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CHAPTER 10
Making Capital Investment Decisions
Answers to Concepts Review and Critical Thinking Questions
1. An opportunity cost is the most valuable alternative that is foregone if a particular project is undertaken. The
relevant opportunity cost is what the asset or input is actually worth today, not, for example, what it cost to
acquire.
2. It’s probably only a mild over-simplification. Current liabilities will all be paid presumably. The cash portion
of current assets will be retrieved. Some receivables won’t be collected, and some inventory will not be sold,
of course. Counterbalancing these losses is the fact that inventory sold above cost (and not replaced at the end
of the project’s life) acts to increase working capital. These effects tend to offset.
3. The EAC approach is appropriate when comparing mutually exclusive projects with different lives that will be
replaced when they wear out. This type of analysis is necessary so that the projects have a common life span
over which they can be compared; in effect, each project is assumed to exist over an infinite horizon of N-year
repeating projects. Assuming that this type of analysis is valid implies that the project cash flows remain the
same forever, thus ignoring the possible effects of, among other things: (1) inflation, (2) changing economic
conditions, (3) the increasing unreliability of cash flow estimates that occur far into the future, and (4) the
possible effects of future technology improvement that could alter the project cash flows.
4. Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thus depreciation causes
taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield t cD. A
reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the
depreciation tax shield must be included to get the total incremental aftertax cash flows.
5. There are two particularly important considerations. The first is erosion. Will the essentialized book simply
displace copies of the existing book that would have otherwise been sold? This is of special concern given the
lower price. The second consideration is competition. Will other publishers step in and produce such a
product? If so, then any erosion is much less relevant. A particular concern to book publishers (and producers
of a variety of other product types) is that the publisher only makes money from the sale of new books. Thus, it
is important to examine whether the new book would displace sales of used books (good from the publisher’s
perspective) or new books (not good). The concern arises any time there is an active market for used product.
6. This market was heating up rapidly, and a number of other competitors were planning on entering. Any
erosion of existing services would be offset by an overall increase in market demand.
7. Air Canada should have realized that abnormally large profits would dwindle as more supply of services came
into the market and competition became more intense.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to
space and readability constraints, when these intermediate steps are included in this solutions manual, rounding
may appear to have occurred. However, the final answer for each problem is found without rounding during any
step in the problem.
Basic
1. The $5 million acquisition cost of the land six years ago is a sunk cost. The $5.4 million current aftertax value
of the land is an opportunity cost if the land is used rather than sold off. The $10.4 million cash outlay and
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$650,000 grading expenses are the initial fixed asset investments needed to get the project going. Therefore,
the proper year zero cash flow to use in evaluating this project is
$5,400,000 + 10,400,000 + 650,000 = $16,450,000
2. Sales due solely to the new product line are:
21,000($12,000) = $252,000,000
Increased sales of the motor home line occur because of the new product line introduction; thus:
5,000($45,000) = $225,000,000
in new sales is relevant. Erosion of luxury motor coach sales is also due to the new mid-size campers; thus:
1,300($85,000) = $110,500,000 loss in sales
is relevant. The net sales figure to use in evaluating the new line is thus:
$252,000,000 + 225,000,000 – 110,500,000 = $366,500,000
3. We need to construct a basic income statement. The income statement is:
Sales $ 650,000
Variable costs 390,000
Fixed costs 158,000
Depreciation 75,000
EBT $ 27,000
Taxes@35% 9,450
Net income $ 17,550
4. To find the OCF, we need to complete the income statement as follows:
Sales $ 912,400
Costs 593,600
Depreciation 135,000
EBT $ 183,800
Taxes@34% 62,492
Net income $ 121,308
The OCF for the company is:
OCF = EBIT + Depreciation – Taxes
OCF = $183,800 + 135,000 – 62,492
OCF = $256,308
The depreciation tax shield is the depreciation times the tax rate, so:
Depreciation tax shield = tcDepreciation
Depreciation tax shield = .34($135,000)
Depreciation tax shield = $45,900
The depreciation tax shield shows us the increase in OCF by being able to expense depreciation.
5. To calculate the OCF, we first need to calculate net income. The income statement is:
354
Sales $ 85,000
Variable costs 43,000
Depreciation 3,000
EBT $ 39,000
Taxes@40% 15,600
Net income $ 23,400
Using the most common financial calculation for OCF, we get:
OCF = EBIT + Depreciation – Taxes = $39,000 + 3,000 – 15,600
OCF = $26,400
The top-down approach to calculating OCF yields:
OCF = Sales – Costs – Taxes = $85,000 – 43,000 – 15,600
OCF = $26,400
The tax-shield approach is:
OCF = (Sales – Costs)(1 – tC) + tCDepreciation
OCF = ($85,000 – 43,000)(1 – .40) + .40(3,000)
OCF = $26,400
And the bottom-up approach is:
OCF = Net income + Depreciation = $23,400 + 3,000
OCF = $26,400
All four methods of calculating OCF should always give the same answer.
