with stand-alone risk. Managers who have large stockholdings in their companies are an example. They get stock (or options) as incentive compensation or else because they founded the company, and they are often constrained from selling to diversify. Note too that years ago brokerage costs and administrative hassle kept people from diversifying, but today mutual funds enable small investors to diversify efficiently.

2-2 Diversification can eliminate unsystematic risk, but market risk will remain. See Figure 2-8 for a picture of what happens as stocks are added to a portfolio. The graph shows that the risk of the portfolio as measured by its SD declines as more stocks are added. This is the situation if randomly selected stocks are added, but if stocks in the same industry are added, the benefits of diversification will be lessened.

Conventional wisdom says that about 40 stocks from a number of different industries is sufficient to eliminate most unsystematic risk, but in recent years the markets have become increasingly volatile, so now it takes somewhat more, perhaps 50 or 60. Of course, the more stocks, the closer the portfolio will be to having zero unsystematic risk. Again, this assumes that stocks are randomly selected.

Different diversified portfolios can have different amounts of risk. First, if the portfolio concentrates on a given industry or sector (as sector mutual funds do), then the portfolio will not be well diversified even if it contains 100 stocks. Second, the betas of the individual stocks affect the risk of the portfolio. If the stock with the highest beta in each industry is selected, then the portfolio may not have much unsystematic risk, but it will have a high beta and thus have a lot of market risk. (Note: The market risk of a portfolio is measured by the beta of the portfolio, and that beta is a weighted average of the betas of the stocks in the portfolio.)

2-3 Note: This question is covered in more detail in Chapter 5, but

students should remember this material from their first finance course, so it is a review.

Expected: The rate of return someone expects to earn on a stock. Typically measured as D1/P0 + g for a constant growth stock.

Required: The minimum rate of return that an investor must expect on a stock to induce him or her to buy or hold the stock. Typically measured as ks = krf + b(MRP), where MRP is the market risk premium or the risk premium required for an average stock.

Historical: The average rate of return earned on a stock during some past period. The historical return on an average large stock varied from –3% to +37% during the 1990s, and it was about –15% in 2000. The variations for individual stocks were much greater—the best performer on the NYSE in 2000 gained 413% and the worst performer lost 99.9% of its value.

Are they Equal? 1) Expected and required. For market equilibrium, the expected and

required rate of return as seen by “the marginal investor” must be equal for any given stock and therefore for the entire market. If the expected return exceeds the required return, then investors will buy, push the price up and the expected return down, and thus produce an equilibrium. Of course, any individual investor may believe that a given stock’s expected and required returns differ, so individuals may think there are bargains to be had or dogs to be sold. Also, new information is constantly hitting the market and changing the opinions of marginal investors, and this leads to swings in the market. New technology is causing new information to be disseminated more rapidly, and that is leading to more rapid and violent market swings.

2) Historical. There is no reason whatever to think that the expected and/or required rate of return, for any given year for either one stock or for all stocks on average, will be equal to the historical rate of return. Rational people don’t expect abnormally high or low performance to continue. On the other hand, people do argue that investors expect to earn returns in the future that approximate average past returns. For example, if stocks returned 10% on average in the past (from 1926 to 2000, which is as far back as good data exist), then they may expect to earn about 10% on stocks in the future. Note, though, that this is a controversial issue—the period 1926-2000 covers a lot of very different economic environments, and investors may not expect the future to replicate the past. Certainly investors didn’t expect future returns to equal distant past returns during the height of the 1999 bull market.

2-4 Risk aversion means that someone doesn’t like risk, so if Securities A and B both have an expected return of say 10%, but Security A has less risk than B, then investors will prefer A. As a result, A’s price will be bid up, and B’s price bid down, and in the resulting equilibrium A’s expected rate of return will be below that of B. Of course, A’s required rate of return will also be less than B’s, and in equilibrium the expected and required returns will be equal.

One issue here is the type of risk investors are averse to—unsystematic, market, or both? According to CAPM theory, only market risk as measured by beta is relevant and thus requires a premium. However, empirical tests indicate that investors are also require a premium for bearing unsystematic risk as measured by the stock’s SD.

2-5 CAPM = Capital Asset Pricing Model. The CAPM establishes a metric for measuring the market risk of a stock (beta), and it specifies the relationship between risk as measured by beta and the required rate of return on a stock. Its principal developers (Sharpe, Merton, and Markowitz) won the Nobel Prize for their work.

The key assumptions are spelled out in Chapter 3, but they include (1) all investors focus on a single holding period, (2) investors can lend or borrow unlimited amounts at the risk-free rate, (3) there are no brokerage cost, and (4) there are no taxes. The assumptions are not realistic, so the CAPM may be incorrect. Empirical tests have neither confirmed nor refuted the CAPM with any degree of confidence, so it may or may not provide a valid formula for measuring the required rate of return.

The SML, or Security Market Line (see Figure 2-12), specifies the relationship between risk as measured by beta and the required rate of return, ks = krf + b(MRP). MRP = Expected rate of return on the market – Risk-free rate = km – kfr .

The data requirements are beta, the risk-free rate, and the rate of return expected on the market. Betas are easy to get (by calculating them or from some source such as Value Line or Yahoo!, but a beta show how volatile a stock was in the past, not how volatile it will be in the future, so historical betas may not reflect investors perceptions about the stock’s risk. The risk-free rate is based on either T-bonds or T-bills; these rates are easy to get, but it is not clear which should be used, and there can be a big difference between bill and bond rates, depending on the shape of the yield curve. Finally, it is difficult to determine the rate of return investors expect on an average stock. Some argue that investors expect to earn the same average return in the future that they earned in the past, hence use historical MRPs, but as noted above, that may not reflect investors’ true expectations.

The bottom line is that we cannot be sure that the CAPM-derived estimate of the required rate of return is actually correct.

2-6 a. We used an Excel model to calculate betas for X and Y, and the SML required returns for these stocks:

bx = 0.69; by = 1.66 and kx = 10.7%; ky = 14.6%. Since Y has the higher beta, it has the higher required return.

