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
Basic
1.
The $4.5 million acquisition cost of the land six years ago is a sunk cost. The $625,000 current appraisal of
the land is an opportunity cost if the land is used rather than sold off. The $6 million cash outlay is the
initial fixed asset investment needed to get the project going and the $325,000 in site preparation cost is
relevant. Therefore, the proper year zero cash flow to use in evaluating this project is:
$625,000 + $6,000,000 + $325,000 = $6.95 million.
353
2.
Sales due solely to the new product line are 13,500($10,000) = $135 million. Increased sales of the motor
home line occur because of the new product line introduction; thus 3,500($37,500) = $131.25 million in
new sales is relevant. Erosion of luxury motor coach sales is also due to the new mid-size campers; thus
1,200($62,000) = $74.4 million loss in sales is relevant. The net sales figure to use in evaluating the new
line is thus $135 million + $131.25 million – $74.4 million = $191.85 million.
3.
Sales
Variable costs
Fixed costs
CCA
EBT
Taxes@27%
Net income
$ 825,000.00
453,750.00
200,000.00
60,000.00
$ 111,250.00
30,037.50
$ 81,212.50
4.
Sales
Costs
CCA
EBT
Taxes@30%
Net income
$1,050,000
560,000
115,000
$ 375,000
112,500
$ 262,500
5.
Sales
$175,000.00
Costs
CCA
EBT
Taxes@30%
Net income
85,000.00
4,500.00
$ 85,500.00
25,650.00
$ 59,850.00
6.
7.
OCF = EBIT + D – T
= 375,000 + 115,000 – 112,500 = $377,500
CCA tax shield = tcD
= .30($115,000) = $34,500
a.
b.
c.
OCF = EBIT + D – T = 85,500 + 4,500 – 25,650
OCF = S – C – T = 175,000 – 85,000 – 25,650
OCF = (S – C)(1 – tc) + tcD = (175,000 – 85,000)(1 – .30) + .30(4,500)
= $64,350.00
= $64,350.00
= $64,350.00
d.
OCF = NI + D = 59,850 + 4,500
= $64,350.00
Sales
Variable costs
Fixed costs
CCA
EBIT
Taxes@37%
Net income
$ 800,000
400,000
180,000
92,000
$ 128,000
47,360
$ 80,640
Cash flow year 0 = -830,000
Cash flow years 1 through 5 = 455,000(1 – .37) = $286,650
PV of CCATS = 830,000(.3)(.37) x (1 + .5(.12))
.12 + .3
1 + .12
= $207,606
NPV = -830,000 + 286,650 x PVIFA (5, 12%) + 207,606 = $410,915
354
8.
Cash flow year 0 = -830,000 - 37,500 = -$867,500
Cash flow years 1 through 5 = 455,000(1 – .37) = $286,650
Ending cash flow = 110,000 + 37,500 = $147,500
PV of CCATS = 830,000(.3)(.37) x (1 + .5(.12))
.12 + .3
1 + .12
-110,000(.3)(.37) x
1
.12 + .3
(1.12) 5
= $191,110
NPV = -867,500 + 286,650 x PVIFA(5, 12%) + (147,500)/(1.12) 5 + 191,110 = $440,615
9.
The NPV will be smaller because the Capital Cost Allowances are smaller early on.
PV of CCATS = 830,000(.25)(.37) x (1 + .5(.12))
.12 + .25
1 + .12
-110,000(.25)(.37) x
1
.12 + .25
(1.12) 5
= $180,780
Therefore with a 25% CCA rate, the
NPV = 440,615 + (180,780 – 191,110) = $430,285
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.
As long as there are other assets in the class, the pool remains open and there are no tax effects from the
sale as long as the undepreciated capital cost (UCC) of the class does not become negative as a result of the
sale. We have no information about the other assets in the pool and therefore make the reasonable
assumption that the company should be considered as a going concern. This implies that there are other
assets in this class.