6. Sales $ 900,000
Variable costs 468,000
Fixed costs 190,000
CCA 112,000
EBIT $ 130,000
Taxes@39% 50,700
Net income $ 79,300
7. Cash flow year 0 = -850,000
Cash flow years 1 through 5 = 490,000(1 – .40) = $294,000
PV of CCATS = 850,000(.3)(.4) x (1 + .5(.12))
.12 + .3 1 + .12
= $229,846.94
NPV = -850,000 + 294,000 x PVIFA (12%, 5) + 229,846.94 = $439,651.14
8. Cash flow year 0 = -850,000 - 37,500 = -$887,500
Cash flow years 1 through 5 = 455,000(1 – .4) = $294,000
Ending cash flow = 100,000 + 37,500 = $137,500
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PV of CCATS = 850,000(.3)(.4) x (1 + .5(.12))
.12 + .3 1 + .12
-100,000(.3)(.4) x 1
.12 + .3 (1.12) 5
= $213,635
NPV = -887,500 + 294,000 x PVIFA(12%, 5) + (137,500)/(1.12)5 + 213,635 = $463,960
9. The NPV will be smaller because the Capital Cost Allowances are smaller early on.
PV of CCATS = 850,000(.25)(.4) x (1 + .5(.12))
.12 + .25 1 + .12
-100,000(.25)(.4) x 1
.12 + .25 (1.12) 5
= $202,087
Therefore with a 25% CCA rate, the
NPV = 463,960 + (202,087 – 213,635) = $452,412
10. Neither one is correct. What should be considered is the opportunity cost of using the land, at the very least
what the land could be sold for today.
11. Generally, as long as there are other assets in the class, the pool remains open and there are no tax effects
from the sale. This fact does not hold here since we are told that the there will be no assets left in the class
in 6 years.
Beyond the first year, the UCC at the beginning of the N th year is given by the formula:
d
UCCN C 1 1 d where C = installed capital cost; d = CCA rate. Note that the half-year rule
N 2
2
has been incorporated. In this case:
UCC7 = $400,000 (1 – (0.2/2)) (1-0.2)7-2 = $117,964.80. This is the book value of the asset at the end of the
6th year (beginning of the seventh).
The asset is sold at a (terminal) loss to book value = $117,964.80 – $100,000 = $17,964.80. The terminal
loss acts as a tax shield which the company can use to reduce its taxes. The reduction in taxes is a cash
inflow.
The tax shield = 0.4 $17,964.80 = $7,185.92.
The after tax salvage value = $100,000 + $7,185.92 = $107,185.92.
12. A/R fell by $5,000, and inventory increased by $2,605, so net current assets fell by $2,395. A/P rose by
$4,100.
∆NWC = ∆(CA – CL) = –2,395 – 4,100 = – 6,495
Net cash flow = S – C – ∆NWC = 67,000 – 28,500 – (– 6,495) = $44,995
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13. CCA1 = 0.3($1.76M/2) = $264,000 ; CCA2 = 0.3(1.76M – $264,000) = $448,800 ;
CCA3 = 0.3($1.76M – 264,000 – 448,800) = $314,160.
OCF1 = (S – C)(1 – tc) + tcD = ($2.027M – $595K)(1 – 0.38) + 0.38($264,000) = $988,160
OCF2 = (S – C)(1 – tc) + tcD = ($2.027M – $595K)(1 – 0.38) + 0.38($448,800) = $1,058,384
OCF3 = (S – C)(1 – tc) + tcD = ($2.027M – $595K)(1 – 0.38) + 0.38($314,160) = $1,007,221
14. After-tax net revenue year 0 = -$1,760,000
After-tax net revenue years 1-3 = (S – C)(1 – tC) = ($2,027,000 – 595,000)(1 – 0.38) = $887,840
Ending cash flows (year 3) = salvage value = $733,040
PV of CCATS = 1,760,000(.3)(.38) x (1 + .5(.2))
.2 + .3 1 + .2
-733,040(.3)(.38) x 1
.2 + .3 (1.2)3
= $271,119
NPV = – $1.76M + $887,840(PVIFA20%, 3) + $271,119 + $733,040(PVIF20%, 3)
= $805,551
15. After-tax net revenue year 0 = -$1,760,000 – 300,000 = -$2,060,000
After-tax net revenue years 1-3 = (S – C)(1 – Tc) = ($2,027,000 – 595,000)(1 – 0.38) = $887,840
Ending cash flows (year 3) = recovery of NWC + salvage value = $300,000 + 215,000 = $515,000
PV of CCATS = 1,760,000(.3)(.38) x (1 + .5(.2))
.2 + .3 1 + .2
-215,000(.3)(.38) x 1
.2 + .3 (1.2)3
= $339,472
NPV = –$2.06M + $887,840(PVIFA20%,3) + $339,472 + $515,000/1.23 = $447,723
16. After-tax net revenue year 0 = -625,000 – 160,000 = -$785,000
After-tax net revenue years 1 through 5 = (8,400,000 – 6,000,000 – 205,000)(1 – .38) = $1,360,900
Ending cash flows (year 5) = $160,000
PV of CCATS = 625,000(.25)(.38) x (1 + .5(.17))
.17 + .25 (1 + .17)
= $131,099
NPV = -785,000 + 131,099 + 1,360,900 x PVIFA(17%,5) + 160,000/(1.17)5
= $3,773,067
Since the NPV is positive, it is probably a good project.
