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CHAPTER 8
CAPITAL BUDGETING DECISIONSPART II
8-1 Kinds of Capital Budgeting
Merck can use the same techniques to some extent. Theoretically, it
should evaluate all R&D projects as if they were ordinary capital
expenditures. They are certainly capital expenditures in the sense that the
company expects future returns from current expenditures. The problem is
that estimates of returns for new projects are extremely speculative. As
projects move toward fruition, estimates of returns become more solid and at
some point DCF techniques make sense. But a company that thrives on new
products, especially products with enormous R&D expenditures, must make the
investments based on the best scientific judgment. The following continuum
might be helpful in explaining the point.
|__________________________________________________________________________|Basic Applied P&E for New
research research Development product Replacements
As you move from left to right, estimates of returns, and of required
investments, become less speculative. With the routine decisions to replace
existing plant assets, DCF techniques shine. However, to the left of the
spectrum, other factors become more important.
8-2 Macroeconomic Events and Capital Budgeting
Note to the Instructor: The questions posed by this problem are
designed to encourage students to think about the interrelationships in the
economy and the factors that can affect the attitudes and plans of a given
industry or firm. The depth of the discussion will be affected by thestudents' backgrounds in economics and the instructor's inclination to
encourage students to exercise their reasoning powers. We've provided a
minimum in response to each question. The instructor may want to explore the
trickle-down effects of each factor.
1. Many industries will be affected by such a law. The law would reduce the
investment spending of companies involved with gasoline-related products,
including (but not limited to) companies making gasoline engines.
Manufacturers of electrical charging units would be more inclined to invest.
Further, the law is likely to affect the inclination of a given company to
invest in different kinds of projects. For example, an oil company would
shift its interest from one type of project to another, being more inclined
to invest in a project related to alternative uses of oil.
2. The demand for cotton would increase and for other fibers would decrease.
Companies involved in the processing of raw cotton would increase capital
spending; those of companies using primarily cotton to produce other products
would also increase. Companies using other fibers would reduce their
spending. Companies producing cotton, including cotton farmers, will reduce
their expected investments in production equipment.
3. Capital spending plans of domestic auto makers would probably increase.
Prices of substitute products (foreign autos) are likely to rise unless
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foreign manufacturers are willing to bear the increased cost. Domestic autos
would become relatively lower-priced, which would increase demand. Of
course. a tariff could prompt domestic makers to increase their prices and
try to maintain unit volume at previous levels. Thus, we cannot be certain
that domestic firms would increase capital spending to increase production,
but it is a likely action. If domestic auto makers do increase their capital
spending, their suppliers are likely to do so also. Increases in unit volume
of domestic autos would spur increases in purchases of steel, glass, vinyl,and other components.
4. The expected effect of an increase in corporate income taxes is a reduced
inclination to invest by all firms because of the reduction in future cash
flows associated with any proposed project. (The subject of the incidence of
corporate taxes can be raised if the students want to pursue this point.)
5. Capital spending plans for colleges and universities would be directly
affected, with a general increase in inclination to invest. To a lesser
extent, the plans of textbook publishers and other organizations that provide
school supplies would be affected.
6. Capital spending would fall because the present value of depreciation tax
shields would fall because the flows would come in later.
8-3 Capital BudgetingEffects of Events
1. A property tax increase reduces the acceptability of proposals requiring
some investment in real property. A project considered acceptable before the
tax increase might become unacceptable because of the increased future taxes.
2. Introduction of a tax credit reduces the cash investment required for any
project qualifying for the credit. This should not affect projects already
acceptable. It could, however, make some projects advisable that were
unacceptable under the old tax environment.
3. It seems likely that the expected future cash flows from the project
would be decreased because of either a lower price (to maintain the expectedsales volume) or a lower volume to be expected at the same price. Hence, the
present value of the future returns would decline, and a project heretofore
acceptable might no longer be so.
Note to the Instructor: A change in ranking of acceptable investments
could result in each of the above cases. Projects not involving real estate
investments could rise in rank; projects qualifying for the investment
credit, projects involving new products, or projects involving new products
other than that for which a substitute has been found could also rise in
rank.
8-4 Choosing Depreciation Methods
The general answer is that a company should postpone taking taxdeductions when doing so increases the amounts of the tax savings
sufficiently to offset the delay in their receipt. An expected increase in
the tax rate is the most obvious case. Other possibilities, not all of which
all students will have reason to know, include
(a) The company has operating losses and expects continuing losses (or
only small operating profits) for several years. It might then be unable to
take advantage of the higher deductions now.
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(b) The company is unincorporated, and expected incomes of its owner(s)
from other sources (and the likely marginal tax rates) will increase. The
additional tax savings from straight-line depreciation could then exceed the
penalty for delaying those deductions.
Note to the Instructor: A factor common to some of the circumstances
mentioned in requirement 2 is an understanding that straight-line
depreciation for tax purposes uses ADR lives, which are almost always longerthan the number of years for deductions using MACRS. Instructors with
particular competence in taxation might wish to discuss the influence of the
alternative minimum tax on a decision to forgo the benefits of accelerated
depreciation. (We thank Professor Will Yancey for bringing the last point to
our attention.)
8-5 Comparison of Methods (Extension of 7-15) (5-10 minutes)
Total
Present Profitability
Project Value Investment Index Rank
A $58,935 $70,000 .842 3
B 77,485 70,000 1.107 1
C 69,898 70,000 .999 2
In this case, the rankings are the same as when the projects were analyzed
using the net present value method.
8-6 Basic Investment Analysis (20 minutes)
1. Negative $2,150
Tax Cash Flows
Annual savings ($600,000 x .10) $60,000 $ 60,000
Depreciation ($240,000/10) 24,000
Increase in taxable income $36,000
Increase in taxes at 40% 14,400 14,400
Net cash savings $ 45,600
Present value factor, 10 years, 14% 5.216Present value of future flows $237,850
Cost of project, investment 240,000
Net present value ($ 2,150)
2. $60,687
Net present value, from requirement 1 ($ 2,150)
Divided by present value factor, 10 years, 14% 5.216
Required increase in after-tax annual flows $ 412
Divided by (1 - 40% tax rate) 60%
Equals required increase in before-tax cash savings $ 687
Plus expected savings 60,000
Equals required savings $60,687
A small increase in savings makes the investment worthwhile on a quantitative
basis. If the company has other reasons for making the investment, it should
go ahead even if the expected NPV is negative.
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3. Yes, the advantage is $17,679.
Tax Cash Flow
Savings with new machine $ 60,000 $ 60,000
Extra depreciation:
New machine $24,000
Old machine ($66,000/10) 6,600 17,400
Increase in taxable income $ 42,600
Increase in taxes at 40% 17,040 17,040After-tax cash flow increase $ 42,960
Present value factor, 14%, 10 years 5.216
Present value of future flows $224,079
Cost of new machine:
Cost of machine $240,000
Less proceeds from sale of old machine 12,000
$228,000
Less tax saving, loss on sale of old machine
[($66,000 - $12,000) x 40%] 21,600
Net cost of new machine 206,400
Difference, in favor of new machine $ 17,679
8-7 Basic Replacement Decision (15-20 minutes)
1. $84,800
Tax Cash Flow
Cost of new lathe $100,000
Resale price of existing lathe $12,000 (12,000)
Book value 20,000
Loss for tax purposes $ 8,000
Tax saving at 40% ( 3,200)
Net required investment $ 84,800
2. $91,215 present value, for an NPV of $6,415
Tax Cash Flow
Savings in cash costs ($63,000 - $22,000) $41,000 $ 41,000
Additional depreciation ($25,000 - $5,000) 20,000
Increase in taxable income $21,000Increased income taxes at 40% 8,400 8,400
Net cash flow $ 32,600
Present value factor, 4 years, 16% 2.798
Present value of future cash flows $ 91,215
Cost of new investment (requirement 1) 84,800
Net present value $ 6,415
The net present value is positive and reasonably high. The company
should accept the investment on economic grounds.
3. NPV increases by $1,656, to $8,071. Because salvage value is ignored for
depreciation purposes, nothing changes until the last flow.
Salvage value net of tax ($5,000 x 60%) $ 3,000
Present value factor, single payment, 4 years, 16% .552
Present value of recovery $ 1,656
8-8 Relationships (25 minutes)
1. $65,946 ($250,000/3.791)
2. $76,577. The easiest approach is to recognize, as the chapter shows,
that the $65,946 after-tax cash flow is the result of two things: the tax
saving from depreciation and the operating cash flow after taxes.
