CHAPTER 20: CAPITAL BUDGETING
STUDENT SOLUTIONS MANUAL
STUDENT SOLUTIONS MANUALSTUDENT SOLUTIONS MANUAL
CHAPTER 20: CAPITAL BUDGETING
EXERCISES
20-34Basic Capital Budgeting Techniques (45 min)
a. Project A:
Or, 2 years and 10 months
b. Project B:
After-tax Cumulative
YearCash Inflows
After-tax Cash Inflows
1
$ 500 $ 500
2
1,200
1,700
3
2,000
3,700
4
2,500
Or, 3 years and 7 months
c.Project C:
Depreciation expense per year: $5,000 5 = $1,000
Taxable income each year: $2,500 $1,000 = $1,500
Income taxes each year: $1,500 x 25% = $375
Annual after-tax net cash inflow: $2,500 $375 = $2,125
Or, 2 years and 5 months
20-34 (Continued)d.Project D:
(1)Depreciation expense per year: ($5,000 $500) 5 = $900
Taxable income:
Sales
$4,000
Expenses:
Cash expenditures $1,500
Depreciation 900 2,400
Operating income before taxes
$1,600
Income taxes (25%)
400
Operating income after taxes
$1,200
Book rate of return = ADVANCE \d 7
ADVANCE \u 7$1,200 ( $5,000 = 24.00%
(2) Average book value = ($5,000 + $500) ( 2 = $2,750
Book rate of return = $1,200 ( $2,750 = ADVANCE \d 7
ADVANCE \u 743.64%e.Net Present Values (@8%), rounded:
Project A:($1,800 x 3.993) $5,000 =
$7,187 $5,000 = $2,187
Project B:
After-tax 8% Discount Present
Year Cash Flows
Factor
Values
0
1
$ 5000.926463
2
1,2000.8571,028
3
2,0000.7941,588
4
2,5000.7351,838
5
2,0000.681 1,362
Net Present Value (NPV) =$1,279
Project C: ($2,125 x 3.993) $5,000 =
$8,485 $5,000 = $3,485
Project D:
Present value of cash inflows:
Years 1 through 4
($1,200 + $900) x 3.312 =$6,955
Year 5
($2,100 + $500) x 0.681 = 1,771
Present value of cash inflows=$8,726
Initial investment
= 5,000
Net present value (NPV)
=
$3,726
20-36Future and Present Values Using Excel (20 min)
A.To calculate future values, use the following Excel function:
FV(rate,nper,pmt,pv,type)
1. Between January 1, 1701 and December 31, 2007 there are 614 six-month periods (nper). Thus, at the end of year 2007, at an annual interest rate of 6% compounded semiannually, the $24.00 will have grown to $1,829,225,347, as follows:
FV(0.06/2,614,0,-24,0)
2. FV(0.08/2,614,0,-24,0) = $$689,733,898,953
3.a. FV(0.06/4,1228,0,-24,0) = $2,091,756,483
b.FV(0.08/4,1228,0,-24,0) = $873,418,055,163
4. FV(0.08/2,12,0,-9500000000,0) = $15,209,806,076
B. To calculate present values, use the following Excel function:
PV(rate,nper,pmt,fv,type)
1. For a stream of ten (10) end-of-year payments of $25,200,000 (ordinary annuity) and a discount rate of 12%, we have:
PV(0.12,10,-25200000,0,0) = $142,385,620
2.If the first payment is received the day the contract is assigned (annuity due), we have:
PV(0.12,10,-25200000,0,1) = $159,471,895
3. Given an income-tax rate of 45%, the after-tax cost of (1) above is:
PV(0.12,10,-25200000*0.55,0,0) = $78,312,091.17
20-38 Basic Capital Budgeting Techniques: Uniform Net cash inflows, No Income Taxes, Non-MACRS-Based Depreciation (45 min)
a.Unadjusted Payback Period: As shown above, the payback period occurs between years 4 and 5. Alternatively, the payback period = $500,000 ( $120,000/year = 4.17 years (about 4 years and 2 months)
b.Book (accounting) rate of return:
As indicated above, the average increase in net income over the ten-year period = $700,000/10 years = $70,000/year. Thus, the ARR
(1) On initial investment: $70,000/$500,000 =14.00%
(2)On average investment:
Average investment: ($500,000 + 0)/2 =
$250,000
Book rate of return:$70,000 ( $250,000 =28.00%20-38 (Continued)
c.NPV: using the PV factors from Table 2 (p. 871), NPV = $178,120
Based on the NPV function of Excel, the NPV = $178,027 (the difference in NPV estimates is due to rounding that takes place when using the PV factors provided in the Table 2 rather than the built-in NPV function)
