CHAPTER 10
Making Capital Investment Decisions
Learning Objectives
LO1
LO2
LO3
LO4
LO5
LO6
LO7
LO8
How to determine relevant cash flows for a proposed project.
How to project cash flows and determine if a project is acceptable.
How to calculate operating cash flow using alternative methods.
How to calculate the present value of a tax shield on CCA.
How to evaluate cost-cutting proposals.
How to analyze replacement decisions.
How to evaluate the equivalent annual cost of a project.
How to set a bid price for a project.
Answers to Concepts Review and Critical Thinking Questions
1.
(LO1) 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.
(LO1) 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.
(LO7) 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 Nyear 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.
(LO1) 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.
(LO1) 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.
(LO1) 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.
(LO1) Pistachio should have realized that abnormally large profits would dwindle as more supply of services
came into the market and competition became more intense.
10-1
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.
(LO1) The $6 million acquisition cost of the land six years ago is a sunk cost. The $6.4 million current aftertax
value of the land is an opportunity cost if the land is used rather than sold off. The $14.2 million cash outlay
and $890,000 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
$6,400,000 + 14,200,000 + 890,000 = $21,490,000
2.
(LO1) Sales due solely to the new product line are:
19,000($13,000) = $247,000,000
Increased sales of the motor home line occur because of the new product line introduction; thus:
4,500($53,000) = $238,500,000
in new sales is relevant. Erosion of luxury motor coach sales is also due to the new portable campers; thus:
900($91,000) = $81,900,000 loss in sales
is relevant. The net sales figure to use in evaluating the new line is thus:
$247,000,000 + 238,500,000 – 81,900,000 = $403,600,000
3.
(LO1) We need to construct a basic Statement of Comprehensive Income. The Statement of Comprehensive
Income is:
Sales
Variable costs
Fixed costs
Depreciation
EBT
Taxes@35%
Net income
4.
$ 830,000
498,000
181,000
77,000
$ 74,000
25,900
$ 48,100
(LO3) To find the OCF, we need to complete the Statement of Comprehensive Income as follows:
Sales
Costs
Depreciation
EBIT
Taxes@34%
Net income
$ 824,500
538,900
126,500
$ 159,100
54,094
$ 105,006
The OCF for the company is:
OCF = EBIT + Depreciation – Taxes
OCF = $159,100 + 126,500 – 54,094
10-2
OCF = $231,506
The depreciation tax shield, also called the CCA tax shield, is the depreciation times the tax rate, so:
Depreciation tax shield = tcDepreciation
Depreciation tax shield = .34($126,500)
Depreciation tax shield = $43,010
The depreciation tax shield shows us the increase in OCF by being able to expense depreciation.
5.
(LO3) To calculate the OCF, we first need to calculate net income. The Statement of Comprehensive Income
is:
Sales
Variable costs
Depreciation
EBT
Taxes@35%
Net income
$ 108,000
51,000
6,800
$ 50,200
17.570
$ 32,630
Using the most common financial calculation for OCF, we get:
OCF = EBIT + Depreciation – Taxes
OCF = $50,200 + 6,800 – 17,570
OCF = $39,430
The top-down approach to calculating OCF yields:
OCF = Sales – Costs – Taxes
OCF = $108,000 – 51,000 – 17,570
OCF = $39,430
The tax-shield approach is:
OCF = (Sales – Costs)(1 – tC) + tCDepreciation
OCF = ($108,000 – 51,000)(1 – .35) + .35(6,800)
OCF = $39,430
And the bottom-up approach is:
OCF = Net income + Depreciation
OCF = $32,630 + 6,800
OCF = $39,430
All four methods of calculating OCF should always give the same answer.
6.
(LO1)
Sales
Variable costs
Fixed costs
CCA
EBIT
Taxes@35%
Net income
$ 940,000
385,400
147,000
104,000
$ 303,600
106,260
$ 197,340
10-3
7.
(LO1, 2)
Cash flow year 0 = -990,000
Cash flow years 1 through 5 = 460,000(1 – .40) = $276,000
PV of CCATS = 990,000(.3)(.4) x (1 + .5(.15))
.15 + .3
1 + .15
= $246,782.61
NPV = -990000 + 276,000 x PVIFA (15%, 5) + 246,782.61
= -990,000 + 276,000 x {1 – [1/1+.15]5/.15} + 246,782.61
= $181,977.42
8.
(LO2)
Cash flow year 0 = -990,000 – 47,200 = -$1,037,200
Cash flow years 1 through 5 = 460,000(1 – .4) = $276,000
Ending cash flow = 100,000 + 47,200 = $147,200
PV of CCATS =
990,000(.3)(.4) x (1 + .5(.15)) –
.15 + .3
1 + .15
100,000(.3)(.4) x
1
.15 + .3
(1.15)5
= $233,524.56
NPV = -1,037,200+ 276,000 x PVIFA(15%, 5) + (147,200)/(1.15)5 + 233,524.56 = $194,703.78
9.
(LO2) The NPV will be smaller because the Capital Cost Allowances are smaller early on.
