Solution manual cost accounting by LauderbachCAPITAL BUDGETING DECISIONS PART II
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CHAPTER 8
CAPITAL BUDGETING DECISIONSPART II
81 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.
82 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 the
students' 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
trickledown 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 gasolinerelated 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
foreign manufacturers are willing to bear the increased cost. Domestic autos
would become relatively lowerpriced, 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.
83 Capital Budgeting
Effects 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 expected
sales 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.
84 Choosing Depreciation Methods
The general answer is that a company should postpone taking tax
deductions 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.
(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 straightline 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 straightline
depreciation for tax purposes uses ADR lives, which are almost always longer
than 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.)
85 Comparison of Methods (Extension of 715) (510 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.
86 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% 5.216
Present 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 aftertax annual flows $ 412
Divided by (1 40% tax rate) 60%
Equals required increase in beforetax 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.
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 17,040
Aftertax 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
87 Basic Replacement Decision (1520 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 $21,000
Increased 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
88 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 aftertax cash flow is the result of two things: the tax
saving from depreciation and the operating cash flow after taxes.
Aftertax cash flow $65,946
Less cash flow from tax shield [40% x ($250,000/5)] 20,000
Aftertax cash flow from operations 45,946
Divided by (1 40% tax rate) 60%
Equals pretax cash flow from operations $76,577
89 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) 400,000
Net present value $ 46,262
* ($80,000 + $20,000) x .636
810 Replacement Decision
Working Capital (1520 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 80,000
Loss 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 $ 96,000
Present value factor, 2 years, 14% 1.647
Present value of flows 158,112
Investment 156,480
Net present value $ 1,632
811 Basic MACRS (1015 minutes)
Aftertax 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 1,500,000
Net present value $ 175,440
812 Mutually Exclusive Alternatives (Extension of 721) (1015 minutes)
1. 1.330 for the handfed machine and 1.228 for the semiautomatic machine.
HandFed Semiautomatic
Total present value of future cash
flows (from 722) $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 recommendation
that 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 the
cost of capital, investing in the handfed 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.
813 Investing to Reduce Inventory, JIT (1520 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
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.
814 New Product Decision
Sensitivity Analysis (2025 minutes)
Note to the Instructor: You might want to ask the class whether
Minnie’s might suffer losses in sales of its other doughnuts. We deem this
likely because people probably don’t 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 aftertax cash flow $ 65,250
2. (a) $43,757
Increase in annual aftertax 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 aftertax cash flows $ 11,251
Divided by (1 45% tax rate) 55%
Equals allowable decrease in beforetax 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)
Closest factors for 16%:
For 4 years
3.218
2.798
For 5 years
3.274
5. 43,181 units
Estimated sales, in cases 50,000
Allowable decrease in annual beforetax cash flows (from req 3) $ 20,457
Divided by perunit 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 beforetax 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 percase variable cost.
815 Working Capital (15 minutes)
General Note to the Instructor: This exercise illustrates the principle
that 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 cutoff 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)
816 Mutually Exclusive Investments (20 minutes)
1. (a) $351,900 for the handfed machine, $408,840 for the semiautomatic
machine.
Handfed 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
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% 128,000 128,000
Net 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 handfed, 14% for the semiautomatic
Handfed: $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 handfed and 1.204 for the semiautomatic
Handfed: $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 handfed 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, handfed 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.
817 Sensitivity Analysis (Extension of 816) (20 minutes)
The sales volumes needed to provide a 10% return are $1,431,857 for the
handfed machine and $1,565,188 for the semiautomatic model.
HandFed 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 $ 110,887
Divided 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 breakeven volume, based on NPV's, is higher for that
machine. Thus, the semiautomatic machine is riskier than the handfed one.
However, both breakeven volumes are well below the $1,750,000 anticipated,
so the difference is probably not large enough to change the decision.
818 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 $463,968
Present 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 7year MACRS is worth $46,008 present value ($20,040 + $25,968, or
$162,000 $115,992.
819 Review of Chapters 7 and 8 (2540 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 aftertax cash flows $ 68,000
2. $54,452
Increase in annual aftertax 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 aftertax cash flow of $14,002
Divided by (1 40% tax rate) 60%
Equals allowable decrease in annual beforetax 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 requirement
5
(3.088) is between the factors at 16% for 4 and 5 years (2.798 and 3.274,
respectively).
820 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
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 1.25
Times investment $361,600
Equals total present value of future cash flows 452,000
Less investment 361,600
Net present value $ 90,400
821 Review of Chapters 7 and 8 (4560 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 aftertax 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.
Annual increase in aftertax 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 presentvalue factor for 12% for 4 years 3.037
Equals required annual aftertax 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 13 Year 4
Tax Cash Flow Tax/Cash
Annual 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
Singleamount 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
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 aftertax 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
822 Asset Acquisition and MACRS (1520 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 straightline depreciation over 10 years.
Cash operating savings $ 260,000
Less depreciation ($1,000,000/10) 100,000
Increase 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 straightline depreciation, a decline of
$46,400.
823 Working Capital Investment (1520 minutes)
The NPV is a positive $88,734 and the offer is desirable.
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 $ 682,344
Investment:
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.
824 Replacement Decision (1520 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) 70,000
Increase 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)
825 Sensitivity Analysis and MACRS (Extension of 811) (1020 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 811 $175,440
Divided by present value factor 5.216
Equals allowable decline in aftertax 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
826 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) $ 9,000
Tax on cost savings (40%) 3,600
Net aftertax 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 aftertax savings from Machine B (over Machine A) $ 7,000
Present value factor, 10 years, 10% 6.145
Present value of aftertax 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 beforetax 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
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.
827 Unit Costs (2025 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 200,000
Increased 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 123. 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 of
existing 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.
828 JIT, Inventory (1520 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 aftertax 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
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.
829 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 64,000
Decrease 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)
830 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%.
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.
831 Alternative Production Process (1015 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)
832 Sensitivity Analysis (2530 minutes)
1. 29,027 units
Annual 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 perunit 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 aftertax cash flow $214,439
Less cash savings from tax shield of depreciation
($600,000/4) x 40% 60,000
Equals required aftertax cash flow of nondepreciation items $154,439
Add aftertax effect of cash for fixed cost ($250,000 x 60%) 150,000
Equals required aftertax effect of contribution margin $304,439
Divided by (1 40% tax rate) 60%
Required contribution margin $507,398
Divided by perunit contribution margin $16
Equals required annual volume 31,712
Note to the Instructor: The solution shown above follows the conceptual
approach presented in the solution to 820. 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 Flow
Expected 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 aftertax 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 aftertax increase in expected annual cash flows $ 16,440
Divided 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
833 Determining Required Cost Savings (20 minutes)
1. About $3.89
Investment $150,000
Divided 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 perunit saving $3.891
2. About $4.42. The solution below uses the approach of CVP analysis.
Required aftertax 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
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) 30,000
Increase in taxable income $ 58,000
Increase in taxes (at 40%) 23,200 23,200
Increase in annual aftertax cash flow 64,800
Times present value factor 3.274
Equals present value of future aftertax 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.
834 BenefitCost 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
on their experiences and personal views. Scores of nonquantifiable 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 the
communitytreatment 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 heartdisease victims whose children are more likely
to be selfsupporting. 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 save
one 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 sociopolitical 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.
835 WhentoSell 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 SixYearOld 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.