d. Present value payback period: as indicated in the above schedule, the present value payback period is 6-plus years; this is the time it takes for the present value of future cash inflows to cover the original investment outlay of $500,000
e. Internal rate of return: as indicated in the above schedule, we can use the built-in function in Excel to estimate the IRR for this proposed investment; IRR = 20.18%Alternatively, we can estimate the IRR as follows. We are looking for an interest/discount rate that provides for a NPV = $0 (i.e., a rate that provides a present value of future cash inflows equal in amount to the original investment outlay, $500,000). Thus,
PV of net cash inflows:
At 20% (i.e., a rate too low): $120,000 x 4.192 =$503,040
At 25% (i.e., a rate too high): $120,000 x 3.571 = 428,520
Difference in PV with 5% difference in discount rate = $ 74,520 ADVANCE \u1220-40 Basic Capital Budgeting Techniques: Uneven Net Cash Inflows, Income Taxes, and MACRS Depreciation (60 min)
1. Payback period: as shown by the above schedule, the payback period is between 4 and 5 years. Using a linear interpolation, we estimate the payback period as
20-40 (Continued)
2. Book rate of return (ARR):Average after-tax operating income/year: $812,000/10 = $81,200Book (accounting) rate of return (ARR):
a.On initial investment: $81,200/$500,000 = 16.24%b. On average investment:
Computation of Simple Average Annual Investment:
YearBook Value, Beginning-of-YearDepreciation
Expense for the YearBook Value, End-of-YearAverage BV During the Year
1$500,000$100,000$400,000$450,000
2400,000160,000240,000320,000
3240,00096,000144,000192,000
4144,00057,60086,400115,200
586,40057,60028,80057,600
628,80028,800014,400
7000
8000
9000
10000
Totals$500,000$1,149,200
Average investment: $1,149,200/10 = $114,920
Book rate of return (ARR): $81,200/$114,920 = 70.66%3. Net Present Value (NPV): as indicated in the above schedule, the NPV of the proposed investment is $229,821 (based on PV factors from Table 1, p. 870). Based on the built-in NPV function in Excel, the estimated NPV is $229,743. The difference in estimates is due to the rounding that is embodied in the PV factors taken from Table 1.
4.Internal Rate of Return (IRR): as indicated in the above schedule, we can use the built-in function in Excel to estimate the IRR for this proposed investment; IRR = 21.46%. Alternatively, we can use a linear interpolation procedure to estimate the projects IRR, as follows: we are looking for an interest/discount rate that produces a PV of cash inflows equal to the net original investment outlay ($500,000). Thus,
PV of net cash inflows at 20% (a rate that is too low): $527,875
PV of net cash inflows at 22% (a rate that is too high): $490,273Difference in PV with 2% difference in discount rate: $ 37,602
Thus,
20-42 Capital Budgeting with Tax, Non-MACRS Depreciation, and Sensitivity Analysis (35 min)
Annual after-tax net cash inflow:
Cash revenue
$1,200 x (1 0.35) =$780
Tax saving on depreciation expense($6,000/10) x 0.35 = 210
Total
$990
1. Payback period:
2. Estimated Operating Income per year:
Sales
$1,200
Depreciation
600
Operating income before taxes$ 600
Taxes
210
Operating income
$ 390
Therefore,
3. The maximum initial investment is such that the project at this level of investment would yield a NPV = $0 (i.e., a situation where PV of cash inflows = PV of cash outflows). The appropriate annuity factor for 10 years, 15% is 5.019. Let X = maximum initial investment, then:
X = $990 x 5.019 = $4,969 4. Required annual (pre-tax) cash revenue:
Given an initial investment outlay of $6,000, the after-tax annual cash flow needed per year to generate a return of 15% = $6,000/5.019 =
$1,195
Less: Annual Tax savings on depreciation expense =
210
Required after-tax annual cash revenue
$985
( (1 t)
( 0.65
Annual (pre-tax) cash revenue needed$1,51520-42 (Continued)5.