PV of CCATS = 990,000(.25)(.4) x (1 + .5(.15)) –
.15 + .25
1 + .15
100,000(.25)(.4) x
1
.15 + .25
(1.15)5
= $218,929.28
Therefore with a 25% CCA rate, the
NPV = 194,703.79 + (218,929.28– 233,524.57) = $181,108.50
10.
(LO1) 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.
(LO4) 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 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:
N 2
 d
UCCN  C 1   1  d  where C = installed capital cost; d = CCA rate. Note that the half-year rule has
 2
been incorporated. In this case:
10-4
UCC6 = $548,000 (1 – (0.2/2)) (1-0.2)6-2 = $202,014.72. This is the book value of the asset at the end of the
5th year (beginning of the sixth).
The asset is sold at a (terminal) loss to book value = $202,014.72 – $105,000 = $97,014.72. 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 = 0.35  $97,014.72 = $33,955.15
The after tax salvage value = $105,000 + $33,955.15 = $138,955.15
.
12.
(LO2) A/R fell by $6,140, and inventory increased by $5,640, so net current assets fell by $500. A/P rose by
$6,930.
∆NWC = ∆(CA – CL) = –500 – 6,930 = – 7,430
Net cash flow = S – C – ∆NWC = 102,000 – 43,500 – (– 7,430) = $65,930
13.
(LO3)
CCA1 = 0.3($3.9M/2) = $585,000; CCA2 = 0.3(3.9M – $585,000) = $994,500;
CCA3 = 0.3($3.9M – 585,000 – 994,500) = $696,150.
OCF1 = (S – C)(1 – tc) + tcD = ($2.65M – $840K)(1 – 0.35) + 0.35($585,000) = $1,381,250
OCF2 = (S – C)(1 – tc) + tcD = ($2.65M – $840K)(1 – 0.35) + 0.35($994,500) = $1,524,575
OCF3 = (S – C)(1 – tc) + tcD = ($2.65M – $840K)(1 – 0.35) + 0.35($696,150) = $1,420,152.50
14.
(LO2)
Initial Cash Flow year 0 = -$2,650,000
After-tax net revenue years 1-3 = (S – C)(1 – tC) = ($2,650,000 – 840,000)(1 – 0.35) = $1,176,500
Ending cash flows (year 3) = salvage value = $1,624,350
PV of CCATS = 3,900,000(.3)(.35) x (1 + .5(.12)) –
.12 + .3
1 + .12
1,624,350 (.3)(.35) x
1
.12 + .3
(1.12)3
= $633,722.80
NPV = – $3.9M + $1,176,500(PVIFA12%, 3) + $633,722.80 + $1,624,350/1.123
15.
= $715,657.53
(LO1, 2)
Cash Flow year 0 = -$3,900,000 – 300,000 = -$4,200,000
After-tax net revenue years 1-3 = (S – C)(1 – Tc) = ($2,650,000 – 840,000)(1 – 0.35) = $1,176,500
Ending cash flows (year 3) = recovery of NWC + salvage value = $300,000 + 210,000 = $510,000
PV of CCATS = 3,900,000(.3)(.35) x (1 + .5(.12)) –
.12 + .3
1 + .12
210,000(.3)(.35) x
.12 + .3
1
(1.12)3
= $885,399.39
NPV = –$4.2M + $1,176,500(PVIFA12%,3) + $885,399.39 + $510,000/1.123 = -$125,838.20
10-5
16. (LO1, 2)
Initial Cash Flow year 0 = -785,000 – 140,000 = -$925,000
After-tax net revenue years 1 through 5 = (13,500,000 – 11,700,000 – 215,000)(1 – .35) = $1,030,250
Ending cash flows (year 5) = $140,000
PV of CCATS = 785,000(.25)(.35) x (1 + .5(.19))
.19 + .25
(1 + .19)
= $143,645.55
NPV = -925,000 + 143,645.55 + 1,030,250 x PVIFA(19%,5) + 140,000/(1.19) 5
= $2,427,440.81
Since the NPV is positive, it is probably a good project.
17.
(LO2) Assuming that all outstanding accounts receivable from the previous quarter are collected in the current
quarter, the amount of cash collections in the current quarter is:
$15,200 – 9,500 = $5,700
This can be seen by making collections from current quarter sales a plug number Y in the current quarter’s
cash flow summary for accounts receivable:
Opening balance of A/R
Current quarter sales
Collections of outstanding A/R from previous quarter
Collections from current quarter sales
Closing balance of A/R
X
$15,200
–X
–Y
$15,200 - Y
This gives the equation: 15,200 – Y = X + 9,500
So the total cash collections in the current are:
X + Y = $5,700
18. (LO1) 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. (LO1) The $7.2 million acquisition cost of the land seven years ago is a sunk cost, and so it is not relevant.
The $586,000 grading cost to make the land usable is relevant. The $962,000 current appraisal of the land is an
opportunity cost if the land is used rather than sold off. If the land is sold at $962,000 there will be a capital
loss of (7,200,000 – 962,000) $6,238,000 of which the company can write off 50% of it against any taxable
Capital Gains. This means that at a tax rate of 30% they would be able to write off 30% x $3,119,000 and thus
save $935,700 in taxes.