Note that the points all fall on the trend line. Thus, the two stocks have essentially no diversifiable, unsystematic risk—all of their risk is market risk. If these were real companies, they might have the indicated trend lines and betas, but the points would be scattered about the trend line. See Figure 3-8 in Chapter 3, where data for Wal-Mart are plotted. Although the situation for our Stocks X and Y would never occur for individual stocks, it would occur (approximately) for index funds, if Stock X were an index fund that held stocks with betas that averaged 0.69 and Stock Y were an index fund with b = 1.66 stocks.

b. Here we drop Year 1 and add Year 6, then calculate new betas and k’s. For Stock X, the beta and required return are stable. However, Y’s beta falls from 1.66 to 0.19, and its required return as calculated with the SML falls to 8.8%.

The figures for Y make little sense. The stock fell sharply because investors became worried about its future prospects, which means that it fell because it became riskier. Yet its beta fell. As a riskier stock, its required return should rise, yet the calculated return fell from 14.6% to 8.8%, just above the riskless rate.

The problem is that Y’s low return tilted the regression line down—the point for Year 6 is in the lower right quadrant of the Excel graph. The low R2 and the large standard error as seen in the Excel regression make it clear that the beta, and thus the calculated required return, are not to be trusted.

Note that in April 2001, the same month that PG&E declared bankruptcy, its beta as reported by Finance.Yahoo was only 0.05, so PG&E actually had the same experience as Stock Y. The moral of the story is that the CAPM, like other cost of capital estimating techniques, can be dangerous if used without care and judgment.

One final point on all this. The utilities are regulated, and regulators estimate their cost of capital and use it as a basis for setting electric rates. If the estimated cost of capital is low, then the companies are only allowed to earn a low rate of return on their invested capital. At times, utilities like PG&E become more risky, have resulting low betas, and are then in danger of having some squirrelly finance “expert” argue that they should be allowed to earn an improper CAPM rate of return. In the industrial sector, a badly trained financial analyst could make the same mistake, estimate the cost of capital to be below the true cost, and cause the company to make investments that it should not have made.

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A B C D E F G H IWorksheet for BOC Question 2-6 4/8/01

We use BOC Q2-6 to illustrate some points about the CAPM, the SML, and Excel. For a morecomplete treatment of Excel, see the Tool Kit for Chapter 2 and also those for the other chapters.

We provide some instructions for creating the Excel model below on the tab labeled Inst.We print out this sheet, then follow it when we go through the Excel model in class. We oftendelete some of the prepared materials below and then re-create it in class.

Question 6.Percentage Returns

Year Market Stock X Stock Y1 20% 16% 28%2 8% 8% 8%3 15% 12% 20%4 -6% -2% -15%5 23% 18% 33%6 20% 16% -70%

Average 12.0% 10.4% 14.8%

Beta X: 0.69Beta Y: 1.66

SML Analysis:Risk-free rate: 8.0%Market return: 12.0%

k(X) = k(rf) + b(k(Market) - k(fr))8.0% + 2.7% = 10.7% = Predicted return for X.

k(Y) = k(rf) + b(k(Market) - k(fr))8.0% + 6.6% = 14.6% = Predicted return for Y.

New Beta Y: 0.19

New k(y): 8.8%

Note that the R-square for the regressiondropped from 0.99 to 0.0029, and thestandard error rose sharply. This indicates

that the beta, and the CAPM requiredreturn, are being measured with a lot of error.

So, we cannot trust the accuracy of theestimated required return.

Beta Graph

-10% 0% 10% 20% 30% 40%Market Return (%)

-10% 0% 10% 20% 30%

ANSWERS TO END-OF-CHAPTER QUESTIONS

2-1 a. Stand-alone risk is only a part of total risk and pertains to the risk an investor takes by holding only one asset. Risk is the chance that some unfavorable event will occur. For instance, the risk of an asset is essentially the chance that the asset’s cash flows will be unfavorable or less than expected. A probability distribution is a listing, chart or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome. When in graph form, the tighter the probability distribution, the less uncertain the outcome.

b. The expected rate of return ( ) is the expected value of a probability distribution of expected returns.

c. A continuous probability distribution contains an infinite number of outcomes and is graphed from - and +.

d. The standard deviation () is a statistical measure of the variability of a set of observations. The variance (2) of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation. The coefficient of variation (CV) is equal to the standard deviation divided by the expected return; it is a standardized risk measure which allows comparisons between investments having different expected returns and standard deviations.

e. A risk averse investor dislikes risk and requires a higher rate of return as an inducement to buy riskier securities. A realized return is the actual return an investor receives on their investment. It can be quite different than their expected return.

f. A risk premium is the difference between the rate of return on a risk-free asset and the expected return on Stock I which has higher risk. The market risk premium is the difference between the expected return on the market and the risk-free rate.

g. CAPM is a model based upon the proposition that any stock’s required rate of return is equal to the risk free rate of return plus a risk premium reflecting only the risk remaining after diversification.

h. The expected return on a portfolio. p, is simply the weighted-average expected return of the individual stocks in the portfolio, with the weights being the fraction of total portfolio value invested in each stock. The market portfolio is a portfolio consisting of all stocks.

i. Correlation is the tendency of two variables to move together. A correlation coefficient (r) of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of -1.0 means the variables always move in opposite directions. A correlation coefficient of zero suggests that the two variables are not related to one another; that is, they are independent.

j. Market risk is that part of a security’s total risk that cannot be eliminated by diversification. It is measured by the beta coefficient. Diversifiable risk is also known as company specific risk, that part of a security’s total risk associated with random events not affecting the market as a whole. This risk can be eliminated by proper diversification. The relevant risk of a stock is its contribution to the riskiness of a well-diversified portfolio.

k. The beta coefficient is a measure of a stock’s market risk, or the extent to which the returns on a given stock move with the stock market. The average stock’s beta would move on average with the market so it would have a beta of 1.0.

l. The security market line (SML) represents in a graphical form, the relationship between the risk of an asset as measured by its beta and the required rates of return for individual securities. The SML equation is essentially the CAPM, ki = kRF + bi(kM - kRF).

m. The slope of the SML equation is (kM - kRF), the market risk premium. The slope of the SML reflects the degree of risk aversion in the economy. The greater the average investors aversion to risk, then the steeper the slope, the higher the risk premium for all stocks, and the higher the required return.