Beyond the first year, the UCC at the beginning of the N th year is given by the formula:
N 2
 d
UCCN  C 1   1  d  where C = installed capital cost; d = CCA rate. Note that the half-year rule
 2
has been incorporated. In this case:
UCC7.= $350,000 (1 – (0.2/2)) (1-0.2)7-2 = $103,219.20 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 gain to book value and the UCC of the class is reduced by the value of the sale. There
are no direct tax effects. Therefore: After-tax salvage value = $100,000
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 = 65,500 – 26,400 – (– 6,495) = $45,595
355
13.
CCA1 = 0.3($1.65M/2) = $247,500 ; CCA2 = 0.3(1.65M – $247,500) = $420,750 ;
CCA3 = 0.3($1.65M – 247,500 – 420,750) = $294,525.
OCF1 = (S – C)(1 – tc) + tcD = ($1.925M – $595K)(1 – 0.4) + 0.4($247,500) = $897,000
OCF2 = (S – C)(1 – tc) + tcD = ($1.925M – $595K)(1 – 0.4) + 0.4($420,750) = $966,300
OCF3 = (S – C)(1 – tc) + tcD = ($1.925M – $595K)(1 – 0.4) + 0.4($294,525) = $915,810
14.
After-tax net revenue year 0 = -$1,650,000
After-tax net revenue years 1-3 = (S – C)(1 – Tc) = ($1,925,000 – 595,000)(1 – 0.4) = $798,000
Ending cash flows (year 3) = salvage value = $687,225
PV of CCATS = 1,650,000(.3)(.4) x (1 + .5(.22))
.22 + .3
1 + .22
-687,225(.3)(.4) x
.22 + .3
1
(1.22) 3
= $259,101
NPV
= – $1.65M + $798,000(PVIFA22%, 3) + $259,101 + $687,225(PVIF22%, 3)
= $617,269
15.
After-tax net revenue year 0 = -$1,650,000 – 245,000 = -$1,895,000
After-tax net revenue years 1-3 = (S – C)(1 – Tc) = ($1,925,000 – 595,000)(1 – 0.4) = $798,000
Ending cash flows (year 3) = recovery of NWC + salvage value = $245,000 + 450,000 = $695,000
PV of CCATS = 1,650,000(.3)(.4) x (1 + .5(.22))
.22 + .3
1 + .22
-450,000(.3)(.4) x
.22 + .3
1
(1.22) 3
= $289,249
NPV = –$1.895M + $798,000(PVIFA22%,3) + $289,249 + $695,000/1.223 = $406,699
16. After-tax net revenue year 0 = -600,000 – 150,000 = -$750,000
After-tax net revenue years 1 through 5 = (6,450,000 – 4,500,000 – 195,000)(1 – .37) = $1,105,650
Ending cash flows (year 5) = $150,000
PV of CCATS = 600,000(.25)(.37) x (1 + .5(.17))
.17 + .25
(1 + .17)
= $122,543
NPV = -750,000 + 122,543 + 1,105,650 x PVIFA(17%,5) + 150,000/(1.17) 5
= $2,978,317
Since the NPV is positive, it is probably a good project.
17. $7,500 – 4,300 = $3,200
356
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 $965,000 current appraisal of
the land is an opportunity cost if the land is used rather than sold off. The $20.45 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 $21.415 million.
20. Currently the firm has sales of 17,500($11,000) + (36,500) ($41,600) = $1,710,900,000. With the introduction
of a new mid-sized car its sales will change by (24,000) ($31,500) + (9,000) ($11,000) – (7,500) ($41,600) =
$543,000,000. 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 = -425,000 – 23,500 = -$448,500
After-tax net revenue years 1 through 6 = (104,500) (1 – .37) = $65,835
Ending cash flows (year 6) = $100,000 + 23,500 = $123,500
PV of CCATS = 425,000(.2)(.37) x (1 + .5(.11)) – 100,000(.2)(.37) x
1
.11 + .2
(1 + .11)
.11 + .2
(1.11) 6
= $83,662
NPV = -448,500 + 83,662 + 65,835 x PVIFA(11%, 6) + 123,500/(1.11) 6
= -$20,292
22. After-tax net revenue year 0 = -1,100,000 + 100,000 = -$1,000,000
After-tax net revenue years 1 through 5 = (375,000)(1 – .34) = $247,500
Ending cash flows (year 5) = $250,000 – 100,000 = $150,000
PV of CCATS = $235,000
NPV = 0 = -1,000,000 + 235,000 + 247,500 x PVIFA(IRR%,5) + 150,000/(1+IRR) 5
IRR = 21.96%
23. $350,000 cost saving case
After-tax net revenue year 0 = -$1,000,000
After-tax net revenue years 1 through 5 = (350,000)(1 – .34) = $231,000
Ending cash flows (year 5) = $250,000 – 100,000 = $150,000
PV of CCATS = $204,899
NPV = -1,000,000 + 204,899 + 231,000 x PVIFA(15%,5) + 150,000/(1+.15) 5 = $53,823.34 Accept the project.