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After-tax cash flow $65,946
Less cash flow from tax shield [40% x ($250,000/5)] 20,000
After-tax cash flow from operations 45,946
Divided by (1 - 40% tax rate) 60%
Equals pre-tax cash flow from operations $76,577
8-9 Working Capital Investment (20 minutes)
$46,262
Tax Cash Flow
Contribution margin [60,000 x ($9 - $4)] $300,000 $300,000
Cash fixed costs 140,000 140,000
Pretax cash flow 160,000 160,000
Depreciation ($300,000/4) 75,000
Increase in taxable income $ 85,000
Increased income taxes at 40% 34,000 34,000
Net cash flow 126,000
Present value factor, 4 years, 12% 3.037
Present value of operating flows $382,662
Present value of return on working capital* 63,600
Total present value 446,262
Investment ($300,000 + $80,000 + $20,000) 400,000Net present value $ 46,262
* ($80,000 + $20,000) x .636
8-10 Replacement DecisionWorking Capital (15-20 minutes)
$1,632, not a huge margin, so the company might not make the investment if
its managers are uncertain about their estimates.
Investment:
Tax Cash Flow
Purchase price $200,000
Sale price of existing machine $50,000 (50,000)
Tax basis 80,000Loss 30,000
Tax benefit at 40% (12,000) (12,000)
Net investment in machinery $138,000
Working capital investment 80,000
Recovery ($80,000 x .769) ( 61,520)
Total investment $156,480
Annual savings:
Tax Cash Flow
Cash savings ($180,000 - $60,000) $120,000 $120,000
Increased depreciation ($100,000 - $40,000) 60,000
Increase in taxable income 60,000
Increased tax at 40% 24,000 24,000
Annual net cash flow $ 96,000Present value factor, 2 years, 14% 1.647
Present value of flows 158,112
Investment 156,480
Net present value $ 1,632
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8-11 Basic MACRS (10-15 minutes)
After-tax cash flow ($400,000 x .60) $ 240,000
Present value factor, 10 years, 14% 5.216
Present value of operating flows $1,251,840
MACRS shield ($1,500,000 x .40 x .706) 423,600
Total present value 1,675,440
Less investment 1,500,000Net present value $ 175,440
8-12 Mutually Exclusive Alternatives (Extension of 7-21) (10-15 minutes)
1. 1.330 for the hand-fed machine and 1.228 for the semiautomatic machine.
Hand-Fed Semiautomatic
Total present value of future cash
flows (from 7-22) $1,063,610 $1,719,260
Divided by investment $ 800,000 $1,400,000
Equals PI 1.330 1.228
2. The memo should include (a) reference to the results of analyzing the
alternatives using discounted cash flow techniques, and (b) a recommendationthat the choice depends on the projected returns for opportunities available
for investing the $600,000 incremental outlay for the semiautomatic machine.
Note to the Instructor: Class coverage of this assignment can be
expanded by determining the return on the incremental outlay, and students'
memos might include such an analysis. As shown below, the IRR on the
$600,000 incremental outlay is over 18%, well above the 14% cost of capital.
Incremental investment $600,000
Divided by incremental cash flow $225,000
Equals present value factor for 4 years 2.667
Factor for 18% 2.690
If expected returns from other available uses of the $600,000 approximate thecost of capital, investing in the hand-fed machine plus those other projects
would produce the same total NPV available by acquiring the semiautomatic
machine but with the additional risk accompanying reliance on more estimates.
In an undergraduate introductory course, we try to avoid extended
discussions of the concept of cost of capital and the conceptual issues
differentiating the NPV and IRR approaches to evaluating investments. Some
instructors might, however, choose to introduce reinvestment assumptions and
other issues relating to these approaches.
8-13 Investing to Reduce Inventory, JIT (15-20 minutes)
About $24.2 million, so the investment is desirable.
(in millions)
Tax Cash Flow
Additional cash operating costs $1.50 $ 1.50
Plus depreciation ($8.5/5) 1.70
Decrease in taxable income $3.20
Reduced income tax at 40% 1.28 1.28
Net cash outflow $ 0.22
Present value factor, 5 years, 12% 3.605
Present value of future outflows $ 0.793
Investment, net inflow, $8.5 - $43.7 + $10.2 25.000
Net present value $24.207
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Note to the Instructor: You might wish to point out how the cash operating
costs and depreciation tax shield nearly offset one another. This result is
purely a function of the numbers we used, not a generalizable conclusion.
8-14 New Product DecisionSensitivity Analysis (20-25 minutes)
Note to the Instructor: You might want to ask the class whether
Minnies might suffer losses in sales of its other doughnuts. We deem thislikely because people probably dont increase their doughnut consumption
every time a new product comes out. We deliberately did not mention this
possibility in the text so that you could ignore it or deal with it as you
choose.
1. $65,250
Tax Cash Flow
Additional contribution margin (50,000 x $3) $150,000 $150,000
New cash fixed costs 60,000 60,000
Increase in income before depreciation $ 90,000 90,000
New depreciation (210,000/6) 35,000
Increase in taxable income $ 55,000
Increase in taxes, at 45% 24,750 24,750
Increase in annual after-tax cash flow $ 65,250
2. (a) $43,757
Increase in annual after-tax cash flow (from requirement 1) $ 65,250
Present value factor, 14%, 6 years 3.889
Total present value of future cash flows $253,757
Less investment 210,000
NPV $ 43,757
(b) About 21.3%. Students using tables will find
Investment $210,000
Divided by annual cash flow $ 65,250
Equals present value factor for 6 years 3.218
Closest factors: For 20% 3.326
For 22% 3.167
(c) 1.208 ($253,757/$210,000)
3. $80,457
NPV (from 2a) $ 43,757
Divided by present value factor, 14%, 6 years 3.889
Allowable decrease in annual after-tax cash flows $ 11,251
Divided by (1 - 45% tax rate) 55%
Equals allowable decrease in before-tax cash flows $ 20,457
Cash fixed operating costs 60,000
Allowable total cash fixed operating costs $ 80,457
4. More than 4 but less than 5 years.
Present value factor (computed in 2b) 3.218
Closest factors for 16%:
For 4 years 2.798
For 5 years 3.274
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5. 43,181 units
Estimated sales, in cases 50,000
Allowable decrease in annual before-tax cash flows (from req 3) $ 20,457
Divided by per-unit contribution margin $3
Allowable decline in number of units sold 6,819
Case sales to achieve 14% IRR 43,181
6. Variable cost could increase about $0.41, to $5.41.
Allowable decrease in annual before-tax cash flows (from req 3) $ 20,457
Divided by expected volume in cases 50,000
Allowable decrease in contribution margin per unit $ 0.41
Note to the Instructor: To remind students of the components of
contribution margin, you might ask the class how much the expected selling
price could fall and the project still return 14%. Of course, the answer is
the same as for requirement 6, $0.41, because a lower selling price has the
same effect on contribution margin as an increase in per-case variable cost.
8-15 Working Capital (15 minutes)
General Note to the Instructor: This exercise illustrates the principlethat any delay in receiving cash flows involves the opportunity cost on the
investment, whether or not there are capital expenditures. The exercise is
simple enough that students should have little problem determining that there
is a negative NPV. Some students might inquire as to the difference between
this exercise and the principles in Chapter 5. Here we have a full year,
just at the cut-off we mentioned in Chapter 5. More importantly, here the
time value of money is significant.
Present value of inflow (30,000 x $20 x .862) $517,200
Investment 540,000
NPV ($ 22,800)
8-16 Mutually Exclusive Investments (20 minutes)
1. (a) $351,900 for the hand-fed machine, $408,840 for the semiautomatic
machine.
Hand-fed machine
Tax Cash Flows
Revenue $1,750,000 $1,750,000
Cash operating costs 1,450,000 1,450,000
Pretax cash flow 300,000 300,000
Depreciation ($1,000,000/10) 100,000
Increase in taxable income $ 200,000
Increase in taxes at 40% 80,000 80,000
Net cash flow $ 220,000
Present value factor, 10 years, 10% 6.145
Present value of future flows $1,351,900
Less investment 1,000,000
Net present value $ 351,900
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Semiautomatic machine
Tax Cash Flows
Revenue $1,750,000 $1,750,000
Cash operating costs 1,230,000 1,230,000
Pretax cash flow 520,000 520,000
Depreciation ($2,000,000/10) 200,000
Increase in taxable income $ 320,000
Increase in taxes at 40% 128,000 128,000Net cash flow $ 392,000
Present value factor, 10 years, 10% 6.145
Present value of future flows $2,408,840
Less investment 2,000,000
Net present value $ 408,840
(b) About 18% for the hand-fed, 14% for the semiautomatic
Hand-fed: $1,000,000/$220,000 = 4.545, which is close to the factor for 18%
Semiautomatic: $2,000,000/$392,000 = 5.102, which is close to the factor
for 14%
(c) 1.352 for the hand-fed and 1.204 for the semiautomatic
Hand-fed: $1,351,900/$1,000,000 = 1.352
Semiautomatic: $2,408,840/$2,000,000 = 1.204
2. The semiautomatic machine is the better choice because its NPV is higher
than that of the hand-fed machine.
Note to the Instructor: One way to illustrate the acceptability of the
incremental investment in the semiautomatic machine is to demonstrate, as
below, the NPV (at cost of capital) for the incremental investment.
