Problem 14-22 Basic Net Present Value AnalysisGiven:Renfree Mines, Inc., owns the mining rights to a large tract of land in a mountainous area. Thetract contains a mineral deposit that the company believes might be commercially attractive tomine and sell. An engineering and cost analysis has been made, and it is expected that thefollowing cash flows would be associated with opening and operating a mine in the area:

Cost of equipment required $850,000 $804,920.93 Net annual cash receipts $230,000 *** Cost (NPV = 0)

Working capital required $100,000 Cost of road repairs in three years $60,000 Salvage value of equipment in five years $200,000

*** Receipts from sales of ore, less out-of-pocket costs for salaries, utilities, insurance,and so forth.

It is estimated that the mineral deposit would be exhausted after five years of mining. At thatpoint, the working capital would be released for reinvestment elsewhere. The Company's required rate of return is 14%.

Required: Ignore income taxes.Determine the net present value of the proposed mining project. Should the project be accepted?Explain.

Timing of Cash 14% PV ofCash Flow PV Table Cash

Relevant Items: Flows Amounts Factor FlowsCost of equipment required Now ($850,000) 1.000000 ($850,000.00)Working capital required Now ($100,000) 1.000000 ($100,000.00)Net annual cash receipts End of Ys 1-5 $230,000 3.433082 $789,608.86 Cost of road repairs in three years End of Year 3 ($60,000) 0.674972 ($40,498.32)Salvage value of equipment in 5 years End of Year 5 $200,000 0.519369 $103,873.80 Working capital released End of Year 5 $100,000 0.519369 $51,936.90

Net Present Value ($45,078.76)

No, the project should not be accepted; it has a negative net present value. This means that therate of return on the investment is less than the company's required rate of return of 14%

Timing of Yearly Cash 14% PV ofCash Flow PV Table CashFlows Amounts Factor FlowsNow ($950,000.00) 1.000000 ($950,000.00)

End of Y1 $230,000.00 0.877193 $201,754.39 End of Y2 $230,000.00 0.769468 $176,977.64 End of Y3 $170,000.00 0.674972 $114,745.24 End of Y4 $230,000.00 0.592080 $136,178.40 End of Y5 $530,000.00 0.519369 $275,265.57

($45,079.07) 3.433082 ($45,078.76)

12.246555% IRR

($39,543.0428)Note: Wrong NPV

Excel formula is wrong

Exercise 14-11 Internal Rate of Return and Net Present ValueGiven:Scalia's Cleaning Service is investigating the purchase of an ultrasound machine for cleaning window

to operate it. Scalia's has estimated that the new machine would increase the company's cash flows,

salvage value.

Required: Ignore income taxes1. Compute the machine's internal rate of return to the nearest whole percent.

operating the car.

IRR = the interest rate that yields a NPV = 0

5.468

From PV of an Annuity Table, scanning along the row for 14 periods yields 5.468 for an IRR equal to 16%

2. Compute the machine's net present value. Use a discount rate of 16% and the format shown inExhibit 14-5. Why do you have a zero net present value?

Amount of 16% PresentItem Year(s) Cash flow Table Factor ValueInitial Investment Now ($136,700) 1.00000 ($136,700)Net annual cash inflows 1-14 $25,000 5.468 $136,700 Net present value $0

The NPV is equal to zero because the discount rate used (16%) is also the IRR.

3. Suppose that the new machine would increase the company's annual cash flows, net of expenses,by only $20,000 per year. Under these conditions, compute the internal rate of return to the nearestwhole percent.

IRR = the interest rate that yields a NPV = 0

6.835

From PV of an Annuity Table, scanning along the row for 14 periods yields:

12% 6.628168X ?% 6.835000 -0.206832

0.01 11% 6.981865 -0.353697

X = 0.2068320.01 0.353697

blinds. The machine would cost $136,700, including invoice cost, freight, and training of employees

net of expenses, by $25,000 per year. The machine would have a 14-year useful life with no expected

Annual cash inflows X Table Value ( Y%, 14 years) from PV of an Annuity Table - Cost = 0$25,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table - $136,700 = 0$25,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table = $136,700 Table Value (Y%, 14 years) from PV of an Annuity Table = $136,700/$25,000

Annual cash inflows X Table Value ( Y%, 14 years) from PV of an Annuity Table - Cost = 0$20,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table - $136,700 = 0$20,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table = $136,700 Table Value (Y%, 14 years) from PV of an Annuity Table = $136,700/$20,000

0.353697 (X) = (0.01)(.206832)0.353697 (X) = 0.00207

X = 0.00585 X = 0.5848%

?% = 12% - 0.5848% = 11.4152%Rounded to nearest whole % = 11% IRR

NPV

From PV of an Annuity Table, scanning along the row for 14 periods yields 5.468 for an IRR equal to 16%

(136,700) (136,700)20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000

20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000 20,000 25,000

11.405% 15.998%0.000 0.000

Exercise 14-3 Uncertain Future Cash FlowsGiven:Union Bay Plastics is investigating the purchase of automated equipment that would save

intangible benefits such as greater flexibility and higher-quality output that are difficult to estimate and yet are quite significant.