$250,000 cost saving case
After-tax net revenue year 0 = -$1,000,000
After-tax net revenue years 1 through 5 = (250,000)(1 – .34) = $165,000
Ending cash flows (year 5) = $250,000 – 100,000 = $150,000
PV of CCATS = $204,899
NPV = -1,000,000 + 204,899 + 165,000 x PVIFA(15%,5) + 150,000/(1+.15) 5 = -$167,418.90 Reject the
project.
Required pretax cost saving case (RCS)
After-tax net revenue year 0 = -$1,000,000
Ending cash flows (year 5) = $250,000 – 100,000 = $150,000
357
PV of CCATS = $204,899
NPV = 0 = -1,000,000 + 204,899 + RCS(1 – .34) x PVIFA(15%,5) + 150,000/(1+.15)5 Solve for RCS
RCS = Required pretax cost saving = $325,672.21.
24.
Capital Spending
Salvage
Additions to NWC
Cash flow
-750,000
375,000
-175,000
175,000
Year
0
3
0
3
1 to 3
Aftertax operating income
Tax shield on CCA*
NPV
Solving for PV of after-tax operating income we obtain:
Dividing by PVIFA(20%,3) we find that annual after-tax
operating income must be $246,702
PV @ 20%
-$750,000
217,014
-175,000
101,273
?
87,040
0
$ 519,673
Consequently, sales must be $246,702 / (1 – .37) + 50($75,000) = $4,141,590 in order to break even. Therefore the
selling price should be no less than $4,141,590/50 or $82,832 per system.
*PV of CCATS = 750,000(.2)(.37) x (1 + .5(.2))
.2 + .2
1 + .2
- 375,000(.2)(.37) x
1
.2 + .2
(1.2) 3
= $87,040
Note:
Problems related to Equivalent Annual Cost (EAC) have been solved under the assumption that
from the firm’s point of view, a cost is an outflow. Accordingly, for these problems (#25, #26, #27,
#28, #29, #30, #36, #39, #40 and #50), the negative signs for EAC and PV(Costs) have been dropped.
This treatment is inconsistent with that of the textbook (where negative signs have been retained).
An adjustment will be made in the next edition of the textbook.
25.
Method 1: PV @12%(Costs) = $6,565
Method 2: PV @12%(Costs) = $10,040
Difference= $3,475 in favour of Method 1
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 $3,475.
With replacement:
Method 1: EAC=$2,733
Method 2: EAC=$3,306
On this basis, Method 2 is more expensive.
26.
Method 1: CF0 = -$5,700
PVCCATS = (5,700)(.35)(.25)(1.06)/[(.12 + .25)(1.12)] = $1,275.76
PV(Costs) = 360(1 – .35)PVIFA (12%, 3) + 5,700 – 1,276 = $4,986
EAC = $4,986/PVIFA(12%, 3) = $2,076
358
Method 2: CF0 = -$8,400
PVCCATS = (8,400)(.35)(.25)(1.06)/[(.12 + .25)(1.12)] = $1,880
PV(Costs) = 540(1 – .35)PVIFA (12%, 4) + 8,400 – 1,880 = $7,586
EAC = $7,586/PVIFA(12%, 4) = $2,498
Method 2 is more expensive.