2-2 a. The probability distribution for complete certainty is a vertical line.

b. The probability distribution for total uncertainty is the X axis from - to +.

2-3 Security A is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks. In a single-asset portfolio, Security A would be more risky because A > B and CVA > CVB.

2-4 a. No, it is not riskless. The portfolio would be free of default risk and liquidity risk, but inflation could erode the portfolio’s purchasing power. If the actual inflation rate is greater than that expected, interest rates in general will rise to incorporate a larger inflation premium (IP) and the value of the portfolio would decline.

b. No, you would be subject to reinvestment rate risk. You might expect to “roll over” the Treasury bills at a constant (or even increasing) rate of interest, but if interest rates fall, your investment income will decrease.

c. A U.S. government-backed bond that provided interest with constant purchasing power (that is, an indexed bond) would be close to riskless.

2-5 a. The expected return on a life insurance policy is calculated just as for a common stock. Each outcome is multiplied by its probability of occurrence, and then these products are summed. For example, suppose a 1-year term policy pays $10,000 at death, and the probability of the policyholder’s death in that year is 2 percent. Then, there is a 98 percent probability of zero return and a 2 percent probability of $10,000:

Expected return = 0.98($0) + 0.02($10,000) = $200.

This expected return could be compared to the premium paid. Generally, the premium will be larger because of sales and administrative costs, and insurance company profits, indicating a negative expected rate of return on the investment in the policy.

b. There is a perfect negative correlation between the returns on the life insurance policy and the returns on the policyholder’s human capital. In fact, these events (death and future lifetime earnings capacity) are mutually exclusive.

c. People are generally risk averse. Therefore, they are willing to pay a premium to decrease the uncertainty of their future cash flows. A life insurance policy guarantees an income (the face value of the policy) to the policyholder’s beneficiaries when the policyholder’s future earnings capacity drops to zero.

2-6 The risk premium on a high beta stock would increase more.

RPj = Risk Premium for Stock j = (kM - kRF)bj.

If risk aversion increases, the slope of the SML will increase, and so will the market risk premium (kM – kRF). The product (kM – kRF)bj is the risk premium of the jth stock. If b j is low (say, 0.5), then the product will be small; RPj will increase by only half the increase in RPM. How-ever, if bj is large (say, 2.0), then its risk premium will rise by twice the increase in RPM.

2-7 According to the Security Market Line (SML) equation, an increase in beta will increase a company’s expected return by an amount equal to the market risk premium times the change in beta. For example, assume that the risk-free rate is 6 percent, and the market risk premium is 5 percent. If the company’s beta doubles from 0.8 to 1.6 its expected return increases from 10 percent to 14 percent. Therefore, in general, a company’s expected return will not double when its beta doubles.

2-8 Yes, if the portfolio’s beta is equal to zero. In practice, however, it may be impossible to find individual stocks that have a nonpositive beta. In this case it would also be impossible to have a stock portfolio with a zero beta. Even if such a portfolio could be constructed, investors would probably be better off just purchasing Treasury bills, or other zero beta investments.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

2-1 = (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)= 11.40%.

2 = (-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4) + (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1)

2 = 712.44; = 26.69%.

CV = = 2.34.

2-2 Investment Beta $35,000 0.8 40,000 1.4

Total $75,000

($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.

2-3 kRF = 5%; RPM = 6%; kM = ?

kM = 5% + (6%)1 = 11%.

ks when b = 1.2 = ?

ks = 5% + 6%(1.2) = 12.2%.

2-4 kRF = 6%; kM = 13%; b = 0.7; ks = ?

ks = kRF + (kM - kRF)b= 6% + (13% - 6%)0.7= 10.9%.

2-5 a. = (0.3)(15%) + (0.4)(9%) + (0.3)(18%) = 13.5%.

= (0.3)(20%) + (0.4)(5%) + (0.3)(12%) = 11.6%.

b. M = [(0.3)(15% - 13.5%)2 + (0.4)(9% - 13.5%)2 + (0.3)(18% -13.5%)2]1/2

= = 3.85%.J = [(0.3)(20% - 11.6%)2 + (0.4)(5% - 11.6%)2 + (0.3)(12% - 11.6%)2]1/2

= = 6.22%.

c. CVM = = 0.29.

CVJ = = 0.54.

2-6 a.

= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)

= 14% versus 12% for X.

= (-10% - 12%)2(0.1) + (2% - 12%)2(0.2) + (12% - 12%)2(0.4)

+ (20% - 12%)2(0.2) + (38% - 12%)2(0.1) = 148.8%.

X = 12.20% versus 20.35% for Y.

CVX = X/ X = 12.20%/12% = 1.02, while

CVY = 20.35%/14% = 1.45.

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

2-7 a. kA = kRF + (kM - kRF)bA

12% = 5% + (10% - 5%)bA

12% = 5% + 5%(bA) 7% = 5%(bA)1.4 = bA.

b. kA = 5% + 5%(bA)kA = 5% + 5%(2)kA = 15%.

2-8 a. ki = kRF + (kM - kRF)bi = 9% + (14% - 9%)1.3 = 15.5%.

b. 1. kRF increases to 10%:

kM increases by 1 percentage point, from 14% to 15%.

ki = kRF + (kM - kRF)bi = 10% + (15% - 10%)1.3 = 16.5%.

2. kRF decreases to 8%:

kM decreases by 1%, from 14% to 13%.

ki = kRF + (kM - kRF)bi = 8% + (13% - 8%)1.3 = 14.5%.

c. 1. kM increases to 16%:

ki = kRF + (kM - kRF)bi = 9% + (16% - 9%)1.3 = 18.1%.