Required:1. What dollar value per year would the intangible benefits have to be worth in order to make

the equipment an acceptable investment? (Ignore income taxes).

If the NPV = 0, then the investment would be earning a return of exactly 15% if the discount

Therefore:

Annual cash inflows = $149,432.16

Thus the dollar value per year of the intangible benefits must be worth at least:

Annual cash inflows required $149,432.16 Less known yearly savings 100,000.00 Minimum yearly intangible benefits $49,432.16

$100,000 each year in direct labor and inventory carrying costs. This equipment costs $750,000and is expected to have a 10-year useful life with no salvage value. The company requires a minimum 15% rate of return on all equipment purchases. This equipment would provide

rate is 15%.

Annual cash inflows X Table Value (15%, 10 years) from PV of an Annuity Table - Cost = 0(Annual cash inflows X 5.019) - $750,000 = 05.019 (Annual cash inflows) = $750,000Annual cash inflows = $750,000/5.019

Exercise 14-5: Payback MethodGiven:The management of Weimar Inc., a civil engineering design company, is consideringan investment in a high-quality blueprint printer with the following cash flows:

InvestmentCash Cash

Year Outflow Inflow1 $38,000 $2,000 2 $6,000 $4,000 3 $8,000 4 $9,000 5 $12,000 6 $10,000 7 $8,000 8 $6,000 9 $5,000

10 $5,000

Required:1. Determine the payback period of the investment.

InvestmentCash Cash Unrecovered

Year Outflow Inflow Investment1 $38,000 $2,000 $36,000 2 $6,000 $4,000 $38,000 3 $8,000 $30,000 4 $9,000 $21,000 5 ***** $12,000 $9,000 6 ***** $10,000 ($1,000)7 $8,000 ($9,000)8 $6,000 ($15,000)9 $5,000 ($20,000)

10 $5,000 ($25,000)

Payback = 5 0.9 5.9 years

2. Would the payback period be affected if the cash inflowin the last year were several times larger?

Since the investment is recovered prior to the last year, the amount of the cash inflow in the last year has no effect on the payback period.

Exercise 14-19: Payback Period and Simple Rate of ReturnGiven:The Heritage Amusement Park would like to construct a new ride called the Sonic Boom, which

estimates that the following annual costs and revenues would be associated with the ride:

Ticket revenues $250,000 Less operating expenses:

Maintenance $40,000 Salaries 90,000 $945,000 Depreciation 27,000 Insurance 30,000

Total Operating Expenses 187,000 Net Operating Income $63,000

Required: Ignore income taxes1. Assume that the Heritage Amusement Park will not construct a new ride unless the ride

provides a payback period of six years or less. Does the Sonic Boom ride satisfy thisrequirement?

Payback period = Investment Required / Net Uniform Annual Cash Inflow

Net Uniform Annual Cash InflowNet Operating Expenses $63,000 Depreciation 27,000

Net Uniform Annual Cash Inflow $90,000

Payback period = $450,000 / $90,000

Payback period = 5.00 years

The Sonic Boom has a payback less than the maximum 6-year limit.The Sonic Boom satisfies the payback criterion.

2. Compute the simple accounting rate of return promised by the new ride. If Heritage Amusement

criterion?

Simple accounting rate of return = AROR

AROR = Annualized incremental NOI / Initial Investment Required

AROR = $63,000 / $450,000

AROR = 14.00%

The Sonic Boom has an AROR greater than the minimum 12% requirement. The Sonic Boom satisfies the simple accounting rate or return criterion.

the park management feels would be very popular. The ride would cost $450,000 to construct,and it would have a 10% salvage value at the end of its 15-year useful life. The company

Park requires a simple rate of return of at least 12%, does the Sonic Boom ride meet this

($450,000)900009000090000900009000090000900009000090000900009000090000900009000090000

18.415% IRRCompute the simple accounting rate of return promised by the new ride. If Heritage Amusement

Problem 14-26: Preference Ranking of Investment Projects

Given:Austin Company is investigating four different investment opportunities. Information on thefour projects under study is given below:

Project Number 1 2 3 4Investment required ($480,000) ($360,000) ($270,000) ($450,000)Present value of cash inflows (10%) 567,270 433,400 336,140 522,970 Net present value $87,270 $73,400 $66,140 $72,970 Life of Project (in years) 6 12 6 3Internal Rate of Return 16% 14% 18% 19%

NPV calculations above. Limited funds are available for investment, so the company can not accept all of the available projects.

Required:1. Compute the project profitability index for each investment project.