The $25 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 = $0.962M + $25M + .586M - $.9357M=
$25,612,300.
20. (LO1) Currently the firm has sales of 23,000($14,690) + (38,600) ($43,700) = $2,024,690,000. With the
introduction of a new mid-sized car its sales will change by (28,500) ($33,600) + (12,500) ($14,690) – (8,200)
10-6
($43,700) = $782,885,000. This amount is the incremental sales and is the amount that should be considered
when evaluating the project.
21. (LO1, 2)
Initial Cash Flow 0 = -560,000 – 29,000 = -$589,000
After-tax savings in Operating Costs years 1 through 5 = (165,000) (1 – .34) = $108,900
Ending cash flows (year 5) = $85,000 + 29,000 = $114,000
PV of CCATS = 560,000(.2)(.34) x (1 + .5(.10)) – 85,000(.2)(.34) x
.10 + .2
(1 + .10)
.10 + .2
1
(1.10)5
= $109,200.55
NPV = -589,000 + 109,200.55+ 108,900 x PVIFA(10%, 5) + 114,000/(1.10)5
= $3,802.26
22. (LO1, 2)
Initial cash flow net revenue year 0 = -720,000+ 110,000 = -$610,000
After-tax savings in order processing costs years 1 through 5 = (350,000)(1 – .35) = $227,500
Ending cash flows (year 5) = $280,000 – 110,000 = $170,000
PV of CCATS = $260,000
NPV = 0 = -610,000 + 260,000 + 227,500 x PVIFA(IRR%,5) + 170,000/(1+IRR)5
NPV = 0 = -610,000 + 260,000 + 227,500 x ({1-[1/(1+IRR)]5}/IRR) + 170,000/(1+IRR)5
IRR = 61.85%
23. (LO1, 2)
$300,000 cost saving case
Initial Costs year 0 = -720,000+110,000 = -$610,000
After-tax savings in processing costs years 1 through 5 = (300,000)(1 – .35) = $195,000
Ending cash flows (year 5) = $280,000 – 110,000 = $170,000
PV of CCATS = $114,969.60
NPV = -610,000 + 114,969.60 + 195,000 x PVIFA(20%,5) + 170,000/(1+.20)5 = $156,458.15 Accept the
project.
$240,000 cost saving case
Initial cash flow year 0 = -$610,000
After tax savings in order processing costs years 1 through 5 = (240,000)(1 – .35) = $156,000
Ending cash flows (year 5) = $280,000 – 110,000 = $170,000
PV of CCATS = $114,969.60
NPV = -610,000 + 114,969.60 + 156,000 x PVIFA(20%,5) + 170,000/(1+.20)5 = $39,824.28 Accept the
project.
Required pretax cost saving case (RCS)
Initial cash flow year 0 = -$610,000
Ending cash flows (year 5) = $280,000 – 110,000 = $170,000
PV of CCATS = $114,969.60
NPV = 0 = -610,000 + 114,969.60 + RCS(1 – .35) x PVIFA(20%,5) + 170,000/(1+.20)5 Solve for RCS
10-7
RCS = Required pretax cost saving = $219,513.18.
24.
(LO8)
PV @ 20%
-$1,300,000
376,157.41
-340,000
196,759.26
Aftertax operating income
?
Tax shield on CCA*
146,791.67
NPV
0
Solving for PV of after-tax operating income we obtain:
$ 920,291.67
Dividing by PVIFA(20%,3) we find that annual after-tax operating income must be $436,885.71
Capital Spending
Salvage
Additions to NWC
Cash flow
-1,300,000
650,000
-340,000
340,000
Year
0
3
0
3
1 to 3
Consequently, sales must be $436,885.71/ (1 – .36) + 89($96,000) = $9,226,633.93 in order to break even.
Therefore the selling price should be no less than $9,226,633.92 / 89 or $103,670.04 per system.
*PV of CCATS = 1,300,000(.2)(.36) x (1 + .5(.2))
.2 + .2
1 + .2
– 650,000(.2)(.36) x
1
3
.2 + .2
(1.2)
= $146,791.67
25.
(LO3)
a. EBIT = Sales – cost – depreciation = $425,000 – $96,000 – $375,000  0.2 = $254,000
b. According to the bottom-up approach:
OCF = (S – C – D)(1 – T) + D = $254,000  (1 – 0.35) + $75,000 = $ 240,100
c. According to the tax shield approach:
OCF = (S – C)(1 – T) + TD = ($425,000 – $96,000)  (1 – 0.35) + 0.35  $75,000 = $240,100
26.
(LO3)
Depreciation = $280,000/2 .25 = $35,000
According to the top down approach:
OCF = (S – C) – (S – C – D)  T = ($650,000 – $490,000) – (650,000 – $490,000 – $35,000)  0.38
= $112,500
According to the tax shield approach:
OCF = (S – C)(1 – T) + TD = ($650,000 – $490,000)  (1 – 0.38) + 0.38  $35,000 = $112,500
27.