357
17. $8,000 – 4,500 = $3,500
18. Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since any one
particular project could be financed entirely with equity, another project could be financed with debt, and the
firm’s overall capital structure remains unchanged, financing costs are not relevant in the analysis of a
project’s incremental cash flows according to the stand-alone principle.
19. The $7.5 million acquisition cost of the land eight years ago is a sunk cost. The $985,000 current appraisal of
the land is an opportunity cost if the land is used rather than sold off. The $19.425 million cash outlay is the
initial fixed asset investment needed to get the project going. Therefore, the proper year zero cash flow to use
in evaluating this project is = $0.985M + $19.425M = $20.41 million.
20. Currently the firm has sales of 18,000($12,500) + (36,700) ($42,600) = $1,788,420,000. With the introduction
of a new mid-sized car its sales will change by (24,500) ($31,500) + (9,000) ($12,500) – (7,500) ($42,600) =
$564,750,000. This amount is the incremental sales and is the amount that should be considered when
evaluating the project.
21. After-tax net revenue year 0 = -450,000 – 23,500 = -$473,500
After-tax net revenue years 1 through 6 = (105,000) (1 – .37) = $66,150
Ending cash flows (year 6) = $100,000 + 23,500 = $123,500
PV of CCATS = 450,000(.2)(.37) x (1 + .5(.125)) – 100,000(.2)(.37) x 1
.125 + .2 (1 + .125) .125 + .2 (1.125)6
= $85,538
NPV = -473,500 + 85,538 + 66,150 x PVIFA(12.5%, 6) + 123,500/(1.125)6
= -$58,882
22. After-tax net revenue year 0 = -1,100,000 + 104,000 = -$996,000
After-tax net revenue years 1 through 5 = (364,000)(1 – .35) = $236,600
Ending cash flows (year 5) = $260,000 – 104,000 = $156,000
PV of CCATS = $240,000
NPV = 0 = -996,000 + 240,000 + 236,600 x PVIFA(IRR%,5) + 156,000/(1+IRR)5
IRR = 20.80%
23. $350,000 cost saving case
After-tax net revenue year 0 = -$996,000
After-tax net revenue years 1 through 5 = (350,000)(1 – .35) = $227,500
Ending cash flows (year 5) = $260,000 – 104,000 = $156,000
PV of CCATS = $205,514
NPV = -996,000 + 205,514 + 227,500 x PVIFA(16%,5) + 156,000/(1+.16)5 = $28,690 Accept the project.
$275,000 cost saving case
After-tax net revenue year 0 = -$996,000
After-tax net revenue years 1 through 5 = (275,000)(1 – .35) = $178,750
Ending cash flows (year 5) = $260,000 – 104,000 = $156,000
PV of CCATS = $205,514
NPV = -996,000 + 205,514 + 178,750 x PVIFA(16%,5) + 156,000/(1+.16)5 = -$131,751 Reject the project.
358
Required pretax cost saving case (RCS)
After-tax net revenue year 0 = -$996,000
Ending cash flows (year 5) = $260,000 – 104,000 = $156,000
PV of CCATS = $205,514
NPV = 0 = -996,000 + 205,514 + RCS(1 – .35) x PVIFA(16%,5) + 156,000/(1+.16)5 Solve for RCS
RCS = Required pretax cost saving = $336,520.
24.
Cash flow Year PV @ 20%
Capital Spending -725,000 0 -$725,000
Salvage 362,500 3 209,780
Additions to NWC -175,000 0 -175,000
175,000 3 101,273
Aftertax operating income 1 to 3 ?
Tax shield on CCA* 86,413
NPV 0
Solving for PV of after-tax operating income we obtain: $ 502,534
Dividing by PVIFA(20%,3) we find that annual after-tax
operating income must be $238,566
Consequently, sales must be $238,566 / (1 – .38) + 50($75,000) = $4,134,783 in order to break even. Therefore the
selling price should be no less than $4,134,783/50 or $82,696 per system.