2. kM decreases to 13%:

ki = kRF + (kM - kRF)bi = 9% + (13% - 9%)1.3 = 14.2%.

2-9 Old portfolio beta = (b) + (1.00)

1.12 = 0.95b + 0.05 1.07 = 0.95b 1.13 = b.

New portfolio beta = 0.95(1.13) + 0.05(1.75) = 1.16.

Alternative Solutions:

1. Old portfolio beta = 1.12 = (0.05)b1 + (0.05)b2 +...+ (0.05)b20

1.12 = (bi)(0.05)bi = 1.12/0.05 = 22.4.

New portfolio beta = (22.4 - 1.0 + 1.75)(0.05) = 1.1575 = 1.16.

2. bi excluding the stock with the beta equal to 1.0 is 22.4 - 1.0 = 21.4, so the beta of the portfolio excluding this stock is b = 21.4/19 = 1.1263. The beta of the new portfolio is:

1.1263(0.95) + 1.75(0.05) = 1.1575 = 1.16.

2-10 Portfolio beta = (1.50) + (-0.50)

+ (1.25) + (0.75)

= 0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75) = 0.15 - 0.075 + 0.3125 + 0.375 = 0.7625.

kp = kRF + (kM - kRF)(bp) = 6% + (14% - 6%)(0.7625) = 12.1%.

Alternative solution: First compute the return for each stock using the CAPM equation [k RF + (kM - kRF)b], and then compute the weighted average of these returns.

kRF = 6% and kM - kRF = 8%.

Stock Investment Beta k = kRF + (kM - kRF)b Weight A $ 400,000 1.50 18% 0.10 B 600,000 (0.50) 2 0.15 C 1,000,000 1.25 16 0.25 D 2,000,000 0.75 12 0.50Total $4,000,000 1.00

kp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.

2-11 First, calculate the beta of what remains after selling the stock:

bp = 1.1 = ($100,000/$2,000,000)0.9 + ($1,900,000/$2,000,000)bR

1.1 = 0.045 + (0.95)bR

bR = 1.1105.

bN = (0.95)1.1105 + (0.05)1.4 = 1.125.

2-12 We know that bR = 1.50, bS = 0.75, kM = 13%, kRF = 7%.

ki = kRF + (kM - kRF)bi = 7% + (13% - 7%)bi.

kR = 7% + 6%(1.50) = 16.0%kS = 7% + 6%(0.75) = 11.5 4.5 %

2-13 a. ($1 million)(0.5) + ($0)(0.5) = $0.5 million.

b. You would probably take the sure $0.5 million.

c. Risk averter.

d. 1. ($1.15 million)(0.5) + ($0)(0.5) = $575,000, or an expected profit of $75,000.

2. $75,000/$500,000 = 15%.

3. This depends on the individual’s degree of risk aversion.

4. Again, this depends on the individual.

5. The situation would be unchanged if the stocks’ returns were perfectly positively correlated. Otherwise, the stock portfolio would have the same expected return as the single stock (15%) but a lower standard deviation. If the correlation coefficient between each pair of stocks was a negative one, the portfolio would be virtually riskless. Since r for stocks is generally in the range of +0.6 to +0.7, investing in a portfolio of stocks would definitely be an improvement over investing in the single stock.

2-14 a. = 0.1(7%) + 0.2(9%) + 0.4(11%) + 0.2(13%) + 0.1(15%) = 11%.

kRF = 6%. (given)

Therefore, the SML equation is

ki = kRF + (kM - kRF)bi = 6% + (11% - 6%)bi = 6% + (5%)bi.

b. First, determine the fund’s beta, bF. The weights are the percentage of funds invested in each stock.

A = $160/$500 = 0.32 B = $120/$500 = 0.24 C = $80/$500 = 0.16 D = $80/$500 = 0.16 E = $60/$500 = 0.12

bF = 0.32(0.5) + 0.24(2.0) + 0.16(4.0) + 0.16(1.0) + 0.12(3.0) = 0.16 + 0.48 + 0.64 + 0.16 + 0.36 = 1.8.

Next, use bF = 1.8 in the SML determined in Part a:

= 6% + (11% - 6%)1.8 = 6% + 9% = 15%.

c. kN = Required rate of return on new stock = 6% + (5%)2.0 = 16%.

An expected return of 15 percent on the new stock is below the 16 percent required rate of return on an investment with a risk of b = 2.0. Since kN = 16% > N = 15%, the new stock should not be purchased. The expected rate of return that would make the fund indifferent to purchasing the stock is 16 percent.

2-15 The answers to a, b, c, and d are given below:

kA kB Portfolio 1997 (18.00%) (14.50%) (16.25%) 1998 33.00 21.80 27.40 1999 15.00 30.50 22.75 2000 (0.50) (7.60) (4.05) 2001 27.00 26.30 26.65

Mean 11.30 11.30 11.30 Std Dev 20.79 20.78 20.13 CV 1.84 1.84 1.78

e. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated (rAB = 0.88).

2-16 a. bX = 1.3471; bY = 0.6508.

b. kX = 6% + (5%)1.3471 = 12.7355%. kY = 6% + (5%)0.6508 = 9.2540%.

c. bp = 0.8(1.3471) + 0.2(0.6508) = 1.2078.

kp = 6% + (5%)1.2078 = 12.04%.Alternatively,kp = 0.8(12.7355%) + 0.2(9.254%) = 12.04%.

d. Stock X is undervalued, because its expected return exceeds its required rate of return.

SOLUTION TO SPREADSHEET PROBLEMS

2-17 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM (in the file Solution to Ch 02-17 Build a Model.xls) and on the instructor’s side of the accompanying book site, http://www.harcourtcollege.com/finance/ifm.