(LO7)
Method 1: PV @ 13%(Costs) = -$6,700 – 400  PVIFA (13%, 3) = -$7,644.46
Method 2: PV @ 13%(Costs) = -$9,900 – 620  PVIFA (13%, 4) = -$11,744.17
Difference= $4,099.71 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 $4,099.71.
10-8
With replacement:
Method 1: EAC = -7,644.46/PVIFA(13%,3) = -$3,237.60
Method 2: EAC = -11,744.17/PVIFA(13%,4) = -$3,948.32
On this basis, Method 2 is again more expensive.
28.
(LO7)
Method 1: CF0 = -$6,700
PVCCATS = (6,700)(.39)(.25)(1.065)/[(.13 + .25)(1.13)] = $1,620.19
PV(Costs) = -400(1 – .39)PVIFA (13%, 3) – 6,700 + 1,620.19 = -$5,655.93
EAC = -$5,655.93/PVIFA(13%, 3) = -$2,395.41
Method 2: CF0 = -$9,900
PVCCATS = (9,900)(.39)(.25)(1.065)/[(.13 + .25)(1.13)] = $2,394.02
PV(Costs) = -620(1 – .39)PVIFA (13%, 4) – 9,900 + 2,394.02 = -$8,630.93
EAC = -$8,630.93/PVIFA(13%, 4) = -$2,901.67
Method 2 is more expensive.
29. (LO7) To calculate the EAC of the project, we first need the NPV of the project. Notice that we include the
NWC expenditure at the beginning of the project, and recover the NWC at the end of the project. The NPV of
the project is:
NPV = –$270,000 – 25,000 – $42,000(PVIFA11%,5) + $25,000/1.115 = –$435,391.39
Now we can find the EAC of the project. The EAC is:
EAC = –$435,391.39 / (PVIFA11%,5) = –$117,803.98
30. (LO7)
Assuming a carry-forward on taxes:
Both cases: salvage value = $40,000
Techron I: After-tax operating costs = $67,000(1 – 0.35) = $43,550
PVCCATS = (290,000)(.35)(.20)(1.05)/[(.10 + .20)(1.10)] – {[(40,000)(0.20)(0.35)/[0.10 + 0.20]]
(1/1.10)3}= $57,578.64
PV(Costs) = -$290,000 – 43,550(PVIFA10%,3) + (40,000/1.103) + 57,578.64 = -$310,671.17
EAC = -$310,671.17 / (PVIFA10%,3) = -$124,925.48
Techron II: After-tax operating costs = $35,000(1 – 0.35) = $22,750
PVCCATS = (510,000)(.35)(.20)(1.05)/[(.10 + .20)(1.10)] – {[(40,000)(0.20)(0.35)/[0.10 + 0.20]]
(1/1.10)5}= $107,795.64
PV(Costs) = -$510,000 – 22,750(PVIFA10%,5) + (40,000/1.105) + 107,7795.64 = -$463,607.90
EAC = -$463,607.90 / (PVIFA10%,5) = -$122,298.60
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.
(LO7)
Pre-fab segments
Given: Initial cost = $6.5M; d = 4%; k = 11%; T = 35%; S = .25 x $6.5M = $1,625,000;
n = 25
PVCCATS = $565,442.71
Assuming end of year costs: PV(Costs) = -$150,000x(1-.35) x PVIFA(11%, 25) = -$821,120.11
10-9
Total PV(Costs) = -$6,500,000 – $821,120.11 + $565,442.71 + $1,625,000PVIF(11%, 25)
= -$6,636,064.25
EAC = -$6,636,064.25/PVIFA(11%, 25) = -$787,967.88
Carbon-fibre technology
Given: Initial cost = $8.2M; d = 4%; k = 11%; T = 35%; S = .25 x $8.2M = $2,050,000;
n = 40
PVCCATS = $724,467.86
Assuming end of year costs:
PV(Costs) = -$650,000x(1-.35)x[PVIF(11%, 10) + PVIF(11%, 20) + PVIF(11%, 30) + PVIF(11%,
40)] = -$226,158.17
Total PV(Costs) = -$8,200,000 – $226,158.17 + $724,467.86 + $2,050,000PVIF(11%, 40)
= -$7,670,152.27
EAC = -$7,670,152.27/PVIFA(11%, 40) = -$856,899.65
The pre-fab segments represent a lower cost choice.
32. (LO7) The present value of the operating costs can be evaluated as a growing annuity. The first annual aftertax operating cost = C =$32,000(1 – .35) = $20,800. We know that:
PV(Growing annuity) =
C
x (1 – (1+g/1+R)n) = $20,800 x (1 - (1.02/1.11)7) = $103,243,32
(R – g)
(.11-.02)
PVCCATS = $96,023.55
PV(Costs) = -$550,000 + $96,023.55 – $103,243.32 + $98,000/(1.11)7 = -$510,017.24
EAC = -$510,017.24/PVIFA(11%,7) = -$108,233.45
33. (LO8)
Given: Initial cost = $940,000; d = 30%; k = 12%; T = 35%; S = $70,000; n = 5; NWC=$75,000
PVCCATS = $212,480.74
NPV = $0 = – $940,000 – 75,000 + 212,480.74 + (After-tax net revenue)(PVIFA12%,5) +
[(75,000 + 70,000) / 1.125]
After-tax net revenue = $720,242.36 / PVIFA12%,5 = $199,802.24
$199,802.24 = [ (P–v)Q – FC ](1 – tc) = [(P – 9.25)185,000 – 305,000](.65)
Solve for P to find:
P = $12.56
34. (LO5)
PVCCATS = $115,911.97
Annual after-tax savings = $210,000(1 – .35) = $136,500
There is an initial increase in inventory of $20,000, and in each year there is any additional cash outflow of
$3,000 to finance inventory costs. At the end of the project, there is a recovery of the initial and annual
outflows = $20,000 + 4($3,000) = $32,000.