27.
PV(Costs) = $210,000 + $45,000 + 17,500(PVIFA14%,6) – $45,000/1.146 = $302,550.29
EAC = $302,550.29 / (PVIFA14%,6) = $77,803.07
28. Assuming a carry-forward on taxes:
Both cases: salvage value = $50,000
Techron I: After-tax operating costs = $37,000(1 – 0.4) = $22,200
PVCCATS = (250,000)(.4)(.20)(1.10)/[(.20 + .20)(1.20)] – {[(50,000)(0.20)(0.40)/[0.20 + 0.20]]
(1/1.20)3}= $40,046.30
PV(Costs) = $250,000 + 22,200(PVIFA20%,3) – (50,000/1.203) – 40,046.30 = $227,782.40
EAC = $227,782.40 / (PVIFA20%,3) = $108,134
Techron II: After-tax operating costs = $15,000(1 – 0.4) = $9,000
PVCCATS = (375,000)(.4)(.20)(1.10)/[(.20 + .20)(1.20)] – {[(50,000)(0.20)(0.40)/[0.20 + 0.20]]
(1/1.20)6}= $65,401.02
PV(Costs) = $375,000 + 9,000(PVIFA20%,6) – (50,000/1.206) – 65,401.02 = $322,783.67
EAC = $322,783.67 / (PVIFA20%,6) = $97,063
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.
29. Pre-fab segments
Given: Initial cost = $4.5M; d = 4%; k = 15%; T = 40%; S = .25 x $4.5M = $1,125,000; n = 20
PVCCATS = $348,444.96
Assuming end of year costs: PV(Costs) = $100,000 x PVIFA(15%, 20) = $625,933.15
Total PV(Costs) = $625,933.15 – $348,444.96 – $1,125,000PVIF(15%, 20) = $208,750.38
EAC = $208,750.38/PVIFA(15%, 20) = $33,350
Carbon-fibre technology
Given: Initial cost = $6.0M; d = 4%; k = 15%; T = 40%; S = .25 x $6.0M = $1,500,000; n = 40
PVCCATS = $471,839.65
Assuming end of year costs:
PV(Costs) = $500,000[PVIF(15%, 10) + PVIF(15%, 20) + PVIF(15%, 30) + PVIF(15%, 40)] = $163,560.64
Total PV(Costs) = $163,560.64 – $471,839.65 – $1,500,000PVIF(15%, 40) = -$313,878.88
EAC = -$313,878.88/PVIFA(15%, 40) = -$47,258.26 or an annual gain
The carbon-fibre technology is the better choice.
30. The present value of the operating costs can be evaluated as a growing annuity. The first annual after-tax
operating cost = C =$15,000(1 – .34) = $9,900. We know that:
T
7
C   1  g   $9,900   1  .04  
PV(Growing annuity) =
1  
1  
 
   $50, 086.49
r  g   1  r   .12  .04   1  .12  
PVCCATS = $45,086.58
PV(Costs) = $300,000 – $45,086.58 + $50,086.49 – $100,000/(1.12)7 = $259,764.99
EAC = $259,764.99/PVIFA(12%,7) = $56,919.12
31. Given: Initial cost = $555,000; d = 30%; k = 20%; T = 35%; S = $80,000; n = 5
PVCCATS = $100,085.96
NPV = $0 = – $555,000 – 77,000 + 100,085.96 + (After-tax net revenue)(PVIFA20%,5) +
[(77,000 + 80,000) / 1.205]
After-tax net revenue = $468,819.26 / PVIFA20%,5 = $156,763.65
$156,763.65 = [ (P–v)Q – FC ](1 – tc) = [(P – 6.50)175,000 – 180,000](.65)
359
Solve for P to find: P = $8.91
Intermediate
32. PVCCATS = $66,183.28
Annual after-tax savings = $160,000(1 – .37) = $100,800
In each year there is any additional cash outflow of $2,500 to finance inventory costs. At the end of the
project, there is a recovery of the initial and annual outflows = $21,000 + 4($2,500) = $31,000.