Net cash flow, semiautomatic $ 392,000
Net cash flow, hand-fed 220,000
Incremental net cash flow from semiautomatic $ 172,000
Present value factor, 10%, 10 years 6.145 Present value of incremental flows $1,056,940
Incremental investment ($2,000,000 - $1,000,000) 1,000,000
Net present value of incremental investment $ 56,940
The depth of the discussion depends on how deeply you wish to explore
the concepts underlying the decision criteria, particularly their assumptions
about reinvestment of cash flows. The only clue students have from the text
is that the project with the higher NPV should be accepted unless doing so
would force rejection of other projects returning more than cost of capital.
8-17 Sensitivity Analysis (Extension of 8-16) (20 minutes)
The sales volumes needed to provide a 10% return are $1,431,857 for the
hand-fed machine and $1,565,188 for the semiautomatic model.
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Hand-Fed Semiautomatic
Net present value, from previous assignment $ 351,900 $ 408,840
Divided by present value factor, 10 years, 10% 6.145 6.145
Equals allowable decline in net cash flow $ 57,266 $ 66,532
Divided by (1 - the 40% tax rate) .60 .60
Equals allowable decline in pretax cash flow
and contribution margin $ 95,443 $ 110,887Divided by contribution margin percentages* 30% 60%
Equals allowable decline in sales volume $ 318,143 $ 184,812
Expected sales $1,750,000 $1,750,000
Minus allowable decline, above 318,143 184,812
Sales to yield 10% $1,431,857 $1,565,188
* 100% minus 70%, and minus 40%.
The decision to acquire the semiautomatic machine appears somewhat less
desirable because break-even volume, based on NPV's, is higher for that
machine. Thus, the semiautomatic machine is riskier than the hand-fed one.
However, both break-even volumes are well below the $1,750,000 anticipated,
so the difference is probably not large enough to change the decision.
8-18 Basic MACRS (15 minutes)
1. NPV is a negative $20,040.
Present value of operating flows ($160,000 x 60% x 4.833) $463,968
Present value of tax shield ($600,000/10 x 40% x 4.833) 115,992
Total present value 579,960
Less investment 600,000
Net present value ($
20,040)
2. NPV becomes positive by $25,968.
Present value of operating flows, above $463,968Present value of tax shield ($600,000 x 40% x .675) 162,000
Total present value 625,968
Less investment 600,000
Net present value $ 25,968
Using 7-year MACRS is worth $46,008 present value ($20,040 + $25,968, or
$162,000 - $115,992.
8-19 Review of Chapters 7 and 8 (25-40 minutes)
1. $68,000
Tax Cash Flow
Contribution margin [60,000 x ($11 - $8)] $180,000 $180,000
Less cash fixed costs 90,000 90,000
Increased income before depreciation 90,000 90,000
Less depreciation ($210,000/6) 35,000
Increase in taxable income $ 55,000
Increased taxes at 40% 22,000 22,000
Increase in annual after-tax cash flows $ 68,000
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2. $54,452
Increase in annual after-tax cash flows (requirement 1) $ 68,000
Times present value factor, 6 years, 14% 3.889
Equals total present value $264,452
Less investment required 210,000
Equals NPV $ 54,452
3. $32,692
Total present value (computed in requirement 2) $264,452
Add present value of return of investment in
working capital ($40,000 x .456) 18,240
Total present value of future receipts 282,692
Less, investment required ($210,000 + $40,000) 250,000
Net present value $ 32,692
4. 1.26 $264,452 from requirement 2/$210,000
5. 3.1 years $210,000/$68,000
6. Between 22% and 24%. The present value factor of 3.088 (requirement 5)is between the factors 3.167 and 3.020, for 22% and 24%, respectively.
7. 52,221 units
Net present value, requirement 2 $54,452
Divided by present value factor, 6 years, 14% 3.889
Equals allowable decrease in annual after-tax cash flow of $14,002
Divided by (1 - 40% tax rate) 60%
Equals allowable decrease in annual before-tax cash flow $23,337
Divided by contribution margin per unit $3
Allowable decrease in volume 7,779
Required volume, 60,000 - 7,779 52,221
8. Between 4 and 5 years. The present value factor computed in requirement5
(3.088) is between the factors at 16% for 4 and 5 years (2.798 and 3.274,
respectively).
8-20 Relationships (25 minutes)
1. (c) $245,680
Annual cash flows $ 40,000
Present value factor, 14%, 15 years 6.142
Equals cost $245,680
(f) $26,779
Cost $245,680
Times profitability index 1.109
Equals total present value of future flows $272,459
Less cost 245,680
Net present value $ 26,779
(d) 12%
Present value of future flows $272,459
Divided by annual flows $ 40,000
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Equals present value factor for 15 years, equals 12% factor 6.811
2. (b) $110,000
Investment $448,470
Divided by present value factor for 8 years, 18% 4.077
Equals annual cash flow $110,000
(f) $29,370
Cash flow $110,000
Times the present value factor for 8 years at 16% 4.344
Equals total present value of future flows $477,840
Less cost 448,470
Net present value $ 29,370
(g) $1.065
Present value (from f) $477,840
Divided by investment $448,470
Profitability index 1.065
3. (a) 10 years
Present value of future flows (from part f) $452,000
Divided by annual flows $ 80,000
Equals present value factor for 12% cost of capital 5.65
That factor is appropriate for 12% and 10 years
(e) Between 16% and 18%. Investment of $361,600 divided by annual
flows of $80,000 produces a factor (4.52) for 10 years that falls
between the factors for 16% and 18%.
(f) $90,400
Profitability index 1.25Times investment $361,600
Equals total present value of future cash flows 452,000
Less investment 361,600
Net present value $ 90,400
8-21 Review of Chapters 7 and 8 (45-60 minutes)
1. Between 10% and 12%.
Tax Cash Flow
Annual cash flow:
Cost savings $100,000 $100,000
Depreciation ($282,000/4) 70,500
Increase in taxable income 29,500
Increase in income taxes, at 30% 8,850 8,850
Increase in annual after-tax cash flows $ 91,150
Investment 282,000
Present value factor, $282,000/$91,150 3.094
Closest factors:
For 10% 3.170
For 12% 3.037
2. Negative $5,177.
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Annual increase in after-tax cash flows (requirement 1) $ 91,150
Present value factor, 12%, 4 years 3.037
Total present value of increase in future cash flows $276,823
Less investment 282,000
Net present value ($ 5,177)
3. .982 $276,823 from requirement 2/$282,000
4. $102,436
Net present value, above ($
5,177)
Divided by present-value factor for 12% for 4 years 3.037
Equals required annual after-tax cash flows $ 1,705
Divided by (1 - 30% tax rate) 70%
Equals required increase in pretax annual cash flow $ 2,436
Plus expected savings 100,000
Equals required savings to achieve 16% return $102,436
5. Negative $1,604
Years 1-3 Year 4
Tax Cash Flow Tax/CashAnnual cash flows:
Savings $100,000 $100,000 $100,000
Depreciation ($282,000/3) 94,000
Taxable income $ 6,000 100,000
Taxes at 30% 1,800 1,800 30,000
Net cash flow $ 98,200 $ 70,000
Applicable present value factors:
Annuity factor for 12% and 3 years 2.402
Single-amount factor for 12%, 4 years .636
Present value $235,876 $ 44,520
Total present value ($235,876 + $44,520) $280,396
Less investment 282,000
NPV ($ 1,604)
Note to the Instructor: This requirement is one of several
opportunities to address the impact of using accelerated depreciation for tax
purposes without going into the specifics of MACRS.
6. NPV decreases $4,368
Decrease in NPV because of additional investment $12,000
Increase in NPV for present value of return of
working capital investment ($12,000 x .636) 7,632
Net decrease $ 4,368
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7. $24,628
Tax Cash Flow
Cost savings $100,000 $100,000
Additional depreciation:
Depreciation on new asset, as above $ 70,500
Depreciation on existing asset ($25,000/4) 6,250 64,250
Increase in taxable income $35,750
Increase in taxes at 30% 10,725 10,725 Increase in annual after-tax cash flow $ 89,275
Present value factor, 12%, 4 years 3.037
Present value of future flows $271,128
Less investment:
Purchase of new equipment $282,000
Sale of old asset:
Cash received $40,000 (40,000)
Less book value 25,000
Tax gain $15,000
Tax on gain at 30% 4,500
Net cost of investment 246,500
NPV $ 24,628
8-22 Asset Acquisition and MACRS (15-20 minutes)
The NPV is $153,800.
Present value of operating cash flows ($260,000 x 60% x 5.65) $ 881,400
Present value of tax shield ($1,000,000 x 40% x .681) 272,400
Total present value 1,153,800
Less investment 1,000,000
Net present value $ 153,800
Note to the Instructor: You might wish to show how the investment would
look if the company had to use straight-line depreciation over 10 years.
Cash operating savings $ 260,000
Less depreciation ($1,000,000/10) 100,000Increase in pretax profit 260,000
Income tax on increase (40% x $160,000) 64,000
Increase in net income 196,000
Plus depreciation 100,000
Net cash flow 296,000
Times present value factor 5.650
Present value of future flows $1,107,400
The NPV drops to $107,400 under straight-line depreciation, a decline of
$46,400.