*PV of CCATS = 725,000(.2)(.38) x (1 + .5(.2))
.2 + .2 1 + .2
- 362,500(.2)(.38) x 1
3
.2 + .2 (1.2)
= $86,413
25. a. EBIT = Sales – cost – depreciation = $150,000 – $80,000 – ($250,000/2) 0.2 = $45,000
b. According to the bottom-up approach:
OCF = (S – C – D)(1 – T) + D = $45,000 (1 – 0.32) + $25,000 = $55,600
c. According to the tax shield approach:
OCF = (S – C)(1 – T) + TD = ($150,000 – $80,000) (1 – 0.32) + 0.32 $25,000 = $55,600
26. According to the top down approach:
OCF = (S – C) – (S – C – D) T = ($400,000 – $305,000) – ($400,000 – $305,000 – $25,000) 0.36
= $69,800
According to the tax shield approach:
OCF = (S – C)(1 – T) + TD = ($400,000 – $305,000) (1 – 0.36) + 0.36 $25,000 = $69,800
27. Method 1: PV @ 12%(Costs) = -$5,800 – 350 PVIFA (12%, 3) = -$6,640.64
Method 2: PV @ 12%(Costs) = -$8,300 – 580 PVIFA (12%, 4) = -$10,061.66
Difference= $3,421.02 in favour of Method 1
359
Without replacement: On this basis we would need to know whether the benefit of 1 more year’s use is
sufficient to offset the additional cost of $3,421.
With replacement: Method 1: EAC = -$2,764.82
Method 2: EAC = -$3,312.65
On this basis, Method 2 is more expensive.
28. Method 1: CF0 = -$5,800
PVCCATS = (5,800)(.37)(.25)(1.06)/[(.12 + .25)(1.12)] = $1,372.32
PV(Costs) = -350(1 – .37)PVIFA (12%, 3) – 5,800 + 1,372.32 = -$4,957.28
EAC = -$4,957.28/PVIFA(12%, 3) = -$2,063.96
Method 2: CF0 = -$8,300
PVCCATS = (8,300)(.37)(.25)(1.06)/[(.12 + .25)(1.12)] = $1,963.84
PV(Costs) = -580(1 – .37)PVIFA (12%, 4) – 8,300 + 1,963.84 = -$7,446.01
EAC = -$7,446.01/PVIFA(12%, 4) = -$2,451.48
Method 2 is more expensive.
5
29. PV(Costs) = -$210,000 – $20,000 + 32,000(PVIFA15%, 5) + $20,000/1.15 = -$112,787.50
EAC = -$112,787.50 / (PVIFA 15%, 5) = -$33,646.27
30. Assuming a carry-forward on taxes:
Both cases: salvage value = $20,000
Techron I: After-tax operating costs = $34,000(1 – 0.35) = $22,100
PVCCATS = (210,000)(.35)(.20)(1.07)/[(.14 + .20)(1.14)] – {[(20,000)(0.20)(0.35)/[0.14 + 0.20]]
(1/1.14)3}= $37,801.20
PV(Costs) = -$210,000 – 22,100(PVIFA14%,3) + (20,000/1.143) + 37,801.20 = -$210,007.44
EAC = -$210,007.44 / (PVIFA14%,3) = -$90,457
Techron II: After-tax operating costs = $23,000(1 – 0.35) = $14,950
PVCCATS = (320,000)(.35)(.20)(1.07)/[(.14 + .20)(1.14)] – {[(20,000)(0.20)(0.35)/[0.14 + 0.20]]
(1/1.14)5}= $59,698.37
PV(Costs) = -$320,000 – 14,950(PVIFA14%,5) – (20,000/1.145) + 59,698.37 = -$301,238.82
EAC = -$301,238.82 / (PVIFA14%,5) = -$87,746
The two milling machines have unequal lives, so they can only be compared by expressing both on an
equivalent annual basis which is what the EAC method does. Thus, you prefer the Techron II because it has the
lower annual cost.
31. Pre-fab segments
Given: Initial cost = $4.8M; d = 4%; k = 15%; T = 38%; S = .25 x $4.8M = $1,200,000; n = 25
PVCCATS = $356,040.27
Assuming end of year costs: PV(Costs) = $100,000 x PVIFA(15%, 25) = $646,414.91
Total PV(Costs) = -$646,414.91 + $356,040.27 + $1,200,000PVIF(15%, 25) = -$253,921.47
EAC = -$253,921.47/PVIFA(15%, 25) = -$39,282
Carbon-fibre technology
Given: Initial cost = $6.0M; d = 4%; k = 15%; T = 38%; S = .25 x $6.0M = $1,500,000; n = 40
PVCCATS = $448,247.66
Assuming end of year costs:
PV(Costs) = $525,000[PVIF(15%, 10) + PVIF(15%, 20) + PVIF(15%, 30) + PVIF(15%, 40)] = $171,738.67
Total PV(Costs) = -$171,738.67 + $448,247.66 + $1,500,000PVIF(15%, 40) = $282,108.85
EAC = $249,396.72/PVIFA(15%, 40) = $42,474.90 or an annual gain
The carbon-fibre technology is a considerably better choice.