NPV = – $400,000 – $21,000 + $66,183.28 + ($100,800 – $2,500)PVIFA(17%,4) + ($75,000 + $31,000)/1.15 4
= -$24,551 Reject project
33.
CF0=-11,300,000 – 950,000 = -12,250,000
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(40%)
1,408,920
1,828,920
2,358,120
2,500,920
862,920
Net profit after-tax
2,113,380
2,743,380
3,537,180
3,751,380
1,294,380
NWC
5,629,550
7,285,300
9,371,545
9,934,500
3,477,075
∆NWC
4,679,550
1,655,750
2,086,245
562,955
-6,457,425
Net profit after-tax
- (∆NWC or NWC
-2,566,170
1,087,630
1,450,935
3,188,425
4,771,455
recovered)
Salvage value
3,390,000
PVCCATS = $1,799,193.67
NPV
= -$12,250,000 + $1,799,194 – $2,566,170*PVIF(20%, 1) + $1,087,630*PVIF(20%, 2) +
$1,450,935*PVIF(20%, 3) + $3,188,425*PVIF(20%, 4) + $4,771,455*PVIF(20%, 5) +
$3,390,000*PVIF(20%, 5)
= -$6,176,787
The project should be rejected.
34. New excavator costs=$775,000 but SV0=$35,000; Therefore, CF0 = $740,000. Operating revenues =$65,000
and SV10=100,000 – 5,000=$95,000.
PV of CCATS = 740,000(.25)(.4) x (1 + .5(.14))
.14 + .25
1 + .14
- 95,000(.25)(.4) x
.14 + .25
1
10
(1.14)
= $171,521.99
NPV = 65,000(1 – .4) x PVIFA (14%, 10) + 95,000 x PVIF (14%, 10) + 171,521.99 – 740,000
= -$339,424 Do not replace the existing excavator.
35. CF0 = 8,500 – 275 = $8,225, SV4 = 1,100 – 150 = $950, and Operating revenues = $7,600.
PV of CCATS = 8,225(.25)(.24) x (1 + .5(.19))
.19 + .5
1 + .19
- 950(.25)(.24) x
.19 + .2
1
4
(1.19)
360
= $967.45
NPV = 7,600(1 – .24) x PVIFA (19%, 4) + 967.45 + 950 x PVIF (19%, 4) – 8,225 = $8,456.66
The student should buy the new equipment.
36. Underground (U): CF0 = $9.5M, annual costs = $55,000, n=20
PV(CostsU) = [$55,000(1 – .36) – ($9.5M/20)(.36)] x PVIFA (12%, 20) + $9.5M = $8,485,649.56
EACU = $8,485,649.56/PVIFA(12%, 20) = $1,136,048
Above ground (A): CF0 = $4.5M, annual costs = $165,000, n = 9
PV(CostsA) = [$165,000(1 – .36) – ($4.5M/9)(.36)] x PVIFA (12%, 9) + $4.5M = $4,103,578.22
EACA = $4,103,578.22/PVIFA(12%, 9) = $770,155
The above ground system is cheaper for the firm.
37. Product A:
PV of CCATS = 376,000(.2)(.40) x (1 + .5(.16))
.2 + .16
1 + .16
+ (96,000/15)(.40) x PVIFA (16%, 15) = $92,066.27
PV (Net cash flows) = (300,500 – 170,000)(1 – .40) x PVIFA (16%, 15) = $436,558.22
NPV = 92,066 + 436,558 – 14,750(1 – .40) x PVIF (16%, 15) – (96,000 + 376,000) = $55,669
Product B:
PV of CCATS = 422,000(.2)(.40) x (1 + .5(.16)) + (177,500/15)(.40) x PVIFA (16%, 15) = $113,701
.2 + .16
1 + .16
PV (Net cash flows) = (373,600 – 212,000)(1 – .40) x PVIFA (16%, 15) = $540,596
NPV = 113,701 + 540,596 – 112,550(1 – .40) x PVIF (16%, 15) – (177,500 + 422,000) = $47,509
Continue to rent:
NPV = 45,000(1 – .40) x PVIFA (16%, 15) = $150,537
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.