NPV Calculations under different assumptions regarding the discount rate (required rate of return) and annual after-tax net cash inflows. Assume a ten-year life and an initial investment outlay of $6,000.
DiscountPV AnnuityAnnual Net After-Tax Cash Flow
RateFactor$500$1,000$2,000
10%6.145($2,928)$145$6,290
15%5.019($3,491)($981)$4,038
20%4.192($3,904)($1,808)$2,384
PROBLEMS
20-44 Equipment Replacement Decision; Strategy (60 min)
1. & 3. PV/
Annuity Present After-tax Cash Flows (000s)
Factor Value 0 1 2 3 4 5
Overhaul AccuDrilOperating Cost1
(48.0)(48.0)(38.4)(38.4)(38.4)
Overhaul cost
(100.0)
Tax savings on deprec.2 4.0 4.0
16.0
16.0
16.0
Other Expenses3
(57.0)(57.0)(57.0)(57.0)(57.0)Net after-tax cash flows:
Year 1 0.893 ($90,193)(101.0)
Year 2 0.797 (160,197)
(201.0)
Year 3 0.712 ( 56,533)
(79.4)
Year 4 0.636 ( 50,498)
(79.4)
Year 5 0.567 ( 45,020)
(79.4)
Total PV
($402,441)Buy RoboDril 1010K
Net Equip. Purchase4 1.000 ($240,000)(240.0)
Operating Cost5 3.605 (86,520)
(24.0)
(24.0)(24.0)(24.0)(24.0)
Tax savings on depr.6 3.605 69,216 19.2 19.2 19.2 19.2 19.2
Other expenses7 3.605 (118,965)
(33.0) (33.0) (33.0) (33.0)(33.0)
Salvage value8 0.567 17,010
30.0
Total PV ($359,259) PV difference in cash flow between alternatives= $402,441 $359,259 = $43,182 in favor of RoboDril20-44 (Continued-1)NOTES
1Years 1 and 2: $10 per hour x 8,000 hours x (1 t) =
$48,000
Years 3, 4, and 5: $48,000 x (1 20%) =
$38,400
2Years 1 and 2:
Depreciation expense per year (SL basis):
($120,000 $20,000) ( 10 =
$10,000
Income Tax Rate (t)
x 0.40
Tax savings on depreciation, Years 1 and 2
$ 4,000 Years 3, 4, and 5:
Book value before overhaul (end of original useful life)
$ 20,000
Overhaul cost, Year 3
100,000
Total amount to be depreciated
$120,000
Number of years
( 3
Depreciation expense per year
$ 40,000
Income Tax Rate (t)
x 40%
Tax savings on depreciation, Years 3, 4, and 5
$ 16,0003 $95,000 x (1 t) = $95,000 x 0.60 = $57,0004 Purchase price
$250,000
Installation, testing, rearrangement, and training
+ 30,000
Subtotal
$280,000
Trade-in allowance for AccuDril
40,000
Net purchase cost
$240,000
5 ($10/hour x 4,000 hours) x (1 t) = $40,000 x 0.60 =
$24,0006 Depreciation expense per year: $240,000 ( 5 Years =
$48,000
Income Tax Rate (t)
x 0.40
Annual Tax savings on depreciation deduction
$19,2007 $55,000 x (1 t) = $55,000 x 0.60 =
$33,0008 ($50,000 - $0) x (1 t) = $50,000 x 0.60 =
$30,00020-44 (Continued-2)2.
