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Ryerson University

Economics

ECN 104

Vikraman Baskaran

Fall

Description

CHAPTER 10
Making Capital Investment Decisions
Learning Objectives
LO1 How to determine relevant cash flows for a proposed project.
LO2 How to project cash flows and determine if a project is acceptable.
LO3 How to calculate operating cash flow using alternative methods.
LO4 How to calculate the present value of a tax shield on CCA.
LO5 How to evaluate cost-cutting proposals.
LO6 How to analyze replacement decisions.
LO7 How to evaluate the equivalent annual cost of a project.
LO8 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 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. (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 tcD.
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 $5 million acquisition cost of the land six years ago is a sunk cost. The $5.3 million current aftertax
value of the land is an opportunity cost if the land is used rather than sold off. The $11.6 million cash outlay
and $425,000 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
$5,300,000 + 11,600,000 + 425,000 = $17,325,000
2. (LO1) Sales due solely to the new product line are:
19,000($12,000) = $228,000,000
Increased sales of the motor home line occur because of the new product line introduction; thus:
4,500($45,000) = $202,500,000
in new sales is relevant. Erosion of luxury motor coach sales is also due to the new mid-size campers; thus:
900($85,000) = $76,500,000 loss in sales
is relevant. The net sales figure to use in evaluating the new line is thus:
$228,000,000 + 202,500,000 – 76,500,000 = $354,000,000
3. (LO1) We need to construct a basic income statement. The income statement is:
Sales $ 740,000
Variable costs 444,000
Fixed costs 173,000
Depreciation 75,000
EBT $ 48,000
[email protected]% 16,800
Net income $ 31,200
4. (LO3) To find the OCF, we need to complete the income statement as follows:
Sales $ 876,400
Costs 547,300
Depreciation 128,000
EBIT $ 201,100
[email protected]% 68,374
Net income $ 132,726
The OCF for the company is:
OCF = EBIT + Depreciation – Taxes
OCF = $201,100 + 128,000 – 68,374
10-2 OCF = $260,726
The depreciation tax shield, also called the CCA tax shield, is the depreciation times the tax rate, so:
Depreciation tax shield =ct Depreciation
Depreciation tax shield = .34($128,000)
Depreciation tax shield = $43,520
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 income statement is:
Sales $ 96,000
Variable costs 49,000
Depreciation 4,500
EBT $ 42,500
[email protected]% 14,875
Net income $ 27,625
Using the most common financial calculation for OCF, we get:
OCF = EBIT + Depreciation – Taxes
OCF = $42,500 + 4,500 – 14,875
OCF = $32,125
The top-down approach to calculating OCF yields:
OCF = Sales – Costs – Taxes
OCF = $96,000 – 49,000 – 14,875
OCF = $32,125
The tax-shield approach is:
OCF = (Sales – Costs)(1 – t ) + t Depreciation
C C
OCF = ($96,000 – 49,000)(1 – .35) + .35(4,500)
OCF = $32,125
And the bottom-up approach is:
OCF = Net income + Depreciation
OCF = $27,625 + 4,500
OCF = $32,125
All four methods of calculating OCF should always give the same answer.
6. (LO1)
Sales $ 860,000
Variable costs 395,600
Fixed costs 162,000
CCA 108,000
EBIT $ 194,400
[email protected]% 68,040
Net income $ 126,360
10-3 7. (LO1, 2)
Cash flow year 0 = -925,000
Cash flow years 1 through 5 = 490,000(1 – .40) = $294,000