38. 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 = ($750K/.15) + ($1,650,000 – $1,100,000) = $5,550,000. Therefore, P 0 = 5,550,000/275,000=$20.18/share.
39. Operating costsA = $127,000(1 – 0.36) = $81,280
PVCCATSA = $109,115.47
PV(CostsA) = $525,000 + $81,280 x PVIFA(18%, 4) – $109,115.47 = $634,533
Operating costsB = $67,500(1 – 0.36) = $43,200
361
PVCCATSB = $124,703.39
PV(CostsB) = $600,000 + $43,200 x PVIFA(18%, 6) – $124,703.39 = $626,393
If the system will not be replaced when it wears out, then system B should be chosen, because it has a lower
present value of costs.
40. EACA = $634,533 / PVIFA(18%, 4) = $235,880
EACB = $626,393 / PVIFA(18%, 6) = $179,092
If the system is replaced, system B should be chosen because it has a smaller EAC.
41. Let: After-tax net revenue = ATNR = [(P–v)Q – FC ](1 – tc)
Opportunity cost of land = $750,000
Capital gains tax = ($750,000 – $600,000)(0.5)(0.38) = $28,500
Opportunity cost of land net of capital gains tax = $750,000 – $28,500 = $721,500
Salvage value = $475,000
PVCCATS = $614,450.62
NPV = 0 = – $721,500 – $3,100,000 – $500,000 + $614,451 + ATNR*PVIFA(17%, 7) –
60,000*PVIFA(17%, 6) + (475,000 + 860,000)*PVIF(17%, 7)
ATNR = $3,046,882 / PVIFA(17%, 7) = $776,794
ATNR = $776,794 = [(P–v)Q – FC ](1 – tc)
$776,794 = [(P – 0.016)(32,500,000) – 475,000](1 – 0.38); P = $0.06917
42.
SAL5000
12 machines needed
cost/machine=$11,500
Op. Costs=$1,500/yr
SV6 = $1,500
DET1000
10 machines needed
cost/machine=$15,000
Op. Costs=$1,200/yr
SV4 = 0
NPVSAL5000=[-1,500 x PVIFA (14%, 6) – 11,500 + 1,500 x PVIF (14%, 6)](12) = -$199,795.46
NPVDET1000=[-1,200 x PVIFA (14%, 4) – 15,000](10) = -$184,964.55
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 = -199,795 – 199,795 x PVIF (14%, 6) = -$290,819
NPVDET1000 = -184,965 – 184,965 x PVIF (14%, 4) – 184,965 x PVIF (14%, 8) = -$359,320
Choose the SAL5000 model.
43.
X:
C0 = 546,000
Savings/yr. = 198,000
n=5
Y:
C0 = 960,000
Savings/yr. = 246,000
n=10
k = 13%
NPVX = 198,000 x PVIFA (13%,5) – 546,000 = $150,412
With replacement chain:
NPVx = 150,412 + 150,412 x PVIF (13%, 5) = $232,050
NPVY = 246,000 x PVIFA (13%, 10) – 960,000 = $374,856
Choose Mixer Y.
362
Challenge
44. a. Assuming the project lasts four years, the NPV is calculated as follows:
Year
0
1
2
3
After-tax profit
$1,600,000
$1,600,000 $1,600,000
Change in NWC
Capital spending
Total cash flow
(1,000,000)
(5,000,000)
($6,000,000)
0
0
$1,600,000
0
0
$1,600,000
0
0
$1,600,000
4
$1,600,000
1,000,000
0
$2,600,000
PVCCATS = $1,310,439.56
Net present value = $805,716.59
b. Abandoned after one year:
Year
After-tax profit
Change in NWC
Capital spending
Total cash flow
0
1
$1,600,000
(1,000,000)
(5,000,000)
($6,000,000)
1,000,000
4,000,000
$6,600,000
PVCCATS = $321,428.57
Net present value = $214,285.71
Abandoned after two years:
Year
After-tax profit
Change in NWC
Capital spending
Total cash flow
0
1
$1,600,000
2
$1,600,000
(1,000,000)
(5,000,000)
($6,000,000)
0
0
$1,600,000
1,000,000
3,500,000
$6,100,000
1
$1,600,000
2
$1,600,000
3
$1,600,000
0
0
$1,600,000
0
0
$1,600,000
1,000,000
1,750,000
$4,350,000
PVCCATS = $537,774.73
Net present value = $829,228.81
Abandoned after three years:
Year
0
After-tax profit
Change in NWC
Capital spending
Total cash flow
(1,000,000)
(5,000,000)
($6,000,000)
PVCCATS = $965,499.90
Net present value = $765,825.61
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.