Net After-tax Cash Flows Difference in Cumulative
Year AccuDril RoboDril Cash Flows Difference
0
$0 ($240,000)($240,000)
($240,000)
1
($101,000)($37,800)$63,200 ($176,800)
2
($201,000)($37,800)$163,200 ($13,600)
3
($79,400)($37,800)$41,600
Thus, the payback period for investing in the new machine is 2-plus years. Using a linear interpolation method, we estimate the payback period as:
4.Among other factors that the firm should consider before the final decision are:
Changes in technology for equipment
Changes in market, especially demand for the product and competitors
Reliability of the new machine and the expected effects of overhaul
Reliability of AccuDril and accuracy of the estimates given
Competitive strategy of the firm
Differences in product qualities manufactured by the two machines
20-46
Comparison of Capital Budgeting Techniques; Sensitivity Analysis (50 min)
1. Effects of the new equipment on operating income after tax:
Sales
$195 x 10,000 = $1,950,000
Cost of goods sold:
Variable manufacturing costs$ 90
Fixed manufacturing costs:
Additional fixed manufacturing overhead:
$250,000/10,000 units = $25
Depreciation on new equipment:
($995,000 $195,000)/4 = $200,000/year
$200,000/10,000 units per year =+ 20 + 45
Manufacturing cost per unit
$135
Times: Number of units x 10,000
Total cost of goods sold
1,350,000
Gross margin
$ 600,000
Operating Expenses:
Variable marketing: Cost per unit $ 10
Number of units x 10,000$100,000
Additional fixed marketing cost + 200,000 300,000 Operating income before taxes
$300,000
Income taxes (@30%)
90,000 Operating income after tax
$210,000Thus, the company will increase its after-tax operating income by $210,000 each year.
2.
Years
1 to 3 Year 4 After-tax operating income
$210,000$210,000
Add: increased depreciation expense
200,000200,000
After-tax cash inflow from disposal of equipment
195,000 Total cash inflow
$410,000$605,000The new machine will increase cash inflows by $410,000 in each of the first three years and $605,000 in Year 4.
3.4.
Average investment = ($995,000 + $195,000)/2 = $595,000
Average after-tax operating income = $210,000
Book rate of return (ARR) based on average investment =
$210,000/$595,000 = 35.29%20-46 (Continued-1)
5.
Using PV and Annuity Tables:
PV of after-tax cash inflows (@14%):
Years 1 through 3: $410,000 x 2.322 =$ 952,020
Year 4 ($410,000 + $195,000): $605,000 x 0.592 = 358,160 Total present value future after-tax cash inflows =$1,310,180
Less: Initial investment outlay
995,000
NPV of the proposed investment
$ 315,180
Using the NPV Function in Excel:
Thus, the estimated NPV of the investment = $315,078 (note the rounding error that occurs when using the PV and annuity factors)
6. Trial-and-Error Approach (initial investment outlay = $995,000):
PV of cash flows @ 25%:
($410,000 x 1.952) + ($605,000 x 0.410) $1,048,370
PV of cash flows @ 30%:
($410,000 x 1.816) + ($605,000 x 0.350)$ 956,310
Difference in PV of after-tax cash inflows$ 92,060
Thus, the estimated IRR for this investment is:
Based on the built-in function in Excel, the estimated IRR of this project = 27.80%, as follows:
20-46 (Continued-2)
7. a.Based on an estimated NPV of $315,078 (part 5, above), the PV of any after-tax increase in variable costs associated with units produced by the new machine = $315,078. Thus, the annual after-tax increase that would be permissible = $315,078/2.914 = $108,126.
To convert this annual cost to a pre-tax basis, we would have to divide by the quantity (1 t), where t = the income-tax rate (30.0%). Thus, the maximum increase in pre-tax variable cost = $108,126/0.70 = $154,466.
Therefore, the variable cost per unit can increase by a maximum of $154,466/10,000 units = $15.45 per unit. At this increase, the new equipment would generate a rate of return of exactly 14%its cost of capital.
b.The maximum pre-tax decrease in selling price = $154,466 (see (a) above). On a per-unit basis, for all units sold, the maximum decrease in unit selling price is therefore equal to $7.72 (rounded), that is, $154,466/20,000 units. This would represent a decrease of approximately 4% ($7.72/$195.00).20-48Capital Budgeting with Sum-of-the-Years-Digits Depreciation; Spreadsheet Application (25 min)
20-50 Determine Initial Investment Based on Internal Rate of Return (10 min)
Let C be the cost of the machine. Then,
after-tax cash flow per year x annuity factor for 6 years, 10% = C
[$20,000 (($20,000 C/6) x 0.20)] x 4.355 = C
[$20,000 $4,000 + 0.03333C] x 4.355 = C
$69,680 + 0.14517C = C
C = $69,680/0.8548 = $81,51620-52 Machine Replacement and Sensitivity Analysis without Taxes
(40 - 50 min)
Net additional cash outlay for the new machine (@ March 5, 2008):
$8,000 $3,000 = $5,0001. a.Payback period: $5,000/$750 = 6.67 years b.