2-18 a. The average return for Stock C is 11.3 percent and the standard deviation of these returns is 20.8 percent. Therefore, Stock C has a coefficient of variation of 1.84.

b. With 33.33 percent in each of Stocks A, B, and C, the following results were obtained from the computerized model:

INPUT DATA: KEY OUTPUT:

Stock A Stock B Stock C Portfolio1997 -18.00% -14.50% 32.00% -0.17%1998 33.00 21.80 -11.75 14.351999 15.00 30.50 10.75 18.752000 -0.50 -7.60 32.25 8.052001 27.00 26.30 -6.75 15.52

11.30% 11.30% 11.30% 11.30%Std Dev 20.8% 20.8% 20.8% 7.5%CV 1.84 1.84 1.84 0.66

From these results, we can see that the portfolio return remained constant, but that the standard deviation and coefficient of variation declined dramatically when Stock C was included in the portfolio.

c. Below we show the results when 25 percent is in Stock A, 25 percent is in Stock B, and 50 percent is in Stock C.

INPUT DATA: KEY OUTPUT:

Stock A Stock B Stock C Portfolio1997 -18.00% -14.50% 32.00% 7.88%1998 33.00 21.80 -11.75 7.831999 15.00 30.50 10.75 16.752000 -0.50 -7.60 32.25 14.102001 27.00 26.30 -6.75 9.95

11.30% 11.30% 11.30% 11.30%Std Dev 20.8% 20.8% 20.8% 4.0%CV 1.84 1.84 1.84 0.35

Harcourt College Publishers Solution to Spreadsheet Problems: 2 - 177

These results occur because all 3 stocks have the same expected return, but Stock C is negatively correlated with Stocks A and B, thus, lowering the standard deviation of the portfolio. From trial and error, we found the portfolio to have the lowest standard deviation, p = 3.3%, when the portfolio consisted of 50 percent Stock A and 50 percent Stock C, and 0 percent in Stock B.

d. These results indicate that Stock C is negatively correlated with Stocks A and B. In fact, the correlation between Stock A and Stock C is -0.95, while the correlation between Stock B and Stock C is -0.84. By the way, the correlation between Stock A and Stock B is +0.88, which explains why the combination of those two stocks produced very little reduction in the standard deviation.

e. A rational investor would prefer to hold a portfolio which contained Stock C rather than a portfolio consisting only of Stocks A and B. As we showed in Part c, however, the best choice is to hold Stocks A and C, and not to hold any of Stock B. If C is negatively correlated with most other stocks and thus with “the market,” C’s beta will be negative, and, hence, its required rate of return will be low. This could lead to buy orders for C, and consequently to a price increase which would drive down its expected future rate of return.

Harcourt College Publishers Solution to Spreadsheet Problems: 2 - 178

CYBERPROBLEM

2-19 The detailed solution for the cyberproblem is available on the instructor’s side of the accompanying book site, http://www.harcourtcollege.com/finance/ifm.

Solution to Cyberproblem: 2 - 179

MINI CASE

ASSUME THAT YOU RECENTLY GRADUATED WITH A MAJOR IN FINANCE, AND YOU JUST LANDED A JOB AS A FINANCIAL PLANNER WITH BARNEY SMITH INC., A LARGE FINANCIAL SERVICES CORPORATION. YOUR FIRST ASSIGNMENT IS TO INVEST $100,000 FOR A CLIENT. BECAUSE THE FUNDS ARE TO BE INVESTED IN A BUSINESS AT THE END OF ONE YEAR, YOU HAVE BEEN INSTRUCTED TO PLAN FOR A ONE-YEAR HOLDING PERIOD. FURTHER, YOUR BOSS HAS RESTRICTED YOU TO THE FOLLOWING INVESTMENT ALTERNATIVES, SHOWN WITH THEIR PROBABILITIES AND ASSOCIATED OUTCOMES. (DISREGARD FOR NOW THE ITEMS AT THE BOTTOM OF THE DATA; YOU WILL FILL IN THE BLANKS LATER.)

RETURNS ON ALTERNATIVE INVESTMENTS ESTIMATED RATE OF RETURN

STATE OF THE T- ALTA REPO AM. MARKET 2-STOCK

ECONOMY PROB. BILLS INDS MEN FOAM PORTFOLIO PORTFOLIORECESSION 0.1 8.0% -22.0% 28.0% 10.0%* -13.0% 3.0%BELOW AVG 0.2 8.0 -2.0 14.7 -10.0 1.0AVERAGE 0.4 8.0 20.0 0.0 7.0 15.0 10.0ABOVE AVG 0.2 8.0 35.0 -10.0 45.0 29.0BOOM 0 .1 8 .0 50 .0 -20 .0 30 .0 43 .0 15 .0

k-HAT ( ) 1.7% 13.8% 15.0%

STD DEV () 0.0 13.4 18.8 15.3

COEF OF VAR (CV)7.9 1.4 1.0

BETA (b)-0.86 0.68

*NOTE THAT THE ESTIMATED RETURNS OF AMERICAN FOAM DO NOT ALWAYS MOVE IN THE SAME DIRECTION AS THE OVERALL ECONOMY. FOR EXAMPLE, WHEN THE ECONOMY IS BELOW AVERAGE, CONSUMERS PURCHASE FEWER MATTRESSES THAN THEY WOULD IF THE ECONOMY WAS STRONGER. HOWEVER, IF THE ECONOMY IS IN A FLAT-OUT RECESSION, A LARGE NUMBER OF CONSUMERS WHO WERE PLANNING TO PURCHASE A MORE EXPENSIVE INNER SPRING MATTRESS MAY PURCHASE, INSTEAD, A CHEAPER FOAM MATTRESS. UNDER THESE CIRCUMSTANCES, WE WOULD EXPECT AMERICAN FOAM’S STOCK PRICE TO BE HIGHER IF THERE IS A RECESSION THAN IF THE ECONOMY WAS JUST BELOW AVERAGE.