8-23 Working Capital Investment (15-20 minutes)
The NPV is a positive $88,734 and the offer is desirable.
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Cash Flow
Sales ($300,000 x 12 months) $3,600,000
Variable cost ($3,600,000 x .85) 3,060,000
Contribution margin 540,000
Cash fixed costs ($18,000 x 12) 216,000
Incremental profit and cash flow $ 324,000
Present value factor, 20%, 3 years 2.106
Present value $ 682,344Investment:
Inventories ($300,000 x .85 x 2) $ 510,000
Receivables ($300,000 x 3) 900,000
Total 1,410,000
Less PV of recovery ($1,410,000 x .579) 816,390 593,610
Net present value of offer $ 88,734
This problem involves no investment in fixed assets, only in working
capital. It is a change of pace from the other assignments and some students
will not see how to approach the solution.
8-24 Replacement Decision (15-20 minutes)
The NPV is a negative $20,644.
Investment:
Purchase price $270,000
Tax benefit of loss on sale:
Tax basis $60,000
Selling price 35,000 (35,000)
Loss $25,000
Tax benefit at 40% ( 10,000) (10,000)
Net investment $225,000
Tax Cash Flow
Annual cash flows:
Savings in operating costs ($130,000 - $20,000) $110,000 $110,000
Additional depreciation ($90,000 - $20,000) 70,000Increase in taxable income $ 40,000
Income tax at 40% 16,000 16,000
Net cash flow $ 94,000
Present value factor, 3 years, 18% 2.174
Present value of future flows $204,356
Less investment, as above 225,000
Net present value ($20,644)
8-25 Sensitivity Analysis and MACRS (Extension of 8-11) (10-20 minutes)
Annual savings of $343,942 in cash operating costs will make the investment
yield just 14%. This is a decline of about 14% from the expected savings of
$400,000 [($400,000 - $343,942)/$400,000].
Net present value from 8-11 $175,440
Divided by present value factor 5.216
Equals allowable decline in after-tax savings $ 33,635
Divided by (1 - 40% tax rate) 60%
Equals allowable decline in pretax savings $ 56,058
Pretax savings required, $400,000 - $56,058 $343,942
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8-26 Comparison of Alternatives (25 minutes)
The memo should include, with supporting analyses, a recommendation to
purchase Machine B. The most direct approach to analyzing the alternatives
is to work with the advantage of Machine B over Machine A and determine if
the additional cost of the former is justified.
Savings in operating cost of B over A ($12,000 - $3,000) $ 9,000Tax on cost savings (40%) 3,600
Net after-tax savings on operating cost alone 5,400
Tax savings due to additional depreciation if B is purchased:
Depreciation on B ($80,000/10) $8,000
Depreciation on A ($40,000/10) 4,000
Additional depreciation 4,000
Tax reduction because of extra depreciation (40%) 1,600
Total after-tax savings from Machine B (over Machine A) $ 7,000
Present value factor, 10 years, 10% 6.145
Present value of after-tax savings from Machine B $43,015
Since the cost of this advantage is $40,000 ($80,000 cost of B vs. $40,000
cost of A), purchase of Machine B is wise. We can also approach the problem
using totals.
Machine A Machine B
Tax Cash Flow Tax Cash Flow
Operating costs $12,000 $12,000 $ 3,000 $ 3,000
Depreciation 4,000 8,000
Tax deductible expenses $16,000 $11,000
Tax savings at 40% 6,400 6,400 4,400 4,400
Net cash outflow (inflow) $ 5,600 ($ 1,400)
Present value factor 6.145 6.145
Present value of flows $34,412 ($ 8,603)
Less investment 40,000 80,000
Total present value $74,412 $71,397
The difference, the advantage to B, is $3,015 ($74,412 - $71,397).
Note to the Instructor: This assignment is particularly interesting
when analyzed using the second of the above approaches because Machine A
produces an annual cash outflow and present value of future flows, while
Machine B produces an annual cash inflow and present value of future flows.
Noting this difference, some students will conclude, without further
consideration, that an increase in cash flow is always preferable to a
decrease as long as some purchase must be made. (That is, students might
arrive at the correct answer for the wrong reason.) It's important that
students recognize that neither a smaller cash outflow nor the mere existence
of a positive cash inflow is sufficient to choose between two alternatives.
To illustrate, suppose that the annual before-tax costs of operating Machine
B are $5,200 rather than the $3,000 in the original problem.
Tax Cash Flow
Annual cash costs $ 5,200 $5,200
Depreciation 8,000
Tax deductible expenses $13,200
Tax savings at 40% 5,280 5,280
Net cash inflow $ 80
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Machine A Machine B
Annual cash flow (increase) $ 5,600 ($ 80)
Present value factor 6.145 6.145
Present value of cash flow (increase) $34,412 ($ 492)
Present value of savings resulting from
adopting Machine B ($34,412 + $492) $34,904
Less cost of adopting Machine B 40,000
NPV $(5,096)
Despite the positive cash flows coming from Machine B, the investment is
unwise.
8-27 Unit Costs (20-25 minutes)
1. Negative $47,804
Tax Cash Flow
Savings:
Materials [200,000 x ($3.50 - $3.40)] $ 20,000 $ 20,000
Direct labor [200,000 x ($7.50 - $6.50)] 200,000 200,000
Variable overhead [200,000 x ($2.50 - $2.15)] 70,000 70,000
Total pretax cash savings 290,000 290,000
Less depreciation 200,000Increased taxable income $ 90,000
Increased tax at 40% 36,000 36,000
Net cash flow $254,000
Present value factor, 3 years, 18% 2.174
Present value of flows $552,196
Less investment 600,000
Net present value ($ 47,804)
2. 12.9% from Lotus 1-2-3. The factor is 2.36 ($600,000/$254,000), which is
closest to 2.322 for 14%.
Note to the Instructor: The above solution assumes it is profitable to
proceed with the new shoes if there is no additional capital investment.
This might not be the case. Such factors as negative effects on sales ofexisting shoes that are more profitable than the new model, or more
profitable uses for the existing facilities, could sway the decision against
the proposed shoe.
8-28 JIT, Inventory (15-20 minutes)
$260.4 thousand
Tax Cash Flow
Savings in cash operating costs $240.0 $ 240.0
Less depreciation ($1,800/10) 180.0
Increase in taxable income $ 60.0
Income tax at 40% 24.0 24.0
Net cash flow 216.0
Present value factor, 10 years, 12% 5.650
Present value of future inflows $1,220.4
Investment:
Investment in fixed assets $1,800.0
Other after-tax investment ($2,900.0 x 60%) 1,740.0
Less reduction in inventory ($2,700.0 - $120.0) (2,580.0)
Total investment 960.0
Net present value $ 260.4
Note to the Instructor: The solution follows the statement in the
chapter that negative effects on inventory at some future date will not
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materialize. Additionally, it's worth pointing out in connection with this
assignment that some benefits of JIT manufacturing are not easily quantified,
particularly those having to do with increased quality of product and
additional manufacturing flexibility. Therefore, the investment might be
desirable even if it had a negative NPV.
8-29 Pollution Control and Capital Budgeting (20 minutes)
The memo should conclude, subject to any expressed reservations about
qualitative issues, that purchasing the CleanAir is the better alternative.
The supporting analysis can be shown in one of two ways. One is to determine
which device has the lower present value of future and current outflows. The
other is to analyze the differences in cash flows. Starting with the first
method, the analysis is as follows.
CleanAir Polcontrol
Annual revenues $ 0 $ 250,000
Annual cash costs 180,000 210,000
Net cash flow before taxes (outflow) ( 180,000) 40,000
Depreciation 100,000 200,000
Net loss for tax purposes 280,000 160,000
Tax savings at 40% of tax loss 112,000 64,000Decrease in net income ( 168,000) ( 96,000)
Plus depreciation 100,000 200,000
Net cash inflow (outflow)* ($ 68,000) $ 104,000
Present value factor 4.833 4.833
Present value of future flows (outflow) ($ 328,644) $ 502,632
Investment ( 1,000,000) ( 2,000,000)
Net present value ($1,328,644) ($1,497,368)
* Combination of net cash flow before taxes and tax savings
The difference between the present values of $168,724 ($1,497,368 -
$1,328,644) can be verified using the second method. Here, the question is
whether it is worthwhile to invest an additional $1,000,000 for the
Polcontrol, given its superiority in annual cash flows.
Difference in flows favoring Polcontrol, $104,000 - (-$68,000) $ 172,000
Present value factor, 10 years, 16% 4.833
Present value of difference in cash flows $ 831,276
Less additional investment 1,000,000
Net present value of additional investment ($
168,724)
8-30 Replacement Decision and Sensitivity Analysis (25 minutes)
1. The investment is desirable; its NPV is $38,825.
Annual cash savings ($45,000 - $20,000) $25,000
Present value factor, annuity for 5 years at 14% 3.433
Present value of future cash savings $85,825
Cost of new equipment:
Purchase price $65,000
Less resale of existing equipment 18,000 47,000
Net present value $38,825
2. Over 25%. The factor is 1.88 ($47,000/$25,000). For 5 years, the lowest
factor in the table is 2.689, the factor for 25%. The actual rate is nearly
45%.