Old New Difference
Depreciation: ($5,000 $600)/11 ($8,000 $400)/10
= $400 = $760 $360
Operating expense (cash)
($750)
Difference in annual pre-tax income (reduction in expenses)
$390
Loss on trade-in of existing asset (at March 5, 2008) =
book value of asset trade-in value = ($5,000 $400) $3,000
= $1,600 (this loss complicates the determination of ARR, but not
NPV or IRR for the proposed investment)
Book values: Old New
3/5/2008 ($5,000 $400 deprec.) $4,600$8,000
3/5/2018
600 400
Average Investment (Book Value)
$2,600$4,200
Therefore, the incremental average investment on the new machine
= $4,200 - $2,600 = $1,600
The average incremental income, including recognition of the loss on disposal of the
existing machine, is $130, as follows:
Ten-Year Difference in Pre-tax Income = 10 x $390 = $3,900
Less: Loss on disposal of existing asset = $4,600 - $3,000 = ($1,600)
Total income difference in favor of new machine = $2,300
Average annual income difference = $230Thus, under the specified treatment of the loss on disposal of the existing machine, the ARR of the proposed replacement decision is slightly over 14%, as follows:
20-52 (Continued)
Students should be alerted to other possible treatments for the loss and to the fact that this is a good example of one of the ambiguities associated with the use of the ARR for capital investment decision-making.
c.NPV= ($750 x 5.650) ($8,000 $3,000) [($600 - $400) x 0.322]
= $4,237.50 $5,000.00 $64.40 = ($826.90) d.Given a negative NPV, we know that the IRR must be less than the discount rate (12%). We are looking for a discount rate that produces a PV of future cash inflows = $5,000 (net investment outlay for the new machine). We try, somewhat arbitrarily, 7% and 8%, as follows:
PV of net cash inflows at 7% = ($750 x 7.024) ($200 x 0.508)= $5,166
PV of net cash inflows at 8% = ($750 x 6.710) ($200 x 0.463)= 4,940
Difference = $ 226
( the estimated IRR = 7.73%, as follows:
2.No, because NPV < $0 (NPV is $826.90). Note that the decision based on the ARR is ambiguous.
3.Because the expected NPV of the project is negative, the firm would have to realize operating cost savings greater than those originally assumed. Let the required pre-tax annual savings = Y. Then, to make NPV = $0, we must have:
PV of Cash Savings = Original Investment Outlay
5.650Y - ($200 x 0.322) = $5,000
5.650Y = $5,064.40
Y = $896.35
(That is, the maximum savings per year before the decision not to invest is changed. This revised amount represents a change of approximately 19.5% above the current estimate of $750. Note that at annual cash savings of $896.35, the IRR on the proposed investment would exactly equal 12%, the companys cost of capital.)20-54Capital Budgeting with Sensitivity Analysis (45 min)
1.Expected annual net cash inflows ($600,000 + $100,000)=
$700,000
Income taxes at 30%
=
210,000After-tax net cash inflows
=
$490,000
The buyer is essentially purchasing an eight-year stream of after-tax rental incomes and income-tax savings associated with the depreciation deduction. Thus, a rational purchase price would be the PV of these future cash flows, using 12% as the discount rate. Note, however, that the depreciation deduction is a function of the purchase price, which we are trying to estimate. Therefore, let P denote the maximum price the buyer would be willing to pay. The amount is approximately $3 million, as follows:
P=[$490,000 x A.12, 8] + [(P/8 x 0.3) x A.12, 8]
P=[$490,000 x 4.968] + [P/8 x 0.3 x 4.968]
P=$2,434,320 + 0.1863P
0.8137P = $2,434,320
P=$2,991,6682.From Meidis perspective, the selling price should be set such that it would cover three things: (1) the PV of the after-tax rental incomes she is foregoing, (2) capital gains taxes she would have to pay on the sale of the real estate, and (3) the sales commission (5%) she has to pay the real estate broker. Thus, if this is the case,
Let S denote the minimum price Meidi would be willing to accept
S=[$460,000 x A.10, 8] + [(S $800,000 0.05S) x 0.40] + 0.05S
S=[$460,000 x 5.335] + [0.38S $320,000] + 0.05S
S=$2,454,100 + 0.43S $320,000
0.57S=$2,134,100
S=$3,744,0353.MACRS depreciation increases to the buyer the PV of the depreciation write-offs (compared to the use of the SL method, as in (1) above). Thus, to the extent the buyer could realize these tax savings, the buyer would be willing to pay a higher price for the property.