Harcourt College Publishers Mini Case: 2 - 180

BARNEY SMITH’S ECONOMIC FORECASTING STAFF HAS DEVELOPED PROBABILITY ESTIMATES FOR THE STATE OF THE ECONOMY, AND ITS SECURITY ANALYSTS HAVE DEVELOPED A SOPHISTICATED COMPUTER PROGRAM WHICH WAS USED TO ESTIMATE THE RATE OF RETURN ON EACH ALTERNATIVE UNDER EACH STATE OF THE ECONOMY. ALTA INDUSTRIES IS AN ELECTRONICS FIRM; REPO MEN INC. COLLECTS PAST-DUE DEBTS; AND AMERICAN FOAM MANUFACTURES MATTRESSES AND VARIOUS OTHER FOAM PRODUCTS. BARNEY SMITH ALSO MAINTAINS AN “INDEX FUND” WHICH OWNS A MARKET-WEIGHTED FRACTION OF ALL PUBLICLY TRADED STOCKS; YOU CAN INVEST IN THAT FUND, AND THUS OBTAIN AVERAGE STOCK MARKET RESULTS. GIVEN THE SITUATION AS DESCRIBED, ANSWER THE FOLLOWING QUESTIONS.

A. WHAT ARE INVESTMENT RETURNS? WHAT IS THE RETURN ON AN INVESTMENT THAT COSTS $1,000 AND IS SOLD AFTER ONE YEAR FOR $1,100?

ANSWER: INVESTMENT RETURN MEASURES THE FINANCIAL RESULTS OF AN INVESTMENT.

THEY MAY BE EXPRESSED IN EITHER DOLLAR TERMS OR PERCENTAGE TERMS.THE DOLLAR RETURN IS $1,100 - $1,000 = $100. THE PERCENTAGE RETURN IS $100/$1,000 = 0.10 =

B. 1. WHY IS THE T-BILL’S RETURN INDEPENDENT OF THE STATE OF THE ECONOMY?

DO T-BILLS PROMISE A COMPLETELY RISK-FREE RETURN?

ANSWER: THE 8 PERCENT T-BILL RETURN DOES NOT DEPEND ON THE STATE OF THE ECONOMY

BECAUSE THE TREASURY MUST (AND WILL) REDEEM THE BILLS AT PAR REGARDLESS

OF THE STATE OF THE ECONOMY.

THE T-BILLS ARE RISK-FREE IN THE DEFAULT RISK SENSE BECAUSE THE 8

PERCENT RETURN WILL BE REALIZED IN ALL POSSIBLE ECONOMIC STATES.

HOWEVER, REMEMBER THAT THIS RETURN IS COMPOSED OF THE REAL RISK-FREE

RATE, SAY 3 PERCENT, PLUS AN INFLATION PREMIUM, SAY 5 PERCENT. SINCE THERE

IS UNCERTAINTY ABOUT INFLATION, IT IS UNLIKELY THAT THE REALIZED REAL RATE

OF RETURN WOULD EQUAL THE EXPECTED 3 PERCENT. FOR EXAMPLE, IF INFLATION

AVERAGED 6 PERCENT OVER THE YEAR, THEN THE REALIZED REAL RETURN WOULD

ONLY BE 8% - 6% = 2%, NOT THE EXPECTED 3%. THUS, IN TERMS OF PURCHASING

POWER, T-BILLS ARE NOT RISKLESS.

ALSO, IF YOU INVESTED IN A PORTFOLIO OF T-BILLS, AND RATES THEN DECLINED,

YOUR NOMINAL INCOME WOULD FALL; THAT IS, T-BILLS ARE EXPOSED TO

REINVESTMENT RATE RISK. SO, WE CONCLUDE THAT THERE ARE NO TRULY

RISK-FREE SECURITIES IN THE UNITED STATES. IF THE TREASURY SOLD INFLATION-

INDEXED, TAX-EXEMPT BONDS, THEY WOULD BE TRULY RISKLESS, BUT ALL ACTUAL

SECURITIES ARE EXPOSED TO SOME TYPE OF RISK.

B. 2. WHY ARE ALTA INDUSTRIES’ RETURNS EXPECTED TO MOVE WITH THE ECONOMY WHEREAS REPO MEN’ ARE EXPECTED TO MOVE COUNTER TO THE ECONOMY?

ANSWER: ALTA INDUSTRIES’ RETURNS MOVE WITH, HENCE ARE POSITIVELY CORRELATED

WITH, THE ECONOMY, BECAUSE THE FIRM’S SALES, AND HENCE PROFITS, WILL

GENERALLY EXPERIENCE THE SAME TYPE OF UPS AND DOWNS AS THE ECONOMY. IF

THE ECONOMY IS BOOMING, SO WILL ALTA INDUSTRIES. ON THE OTHER HAND, REPO

MEN IS CONSIDERED BY MANY INVESTORS TO BE A HEDGE AGAINST BOTH BAD

TIMES AND HIGH INFLATION, SO IF THE STOCK MARKET CRASHES, INVESTORS IN THIS

STOCK SHOULD DO RELATIVELY WELL. STOCKS SUCH AS REPO MEN ARE THUS

NEGATIVELY CORRELATED WITH (MOVE COUNTER TO) THE ECONOMY. (NOTE: IN

ACTUALITY, IT IS ALMOST IMPOSSIBLE TO FIND STOCKS THAT ARE EXPECTED TO

MOVE COUNTER TO THE ECONOMY. EVEN REPO MEN SHARES HAVE POSITIVE (BUT

LOW) CORRELATION WITH THE MARKET.)

C. CALCULATE THE EXPECTED RATE OF RETURN ON EACH ALTERNATIVE AND FILL

IN THE BLANKS ON THE ROW FOR IN THE TABLE ABOVE.

ANSWER: THE EXPECTED RATE OF RETURN, , IS EXPRESSED AS FOLLOWS:

HERE IS THE PROBABILITY OF OCCURRENCE OF THE iTH STATE, IS THE

ESTIMATED RATE OF RETURN FOR THAT STATE, AND n IS THE NUMBER OF STATES.

HERE IS THE CALCULATION FOR ALTA INDUSTRIES:

ALTA INDS = 0.1(-22.0%) + 0.2(-2.0%) + 0.4(20.0%) + 0.2(35.0%) + 0.1(50.0%)

= 17.4%.