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3. About $13,691 $47,000/3.433
4. More than 2 years. The factor is 1.88 (requirement 2); the annuity
factor in the 14% column for two years is 1.647.
8-31 Alternative Production Process (10-15 minutes)
1. $77,000 Data on Cash for
Old Machine New Machine
Cost of new machine, an outflow $100,000
Cash from sale of old machine:
Selling price, a cash inflow $25,000 (25,000)
Less, book value of old machine 20,000
Taxable gain on sale of old machine $ 5,000
Tax on gain (at 40%), an outflow 2,000
Net cash cost of new machine $ 77,000
2. -$2,016
Tax Cash Flow
Savings ($64,000 - $40,000) $24,000 $24,000 Less, additional depreciation:
New machine ($100,000/5) $20,000
Old machine 4,000 16,000
Increase in taxable income $ 8,000
Increased tax at 40% 3,200 3,200
Increase in annual cash flow $20,800
Times present value factor for 12%, 5 years 3.605
Present value of future cash flows $74,984
Net cost of new machine (requirement 1) 77,000
Net present value of investment in alternative method ($ 2,016)
8-32 Sensitivity Analysis (25-30 minutes)
1. 29,027 unitsAnnual net contribution margin required:
Investment $600,000
Divided by present value factor, 4 years, 16% 2.798
Equals net cash flow required $214,439
Plus cash fixed costs 250,000
Equals contribution margin needed $464,439
Divided by per-unit contribution ($30 - $14) $16
Equals annual unit volume required 29,027
2. 31,712 units
Investment $600,000
Divided by the present value factor for 4 years at 10% 2.798
Equals required annual after-tax cash flow $214,439
Less cash savings from tax shield of depreciation
($600,000/4) x 40% 60,000
Equals required after-tax cash flow of nondepreciation items $154,439
Add after-tax effect of cash for fixed cost ($250,000 x 60%) 150,000
Equals required after-tax effect of contribution margin $304,439
Divided by (1 - 40% tax rate) 60%
Required contribution margin $507,398
Divided by per-unit contribution margin $16
Equals required annual volume 31,712
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Note to the Instructor: The solution shown above follows the conceptual
approach presented in the solution to 8-20. This approach differs little
from the shortcut approach we present to deal with MACRS. Some students will
use a longer method that first computes the NPV of the project and then uses
the differential approach shown in the text. For such students, you might
want to go over the steps required (shown below) when using that method.
Tax Cash FlowExpected contribution margin (30,000 x $16), an inflow $480,000 $480,000
Cash fixed costs, an outflow 250,000 250,000
Change in income from cash flows 230,000 230,000
Less depreciation ($600,000/4) 150,000
Increase in taxable income $ 80,000
Increase in taxes (at 40%), an outflow 32,000 32,000
Increase in annual after-tax cash flows $198,000
Times present value factor, 4 years, 10% 2.798
Equals present value of expected cash flows, rounded $554,000
Less investment 600,000
NPV ($
46,000)
Divided by present value factor 2.798
Equals required after-tax increase in expected annual cash flows $ 16,440Divided by (1 - 40% tax rate) 60%
Equals required increase in expected pretax annual cash flows $ 27,400
Plus expected pretax annual cash flows (above) 230,000
Equals required pretax annual cash flows 257,400
Plus known cash fixed costs 250,000
Equals required cash flow from contribution margin $507,400
Divided by contribution margin per unit $16
Equals required unit volume to achieve needed contribution margin 31,712
8-33 Determining Required Cost Savings (20 minutes)
1. About $3.89
Investment $150,000Divided by the present value factor for 16% and 5 years 3.274
Equals required annual net cash flow $ 45,816
Cash fixed operating costs 32,000
Equals required total savings (cash inflow) $ 77,816
Divided by annual unit volume 20,000
Equals required per-unit saving $3.891
2. About $4.42. The solution below uses the approach of CVP analysis.
Required after-tax cash flow (requirement 1) $45,816
Less depreciation 30,000
Equals required net income 15,816
Divided by one minus the tax rate .60
Equals required pretax income 26,360
Plus fixed costs, $30,000 + $32,000 62,000
Equals required variable cost saving, in total 88,360
Divided by expected annual volume 20,000
Equals required unit variable cost saving $4.418
Note to the Instructor: Some students will have serious difficulties
with this assignment because it does not follow the pattern of sensitivity
analyses in the chapter, where one starts with an NPV and determines the
change in the relevant factor. It is possible to solve by a kind of brute
force approach, in which you assume a value for the reduction in variable
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costs, then solve the sensitivity analysis. Suppose we start with a
hypothetical $6.00 per unit saving.
Tax Cash Flow
Savings in variable cost, $6 x 20,000 $120,000 $120,000
Cash operating costs (cash outflow) 32,000 32,000
Pretax cash flow 88,000 88,000
Depreciation ($150,000/5) 30,000Increase in taxable income $ 58,000
Increase in taxes (at 40%) 23,200 23,200
Increase in annual after-tax cash flow 64,800
Times present value factor 3.274
Equals present value of future after-tax cash flows 212,155
Investment required 150,000
Hypothetical NPV $ 62,155
Divided by present value factor 3.274
Equals allowable decline in net cash flow $18,984
Divided by (1 - 40% tax rate) 60%
Equals allowable decline in pretax cash flow $31,640
Divided by expected unit volume 20,000
Equals allowable decline in variable cost savings $ 1.582
Required saving = $6.00 - $1.582 $ 4.418
3. About 22,090 units (rounded)
Required total annual savings (requirement 2) $88,360
Divided by $4 estimated unit savings $4
Equals annual unit volume required 22,090
Note to the Instructor: This problem is a good vehicle for pointing out
to students that requirements 2 and 3 are items they were doing in Chapter 2,
using CVP analysis.
8-34 Benefit-Cost Analysis (25 minutes)
1. Net present values of saved lives: Kidney Heart
Disease Disease
Annual incomes $ 15,000 $ 25,000
Present value factors, 10%:
30 years 9.427
20 years 8.514
Present values of future incomes $141,405 $212,850
Less cost 100,000 150,000
Net present value $ 41,405 $ 62,850
2. If one considers only (perhaps as a first screen) the factors given,
there is a narrow margin favoring the treatment of the heart disease.
Assuming a convenient equal outlay for treatment, say $300,000, and computing
a net present value per dollar spent, three persons could be saved from
kidney disease or two from heart disease.
Kidney Heart
Disease Disease
Present values of:
3 lives saved ($141,405 x 3) $424,215
2 lives saved ($212,850 x 2) $425,700
Less cost 300,000 300,000
Net present value $124,215 $125,700
Note to the Instructor: Students' answers to requirement 2 will depend
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on their experiences and personal views. Scores of non-quantifiable factors
are involved in a decision such as this, and there are other quantifiable
issues as well. Personal views and experiences notwithstanding, the goal of
improving students' analytical skills is served if class discussion includes
coverage of the relatively simple analysis shown above as well as the matters
covered in the analytical comments that follow.
The NPV analysis is conceptually weak because it relates the cost to thecommunity-treatment cost of the department, paid for by taxes, to the incomes
of individuals treated, rather than to the benefits to the community.
Individual incomes influence community benefits in some ways (e.g., receipts
from local income taxes, contributions to charitable and cultural
activities). But individual incomes are not a particularly good measure of
benefits to the community and the issue here is use of community finances.
For example, being younger, victims of kidney disease probably have more
dependents than do the heart-disease victims whose children are more likely
to be self-supporting. Thus, treating kidney disease might produce greater
savings to the community (in social security, welfare, and other payments to
dependents).
Evaluation of community benefits must also consider that (a) more lives
can be saved if kidney disease is treated, because of the lower cost to saveone life; and that (b) treatment of kidney disease will add more years of
life to community members because persons saved from that disease have ten
more years of life than those saved from heart disease. (An important point
to remember is that a decision such as the one in this problem does not
consider the lives of any particular individuals.)
As with any benefit/cost situation under conditions of resource
scarcity, a decision must be made as to who is to benefit from the use of
those resources. This socio-political problem can't be resolved with
quantifiable factors alone. That this particular decision involves human
lives does not negate the need for a decision about what the community is to
do with its limited resources. The community can choose to increase the
available resources, but it is still likely to set some limit short of taxing
its members to a subsistence level.
8-35 When-to-Sell Decisions (20 minutes)
1. About 14%. The choice is between $700 now and $1,170 in four years.
The present value factor is .598 ($700/$1,170), which is closest to .592 for
four years and 14%.
2. About $1,100, which is $700/.636, the present value divided by the factor
for four years and 12%.