PV of CCATS = 925,000(.3)(.4) x (1 + .5(.12))
.12 + .3 1 + .12
= $250,127.55
NPV = -925,000 + 294,000 x PVIFA (12%, 5) +5250,127.55
= -925,000 + 294,000 x {1 – [1/1+.12] /.12} + 250,127.55
= $384,931.75
8. (LO2)
Cash flow year 0 = -925,000 – 36,200 = -$961,200
Cash flow years 1 through 5 = 490,000(1 – .4) = $294,000
Ending cash flow = 100,000 + 36,200 = $136,200
PV of CCATS = 925,000(.3)(.4) x (1 + .5(.12)) –
.12 + .3 1 + .12
100,000(.3)(.4) x 1
.12 + .3 (1.12)
= $233,915.36
NPV = -961,200 + 294,000 x PVIFA(12%, 5) + (136,200)/(1.12) + 233,915.36 = $409,803.10
9. (LO2) The NPV will be smaller because the Capital Cost Allowances are smaller early on.
PV of CCATS = 925,000(.25)(.4) x (1 + .5(.12)) –
.12 + .25 1 + .12
100,000(.25)(.4) x 1
.12 + .25 (1.12)5
= $221,271.28
Therefore with a 25% CCA rate, the
NPV = 409803.1 + (221,271 – 233,915) = $397,159
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 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 year is given by the formula:
UCC = C 1− d (−d )N −2
N 2 where C = installed capital cost; d = CCA rate. Note that the half-year rule has
been incorporated. In this case:
10-4 UCC =6$468,000 (1 – (0.2/2)) (1-0.2) 6-2= $172,523.52. This is the book value of the asset at the end of the 5 th
year (beginning of the sixth).
The asset is sold at a (terminal) loss to book value = $172,523.52 – $72,000 = $100,523.52. 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 × $100,523.52 = $35,183.23.
The after tax salvage value = $72,000 + $35,183.23 = $107,183.23.
12. (LO2) A/R fell by $5,140, and inventory increased by $3,640, so net current assets fell by $1,500. A/P rose
by $5,930.
∆NWC = ∆(CA – CL) = –1,500 – 5,930 = – 7,430
Net cash flow = S – C – ∆NWC = 67,000 – 28,500 – (– 7,430) = $45,930
13. (LO3)
CCA = 0.3($4.2M/2) = $630,000 ; CCA = 0.3(4.2M – $630,000) = $1,071,000;
1 2
CCA =30.3($4.2M – 630,000 – 1,071,000) = $749,700.
OCF =1(S – C)(1 – t )c+ t Dc= ($3.1M – $990K)(1 – 0.35) + 0.35($630,000) = $1,592,000
OCF =2(S – C)(1 – t )c+ t Dc= ($3.1M – $990K)(1 – 0.35) + 0.35($1,071,000) = $1,746,350
OCF =3(S – C)(1 – t ) + t D = ($3.1M – $990K)(1 – 0.35) + 0.35($749,700) = $1,633,895
c c
14. (LO2)
After-tax net revenue year 0 = -$4,200,000
After-tax net revenue years 1-3 = (S – C)(1 – t C = ($3,100,000 – 990,000)(1 – 0.35) = $1,371,500
Ending cash flows (year 3) = salvage value = $1,749,000
PV of CCATS = 4,200,000(.3)(.35) x (1 + .5(.12)) –
.12 + .3 1 + .12
1,749,300(.3)(.35) x 1
.12 + .3 (1.12)3
= $682,470.70
NPV = – $4.2M + $1,371,500(PVIFA 12%, 3 + $682,471 + $1,749,000/1.12 3
= $1,021,699
15. (LO1, 2)
After-tax net revenue year 0 = -$4,200,000 – 300,000 = -$4,500,000
After-tax net revenue years 1-3 = (S – C)(1 – T )c= ($3,100,000 – 990,000)(1 – 0.35) = $1,371,500
Ending cash flows (year 3) = recovery of NWC + salvage value = $300,000 + 210,000 = $510,000
PV of CCATS = 4,200,000(.3)(.35) x (1 + .5(.12)) –
.12 + .3 1 + .12
210,000(.3)(.38) x 1
.12 + .3 (1.12)3
= $956,381.54
10-5 NPV = –$4.5M + $1,371,000(PVIFA 12%,3+ $956,382 + $510,000/1.12 = $113,501
16. (LO1, 2)
After-tax net revenue year 0 = -715,000 – 140,000 = -$855,000
After-tax net revenue years 1 through 5 = (9,100,000 – 7,700,000 – 195,000)(1 – .35) = $783,250
Ending cash flows (year 5) = $140,000
PV of CCATS = 715,000(.25)(.35) x (1 + .5(.19))
.19 + .25 (1 + .19)
= $130,836.40
5
NPV = -855,000 + 130,836 + 783,250 x PVIFA(19%,5) + 140,000/(1.19)