32. The present value of the operating costs can be evaluated as a growing annuity. The first annual after-tax
operating cost = C =$16,000(1 – .35) = $10,400. We know that:
360
C 1 g $10, 400 1 .03
T 7
PV(Growing annuity) = 1 1 $52,118.37
r g 1 r .115 .03 1 .115
PVCCATS = $56,054.72
PV(Costs) = -$350,000 + $56,054.72 – $52,118.37 – $105,000/(1.115)7 = -$297,055.85
EAC = -$297,055.85/PVIFA(11.5%,7) = -$64,062
33. Given: Initial cost = $570,000; d = 30%; k = 20%; T = 37%; S = $77,000; n = 5
PVCCATS = $109,125.30
NPV = $0 = – $570,000 – 75,000 + 109,125.30 + (After-tax net revenue)(PVIFA20%,5) +
[(75,000 + 77,000) / 1.205]
After-tax net revenue = $474,789.31 / PVIFA20%,5 = $158,759.91
$158,759.91 = [ (P–v)Q – FC ](1 – tc) = [(P – 6.25)175,000 – 182,000](.63)
Solve for P to find: P = $8.73
34. PVCCATS = $71,430.40
Annual after-tax savings = $150,000(1 – .36) = $96,000
In each year there is any additional cash outflow of $2,000 to finance inventory costs. At the end of the
project, there is a recovery of the initial and annual outflows = $22,000 + 4($2,000) = $30,000.
NPV = -$450,000 – $22,000 + $71,430.40 + ($96,000 – $2,000)PVIFA(18%,4) + ($75,000 + $30,000)/1.184 =
-$93,546 Reject the project
Intermediate
35. CF0=-11,300,000 – 975,000 = -12,275,000
1 2 3 4 5
Sales 15,215,000 19,690,000 25,328,500 26,850,000 9,397,500
Variable costs 11,645,000 15,070,000 19,385,500 20,550,000 7,192,500
Fixed costs 47,700 47,700 47,700 47,700 47,700
Net profit 3,522,300 4,572,300 5,895,300 6,252,300 2,157,300
Taxes(37%) 1,303,251 1,691,751 2,181,261 2,313,351 798,201
Net profit after-tax 2,219,049 2,880,549 3,714,039 3,938,949 1,359,099
NWC = (37% × 5,629,550 1,655,750 2,086,245 562,955 -6,457,425
Sales)
NWC 4,654,550 -3,973,800 430,495 -1,523,290 -562,955
Net profit after-tax
- (NWC or NWC -2,435,501 6,854,349 3,283,544 5,462,239 1,922,054
recovered)
Salvage value 2,825,000
PVCCATS = $1,706,260.40
NPV = -$12,275,000 + $1,706,260 – $2,435,501*PVIF(20%, 1) + $6,854,349*PVIF(20%, 2) +
$3,283,544*PVIF(20%, 3) + $5,462,239*PVIF(20%, 4) + $1,922,054*PVIF(20%, 5) +
$2,825,000*PVIF(20%, 5)
= -$1,396,244
The project should be rejected.
36. New excavator costs=$700,000 but SV0=$35,000; Therefore, CF0 = $665,000. Operating revenues =$65,000
and SV10=115,000 – 5,000=$110,000.
PV of CCATS = 700,000(.25)(.39) x (1 + .5(.14)) - 110,000(.25)(.4) x 1
10
.14 + .25 1 + .14 .14 + .25 (1.14)
= $148,623.71
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NPV = 65,000(1 – .39) x PVIFA (14%, 10) + 110,000 x PVIF (14%, 10) + 148,623.71 – 665,000
= -$279,885 Do not replace the existing excavator.
37. CF0 = 8,000 – 300 = $7,700, SV4 = 1,100 – 150 = $950, and Operating revenues = $8,000.
PV of CCATS = 7,700(.25)(.22) x (1 + .5(.17))
.17 + .25 1 + .17
- 950(.25)(.22) x 1
4
.17 + .25 (1.17)
= $868.69
NPV = 8,000(1 – .22) x PVIFA (17%, 4) + 868.69 + 950 x PVIF (17%, 4) – 7,700 = $10,793.44
The student should buy the new equipment.
38. Underground (U): CF0 = $9.5M, annual costs = $62,000, n=20
PV(CostsU) = [-$62,000(1 – .37) + ($9.5M/20)(.37)] x PVIFA (10.5%, 20) – $9.5M = -$8,374,917.06
EACU = -$8,374,917.06/PVIFA(10.5%, 20) = -$1,017,496
Above ground (A): CF0 = $5.0M, annual costs = $165,000, n = 9
PV(CostsA) = [-$165,000(1 – .37) + ($5M/9)(.37)] x PVIFA (10.5%, 9) – $5M = -$4,426,302.13
EACA = -$4,426,302.13/PVIFA(10.5%, 9) = -$783,926
The above ground system is cheaper for the firm.