As in (1) above, we represent the maximum price the buyer would be willing to pay as the sum of two components: the PV of after-tax rental incomes ($2,434,320) plus the PV of the tax savings due to the depreciation deductions over the life of the property. This second component is represented as 0.2214397P (where P represents the purchase price, and therefore depreciable cost, of the property), as follows:
20-54 (Continued)
(1)
MACRS (2) (3)
(2) x (3)
Year Depreciation1 Tax Effect2PV Factor Present Value
1 0.2000P0.06000P0.8930.0535800P
2 0.3200P0.09600P0.7970.0765120P
3 0.1920P0.05760P0.7120.0410112P
43 0.1152P0.03456P0.6360.0219801P
5 0.1152P0.03456P0.5670.0195955P
6 0.0576P0.01728P0.5070.0087609P
0.2214397P
Notes:
1See text, Exhibit 20.6 for MACRS depreciation rates, 5-year property
2Assuming a 30% marginal income-tax rate.
3First year of switching to SL depreciation method.
Thus, the maximum amount that a rational buyer would be willing to pay has increased to $3,126,694, as follows:
P= $2,434,320 + 0.2214397P
0.7785603P= $2,434,320
P= $3,126,694 (an increase of $135,026 over the amount calculated above in (1))
20-56 Machine Replacement with Tax Considerations (30 - 45 min)Present Value of Costs with the Original Equipment:
Present value of tax savings from depreciation deductions:
($2,500,000 ( 4) x 0.45 x 2.577 =
($724,781)
Present value of cash operating costs:
[$1,800,000 x (1 0.45)] x 2.577 = $2,551,230
Present value of salvage value:
[$50,000 x (1 0.45)] x 0.794 = ($21,835) Present value of costs with the original equipment = $1,804,614Present value of Costs with the New Machine:
Initial outlay cost
$2,000,000Present value of tax savings from depreciation deductions:
Beginning Depreciation TaxTax Discount
YearBook Value Expense1 Rate Savings Factor
1
$2,000,000 $1,333,333x 0.45 = $600,000 x 0.926=
($555,600)
2
666,667 444,445x 0.45 = 200,000 x 0.857=
(171,400)
3
222,223 222,223x 0.45 = 100,000 x 0.794=
(79,400)
Cash proceeds from sale of the old machine
($300,000)
Tax savings related to loss on disposal of the old machine:
($1,875,0002 $300,000) x 0.45 = ($708,750)
Present value of cash operating costs: $1,000,000 x (1 0.45) x 2.577 = $1,417,350
Present value of costs with the new machine$1,602,200
Notes:
1DDB depreciation charges were calculated using the VDB function in Excel, as follows:
20-56(Continued)
2Book value of old asset at time of sale =
Original cost accumulated depreciation =
$2,500,000 [($2,500,000/4) x 1 year] =
$2,500,000 $625,000 = $1,875,000
PV of savings from using the new machine:
$1,804,614 $1,602,200 = $202,414The total cost of the new machine, including the purchase cost and the cash operating cost in each of the three years, is in present value terms $202,414 below the total cost of continuing with the original equipment. Therefore, from a purely financial standpoint, the purchase of the new machine is a good investment.