3. Nine years gives the highest IRR.
Price for Expected
Additional Six-Year-Old Future PV Discount Rate for
Holding Period Scotch / Price = Factor Closest Factor
1 (sell at 7) $700 $ 800 .875 14% (.877)
2 700 950 .737 16% (.743)
3 700 1,200 .583 20% (.579)
4 700 1,400 .500 18% (.516)
4. Ten years gives the highest present value and highest net present value
because the investment is $700 under all choices.
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Additional Expected PV
Holding Future Factor Present
Period Price x at 12% = Value
1 $ 800 .893 $714
2 950 .797 757
3 1,200 .712 854
4 1,400 .636 890
Note to the Instructor: Requirements 3 and 4 are contrived to give
different decisions under the two criteria, IRR and NPV. As discussed in the
chapter, in most cases the NPV criterion will give the better decision where
mutually exclusive investments are under consideration. That conclusion is
not always correct, because it depends on the assumed rate of return earned
by the incoming cash flows.
In this particular case, if the proceeds from sale after nine years
could be reinvested at 20%, the IRR earned if the Scotch is held until it is
nine years old, the company would have at the end of the fourth year $1,440
($1,200 x 1.20), which is more than it would have if it held the Scotch until
the end of year four. If the company could earn only the cost of capital of
9%, it would have $1,308 at the end of year four, which is less than it wouldhave if it held the Scotch until it was ten years old ($1,400).
8-36 Increased Sales and Working Capital (25-30 minutes)
The decision is a tossup. The NPV is a negative $437, $160,000 -
$159,563, which is within rounding errors.
Investment required:
Outlay for the machine $ 80,000
Increase in working capital 80,000
Total current outlay $160,000
Present value of cash flows:
Annual returns of $26,450 for 10 years at 14%
$26,450 (from below) x 5.216 $137,963 Return of the investment in working capital,
at the end of the 10th year ($80,000 x .270) 21,600
Total present value $159,563
Computation of Cash Flows for 10 Years
Existing Proposed
Conditions Conditions
Revenues:
80,000 x $8 $640,000
105,000 x $7 $735,000
Variable costs:
Labor:
Currently ($2.25 x 80,000 units) 180,000
Future (labor force constant) 180,000
Other:
80,000 x $2.25 180,000
105,000 x $2.25 ________ 236,250
Total variable costs 360,000 416,250
Contribution margin $280,000 $318,750
Increase in contribution margin $38,750
Depreciation ($80,000/10) 8,000
Increase in taxable income $30,750
Tax on above increase (40%) 12,300
Net increase in after-tax cash flow $26,450
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8-37 Sensitivity Analysis (Extension of 7-33) (20 minutes)
1. 207,527 units, a drop of 42,473
Net present value, from 8-34 $262,458
Divided by present value factor, 5 years, 14% 3.433
Equals allowable decrease in net cash flow $ 76,452
Divided by (1 - 40% tax rate) 60%Equals allowable decrease in pretax cash flow and income $127,420
Divided by contribution margin per unit ($4 - $1) $3
Equals allowable decrease in unit volume 42,473
Expected unit volume 250,000
Less allowable decrease in unit volume 42,473
Equals unit volume required to earn 14% IRR 207,527
2. Pitcairn's managers might be more inclined to make the investment after
seeing that it would take a drop of 42,473 units in volume to bring the net
present value to zero. The required volume is about 17% below the expected
level of 250,000 units, which is a fairly large decrease.
8-38 Backing a Play (30 minutes)
1. The play appears to be a good investment, with a $325,851 NPV.
Tax Cash Flow
Annual gross receipts $1,500,000 $1,500,000
Cash expenses:
Salaries 600,000 600,000
Rent [$20,000 + (5% x $1,500,000)] 95,000 95,000
Royalties (10% x $1,500,000) 150,000 150,000
Other cash expenses 140,000 140,000
Total cash expenses 985,000 985,000
Pretax cash flow 515,000 515,000
Depreciation ($500,000/4) 125,000
Taxable income $ 390,000
Tax at 40% 156,000Annual cash flow $ 359,000
Present value factor, 20%, 4 years 2.589
Total present value of future annual returns $ 929,451
Present value of return of working capital investment
$200,000 x 0.482 96,400
Total present value 1,025,851
Less investment 700,000
Net present value $ 325,851
2. $1,253,215
Net present value, computed in requirement 1 $ 325,851
Divided by present value factor for 4 years at 20% 2.589
Equals allowable decline in net cash flow $ 125,860
Divided by (1 - 40% tax rate) 60%
Equals allowable decline in pretax income and revenue $ 209,767
Divided by contribution margin (100% less variable costs of
5% for rent and 10% for royalty) 85%
Equals allowable decline in gross receipts $ 246,785
Expected revenue $1,500,000
Less allowable decline 246,785
Equals revenue needed for 20% IRR $1,253,215
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The decline is 16.5% of revenue, so the decision is not extremely
sensitive to the estimate of revenue. You might very well elect not to back
the play for that reason, given that plays are probably riskier investments
than most.
8-39 Replacement Decision (25 minutes)
1. $19,900
Purchase price, outflow $37,300
Tax saving from loss on sale of old machine:
Sale of old machine, a cash inflow $12,000 (12,000)
Book value of old machine 18,000
Tax loss $ 6,000
Tax saving at 40%, a cash inflow ( 2,400)
Saved cost of repairs, net of tax ($5,000 x 60%) ( 3,000)
Net cost $19,900
2. The new machine should be a wise investment because it involves a cash
outlay of $19,900 with anticipated returns of $26,866 computed as below.
Tax Cash FlowCash savings due to greater speed $ 6,000 $ 6,000
Change in depreciation:
Depreciation on new asset ($37,300/10) $3,730
Depreciation on old asset 1,800
Additional depreciation from new asset 1,930
Increase in taxable income $ 4,070
Tax on increased income, at 40% 1,628 1,628
Increase in net cash flow $ 4,372
Present value factor, 10 years, 10% 6.145
Total present value of savings $ 26,866
8-40 Valuing a Football Team (25-35 minutes)
1. $17,591,288 calculated as follows.
After-tax operating cash flow ($4,000,000 x .72) $ 2,880,000
Present value factor, 10 years, 14% 5.216
Present value of operating flows $15,022,080
Let M = the maximum investment. The amortization tax shield is [(M/10) x .28
x 5.216], which is subtracted from M along with the present value of the
operating flows. Thus,
M = $15,022,080 + [(M/10) x .28 x 5.216]
M = $15,022,080 + .14605M
.85395M = $15,022,080
M = $17,591,288
As proof,
Tax Cash Flows
Operating $4,000,000 $ 4,000,000
Amortization ($17,591,288/10) 1,759,129
Pretax profit $2,240,871
Tax at 28% 627,444
Net cash flow $ 3,372,556
Present value factor 5.216
Present value $17,591,252
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The difference between the $17,591,252 and the $17,591,288 is from rounding.
2. $16,250,627. The tax shield here is a lump sum at the end of 10 years,
so the shield = M x .28 x .270. (The .270 is the present value of a single
payment in 10 years.) Thus,
M = $15,022,080 + (M x .28 x .27)
M = $15,022,080 + .0756M .9244M = $15,022,080
M = $16,250,627
As proof,
Present value of operating flows, above $15,022,080
Present value of write-off ($16,250,627 x .28 x .27) 1,228,547
Equals investment $16,250,627
8-41 Investing in Quality, JIT, Declining Base (15-20 minutes)
About $1,221 thousand dollars.
Tax Cash Flow
Saved contribution margin ($1,500.0 x 60%) $ 900.0 $ 900.0Less additional cash fixed costs 700.0 700.0
Pretax cash inflow 200.0 200.0
Depreciation ($5,500.0/10) 550.0
Decrease in taxable income $ 350.0
Reduced income tax at 40%, a cash inflow 140.0
Net cash inflow $ 340.0
Present value factor, 10 years, 12% 5.650
Present value of future flows $1,921.0
Less investment ($5,500.0 - $4,800.0) 700.0
Net present value $1,221.0
Note to the Instructor: The solution follows the position in the
chapter of assuming that there is no negative effect on inventory at some
future date. This assignment also involves no additional cash inflows fromsales but rather a halt in the decline of sales. Some students will not see
this point and will wonder what the benefits are.
If the point hasn't been made in connection with other assignments, it's
worth pointing out here that some benefits of JIT operations are not easily
quantified, particularly those having to do with increased quality of product
and additional manufacturing flexibility.
8-42 Attracting Industry (20-25 minutes)
1. Looking only at the receipts and costs for the town, the investment will
not return enough to meet the 9% required rate of return.
Receipts:
Rent $ 150,000
Sales tax ($6,000,000 x 1%) 60,000
Property taxes [($4,400,000/$1,000) x $80] 352,000
Total receipts 562,000
Additional costs 105,000
Annual net cash inflow $ 457,000
Present value factor, 9%, 20 years 9.129
Present value of future cash inflows $4,171,953
Less investment 4,300,000
Net present value ($ 128,047)
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2. The above analysis considers only the receipts and costs of the town
itself. The state, as well as the town, would benefit from the new plant,
because the state would save some of the money it now spends on unemployed
people. Hence, it's possible the state might be willing to share some of the
cost of this project.