45. Cash flows for year 0 = -$250,000
Cash flows for years 1-5 = (25,000 + 26,000)(1 – .38) + (250,000/5)(.38)
= $50,620
PV of after-tax cash flows = $50,620*PVIFA(11%, 5) = $187,086
NPV
= $187,086 – $250,000 = -$62,914
No, they should not renovate.
363
46. PV of CCATS = 175,500(.20)(.40) x (1 + .5(.15)
.15 + .20
(1 + .15)
= $37,498
a.
175,500 – 37,498.14 = PMT x PVIFA(15%, 5)
PMT = $41,168.10
Cost savings = 41,168.10/.6 = $68,613.50
b.
PV of CCATS = 175,500(.20)(.40) x (1 + .5(.15) - 28,500(.20)(.40) x 1
.15 + .20
(1 + .15)
.15 + .20
(1.15)5
= $34,259.39
175,500 – 34,259.39 = PMT x PVIFA (15%, 5) + 28,500/(1.15) 5
PMT = $37,907.28
Cost savings = 37,907.28/.6 = $63,179
47. Cash flow year 0 = -85,000,000 – 4,600,000 – 16,500,000 – 3,300,000(1 – .38) = -$108,146,000
Cash flow years 1-7 = [(17,600)(23,500 – 19,300) – 28,000,000](1 – .38) = $28,470,400
Cash flow year 8 = 28,470,400 + 20,200,000 + 16,500,000 = $65,170,400
PVCCATS (Class 3) = 10,000,000(.05)(.38) x (1 + .5(.15)) - 7,000,000(.05)(.38) x 1
8
.15 + .05
(1 + .15)
.15 + .05
(1.15)
= $670,654
PVCCATS (Class 8) = 75,000,000(.20)(.38) x (1 + .5(.15)) - 8,600,000(.20)(.38) x
1
8
.15 + .20
(1 + .15)
.15 + .20
(1.15)
= $14,613,137
NPV = -108,146,000 + 28,470,400*PVIFA(15%, 7) + 65,170,400*PVIF(15%, 8) + 670,654 + 14,613,137
= $46,890,924
The net present value is positive, so they should produce the robots.
48.
Year
Units/year
Price/unit
Variable cost/unit
Sales
Variable costs
Fixed costs
Net revenue
Taxes (40%)
(S – C)(1 – T)
Year
1
90,000
$360
$227
$32,400,000
(20,430,000)
(175,000)
11,795,000
(4,718,000)
$ 7,077,000
0
2
100,000
$360
$227
3
110,000
$360
$227
$36,000,000
$39,600,000
(22,700,000)
(24,970,000)
(175,000)
(175,000)
13,125,000
14,455,000
(5,250,000)
(5,782,000)
$ 7,875,000
$ 8,673,000
1
2
3
364
4
117,000
$360
$227
$42,120,000
(26,559,000)
(175,000)
15,386,000
(6,154,400)
$ 9,231,600
4
5
65,000
$360
$227
$23,400,000
(14,755,000)
(175,000)
8,470,000
(3,388,000)
$ 5,082,000
5
After-tax revenue
$0
$7,077,000 $7,875,000
$8,673,000 $9,231,600
$5,082,000
Change in NWC
(550,000)
(1,260,000) (1,260,000)
(882,000)
0
3,952,000
Capital spending
(14,200,000)
0
0
0
0
3,550,000
PVCCATS
2,065,198
Total cash flow
($12,684,802) $5,817,000 $6,615,000
$7,791,000 $9,231,600
$12,584,000
Net present value = $8,096,178; 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 = 49.64%. 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 = 46.59019%.