NPV = -$560,000 – $20,000 + $115,911.97+ ($136,500 – $3,000)PVIFA(9%,4) + ($80,000 + $32,000)/1.094 =
$47,758.20
Accept the project.
10-10
Intermediate
35. (LO2) CF0 = -24,000,000 – 1,800,000 = -$25,800,000
ΔNWC= (15% × ΔSales) = – 15% (next period sales – current period sales)
Sales
Variable costs
Fixed costs
Net profit
Taxes(35%)
Net profit after-tax
ΔNWC= (15% × ΔSales)
NWC balance
Cash flow = Net profit
after-tax + (ΔNWC) or
NWC recovered
Salvage value (20%)
Total cash flow
PV(t = 0)
1
35,340,000
24,645,000
1,200,000
9,495,000
3,323,250
6,171,750
-684,000
-2,484,000
5,487,750
2
39,900,000
27,825,000
1,200,000
10,875,000
3,806,250
7,068,750
-1,311,000
-3,795,000
5,757,750
3
48,640,000
33,920,000
1,200,000
13,520,000
4,732,000
8,788,000
-342,000
-4,137,000
8,446,000
4
50,920,000
35,510,000
1,200,000
14,210,000
4,973,500
9,236,500
2,679,000
-1,458,000
11,915,500
5
33,060,000
23,055,000
1,200,000
8,805,000
3,081,750
5,723,250
1,458,000
0
7,181,250
5,487,750
4,650,635.59
5,757,750
4,135,126.40
8,446,000
5,140,496.35
11,915,500
6,145,882.34
4,800,000
11,981,250
5,237,114.80
PVCCATS = $3,697,357.13
NPV
= -$25,800,000 + $3,697,357.13 + $4,650,635.59+ $4,135,126.40+ $5,140,496.35+ $6,145,882.34
+ $5,237,114.80
= $3,206,612.61
The project should be accepted because NPV is positive.
36. (LO6) New excavator costs=$950,000 but SV0=$50,000; Therefore, CF0 = $900,000. Operating revenues
=$90,000 and SV10=175,000 – 3,000=$172,000.
PV of CCATS = 900,000(.25)(.35) x (1 + .5(.14)) - 172,000(.25)(.35) x
1
10
.14 + .25
1 + .14
.14 + .25
(1.14)
= $179,114.95
NPV = 90,000(1 – .35) x PVIFA (14%, 10) + 172,000 x PVIF (14%, 10) + 179,114.95 – 900,000
= -$369,345.35
Do not replace the existing excavator.
37. (LO6)
CF0 = 12,000 – 500 = $11,500, SV4 = 1,600 – 250 = $1,350, and Operating revenues = $8,000.
PV of CCATS = 11,500(.25)(.22) x (1 + .5(.15))
.15 + .25
1 + .15
– 1,350(.25)(.22) x
1
4
.15 + .25
(1.15)
= $1372
NPV = 8,000(1 – .22) x PVIFA (15%, 4) +1372 + 1,350 x PVIF (15%, 4) – 11,500
= $8,458.93
The student should buy the new equipment.
10-11
38. (LO7) Underground (U): CF0 = $9.2M, annual costs = $80,000, n=20
PV(CostsU) = [-$80,000(1 – .39) + ($9.2M/20)(.39)] x PVIFA (13%, 20) – $9.2M = -$7,988,559.57
EACU = -$7,988,559.57/PVIFA(13%, 20) = -$1,137,201.72
Above ground (A): CF0 = $6.8M, annual costs = $190,000, n = 9
PV(CostsA) = [-$190,000(1 – .39) + ($6.8M/9)(.39)] x PVIFA (13%, 9) – $6.8M = -$5,403,772.29
EACA = -$5,403,772.29/PVIFA(13%, 9) = -$1,053,027.17
The above ground system is cheaper for the firm.