39. Product A:
PV of CCATS = 372,000(.2)(.39) x (1 + .5(.15))
.2 + .15 1 + .15
+ (99,000/15)(.39) x PVIFA (15%, 15) = $92,547.28
PV (Net cash flows) = (301,900 – 169,500)(1 – .39) x PVIFA (15%, 15) = $472,257.00
NPV = 92,547 + 472,257 – 14,750(1 – .39) x PVIF (15%, 15) – (99,000 + 372,000) = $92,699
Product B:
PV of CCATS = 428,000(.2)(.39) x (1 + .5(.15)) + (180,850/15)(.39) x PVIFA (15%, 15) = $116,657.16
.2 + .15 1 + .15
PV (Net cash flows) = (375,000 – 210,500)(1 – .39) x PVIFA (15%, 15) = $586,754.35
NPV = 116,657 + 586,754 – 112,550(1 – .39) x PVIF (15%, 15) – (180,850 + 428,000) = $86,124
Continue to rent:
NPV = 45,000(1 – .39) x PVIFA (15%, 15) = $160,510
362
Continue to rent the building (highest NPV). Note: If the lost rent from renovations is included as an
opportunity cost in the evaluation of Products A and B, their NPVs would be negative, indicating that the firm
should not produce either of those items and, instead, continue to rent the facility.
40. The rule is to discount nominal cash flows using nominal rates and real cash flows using real rates. Our choice
is simple here. We should use nominal values for cash flows and rates since the rate of inflation is not
provided.
V = ($700K/.17) + ($1,800,000 – $1,100,000) = $4,817,647.
Therefore, P0 = $4,817,647/275,000=$17.52/share.
41. Operating costsA = $120,000(1 – 0.34) = $79,200
PVCCATSA = $80,410.00
PV(CostsA) = -$430,000 – $79,200 x PVIFA(20%, 4) + $80,410.00 = -$554,617.78
Operating costsB = $80,000(1 – 0.34) = $51,200
PVCCATSB = $100,980.00
PV(CostsB) = -$540,000 – $51,200 x PVIFA(20%, 6) + $100,980.00 = -$609,286.12
If the system will not be replaced when it wears out, then system A should be chosen, because it has a lower
present value of costs.
42. EACA = -$554,617.78 / PVIFA(20%, 4) = -$214,243
EACB = -$609,286.12 / PVIFA(20%, 6) = -$183,216
If the system is replaced, system B should be chosen because it has a smaller EAC.
43. Let: After-tax net revenue = ATNR = [(P–v)Q – FC ](1 – tc)
Opportunity cost of land = $1,200,000
Capital gains tax = ($1,200,000 – $1,000,000)(0.5)(0.34) = $34,000
Opportunity cost of land net of capital gains tax = $1,200,000 – $34,000 = $1,166,000
Salvage value = $600,000
PVCCATS = ($3,100,000/5)(0.34)PVIFA(15%, 5) = $706,634.29
NPV = 0 = – $1,166,000 – $3,100,000 – $600,000 + $706,634 + ATNR*PVIFA(15%, 5) –
50,000*PVIFA(15%, 4) + (600,000 + 800,000)*PVIF(15%, 5)
ATNR = $3,606,067 / PVIFA(15%, 5) = $1,075,746
ATNR = $1,075,746 = [(P–v)Q – FC ](1 – tc)
$776,794 = [(P – 0.0075)(80,000,000) – 800,000](1 – 0.34); P = $0.0379
44. SAL5000 DET1000
12 machines needed 10 machines needed
cost/machine=$12,000 cost/machine=$14,000
Op. Costs=$1,750/yr Op. Costs=$1,400/yr
SV6 = $1,200 SV4 = 0
NPVSAL5000=[-1,750 x PVIFA (15%, 6) – 12,000 + 1,200 x PVIF (15%, 6)](12) = -$217,248.62
NPVDET1000=[-1,400 x PVIFA (15%, 4) – 14,000](10) = -$179,969.70
Using a replacement chain, we effectively assume that each alternative is duplicated over identical future
periods of time until they both meet at the same point in time. If the SAL5000 is repeated once it will extend
out to 12 years. If the DET1000 is repeated twice (two subsequent four-year periods) it will also extend out to
the same point in time thus allowing for a more reasonable comparison between the two.
NPVSAL5000 = -217,248.62 – 217,248.62 x PVIF (15%, 6) = -$311,171.19
NPVDET1000 = -179,969.70 – 179,969.70 x PVIF (15%, 4) – 179,969.70 x PVIF (15%, 8) = -$341,700.37
Choose the SAL5000 model.