49.
PVCCATS(class 8) = 540,000 x 0.20 x 0.37 x (1+0.5(0.11))
0.20+0.11
1.11
-95,000 x 0.20 x 0.37 x 1/(1.11)5
0.20 + 0.11
= $109,058
NPV = 0 = -$540,000 – $20,000+ (S-C)(0.63)*PVIFA(11%, 5) + $109,058 +
($95,000 + $20,000)/1.115
(S-C)(0.63)*PVIFA(11%, 5) = $382,695
(S-C) = $164,359
50. a.
For the new computer:
For the old computer:
PVCCATS = $143,597.80
$60, 000(.36) $60, 000(.36)

 $36,505.10
PVCCATS =
1.12
(1.12)2
Difference in PVCCATS = $107,092.70
If old computer is replaced now:
Year
0
After-tax cost savings
(S – C)(1 – T)
Capital spending
Total cash flow
(392,907)*
($392,907)
1
70,400
2
70,400
3
70,400
4
70,400
5
70,400
0
$70,400
(75,000)
($4,600)
0
$70,400
0
$70,400
100,000
$170,400
*Initial Capital spending
= Payment for new computer + resale of old computer + gain in PVCCATS
= ($650,000) + $150,000 + $107,092.70 = ($392,907.30)
NPV = -$142,177.61. Do not replace the old computer now.
b.
New Computer:
Year
Cost savings
PVCCATS
Capital spending
Total cash flow
0
143,598
(650,000)
($506,402)
1
70,400
2
70,400
3
70,400
4
70,400
5
70,400
0
$70,400
0
$70,400
0
$70,400
0
$70,400
100,000
$170,400
Net present value = –$195,883.07; EAC = $54,339.87
365
Old Computer:
Year
0
1
2
3
4
5
Depreciation tax shield
Change in NWC
0
Capital spending
(150,000)
Total cash flow
($150,000)
21,600
0
0
$21,600
21,600
0
75,000
$96,600
0
0
0
$0
0
0
0
$0
0
0
0
$0
Net present value = –$53,705.36; EAC = $31,777.36
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.
51.
a. Assume price per unit = $10 and units/year = 175,000
After-tax net revenue/yr. = [(P-V)Q  FC](1  Tc) = [($10 – 6.50)(175,000) – 180,000](0.65) = $281,125
PVCCATS = $100,086; Salvage value = $80,000; Initial working capital increase = $77,000
NPV
= -$555,000 – 77,000 + 100,086 + 281,125*PVIFA(20%, 5) + (77,000 + 80,000)*PVIF(20%, 5)
= $371,917
To break even the number of cartons sold must be less than 175,000.
b. NPV = $0 = -$555,000 – 77,000 + 100,086 + [($10 – 6.50)(Q) – 180,000](0.65)*PVIFA(20%, 5) +
(77,000 + 80,000)*PVIF(20%, 5)
Solve for Q to find: Q  120,336 cartons. At Q = 120,336: NPV = $2.30  $0
c. NPV = $0 = -$555,000 – 77,000 + 100,086 + [($10 – 6.50)(175,000) – FC](0.65)*PVIFA(20%, 5) +
(77,000 + 80,000)*PVIF(20%, 5)
Solve for FC to find: FC  $371,325. At FC = $371,325: NPV = $0.35  $0
Appendix 10A
A1. Nominal discount rate = 12%; Inflation rate = 3%
Real rate = (1.12/1.03) – 1 = 0.0873786 = 8.73786%
Year
0
1
2
3
4
Real Cash Flows
Method 1
Method 2
$5,700.00 $8,400.00
349.51
524.27
339.33
509.00
329.45
494.18
479.78
Discounting the real cash flows at the real rate we get:
Method 1: PV(Costs) = $6,565
Method 2: PV(Costs) = $10,040
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 = $2,733
Method 2: EAC = $3,306
366