Project profitability index = NPV / Investment Required

Project Number 1 2 3 4Net present value $87,270 $73,400 $66,140 $72,970 Investment required $480,000 $360,000 $270,000 $450,000 Project profitability index 0.1818125 0.20388889 0.24496296 0.16215556

2. Rank the four projects according to preference, in terms of:Project Number 1 2 3 4a. NPV 1 2 4 3b. PPI 3 2 1 4c. IRR 3 4 2 1

3. Which ranking do you prefer? Why?

Which ranking is best will depend on the company's opportunities for reinvesting fundsas they are released from a project.

IRR: The internal rate of return method assumes that any released funds are reinvestedat the internal rate of return.

This means that funds released from project #4 would have to be reinvested at arate or return of 19%, but another project yielding such a high rate of return mightbe difficult to find.

PPI: The project profitability index approach assumes that funds released from a projectare reinvested at a rate of return equal to the discount rate, which in this case is only10%. On balance, the PPI is generally regarded as the most dependable method ofranking competing projects.

Since the company's required rate of return is 10%, a 10% discount rate has been used tn the

NPV: The net present value is inferior to the project profitability index as a ranking devicebecause it does not properly consider the amount of investment.

For example, it ranks project #3 fourth because of its low NPV; yet this project isthe best in terms of the amount of cash inflow generated per dollar invested.

Problem 14-37: Net Present Value Analysis Including Income Taxes

Given:The Crescent Drilling Company owns the drilling rights to several tracts of land on which natural gas has been found. The amount of gas on some of the tracts is somewhat marginal,and the company is unsure whether it would be profitable to extract and sell the gas that thesetracts contain. One such tract is tract 410, on which the following information has been gathered:

Investment in equipment needed for extraction work $600,000 Working capital investment needed $85,000 Annual cash receipts from sale of gas, net of related cash

operating expenses (before taxes) $110,000 Cost of restoring the land at completion of extraction work $70,000

extraction was completed. For tax purposes, the company would depreciate the equipment

for use elsewhere at the completion of the project.

Required:1. Compute the NPV of tract 410.

Timing of Cash After CashCash Flow Tax Flow

Normal Acctg. Approach Flows Amounts Effect AmountsInvestment in equipment Now ($600,000) None ($600,000)Working capital required Now ($85,000) None ($85,000)Net annual cash receipts End of Ys 1-10 $110,000 70% $77,000 Tax Savings (Depreciation tax shield) End of Ys 1-10 $60,000 30% $18,000 Restoration Expense End of Year 10 ($70,000) 70% ($49,000)Salvage value of equipment in 5 years End of Year 10 $90,000 None $90,000 Tax Outflow from Salvage Gain End of Year 10 $90,000 30% ($27,000)Working capital released End of Year 10 $85,000 None $85,000

Net Present Value

Normal Finance Approach Year 0 (Now) Year 1 Year 2 Year 3Net annual cash receipts $110,000 $110,000 $110,000 Less Depreciation Expense (60,000.00) (60,000.00) (60,000.00)Less Restoration ExpenseTaxable Salvage GainIncome Before Taxes $50,000 $50,000 $50,000 Less Income Taxes (30%) (15,000) (15,000) (15,000)Net Income $35,000 $35,000 $35,000 Add back depreciation 60,000 60,000 60,000 Operating Cash Flow $95,000 $95,000 $95,000 Working capital releasedCash Inflow $95,000 $95,000 $95,000 Table Factor 10% (PV of $1 Table) 0.909091 0.826446 0.751315 PV of cash inflows $621,902.53 $86,363.65 $78,512.37 $71,374.93

The natural gas in tract 410 would be exhausted after 10 years of extraction work. The equipmentwould have a useful life of 15 years, but it could be sold for only 15% of its original cost when

over 10 years using straight-line depreciation and assuming zero salvage value. The tax rateis 30%, and the company's after-tax discount rate is 10%. The working capital would be released

Initial Investment in equipment (600,000.00)Initial Investment in Working Capital (85,000.00)Net Present Value ($63,097.47)

Net Present Value (Adj. Excel Formula) ($63,097.34)

2. Would you recommend that the investment project be undertaken?

No, the investment project should not be undertaken. The NPV is negative.