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45. X: Y:
C0 = 550,000 C0 = 950,000
Savings/yr. = 195,000 Savings/yr. = 247,000
n=5 n=10
k = 14.5%
NPVX = 195,000 x PVIFA (14.5%,5) – 550,000 = $111,483.92
With replacement chain:
NPVx = 111,483.92 + 111,483.92 x PVIF (14.5%, 5) = $168,131.94
NPVY = 247,000 x PVIFA (14.5%, 10) – 950,000 = $313,629.18
Choose Mixer Y.
Challenge
46. a. Assuming the project lasts four years, the NPV is calculated as follows:
Year 0 1 2 3 4
After-tax profit $1,600,000 $1,600,000 $1,600,000 $1,600,000
Change in NWC (1,000,000) 0 0 0 1,000,000
Capital spending (5,000,000) 0 0 0 0
Total cash flow ($6,000,000) $1,600,000 $1,600,000 $1,600,000 $2,600,000
PVCCATS = $1,280,347.30
Net present value = $652,820.15
b. Abandoned after one year:
Year 0 1
After-tax profit $1,600,000
Change in NWC (1,000,000) 1,000,000
Capital spending (5,000,000) 4,000,000
Total cash flow ($6,000,000) $6,600,000
PVCCATS = $318,584.07
Net present value = $159,292.03
Abandoned after two years:
Year 0 1 2
After-tax profit $1,600,000 $1,600,000
Change in NWC (1,000,000) 0 1,000,000
Capital spending (5,000,000) 0 3,340,000
Total cash flow ($6,000,000) $1,600,000 $5,940,000
PVCCATS = $569,663.85
Net present value = $637,484.35
364
Abandoned after three years:
Year 0 1 2 3
After-tax profit $1,600,000 $1,600,000 $1,600,000
Change in NWC (1,000,000) 0 0 1,000,000
Capital spending (5,000,000) 0 0 1,500,000
Total cash flow ($6,000,000) $1,600,000 $1,600,000 $4,100,000
PVCCATS = $997,896.67
Net present value = $508,366.23
The decision to abandon is an important variable when evaluating the NPV of a project.
This project should be abandoned after two years since the NPV is larger than at any other year-end.
47. Cash flows for year 0 = -$240,000
Cash flows for years 1-5 = (25,000 + 30,000)(1 – .38) + (240,000/5)(.38)
= $52,340
PV of after-tax cash flows = $52,340*PVIFA(13%, 5) = $184,091.88
NPV = $184,091.88 – $240,000 = -$55,908.12
No, they should not renovate.
48. PV of CCATS = 190,000(.20)(.37) x (1 + .5(.14)
.14 + .20 (1 + .14)
= $38,813.73
a. 190,000 – 38,813.73 = PMT x PVIFA(14%, 5)
PMT = $44,038.07
Cost savings = 44,038.07/.63 = $69,901.70
b. PV of CCATS = 190,000(.20)(.37) x (1 + .5(.14) - 28,500(.20)(.37) x 1
5
.14 + .20 (1 + .14) .14 + .20 (1.14)
= $35,592.11
5
190,000 – 35,592.11 = PMT x PVIFA (14%, 5) + 28,500/(1.1)
PMT = $40,664.90
Cost savings = 40,664.90/.63 = $64,547.46
49. Cash flow year 0 = -85,500,000 – 4,500,000 – 16,300,000 – 3,300,000(1 – .37) = -$108,379,000
Cash flow years 1-7 = [(16,900)(23,900 – 20,000) – 28,400,000](1 – .37) = $23,631,300
Cash flow year 8 = 23,631,300 + 20,900,000 + 16,300,000 = $60,831,300
PVCCATS (Class 3) = 10,000,000(.05)(.37) x (1 + .5(.16)) - 7,700,000(.05)(.37) x 1
8
.16 + .05 (1 + .16) .16 + .05 (1 + .16)
= $613,288.11
PVCCATS (Class 8) = 75,500,000(.20)(.37) x (1 + .5(.16)) - 8,700,000(.20)(.37) x 1
8
.16 + .20 (1 + .16) .16 + .20 (1 +.16)
= $13,903,650.74
NPV = -108,379,000 + 23,631,300*PVIFA(16%, 7) + 60,831,300*PVIF(16%, 8) + 613,288 + 13,903,651
= $20,129,585
The net present value is positive, so they should produce the robots.
365
50.
Year 1 2 3 4 5
Units/yr 95,000 105,000 105,000 112,000 62,500
Price/unit 360 360 360 360 360
Vcost/unit 240 240 240 240 240
Sales 34,200,000 37,800,000 37,800,000 40,320,000 22,500,000
VC -22,800,000 -25,200,000 -25,200,000 -26,880,000 -15,000,000
FC -160,000 -160,000 -160,000 -160,000 -160,000
Net Rev 11,240,000 12,440,000 12,440,000 13,280,000 7,340,000
Taxes -4,496,000 -4,976,000 -4,976,000 -5,312,000 -2,936,000
(S-C)(1-T) 6,744,000 7,464,000 7,464,000 7,968,000 4,404,000
Year 0 1 2 3 4 5
A-T Rev 0 6,744,000 7,464,000 7,464,000 7,968,000 4,404,000
Ch in NWC -600,000 -1,260,000 0 -882,000 0 2,742,000
Cap Spend -16,700,000 0 0 0 0 4175000
PVCCATS 2,599,908
Total CF -14,700,092 5,484,001 7,464,002 6,582,003 7,968,004 11,321,005
Net present value = $6,220,041; An approximate solution for the IRR can be found by assuming that the
PVCCATS is discounted at the cost of capital of the firm. In this case: IRR = 38.55%. The alternative is to
enter the data into a spreadsheet and search for the rate that produces a NPV = 0. In this case we find that
IRR = 38.08769%.