= $1,729,396
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:
$9,200 – 5,500 = $3,700
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 X
Current quarter sales $9,200
Collections of outstanding A/R from previous quarter –X
Collections from current quarter sales –Y
Closing balance of A/R X + $5,500
This gives the equation: 9,200 – Y = X + 5,500
So the total cash collections in the current are:
X + Y = $3,700
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 $6.5 million acquisition cost of the land seven years ago is a sunk cost, and so it is not relevant.
The $515,000 grading cost to make the land usable is also not relevant, because that cost is already reflected in
the appraised market value of the land. The $985,000 current appraisal of the land is an opportunity cost if the
land is used rather than sold off. The $22 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 +
$22M = $22.985 million.
20. (LO1) Currently the firm has sales of 23,000($11,850) + (35,200) ($41,800) = $1,743,910,000. With the
introduction of a new mid-sized car its sales will change by (24,500) ($30,600) + (9,500) ($11,850) – (6,200)
($41,800) = $603,115,000. This amount is the incremental sales and is the amount that should be considered
when evaluating the project.
10-6 21. (LO1, 2)
After-tax net revenue year 0 = -440,000 – 34,000 = -$474,000
After-tax net revenue years 1 through 5 = (130,000) (1 – .34) = $85,800
Ending cash flows (year 6) = $60,000 + 34,000 = $94,000
PV of CCATS = 440,000(.2)(.34) x (1 + .5(.10)) – 60,000(.2)(.34) x 1
.10 + .2 (1 + .10) .10 + .2 (1.10)5
= $81,333.25
NPV = -474,000 + 86,755 + 85,800 x PVIFA(10%, 5) + 94,000/(1.10) 5
= -9050.64
22. (LO1, 2)
After-tax net revenue year 0 = -840,000+ 125,000 = -$715,000
After-tax net revenue years 1 through 5 = (330,000)(1 – .35) = $214,500
Ending cash flows (year 5) = $260,000 – 125,000 = $135,000
PV of CCATS = $240,000
5
NPV = 0 = -715,000 + 240,000 + 214,500 x PVIFA(IRR%,5) + 135,000/(1+IRR)
NPV = 0 = -715,000 + 240,000 + 214,500 x ({1-[1/(1+IRR)] }/IRR) + 135,000/(1+IRR) 5
IRR = 38.42%
23. (LO1, 2)
$380,000 cost saving case
After-tax net revenue year 0 = -840,000+125,000 = -$715,000
After-tax net revenue years 1 through 5 = (380,000)(1 – .35) = $247,000
Ending cash flows (year 5) = $260,000 – 125,000 = $135,000
PV of CCATS = $139,757
NPV = -715,000 + 139,757 + 247,000 x PVIFA(20%,5) + 135,000/(1+.20) = $217,692 Accept the project.
$280,000 cost saving case
After-tax net revenue year 0 = -$715,000
After-tax net revenue years 1 through 5 = (280,000)(1 – .35) = $182,000
Ending cash flows (year 5) = $260,000 – 125,000 = $135,000
PV of CCATS = $139,757
5
NPV = -715,000 + 139,757 + 182,000 x PVIFA(20%,5) + 135,000/(1+.20) = $23,302 Accept the project.
Required pretax cost saving case (RCS)
After-tax net revenue year 0 = -$715,000
Ending cash flows (year 5) = $260,000 – 125,000 = $135,000
PV of CCATS = $139,757
5
NPV = 0 = -715,000 + 139,757 + RCS(1 – .35) x PVIFA(20%,5) + 135,000/(1+.20) Solve for RCS
RCS = Required pretax cost saving = $268,013.
10-7 24. (LO8)
Cash flow Year PV @ 20%
Capital Spending -1,000,000 0 -$1,000,000
Salvage 500,000 3 289,351
Additions to NWC -220,000 0 -220,000
220,000 3 127,315
Aftertax operating income 1 to 3 ?
Tax shield on CCA* 112,917
NPV 0
Solving for PV of after-tax operating income we obtain: $ 690,417