WE USE THE SAME FORMULA TO CALCULATE K’S FOR THE OTHER ALTERNATIVES:

T-BILLS = 8.0%.

REPO MEN = 1.7%.

AM FOAM = 13.8%.

M = 15.0%.

D. YOU SHOULD RECOGNIZE THAT BASING A DECISION SOLELY ON EXPECTED

RETURNS IS ONLY APPROPRIATE FOR RISK-NEUTRAL INDIVIDUALS. SINCE YOUR

CLIENT, LIKE VIRTUALLY EVERYONE, IS RISK AVERSE, THE RISKINESS OF EACH

ALTERNATIVE IS AN IMPORTANT ASPECT OF THE DECISION. ONE POSSIBLE

MEASURE OF RISK IS THE STANDARD DEVIATION OF RETURNS.

1. CALCULATE THIS VALUE FOR EACH ALTERNATIVE, AND FILL IN THE BLANK ON

THE ROW FOR IN THE TABLE ABOVE.

ANSWER: THE STANDARD DEVIATION IS CALCULATED AS FOLLOWS:

ALTA INDS = [(-22.0 - 17.4)2(0.1) + (-2.0 - 17.4)2(0.2) + (20.0 - 17.4)2(0.4) + (35.0 - 17.4)2(0.2) + (50.0 - 17.4)2(0.1)]0.5

= = 20.0%.

HERE ARE THE STANDARD DEVIATIONS FOR THE OTHER ALTERNATIVES:

T-BILLS = 0.0%.

REPO MEN = 13.4%.

AM. FOAM = 18.8%.

M = 15.3%.

D. 2. WHAT TYPE OF RISK IS MEASURED BY THE STANDARD DEVIATION?

ANSWER: THE STANDARD DEVIATION IS A MEASURE OF A SECURITY’S (OR A PORTFOLIO’S)

STAND-ALONE RISK. THE LARGER THE STANDARD DEVIATION, THE HIGHER THE

PROBABILITY THAT ACTUAL REALIZED RETURNS WILL FALL FAR BELOW THE

EXPECTED RETURN, AND THAT LOSSES RATHER THAN PROFITS WILL BE INCURRED.

D. 3. DRAW A GRAPH WHICH SHOWS ROUGHLY THE SHAPE OF THE PROBABILITY

DISTRIBUTIONS FOR ALTA INDUSTIRES, AMERICAN FOAM, AND T-BILLS.

ANSWER:

BASED ON THESE DATA, ALTA INDUSTRIES IS THE MOST RISKY INVESTMENT, T-BILLS

THE LEAST RISKY.

E. SUPPOSE YOU SUDDENLY REMEMBERED THAT THE COEFFICIENT OF VARIATION

(CV) IS GENERALLY REGARDED AS BEING A BETTER MEASURE OF STAND-ALONE

RISK THAN THE STANDARD DEVIATION WHEN THE ALTERNATIVES BEING

CONSIDERED HAVE WIDELY DIFFERING EXPECTED RETURNS. CALCULATE THE

MISSING CVs, AND FILL IN THE BLANKS ON THE ROW FOR CV IN THE TABLE

ABOVE. DOES THE CV PRODUCE THE SAME RISK RANKINGS AS THE STANDARD

DEVIATION?

ANSWER: THE COEFFICIENT OF VARIATION (CV) IS A STANDARDIZED MEASURE OF DISPERSION

ABOUT THE EXPECTED VALUE; IT SHOWS THE AMOUNT OF RISK PER UNIT OF

RETURN.

CV = .

CVT-BILLS = 0.0%/8.0% = 0.0.

CVALTA INDS = 20.0%/17.4% = 1.1.

CVREPO MEN = 13.4%/1.7% = 7.9.

CVAM FOAM = 18.8%/13.8% = 1.4.

CVM = 15.3%/15.0% = 1.0.

WHEN WE MEASURE RISK PER UNIT OF RETURN, REPO MEN, WITH ITS LOW

EXPECTED RETURN, BECOMES THE MOST RISKY STOCK. THE CV IS A BETTER

MEASURE OF AN ASSET’S STAND-ALONE RISK THAN BECAUSE CV CONSIDERS BOTH

THE EXPECTED VALUE AND THE DISPERSION OF A DISTRIBUTION--A SECURITY WITH

A LOW EXPECTED RETURN AND A LOW STANDARD DEVIATION COULD HAVE A

HIGHER CHANCE OF A LOSS THAN ONE WITH A HIGH BUT A HIGH .

F. SUPPOSE YOU CREATED A 2-STOCK PORTFOLIO BY INVESTING $50,000 IN ALTA INDUSTRIES AND $50,000 IN REPO MEN.

1. CALCULATE THE EXPECTED RETURN ( ), THE STANDARD DEVIATION (p), AND

THE COEFFICIENT OF VARIATION (CVp) FOR THIS PORTFOLIO AND FILL IN THE

APPROPRIATE BLANKS IN THE TABLE ABOVE.

ANSWER: TO FIND THE EXPECTED RATE OF RETURN ON THE TWO-STOCK PORTFOLIO, WE FIRST

CALCULATE THE RATE OF RETURN ON THE PORTFOLIO IN EACH STATE OF THE

ECONOMY. SINCE WE HAVE HALF OF OUR MONEY IN EACH STOCK, THE PORTFOLIO’S

RETURN WILL BE A WEIGHTED AVERAGE IN EACH TYPE OF ECONOMY. FOR A

RECESSION, WE HAVE: kp = 0.5(-22%) + 0.5(28%) = 3%. WE WOULD DO SIMILAR

CALCULATIONS FOR THE OTHER STATES OF THE ECONOMY, AND GET THESE

RESULTS:

STATE PORTFOLIORECESSION 3.0%BELOW AVERAGE 6.4AVERAGE 10.0ABOVE AVERAGE 12.5BOOM 15.0

NOW WE CAN MULTIPLY PROBABILITIES TIMES OUTCOMES IN EACH STATE TO

GET THE EXPECTED RETURN ON THIS TWO-STOCK PORTFOLIO, 9.6%.