10% PV ofPV Table Cash

Factor Flows1.000000 ($600,000.00)1.000000 ($85,000.00)6.144567 $473,131.66 6.144567 $110,602.21 0.385543 ($18,891.61)0.385543 $34,698.87 0.385543 ($10,409.66)0.385543 $32,771.16

($63,097.38)

Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10$110,000 $110,000 $110,000 $110,000 $110,000 $110,000 $110,000

(60,000.00) (60,000.00) (60,000.00) (60,000.00) (60,000.00) (60,000.00) (60,000.00)(70,000.00)90,000.00

$50,000 $50,000 $50,000 $50,000 $50,000 $50,000 $70,000 (15,000) (15,000) (15,000) (15,000) (15,000) (15,000) (21,000)$35,000 $35,000 $35,000 $35,000 $35,000 $35,000 $49,000

60,000 60,000 60,000 60,000 60,000 60,000 60,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $109,000

85,000 $95,000 $95,000 $95,000 $95,000 $95,000 $95,000 $194,000

0.683013 0.620921 0.564474 0.513158 0.466507 0.424098 0.385543 $64,886.24 $58,987.49 $53,625.03 $48,750.01 $44,318.17 $40,289.31 $74,795.34

Problem 14-31 Net Present Value Analysis of a Lease or Buy Decision

Given:Blinko Products wants an airplane for use by its corporate staff. The airplane that the company wishes to acquire, a Zephyr II, can be either purchased or leased from the manufacturer. Thecompany has made the following evaluations of the two alternatives:

Purchase alternative.If the Zephyr II is purchased, then the costs incurred by the company would be as follows:

Purchase cost of the plane $850,000 Annual cost of servicing, licenses, and taxes $9,000 Repairs:

First 3 years, per year $3,000 Fourth year $5,000 Fifth year $10,000

The plane would be sold after 5 years. Based on current resale values, the company wouldbe able to sell it for about one-half of its original cost at the end of the five-year period.

Lease alternative.If the Zephyr II is leased, then the company would have to make an immediate deposit of$50,000 to cover any damage during use. The lease would run for five years, at the end ofwhich time the deposit would be refunded. The lease would require an annual rental payment of $200,000 (the first payment is due at the end of Year 1). As part of this leasecost, the manufacturer would provide all servicing and repairs, license the plane, and payall taxes. At the end of the 5-year period, the plane would revert to the manufacturer, asowner.

Blinko Products' required rate of return is 18%

Required: Ignore income taxes.1. Use the total-cost approach to determine the present value of the cash flows associated

with each alternative.Timing of Amount of PV Table

Purchase alternative. Cash Flows Cash Flows Factor (18%)Purchase cost of the plane Now ($850,000) 1.000000Annual cost of servicing, etc. End of Ys 1-5 ($9,000) 3.127171Repairs:

First Three Years End of Ys 1-3 ($3,000) 2.174273Fourth Year End of Year 4 ($5,000) 0.515789Fifth Year End of Year 5 ($10,000) 0.437109

Resale value of the plane End of Year 5 $425,000 0.437109

Timing of Amount of PV TableLease alternative. Cash Flows Cash Flows Factor (18%)Damage Deposit Now ($50,000) 1.000000Annual Lease Payments End of Ys 1-5 ($200,000) 3.127171Refund of Deposit End of Year 5 $50,000 0.437109

Net present value in favor of the leasing option

2. Which alternative would you recommend that the company accept? Why?

The company should accept the leasing alternative. The present value of the cash outflows is less under the leasing option.

Blinko Products wants an airplane for use by its corporate staff. The airplane that the company wishes to acquire, a Zephyr II, can be either purchased or leased from the manufacturer. The

If the Zephyr II is purchased, then the costs incurred by the company would be as follows:

The plane would be sold after 5 years. Based on current resale values, the company would

$50,000 to cover any damage during use. The lease would run for five years, at the end of

cost, the manufacturer would provide all servicing and repairs, license the plane, and pay

PV of Timing of Amount of PV Table PV ofCash Flow Cash Flows Cash Flows Factor (18%) Cash Flow

($850,000.00) Now ($850,000) 1.000000 ($850,000.00)($28,144.54) End of Year 1 ($12,000) 0.847458 ($10,169.50)

End of Year 2 ($12,000) 0.718184 ($8,618.21)($6,522.82) End of Year 3 ($12,000) 0.608631 ($7,303.57)($2,578.95) End of Year 4 ($14,000) 0.515789 ($7,221.05)($4,371.09) End of Year 5 $406,000 0.437109 $177,466.25

$185,771.33 ($705,845.98) ($705,846.07)($705,846.07)

PV of Timing of Amount of PV Table PV ofCash Flow Cash Flows Cash Flows Factor (18%) Cash Flow($50,000.00) Now ($50,000) 1.000000 ($50,000.00)

($625,434.20) End of Year 1 ($200,000) 0.847458 ($169,491.60)$21,855.45 End of Year 2 ($200,000) 0.718184 ($143,636.80)

($653,578.75) End of Year 3 ($200,000) 0.608631 ($121,726.20)

End of Year 4 ($200,000) 0.515789 ($103,157.80)End of Year 5 ($150,000) 0.437109 ($65,566.35)

($653,578.74) ($653,578.75)

$52,267.32 $52,267.23 $52,267.32

The company should accept the leasing alternative. The present value of the cash outflows is less under the leasing option.