If the interest rate for the state is also 9%, it would be worth$27,387,000 ($2,000 x 1,500 reduced unemployment x 9.129, the present value
factor) to the state if the 1,500 people were taken off the unemployment
rolls. Of course, that figure assumes the level of unemployment would stay
at about the same level for the next 20 years if the factory were not built.
At least some of the unemployed are likely to become discouraged and move
away.
The town council and mayor might accept the project if they think it
worthwhile to increase taxes somewhat to cover the required investment. They
might consider it worthwhile to do so if they believe the town would benefit
in noneconomic ways from having fewer unemployed persons. For example, they
might consider the positive effects on the unemployed of being given jobs.
8-43 Dropping a Product (30 minutes)
1. Quickclean should not be dropped.
Tax Cash Flow
Present value of future cash flows:
Contribution margin $700,000 $700,000
Avoidable fixed costs 580,000 580,000
Cash flow before taxes 120,000 120,000
Less depreciation 100,000
Increase in taxable income 20,000
Tax at 40% 8,000 8,000
Net cash flow $112,000
Present value factor, 14%, 5 years 3.433
Present value of future cash flows $384,496
Present value of disposal of equipment:Book value and loss for tax purposes $500,000
Tax savings at 40%, and present value of inflow 200,000
Net present value in favor of keeping Quickclean $184,496
2. Quickclean should be dropped.
Tax Cash Flow
Selling price of machinery $350,000 $350,000
Book value 500,000
Loss for tax purposes 150,000
Tax saving at 40% rate 60,000 60,000
Total present value of disposal $410,000
Present value of future inflows, requirement 1 384,496
Net present value of dropping Quickclean $ 25,504
8-44 New ProductComplementary Effects (35 minutes)
1. The product should not be introduced. The NPV is a negative $155,160.
Investment required:
Machinery $2,000,000
Inventories 500,000
Receivables (10,000 units per month x 2 x $20) 400,000
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Total investment $2,900,000
Tax Cash Flows
Present value of future cash flows:
Contribution margin [120,000 x ($20 - $9)] $1,320,000 $1,320,000
Less:
Additional fixed costs $300,000
Forgone rent of space 120,000 420,000 420,000
Cash flow before taxes 900,000 900,000 Depreciation ($2,000,000/10) 200,000
Taxable income $ 700,000
Income tax at 40% 280,000
Net operating cash flow, years 1-10 $ 620,000
Present value factor, 10 years, 20% 4.192
Present value of future operating cash flows $2,599,040
Recovery of working capital investment
(computed above) in year 10 $ 900,000
Present value factor, single payment in 10 years
at 20% .162 145,800
Total present value of future cash flows $2,744,840
Less investment required, above 2,900,000
Net present value ($ 155,160)
2. The complementary effects make the new product desirable. The positive
present value of the future flows from increased sales of the existing
product, less the additional investment in inventory and receivables, is
$251,544, which is more than enough to offset the $155,160 deficiency in NPV
considering the new product by itself as in requirement 1.
Contribution margin [30,000 x ($10 - $6)] $ 120,000
Less additional income tax at 40% 48,000
Cash flow 72,000
Present value factor, 10 years, 20% 4.192
Present value of future operating flows $ 301,824
Recovery of additional investment in working
capital $60,000
Single payment factor, 10 years, 20% .162 9,720Total present value of future inflows 311,544
Less additional investment in receivables and inventory 60,000
Net present value of increased sales $ 251,544
8-45 Closing a PlantExternalities (35 minutes)
1. A $268,800 difference in present values favors closing the plant.
Total Project Approach
Close plant:
Increased shipping costs $ 900,000
Tax at 40% 360,000
Net cash outflow 540,000 Present value factor, 10 years, 14% 5.216
Present value of increased shipping costs 2,816,640
Severance pay, net of tax, $800,000 - $320,000 480,000
Subtotal 3,296,640
Less selling price of plant 400,000
Present value of future cash flows $2,896,640
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Keep plant open:
Investment required $4,000,000
Depreciation tax shield, $4,000,000/10 x 40% $ 160,000
Present value factor, 10 years, 14% 5.216
Present value of future cash inflows 834,560
Present value of future cash outflows $3,165,440
Difference favoring closing plant, $3,165,440 - $2,896,640 $ 268,800
The investment in equipment produces a net annual cash inflow from tax
savings from the depreciation deduction. Some of the flows could be treated
differently. For example, the severance pay and sale price of the plant
could be treated as savings (avoided costs) under the alternative of keeping
the plant open.
Incremental Approach
Tax Cash Flows
Annual savings from keeping open:
Shipping costs saved $900,000 $ 900,000
Less depreciation expense 400,000
Difference in taxable income 500,000 Difference in taxes at 40% 200,000 200,000
Net annual savings $ 700,000
Present value factor, 10 years, 14% 5.216
Present value of future savings $3,651,200
Net investment required:
Equipment $4,000,000
Foregone selling price 400,000
Avoided severance pay, net of tax (480,000)
Net amount of investment 3,920,000
Net present value favoring closing ($ 268,800)
2. Some of the factors also to be considered follow.
(a) Both the company's managers and city officials must consider the impactof the closing on the city of Vesalia. Nearly 400 people will be put out of
work. How many of those people will find other employment is influenced by
the availability of other employment locally. Some may leave the area; some
of those who stay may require additional assistance from the city. Offering
employees the opportunity to move to the new location might help those
employees but could still have negative effects on the city.
(b) The company's managers should assess the likelihood of reaching some
type of compromise if the relevant information is shared with city officials
and possibly with persons representing the company's employees. Managers
could try to negotiate some assistance from the city, perhaps in the form of
lower property taxes. Managers could also try to negotiate wage concessions
from employees. (As an example, consider the wage concessions negotiated by
troubled airlines in the early 1990s.)
If the pollution standards were established locally, city officials
might not have considered the costs to the city of the increase in unemployed
citizens or the potential for reduced property-tax revenues. As interested
parties, city officials might reconsider the standards when better informed
of the company's situation. If the pollution standards were established at
the national level, concessions on property taxes and/or wages might still be
negotiated to offset the monetary advantage of closing the plant.
(c) The company's managers might not have considered whether the Montclair
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area has the additional workers needed to handle the increase in production
at the Montclair plant.
Note to the Instructor: Apart from the difficulties presented by the
qualitative issues in it, this problem is difficult for many students because
of the number of cash flow items involved. We've assumed the company
considered all the discernible monetary aspects of the situation. As
examples, we assumed that (1) the company's calculations include any changesin selling and administrative costs that would result from eliminating one of
its locations; (2) no opportunities exist for reducing operating costs at the
Vesalia plant other than the tax and wage concessions mentioned in
requirement 2; (3) transferring production from the Vesalia to the Montclair
plant would not affect any company plans for future use of the currently
unused capacity at the Montclair plant; and (4) closing the Montclair plant
and transferring its production to the Vesalia plant is financially unwise.
An interesting aspect of this problem is that the analysis does not
involve contribution margin. The inability to change selling price is a
reasonable assumption in a competitive industry. The cost structures and
relative sizes of the two plants are unknown. If the Montclair plant can
handle the increased production, one must wonder about the implications of
the assertion that cash production costs at the two plants are equal.
8-46 Modification of Equipment (35 minutes)
The memo should recommend that the new equipment be purchased and the
old equipment sold. The computations submitted in support of the
recommendation could be either of the two approaches shown below.
Total-project approach
The present value of the future outflowsof buying new equipment is $96,080
less than that of modifying the existing equipment ($284,160 - $188,080).
Tax Cash Flow
Modify existing equipment:Annual cash OUTFLOW, excess of operating costs
over new equipment* ($ 50,000) ( 50,000)
Depreciation [$100,000 + ($300,000/4)] 175,000
Total tax deductible expense 225,000
Tax saving at 40% 90,000 90,000
Net after-tax cash flow (inflow) ($ 40,000)
Present value factor, 16%, 4 years 2.798
Present value of future cash savings ($111,920)
Less investment required 300,000
Present value of future cash inflows $188,080
* This amount could also be shown as a reduction under the "buy new
equipment" alternative.
Tax Cash Flow
Buy new equipment:
Depreciation ($800,000/4) $200,000
Tax savings at 40% 80,000 ($ 80,000)
Present value factor, 16%, 4 years 2.798
Present value of tax shield ($223,840)
Investment:
Price of new equipment $800,000
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Less proceeds on sale of existing equipment $220,000 (220,000)
Book value of equipment 400,000
Loss for tax purposes $180,000
Tax saving at 40% ( 72,000)
Net investment 508,000
Less present value of depreciation tax shield, above 223,840
Present value of future cash outflows $284,160
Incremental approach--buy rather than modify
Tax Cash Flow
Operating savings, a cash inflow $ 50,000 $ 50,000
Increased depreciation ($200,000 - $175,000) 25,000
Reduction in tax deductible expenses 25,000
Lost tax savings at 40%, an outflow 10,000 10,000
Net cash inflow favoring modification $ 40,000
Times relevant present value factor 2.798
Present value of future savings $111,920
Net investment required:
Net purchase price (above) $508,000
Modifications avoided 300,000
Net outlay 208,000
Difference in favor of buying $ 96,080
8-47 Mutually Exclusive Investments (50 minutes)
The company should buy the Rapidgo 350 and replace it in five years.
