capital budgeting decisions - part ii

8/13/2019 Capital Budgeting Decisions - Part II

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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


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


Increased income taxes at 40% 34,000 34,000

Net cash flow 126,000


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



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8-11 Basic MACRS (10-15 minutes)

After-tax cash flow ($400,000 x .60) $ 240,000


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 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 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


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


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


Depreciation ($1,000,000/10) 100,000


Increase in taxes at 40% 80,000 80,000



Present value of future flows $1,351,900

Less investment 1,000,000



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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


Depreciation ($2,000,000/10) 200,000


Increase in taxes at 40% 128,000 128,000Net cash flow $ 392,000





(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



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




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


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


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


Equals allowable decrease in annual after-tax cash flow of $14,002


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


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


(d) 12%


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


(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



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 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


Total present value of increase in future cash flows $276,823



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


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


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 taxes at 30% 10,725 10,725 Increase in annual after-tax cash flow $ 89,275



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




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


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.


15/35

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 $ 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:


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




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


Equals allowable decline in pretax savings $ 56,058

Pretax savings required, $400,000 - $56,058 $343,942


16/35

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 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


17/35

Machine A Machine B

Annual cash flow (increase) $ 5,600 ($ 80)


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


Net cash flow $254,000


Present value of flows $552,196



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 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


18/35

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 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 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:


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%.


19/35

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 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


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


Required contribution margin $507,398

Divided by per-unit contribution margin $16

Equals required annual volume 31,712


20/35

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 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


NPV ($

46,000)


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


21/35

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


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


Equals allowable decline in net cash flow $18,984


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


22/35

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.


23/35

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


Tax on above increase (40%) 12,300

Net increase in after-tax cash flow $26,450


24/35

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


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


Depreciation ($500,000/4) 125,000

Taxable income $ 390,000

Tax at 40% 156,000Annual cash flow $ 359,000


Total present value of future annual returns $ 929,451

Present value of return of working capital investment

$200,000 x 0.482 96,400




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


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


25/35

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


Tax on increased income, at 40% 1,628 1,628

Increase in net cash flow $ 4,372


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



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


26/35

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 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 of future cash inflows $4,171,953




27/35

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


Tax at 40% 8,000 8,000

Net cash flow $112,000


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.


Machinery $2,000,000

Inventories 500,000

Receivables (10,000 units per month x 2 x $20) 400,000


28/35

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 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


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 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 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 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 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 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


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 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



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


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 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




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)


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


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.


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 of future cash flows $ 611,858

Net investment required, from above 306,000


* $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


Investment required 4,000.000


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



Less investment required 5,500,000


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 taxable income $ 150,000

Increased income tax at 40% 60,000 60,000

Increased net cash flow $ 240,000


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

capital budgeting decisions - part ii

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