Dividing by PVIFA(20%,3) we find that annual after-tax operating income must be $327,758
Consequently, sales must be $327,758 / (1 – .36) + 75($80,000) = $6,512,122 in order to break even. Therefore
the selling price should be no less than $6,512,122 / 75 or $86,828.30 per system.
*PV of CCATS = 1,000,000(.2)(.36) x (1 + .5(.2))
.2 + .2 1 + .2
– 500,000(.2)(.36) x 1
.2 + .2 (1.2)
= $112,916.67
25. (LO3)
a. EBIT = Sales – cost – depreciation = $225,000 – $92,000 – ($250,000/2) × 0.2 = $108,000
b. According to the bottom-up approach:
OCF = (S – C – D)(1 – T) + D = $108,000 × (1 – 0.35) + $25,000 = $ 95,200
c. According to the tax shield approach:
OCF = (S – C)(1 – T) + TD = ($225,000 – $92,000) × (1 – 0.35) + 0.35 × $25,000 = $95,200
26. (LO3)
Depreciation = $240,000/2 ×.25 = $30,000
According to the top down approach:
OCF = (S – C) – (S – C – D) × T = ($450,000 – $290,000) – ($450,000 – $290,000 – $30,000) × 0.38
= $110,600
According to the tax shield approach:
OCF = (S – C)(1 – T) + TD = ($450,000 – $290,000) × (1 – 0.38) + 0.38 × $30,000 = $110,600
27. (LO7)
Method 1: PV @ 13%(Costs) = -$6,200 – 400 × PVIFA (13%, 3) = -$7,144.46
Method 2: PV @ 13%(Costs) = -$9,100 – 620 × PVIFA (13%, 4) = -$10,994.17
Difference= $3,799.71 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 $3,799.71.
With replacement: Method 1: EAC = -7,144.46/ PVIFA(13%,3) = -$3.025.84
10-8 Method 2: EAC = -10,994.17/ PVIFA(13%,4) = -$3,679.37
On this basis, Method 2 is again more expensive.
28. (LO7)
Method 1: CF = -$6,200
0
PVCCATS = (6,200)(.39)(.25)(1.065)/[(.13 + .25)(1.13)] = $1,499.28
PV(Costs) = -400(1 – .39)PVIFA (13%, 3) – 6,200 + 1,499.28 = -$5,276.84
EAC = -$5,276.84/PVIFA(13%, 3) = -$2,234.86
Method 2: CF = -09,100
PVCCATS = (9,100)(.39)(.25)(1.065)/[(.13 + .25)(1.13)] = $2,200.56
PV(Costs) = -620(1 – .39)PVIFA (13%, 4) – 9,100 + 2,200.56 = -$8,024.38
EAC = -$8,024.38/PVIFA(13%, 4) = -$2,697.75
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 = –$240,000 – 20,000 – $32,000(PVIFA 11%,5 + $20,000/1.11 = –$366,399.68
Now we can find the EAC of the project. The EAC is:
EAC = –$366,399.68 / (PVIFA 11%,5 = –$99,136.87
30. (LO7)
Assuming a carry-forward on taxes:
Both cases: salvage value = $20,000
Techron I: After-tax operating costs = $41,000(1 – 0.35) = $26,650
PVCCATS = (330,000)(.35)(.20)(1.07)/[(.14 + .20)(1.14)] – {[(20,000)(0.20)(0.35)/[0.14 + 0.20]]
3
(1/1.14) }= $60,990.06
PV(Costs) = -$330,000 – 26,650(PVIFA 14%,3+ (20,000/1.14 ) + 60,996.06 = -$317,376
EAC = -$317,376 / (PVIFA 14%,3 = -$136,703.84
Techron II: After-tax operating costs = $33,000(1 – 0.35) = $21,450
PVCCATS = (480,000)(.35)(.20)(1.07)/[(.14 + .20)(1.14)] – {[(20,000)(0.20)(0.35)/[0.14 + 0.20]]
(1/1.14) }= $90,616.84
5
PV(Costs) = -$480,000 – 21,450(PVIFA 14%,5+ (20,000/1.14 ) + 90,616.84 = -$452,635.37
EAC = -$452,635.37 / (PVIFA 14%,5 = -$131,845.24
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 = $5.2M; d = 4%; k = 12%; T = 35%; S = .25 x $5.2M = $1,300,000;
n = 25
PVCCATS = $423,933.85
Assuming end of year costs: PV(Costs) = -$120,000x(1-.35) x PVIFA(12%, 25) = -$611,764.49
Total PV(Costs) = -$5,200,000 – $611,764.49 + $423,933.85 + $1,300,000PVIF(12%, 25)
= -$5,311,360.34
10-9 EAC = -$5,311,360.34PVIFA(12%, 25) = -$677,198.28
Carbon-fibre technology
Given: Initial cost = $7.0M; d = 4%; k = 12%; T = 35%; S = .25 x $7.0M = $1,750,000;
n = 40
PVCCAT

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