51. PVCCATS(class 8) = 600,000 x 0.20 x 0.37 x (1+0.5(0.125))
0.20 + 0.125 1 + .125
-90,000 x 0.20 x 0.37 x 1/(1.125)5
0.20 + 0.125
= $117,653.83
NPV = 0 = -$600,000 – $20,000+ (S-C)(0.63)*PVIFA(12.5%, 5) + $117,653.83 +
($90,000 + $20,000)/1.1255
(S-C)(0.63)*PVIFA(12.5%, 5) = $441,303.98
(S-C) = $196,733
52. a. For the new computer: PVCCATS = $140,844.22
$62,500(.36) $62,500(.36)
For the old computer: PVCCATS = $38,531.78
1.11 (1.11)2
Difference in PVCCATS = $102,312.44
366
If old computer is replaced now:
Year 0 1 2 3 4 5
After-tax cost savings 64,000 64,000 64,000 64,000 64,000
(S – C)(1 – T)
Capital spending (372,688)* 0 (75,000) 0 0 100,000
Total cash flow ($372,688) $64,000 ($11,000) $64,000 $64,000 $164,000
*Initial Capital spending = Payment for new computer + resale of old computer + gain in PVCCATS
= ($625,000) + $150,000 + $102,312.44 = ($372,687.56)
NPV = -$137,677. Do not replace the old computer now.
b.
New Computer:
Year 0 1 2 3 4 5
Cost savings 64,000 64,000 64,000 64,000 64,000
PVCCATS 140,844
Capital spending (625,000) 0 0 0 0 100,000
Total cash flow ($484,156) $64,000 $64,000 $64,000 $64,000 $164,000
Net present value = -$188,273; EAC = -$50,941
Old Computer:
Year 0 1 2 3 4 5
Depreciation tax shield 22,500 22,500 0 0 0
Change in NWC 0 0 0 0 0 0
Capital spending (150,000) 0 75,000 0 0 0
Total cash flow ($150,000) $22,500 $97,500 $0 $0 $0
Net present value = -$50,596; EAC = -$29,545
Once we consider that there is going to be a planned replacement of the old machine after the second year, we
must compare the EACs. The decision is to still stick with the old computer.
53. a. Assume price per unit = $10 and units/year = 175,000
After-tax net revenue/yr. = [(P-V)Q FC](1 Tc) = [($10 – 6.25)(175,000) – 182,000](0.63) = $298,777.50
PVCCATS = $109,125.30; Salvage value = $77,000; Initial working capital increase = $75,000
NPV = -$570,000 – 75,000 + 109,125.30 + 298,777.50*PVIFA(20%, 5) + (77,000 + 75,000)*PVIF(20%, 5)
= $418,738.31
To break even the number of cartons sold must be less than 175,000.
b. NPV = $0 = -$570,000 – 75,000 + 109,125.30 + [($10 – 6.25)(Q) – 182,000](0.63)*PVIFA(20%, 5) +
(77,000 + 75,000)*PVIF(20%, 5)
Solve for Q to find: Q 115,733 cartons. At Q = 115,733: NPV $0
c. NPV = $0 = -$570,000 – 75,000 + 109,125.30 + [($10 – 6.25)(175,000) – FC](0.63)*PVIFA(20%, 5) +
(77,000 + 75,000)*PVIF(20%, 5)
Solve for FC to find: FC $404,250. At FC = $404,250: NPV $0
367
Appendix 10A
A1. Nominal discount rate = 12%; Inflation rate = 3%
Real rate = (1.12/1.03) – 1 = 0.0873786 = 8.73786%
Real Cash Flows
Year Method 1 Method 2
0 $5,800.00 $8,300.00
1 339.81 563.27
2 329.91 546.71
3 320.30 530.78
4 515.32
Discounting the real cash flows at the real rate we get: Method 1: PV(Costs) = -$6,640.64
Method 2: PV(Costs) = -$10,061.66
As long as the cash flows and the discount rate in the annuity factors that we use to compute the EACs are also
adjusted for inflation, we should obtain the identical value for each EAC as we obtained in the earlier problem.
Method 1: EAC = -$2,764.82
Method 2: EAC = -$3,312.65
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