39. (LO1, 2)
Product A:
PV of CCATS = 382,000(.2)(.36) x (1 + .5(.16))
.2 + .16
1 + .16
+ (102,000/15)(.36) x PVIFA (16%, 15) = $84,779.75
PV (Net cash flows) = (323,100 – 174,700)(1 – .36) x PVIFA (16%, 15) = $529,534.52
NPV = 84,779.75 + 529,534.52 – 19,200(1 – .36) x PVIF (16%, 15) – (102,000 + 382,000) = $61,803.06
Product B:
PV of CCATS = 456,000(.2)(.36) x (1 + .5(.16)) + (192,250/15)(.36) x PVIFA (16%, 15) = $110,635.50
.2 + .16
1 + .16
PV (Net cash flows) = (396,000 – 235,700)(1 – .36) x PVIFA (16%, 15) = $571,997.20
NPV = 110,635.50 + 571,997.20 – 129,250(1 – .36) x PVIF (16%, 15) – (192,250 + 456,000) = $25,454.98
Continue to rent:
NPV = 75,000(1 – .36) x PVIFA (16%, 15) = $267,621.90
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. (LO1, 2) 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 = ($820K/.16) + ($1,900,000 – $1,400,000) = $5,625,000.
Therefore, P0 = $5,625,000/385,000=$14.61/share.
41. (LO1, 2)
Operating costsA = $135,000(1 – 0.34) = $89,100
PVCCATSA = $82,744.90
PV(CostsA) = -$360,000 – $89,100 x PVIFA(12%, 4) + $82,744.90 = -$547,882.93
Operating costsB = $98,000(1 – 0.34) = $64,680
PVCCATSB = $98,834.18
10-12
PV(CostsB) = -$430,000 – $64,680 x PVIFA(12%, 6) + $98,834.18 = -$597,091.64
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. (LO1, 2)
EACA = -$547,882.93 / PVIFA(12%, 4) = -$180,381.93
EACB = -$597,091.85 / PVIFA(12%, 6) = -$145,228.04
If the system is replaced, system B should be chosen because it has a smaller EAC.
43. (LO8)
Let: After-tax net revenue = ATNR = [(P–v)Q – FC ](1 – tc)
v = $0.009 per stamp
Q = 140 million
FC = $961,000
Tax rate = 34%
Required rate of return = 11%
After-tax opportunity cost of land today = $1,800,000
After-tax salvage value of land in 5 years = $1,800,000
Initial investment = $4,600,000
Salvage value = $756,000
NWC 0 = $569,000
NWC 1 – 5 = $68,000
All NWC recoverable in year 5
PV of Tax shield using straight line dep. = (($4,600,000 – 756,000)/5)(0.34)PVIFA(11%, 5) = $966,077.91
NPV = 0 = – $1,800,000 – $4,600,000 – $569,000 + $966,077.91 + ATNR*PVIFA(11%, 5) –
68,000*PVIFA(11%, 5) + (756,000 + (569,000 + 5x 68,000) + 1,800,000)*PVIF(11%, 5)
ATNR = $6,552,020.48 / PVIFA(11%, 5) = $1,772,787.51
ATNR = $1,772,787.51 = [(P–v)Q – FC ](1 – tc)
$1,772,787.51= [(P – 0.009)(140,000,000) – 961,000](1 – 0.34)
P = $0.0351 per stamp
44. (LO7)
SAL5000
12 machines needed
cost/machine=$15,900
Op. Costs=$1,850/yr
SV6 = $1,300
DET1000
10 machines needed
cost/machine=$19,000
Op. Costs=$1,700/yr
SV4 = 0
NPVSAL5000=[-1,850 x PVIFA (15%, 6) – 15,900 + 1,300 x PVIF (15%, 6)](12) = -$268,071.21
NPVDET1000=[-1,700 x PVIFA (15%, 4) – 19,000](10) = -$238,534.63
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 two more times (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 = -268,071.21– 268,071.21 / PVIF (15%, 6) = -$383,965.79
NPVDET1000 = -238,534.63– 238,534.63/ PVIF (15%, 4) – 238,534.63/ PVIF (15%, 8) = -$452,894.98
Choose the SAL5000 model.
10-13
Note that we would have arrived at the same recommendation, namely choose the SAL model, if we had
calculated EAC values for the two alternatives. The EAC method implicitly assumes the replacement chain that
we have used here.
45. (LO7)
X:
C0 = 743,000
Savings/yr. = 296,000
n=6
Y:
C0 = 989,000
Savings/yr. = 279,000
n=10
k = 12%
NPVX = 296,000 x PVIFA (12%,6) – 743,000 = $473,976.57
With replacement chain of 5 links (5 x 6 = 30):
NPVX = 473,976.57+ 473,976.57x PVIF (12%, 6) + 473,976.57x PVIF (12%, 12) + 183,213.43 x PVIF (12%,
18) + 473,976.57x PVIF (12%, 24)
= $928,628.12
NPVY = 279,000 x PVIFA (12%, 10) – 989,000 = $587,412.22
With replacement chain of 3 links (3 x 10 = 30):
NPVY = 587,412.22+ 587,412.22 x PVIF (12%, 10) + 587,412.22 x PVIF (12%, 20)
= 837,438.48
Choose Mixer Y.