Rapidgo 600
Present Values
Original cost $ 90,000
Annual operating costs $15,000
Plus depreciation ($90,000/10) 9,000
Total expenses $24,000
Tax saving at 40% rate $ 9,600
Net cash outflows ($15,000 - $9,600) $ 5,400
Present value factor, 10 years, 16% 4.833
Present value of future annual cash flows 26,098Total present value $116,098
Rapidgo 350
Present Values
Original cost $ 50,000
Annual operating costs, first 5 years $12,000
Depreciation ($50,000/5) 10,000
Total expenses $22,000
Tax saving at 40% $ 8,800
Net cash outflows ($12,000 - $8,800) $ 3,200
Present value factor, 5 years, 16% 3.274
Present value of flows for first 5 years 10,477
Purchase price of replacement machine $60,000
Present value factor, 5 years, 16% .476
Present value of replacement cost 28,560
Annual operating costs, second 5 years $12,000
Depreciation ($60,000/5) 12,000
Total expense $24,000
Tax saving at 40% $ 9,600
Net cash outflows ($12,000 - $9,600) $ 2,400
Present value of flows* 3,742
Total present value $ 92,779
* $2,400 x 1.559, which is the sum of the present value factors for single
payments 6, 7, 8, 9, and 10 years hence (.410 + .354 + .305 + .263 + .
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227).
Cash flow $2,400
Times present value annuity factor, 5 years, 16% 3.274
Equals present value of annuity at beginning of
6th year (5 years from now) $7,858
Present value factor, single payment 5 years, 16% .476
Present value of delayed annuity $3,740
8-48 Replacement Decision, MACRS (30 minutes)
1. Buy
Purchase cost (80,000 x $20) $1,600,000
Less tax saving at 40% 640,000
Net cash outflow $ 960,000
Present value factor, 12%, 8 years 4.968
Present value of buying $4,769,280
Make
Variable costs (80,000 x $9.30*) $ 744,000Cash fixed costs 100,000
Total cash costs 844,000
Less tax savings at 40% 337,600
Net cash flow $ 506,400
Present value factor, 12%, 8 years 4.968
Present value of operating flows $2,515,795
Present value of MACRS ($2,500,000 x .40 x .738) ( 738,000)
Present value of salvage value ($100,000 x 60% x .404) ( 24,240)
Less investment 2,500,000
Total present value of making $4,253,555
* $9.30 = $4.50 + $3.00 + $1.80
2. About 63,831 units (80,000 - 16,169)
Advantage to making ($4,769,280 - $4,253,555) $515,725
Divided by relevant present value factor 4.968
Equals allowable decline in annual net cash flow $103,809
Divided by (1 - 40% tax rate) 60%
Equals allowable decline in annual pretax cash flow $173,015
Divided by difference in variable cost ($20.00 - $9.30) $ 10.70
Equals allowable decline in unit volume 16,170
8-49 Evaluating an Investment Proposal (40 minutes)
The assistant is incorrect; the project should be accepted. The
assistant has made the following errors.
1. The research and development costs and administrative time have already
been incurred and so are sunk costs.
2. Interest on debt specific to this particular project should not be a
component of the cash flow analysis.
3. The tax saving from scrapping the existing equipment has been ignored.
4. The treatment of depreciation is incorrect. The analysis should use the
difference between depreciation on the existing machinery and that on the new
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machinery, not the depreciation on the new machinery.
5. The annual cash flow calculation is incorrect because the calculation
included a deduction for depreciation, which is not a current cash flow.
Depreciation should be added to the $75,000 to arrive at cash flow.
The following analysis corrects the above errors.
Investment required:
Purchase price of machinery $350,000
Tax savings on scrapping
old machinery ($110,000 loss x 40%) 44,000
Net investment required $306,000
Tax Cash Flows
Annual cash flows:
Labor $ 75,000 $ 75,000
Materials 80,000 80,000
Variable overhead 40,000 40,000
$ 195,000 $ 195,000
Less tax at 40% of savings 78,000 78,000
Net saving before tax effect of depreciation $ 117,000 Tax savings from increase in depreciation
($35,000 - $11,000*) x 40% 9,600
Net increase in cash flow $ 126,600
Present value factor, 10 years, 16% 4.833
Present value of future cash flows $ 611,858
Net investment required, from above 306,000
Net present value $ 305,858
* $110,000 book value divided by remaining life of 10 years
8-50 Expanding a Factory (60 minutes)
The smaller expansion, Plan A, should be accepted. The first step is to
determine how to use the additional capacity. The products producecontribution margin per machine-hour as follows: 101-X, $9; 201-X, $6; 305-X,
$8. Therefore, 101-X should be made first, until its sales potential is
reached, then 305-X, and finally, 201-X.
The NPV of Plan A is $497,400. The NPV of Plan B is $353,400, or
$144,000 less than that of Plan A. Plan B can be analyzed in total or
incrementally. Both approaches are shown below.
Analysis of Plan A
Computation of product quantities and contribution margin:
Available machine-hours 200,000
Less production of 30,000 101-Xs (2 x 30,000) 60,000
Hours remaining 140,000
Divided by hours required for 305-X 5
Equals number of 305-Xs to be made 28,000
Contribution margin:
101-X (30,000 x $18) 540,000
305-X (28,000 x $40) 1,120,000
Total contribution margin $1,660,000
Tax Cash Flows
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Computation of NPV:
Contribution margin $1,660,000 $1,660,000
Less additional fixed costs requiring cash 600,000 600,000
Cash flow before taxes 1,060,000 1,060,000
Less depreciation ($4,000,000/10) 400,000
Increased taxable income 660,000
Increase in income taxes (40%) 264,000 264,000
Net cash flow $ 796,000Present value factor, 12%, 10 years 5.650
Present value of future flows $4,497,400
Investment required 4,000.000
Net present value $ 497,400
Analysis of Plan B
Available machine-hours 280,000
Less hours devoted
To 101-X ( 60,000)
To 305-X (140,000)
Hours available in excess of Plan A 80,000
Less hours used for additional production of 305-X
(30,000 - 28,000) x 5 ( 10,000) Hours remaining for production of 201-X 70,000
Divided by hours required to produce 201-X 4
Equals number of 201-Xs to be made 17,500
Contribution margin:
101-X (30,000 x $18) $ 540,000
305-X (30,000 x $40) 1,200,000
201-X (17,500 x $24) 420,000
Total contribution margin $2,160,000
Annual cash flows: Tax Cash Flows
Contribution margin $2,160,000 $2,160,000
Less additional fixed costs requiring cash 800,000 800,000
Cash flow before taxes 1,360,000 1,360,000
Less depreciation ($5,500,000/10) 550,000 Increased taxable income $ 810,000
Increase in income tax, at 40% 324,000 324,000
Net cash flow $1,036,000
Present value factor, 12%, 10 years 5.650
Present value of future flows $5,853,400
Less investment required 5,500,000
Net present value $ 353,400
Incremental analysis
Tax Cash Flows
Increased contribution margin
$2,160,000 - $1,660,000 $ 500,000 $ 500,000
Increased fixed cash costs ($800,000 - $600,000) 200,000 200,000
Increased pretax cash flow 300,000 300,000
Increased depreciation ($550,000 - $400,000) 150,000
Increased taxable income $ 150,000
Increased income tax at 40% 60,000 60,000
Increased net cash flow $ 240,000
Present value factor, 12%, 10 years 5.650
Present value of incremental cash flows $1,356,000
Incremental investment 1,500,000
Net present value of incremental investment ($ 144,000)
The $144,000 is also the difference between the two net present values
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($497,400 - $353,400).
Note to the Instructor: As always, the validity of the analysis depends
on the validity of the estimates. An additional factor some students might
discuss is how pattern of demand might affect production scheduling and,
hence, the decision on the magnitude of the expansion. For example, if
demand is seasonal and inventory carrying costs high, the company might
believe the benefits of volume flexibility with Plan B exceed the benefits ofthe stable production needed to meet demand with the smaller facility.
Some students may pursue a point raised in the problem, the production
manager's comment that the cost per machine hour and investment per machine
hour figures were lower for Plan B than for Plan A. As shown below, the
production manager is correct; but the point is irrelevant to the decision.
Plan A Plan B
Fixed cost per machine-hour
($600,000 + $400,000)/200,000 $ 5.00
($800,000 + $550,000)/280,000 $ 4.82
Investment per machine-hour
$4,000,000/200,000 $20.00
$5,500,000/280,000 $19.64