ALTERNATIVELY, WE COULD APPLY THIS FORMULA,

k = wi x ki = 0.5(17.4%) + 0.5(1.7%) = 9.6%,

WHICH FINDS k AS THE WEIGHTED AVERAGE OF THE EXPECTED RETURNS OF THE

INDIVIDUAL SECURITIES IN THE PORTFOLIO.IT IS TEMPTING TO FIND THE STANDARD DEVIATION OF THE PORTFOLIO AS THE WEIGHTED

AVERAGE OF THE STANDARD DEVIATIONS OF THE INDIVIDUAL SECURITIES, AS FOLLOWS:

p wi(i) + wj(j) = 0.5(20%) + 0.5(13.4%) = 16.7%.

HOWEVER, THIS IS NOT CORRECT--IT IS NECESSARY TO USE A DIFFERENT FORMULA,

THE ONE FOR THAT WE USED EARLIER, APPLIED TO THE TWO-STOCK PORTFOLIO’S

RETURNS.

THE PORTFOLIO’S DEPENDS JOINTLY ON (1) EACH SECURITY’S AND (2) THE

CORRELATION BETWEEN THE SECURITIES’ RETURNS. THE BEST WAY TO APPROACH

THE PROBLEM IS TO ESTIMATE THE PORTFOLIO’S RISK AND RETURN IN EACH STATE

OF THE ECONOMY, AND THEN TO ESTIMATE p WITH THE FORMULA. GIVEN THE

DISTRIBUTION OF RETURNS FOR THE PORTFOLIO, WE CAN CALCULATE THE

PORTFOLIO’S AND CV AS SHOWN BELOW:

p = [(3.0 - 9.6)2(0.1) + (6.4 - 9.6)2(0.2) + (10.0 - 9.6)2(0.4)

+ (12.5 - 9.6)2(0.2) + (15.0 - 9.6)2(0.1)]0.5

= 3.3%.

CVp = 3.3%/9.6% = 0.3.

F. 2. HOW DOES THE RISKINESS OF THIS 2-STOCK PORTFOLIO COMPARE WITH THE

RISKINESS OF THE INDIVIDUAL STOCKS IF THEY WERE HELD IN ISOLATION?

ANSWER: USING EITHER OR CV AS OUR STAND-ALONE RISK MEASURE, THE STAND-ALONE

RISK OF THE PORTFOLIO IS SIGNIFICANTLY LESS THAN THE STAND-ALONE RISK OF

THE INDIVIDUAL STOCKS. THIS IS BECAUSE THE TWO STOCKS ARE NEGATIVELY

CORRELATED--WHEN ALTA INDUSTRIES IS DOING POORLY, REPO MEN IS DOING

WELL, AND VICE VERSA. COMBINING THE TWO STOCKS DIVERSIFIES AWAY SOME OF

THE RISK INHERENT IN EACH STOCK IF IT WERE HELD IN ISOLATION, i.e., IN A 1-STOCK

PORTFOLIO.

OPTIONAL QUESTION (USE ONLY IF YOU HAVE LOTS OF TIME)

DOES THE EXPECTED RATE OF RETURN ON THE PORTFOLIO

DEPEND ON THE PERCENTAGE OF THE PORTFOLIO INVESTED IN

EACH STOCK? WHAT ABOUT THE RISKINESS OF THE PORTFOLIO?

ANSWER: USING A SPREADSHEET MODEL, IT’S EASY TO VARY THE COMPOSITION OF THE PORTFOLIO TO SHOW THE EFFECT ON THE PORTFOLIO’S EXPECTED RATE OF RETURN AND STANDARD DEVIATION:

ALTA INDS. PLUS REPO MEN% IN ALTA INDS.

0% 1.7% 13.4%10 3.3 10.020 4.9 6.730 6.4 3.340 8.0 0.050 9.6 3.360 11.1 6.770 12.7 10.080 14.3 13.490 15.8 16.7

100 17.4 20.0

THE EXPECTED RATE OF RETURN ON THE PORTFOLIO IS MERELY A LINEAR

COMBINATION OF THE TWO STOCK’S EXPECTED RATES OF RETURN. HOWEVER,

PORTFOLIO RISK IS ANOTHER MATTER. p BEGINS TO FALL AS ALTA INDUSTRIES AND

REPO MEN ARE COMBINED; IT REACHES ZERO AT 40% ALTA INDUSTRIES; AND THEN

IT BEGINS TO RISE. ALTA INDUSTRIES AND REPO MEN CAN BE COMBINED TO FORM A

NEAR ZERO RISK PORTFOLIO BECAUSE THEY ARE VERY CLOSE TO BEING PERFECTLY

NEGATIVELY CORRELATED; THEIR CORRELATION COEFFICIENT IS -0.9998. (NOTE:

UNFORTUNATELY, WE CANNOT FIND ANY ACTUAL STOCKS WITH r = -1.0.)

G. SUPPOSE AN INVESTOR STARTS WITH A PORTFOLIO CONSISTING OF ONE RANDOMLY SELECTED STOCK. WHAT WOULD HAPPEN (1) TO THE RISKINESS AND (2) TO THE EXPECTED RETURN OF THE PORTFOLIO AS MORE AND MORE RANDOMLY SELECTED STOCKS WERE ADDED TO THE PORTFOLIO? WHAT IS THE IMPLICATION FOR INVESTORS? DRAW A GRAPH OF THE TWO PORTFOLIOS TO ILLUSTRATE YOUR ANSWER.

ANSWER:

THE STANDARD DEVIATION GETS SMALLER AS MORE STOCKS ARE COMBINED IN THE

PORTFOLIO, WHILE kp (THE PORTFOLIO’S RETURN) REMAINS CONSTANT. THUS, BY

ADDING STOCKS TO YOUR PORTFOLIO, WHICH INITIALLY STARTED AS A 1-STOCK

PORTFOLIO, RISK HAS BEEN REDUCED.