Challenge
46. (LO1, 2)
a. Assuming the project lasts four years, the NPV is calculated as follows:
Year
0
1
2
3
After-tax profit
$1,525,000
$1,525,000 $1,525,000
Change in NWC
Capital spending
Total cash flow
(2,000,000)
(7,000,000)
($9,000,000)
0
0
$1,525,000
0
0
$1,525,000
PVCCATS = $1,941,860.08
Net present value = -$1,295,433.70
b. Abandoned after one year:
Year
After-tax profit
Change in NWC
Capital spending
Total cash flow
0
1
$1,525,000
(2,000,000)
(7,000,000)
($9,000,000)
2,000,000
5,000,000
$8,525,000
PVCCATS = $639,472.37
Net present value = -$816,279.85
10-14
0
0
$1,525,000
4
$1,525,000
2,000,000
0
$3,525,000
Abandoned after two years:
Year
After-tax profit
Change in NWC
Capital spending
Total cash flow
0
1
$1,525,000
2
$1,525,000
(2,000,000)
(7,000,000)
($9,000,000)
0
0
$1,525,000
2,000,000
4,740,000
$8,265,000
1
$1,525,000
2
$1,525,000
3
$1,525,000
0
0
$1,525,000
0
0
$1,525,000
2,000,000
2,600,000
$6,125,000
PVCCATS = $849,237.47
Net present value = -$328,497.67
Abandoned after three years:
Year
0
After-tax profit
Change in NWC
Capital spending
Total cash flow
(2,000,000)
(7,000,000)
($9,000,000)
PVCCATS = $1,411,480.56
Net present value = -$799,730.99
The decision to abandon is an important variable when evaluating the NPV of a project. This particular project
should not proceed because all NPV values are negative, but it can be seen that the option to abandon results in
the maximum NPV occurring after two years.
47. (LO1, 2)
Cash flows for year 0 = -$364,000
Cash flows for years 1-5 = (36,000 + 43,000)(1 – .36) + (364,000/5)(.36)
= $76,768
PV of after-tax cash flows = $76,768*PVIFA(13%, 5) = $270,010.81
NPV
= $270,010.81 – $364,000
= -$93,989.19
No, they should not renovate.
48. (LO5, 8)
PV of CCATS = 620,000(.20)(.35) x (1 + .5(.11)
.11 + .20
(1 + .11)
= $133,063.06
a.
620,000 – 133,063.06 = PMT x PVIFA(11%, 5)
PMT = $131,750.68
Cost savings = 131,750.68 /(1 - .35) = $202,693.35
b.
PV of CCATS = 620,000(.20)(.35) x (1 + .5(.11) - 90,000(.20)(.35) x 1
5
.11 + .20
(1 + .11)
.11 + .20
(1.11)
= $121,002.60
5
620,000 – 121,002.60= PMT x PVIFA (11%, 5) + 90,000/(1.11)
PMT = $120,562.55
Cost savings = 120,562.55/ (1 - .35) = $185,480.85
10-15
49. (LO1, 2)
Cash flow year 0 = -96,500,000 – 7,200,000 – 19,200,000 – 4,600,000(1 – .39) = -$125,706,000
Cash flow years 1-7 = [(19,600)(45,900 – 35,000) – 39,100,000](1 – .39) = $106,469,400
Cash flow year 8 = 106,469,400 + 27,900,000 + 19,200,000 = $153,569,400
PVCCATS (Class 3) = 16,000,000(.05)(.39) x (1 + .5(.17)) - 8,700,000(.05)(.39) x 1
8
.17 + .05
(1 + .17)
.17 + .05
(1 + .17)
= $1,095,545.47
PVCCATS (Class 8) = 80,500,000(.20)(.39) x (1 + .5(.17)) - 12,000,000(.20)(.39) x
1
8
.17 + .20
(1 + .17)
.17 + .20
(1 +.17)
= $15,016,964.95
NPV = -125,706,000 + 106,469,400*PVIFA(17%, 7) + 153,569,400*PVIF(17%, 8) + 1,095,545.47+
15,016,964.95
= $351,753,827.90
The net present value is positive, so they should produce the robots.
50.
(LO2)
Year
Units/yr
Price/unit
Vcost/unit
1
107,000
395
295
2
123,000
395
295
3
134,000
395
295
4
156,000
395
295
5
95,500
395
295
Sales
VC
FC
Net Rev
Taxes
(S-C)(1-T)
42,265,000
31,565,000
192,000
10,508,000
4,203,200
6,304,800
48,585,000
36,285,000
192,000
12,108,000
4,843,200
7,264,800
52,930,000
39,530,000
192,000
13,208,000
5,283,200
7,924,800
61,620,000
46,020,000
192,000
15,408,000
6,163,200
9,244,800
37,722,500
28,172,500
192,000
9,358,000
3,743,200
5,614,800
0
1
6,304,800
2
7,264,800
3
7,924,800
4
9,244,800
5
5,614,800
-800,000
-19,500,000
-2,528,000
-1,738,000
-3,476,000
0
8,542,000
5,850,000
3,776,800
5,526,000
4,448,800
9,246,800
20,006,800
Year
A-T Rev
Ch in NWC
Cap Spend
PVCCATS
Total CF
2,902,121.33
-17,397,878.67
Net present value = $2,861,990.17
An approximate solution for the IRR can be found by assuming that the PVCCATS is discounted at the
23% cost of capital of the firm, so that the PVCCATS value in the table is held constant. In this case: IRR
= 28.04%.