20-58Equipment Replacement with MACRS Depreciation (35 - 45 min)
1.Per-unit profit margin of the additional units:
Sales price per unit
$3,500
Current manufacturing cost
- 2,450Current gross margin per unit
$1,050
Cost savings per unit with the new machine
+ 150Gross margin (cash flow) per unit for the additional units
$1,200
Net cash inflows:
Present Discount
Item Description Value Factor 2010 2011 2012 2013 Purchase cost($608,000)
Installation cost($12,000)
After-tax proceeds from disposing old $30,000
Gross margin/unit (above)
$1,200$1,200$1,200$1,200
Additional units
30 50 50 70Pre-tax cash flow from additional units (000)
$ 36$ 60$ 60$ 84
Efficiency savings (000)
125 125 125 125Total increase in pre-tax incomes/cash flow (000)
$161$185$185$209
Income taxes (000)
64.4 74 74 83.6Increase in after-tax cash flow before depreciation (000)
$96.60$111$111$125.4
After-tax proceeds from disposal ($80,000 x 0.6)
48
Tax savings from depreciation (000)
81.84 111.60 37.20 17.36After-tax cash inflows
$155,2430.870 $178.44
$168,286 0.756
222.60
$97,5160.658
148.20
$109,115 0.572
190.76
Net Present Value (NPV)
($59,840)VacuTech can expect to have a negative NPV of $59,840 if it purchases the new pump.
20-58 (Continued)
2.Other factors the firm needs to consider include:
Maintenance costs of the machines
Reliability of the machines
Changes and timing of newer machine
Effects on production workers
Learning effect on using the new machine
Changes in market
Competitor reaction
20-60Risk and NPV (45 min)
1. PV of future cash inflows @ 12% = $275,000 x 6.194 = $1,703,350
Less: Initial investment outlay, year 0 = $1,500,000
Net present value (NPV) =
$ 203,350
Since the NPV > $0, the project should be accepted.
2. PV of future cash inflows @ 15% = $275,000 x 5.421 = $1,490,775
Less: Investment outlay, year 0 = $1,500,000
Net present value (NPV) = $(9,225)
Since the NPV < $0, the project should not be accepted.
3.The break-even initial investment outlay is the amount that would produce a NPV = $0, given the annual after-tax flows of $275,000 and a discount rate of 15.00%. We can use Excel to solve, in two steps, for this break-even amount = $1,490,670:
Step 1: Estimate the Projects NPV (compare with 2 above)
20-60 (Continued)
Step 2: Complete the following goal seek dialog box: 4.Many firms raise the discount rate in evaluating a particular capital investment in view of uncertainties underlying the investment. This approach allows managers to factor in risks and uncertainties. The higher the risk or uncertainty a project has, the higher the discount rate.
An alternative is to use a direct approach in dealing with risk or uncertainty. For example, if a firm considers that revenues from an investment are likely to differ from the projected figures, the firm should adjust the projected revenues. If the expenses are likely to be higher, adjusting the projected expenses would allow the firm to be aware of the need for a higher amount of cash outflows. Some believe that using a direct approach (if possible) is better than simply using a higher discount rate. In any case, the topic of risk adjustments is handled more completely in financial management textbooks.
20-62 Uneven Cash Flows (40 min)
1.Present value of net cash inflows:
Year 1
-0-
Year 2
$1,000,000 x 0.797 =$ 797,000
Year 3
$1,000,000 x 0.712 = 712,000
Year 4
$2,500,000 x 0.636 =1,590,000
Years 5-10($3,000,000 x 4.111) x 0.636 =7,843,788
Present value of net cash inflows $10,942,788
Less: Initial investment outlay, year 0
15,000,000 NPV (@12%)
$(4,057,212)
Alternatively, the built-in functions in Excel can be used to estimate the NPV and the IRR of this project, as follows:
2. The maximum purchase price the seller would be willing to offer, given a discount rate of 12% and the indicated cash flows, would be slightly less than $11,000,000, as follows:
20-62 (Continued)
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Blocher, Stout, Cokins, Chen, Cost Management, 4/e 20-1 The McGraw-Hill Companies, 2008Blocher, Stout, Cokins, Chen, Cost Management, 4/e 20-4 The McGraw-Hill Companies, 2008Blocher, Stout, Cokins, Chen, Cost Management, 4/e 20-5 The McGraw-Hill Companies 2008
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