The alternative is to enter the data into a spreadsheet and search for the rate that produces a NPV = 0,
where PVCCATS is discounted at the IRR.
10-16
51.
(LO5)
PVCCATS(class 8) = 865,000 x 0.20 x 0.36 x (1+0.5(0.135)) –
0.20 + 0.135
1 + .135
138,000 x 0.20 x 0.36 x 1/(1.135)6
0.20 + 0.135
= $160,980.42
NPV = 0 = -$865,000 – $58,000+ (S-C)(1-.36)*PVIFA(13.5%, 6) + $160,980.42 +
($138,000 + $58,000)/1.1356
(S-C)(0.64)*PVIFA(13.5%, 6) = $670,338.25
(S-C) = $265,669.58
52. (LO6)
a.
For the new computer: PVCCATS = 368,000 x 0.30 x 0.38 x (1+0.5(0.13)) –
0.30 + 0.13
1 + .13
198,000 x 0.30 x 0.38 x 1/(1.13)5 = $63,459.66
0.30 + 0.13
For the old computer: PVCCATS = 140,000(.38) + 140,000(.38)
(1+.13)
(1+.13)2
= $88,743.05
Difference in PVCCATS = -$25,283.39
If old computer is replaced now:
Year
After-tax cost savings
(S – C)(1 – T)
Capital spending
Total cash flow
0
1
80,600
2
80,600
3
80,600
4
80,600
5
80,600
(208,283.39)*
($208,283.39)
0
$80,600
(95,000)
($14,400)
0
$80,600
0
$80,600
198,000
$278,600
*Initial Capital spending
= Payment for new computer + resale of old computer + loss in PVCCATS
= -$368,000 + $190,000 – $25,283.39 = -$208,283.39
NPV = $113,272.98 Replace the old computer now.
b.
New Computer:
Year
Cost savings
PVCCATS
Capital spending
Total cash flow
0
63,459.66
(368,000)
($304,540.34)
1
80,600
2
80,600
3
80,600
4
80,600
5
80,600
0
$80,600
0
$80,600
0
$80,600
0
$80,600
198,000
$278,600
Net present value = $86,414.97
EAC = $24,569.03
10-17
Old Computer:
Year
0
1
2
3
4
5
Depreciation tax shield
Change in NWC
0
Capital spending
(190,000)
Total cash flow
($190,000)
53,200
0
0
$53,200
53,200
0
95,000
$148,200
0
0
0
$0
0
0
0
$0
0
0
0
$0
Net present value = -$26,858.02
EAC = -$16,100.94
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 replace the old computer.
53.
(LO8)
a. Assume price per unit = $15 and units/year = 185,000
After-tax net revenue/yr. = [(P-V)Q  FC](1  Tc) = [($15 – 9.25)(185,000) – 305,000](0.65) = $493,187.50
PVCCATS = $212,480.74; Salvage value = $70,000; Initial working capital increase = $75,000
NPV
= -$940,000 – 75,000 + 212,480.74 + 493,187.50*PVIFA(12%, 5) + (70,000 + 75,000)*PVIF(12%, 5)
= $1,057,588.20
The positive NPV tells us that to break even the number of cartons sold must be less than 185,000, and that
our costs are lower than revenues.
b. NPV = $0 = -$940,000 – 75,000 + 212,480.74 + [($15 – 9.25)(Q) – 305,000](0.65)*PVIFA(12%, 5) +
(70,000 + 75,000)*PVIF(12%, 5)
Solve for Q to find: Q  106,502.27 cartons. At Q = 106,502.27 : NPV  $0
c. NPV = $0 = -$940,000 – 75,000 + 212,480.74 + [($15 – 9.25)(185,000) – FC](0.65)*PVIFA(12%, 5) +
(70,000 + 75,000)*PVIF(12%, 5)
Solve for FC to find: FC  $756,361.94. At FC = $756,361.94: NPV  $0
Appendix 10A
A1. Nominal discount rate = 13%; Inflation rate = 3%
Real rate = (1.13/1.03) – 1 = 0.0970874 = 9.70874%
Year
0
1
2
3
4
Real Cash Flows
Method 1
Method 2
$6,700.00 $9,900.00
388.35
601.94
377.04
584.41
366.06
567.39
550.86
Discounting the real cash flows at the real rate we get:
10-18
Method 1: PV(Costs) = -$7,644.46
Method 2: PV(Costs) = -$11,744.17
Note that these are the identical PV values as obtained in the earlier Problem 27. When nominal cash flows are
discounted by a nominal discount rate, the same PV is obtained as when real cash flows are discounted by a
real discount rate.
However, we do not get the same EAC values as before:
Method 1: EAC = -7,644.46 / PVIFA(9.71%,3) = -$3,058.20
Method 2: EAC = -11,744.17 / PVIFA(9.71%,4) = -$3,681.61
The EAC values from Problem 27 for Method 1 and 2 were -3,237.60 and -3,948.32, respectively. The
differences arise because, with inflation, the PVIFA values with the real rate are larger than with the nominal
rate since the real rate of 9.71% is lower than the nominal rate of 13%.
10-19