Chapter 8, 9, 10 Notes, Questions, and Answers

1 Things to Remember

1. Difference between independent and mutually exclusive.

2. Difference between ordinary payback and discounted payback

3. If project is replacement or expansion.

4. If replacing old machinery with new take into account the incremental cash flows.

2 Chapter 8 Notes

2.1 Capital Budgeting categories:

1. Replacement projects.

2. Expansion projects.

3. New products and services.

4. Regulatory, safety, and environmental projects.

2.2 Principals of Capital Budgeting.

1. Timing of cash flows is crucial. Time Value of Money

2. Incremental Cash Flows.

3. Cash flows are analysed on an after-tax basis.

4. Financing costs are ignored.

5. Cash flows are not net income.

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2.3 Capital budgeting concepts.

1. A sunk cost is one that has already been incurred.

2. An opportunity cost is what a resource is worth in its next-best use.

3. Independent versus mutually exclusive.

2.4 Capital budget procedures

• NPV

• IRR

• Payback Period

• Profitability Index

2.4.1 Drawbacks of Payback

• Does not take into account time value of money

• ignores cash flows after payback.

• Projects with shorter paybacks may have lowest NPV

2.4.2 Pitfalls of IRR

• Borrowing or Lending

• Multiple Rates of Return

• Mutually Exclusive. Differing Cash flow patterns and Scale.

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2.5 NPV and Stock Prices

2.6 Investment Timing

You may purchase a computer anytime within the next five years. While the computer will

save your company money, the cost of computers continues to decline. If your cost of capital

is 10% and given the data listed below, when should you purchase the computer?

3 Chapter 9 Notes

1. Initial Outlay:

Outlay = FCInv + NWCInv (1)

where

• FCINV=investment in new fixed capital.

• NWINV=investment in net working capital.

2. Annual after-tax operating cash flow:

CF = (S − C −D)(1− T ) + D (2)

or

CF = (S − C)(1− T ) + T ∗D (3)

where

• S=Sales

• C=cash operating expenses

• D=depreciation charge

• T=taxes

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3. Terminal year after-tax nonoperating cash flow:

TNOCF = SALT + NWInvT (SalTBT ) (4)

where

• SALT=cash proceeds from sale of fixed capital

• BT=Book value of fixed capital on termination date.

4 Chapter 10 notes

Risk is the measure of the dispersion of outcomes. In this case we measure the riskiness of

a project by the dispersion of NPVs or IRRs.

1. Sensitivity Analysis - Analysis of the effects on project profitability of changes in sales,

costs, etc.

2. Scenario Analysis - Project analysis given a particular combination of assumptions.

3. Simulation Analysis - Estimation of the probabilities of different possible outcomes.

4. Break Even Analysis - Analysis of the level of sales at which the company breaks even.

4.1 Real Options

• Timing options: A company can delay investing.

• Sizing or Abandon: If the cash flow from abandoning a project exceeds the PV of cash

flows from continuing than abandon.

• Flexibility:

• Fundamental option: The payoffs from the investment are contingent on an underlying

asset. Ex. the value of an oil well is contingent on the price of oil.

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5 Chapter 8 Questions

Use Table 1 to answer questions 1-6. The required rate of return is 8%.

Table 1: Capital Budgeting

Year 0 1 2 3 4 5

Cash flow -50,000 15,000 15,000 20,000 10,000 5,000

1. Calculate the NPV.

2. Calculate the IRR.

3. Should you invest?

4. Calculate the payback period.

5. Calculate the discounted payback period.

6. Calculate the profitability index.

Use Table 2 to answer questions 7-8. The required rate of return is 12%.

Table 2: Independent and Mutually Exclusive

Project A Project B

Initial Cost 15,000 20,000

Life 5 years 4 years

Cash inflows 5,000/year 7,500/year

7. If the projects are independent the company should accept both, reject both, accept

A and not B, or accpet B and not A?

8. If the projects are mutually exclusive the company should accept both, reject both,

accept A and not B, or accpet B and not A?

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Use Table 3 to answer question 9.

Table 3: Mutually Exclusive: Magnitude

year 0 1 2 3 4

A -100 50 50 50 50

B -400 170 170 170 170

9. If the two projects in Table 3 are mutually exclusive which one would you choose if

the discount rate is 10%?

10. You are interested in investing in a new computer. The cost today is 950. The cost

next year is 900. The present value of the savings is 1150. The discount rate is 10%.

Should you buy today or next year?

6 CHAPTER 9 QUESTIONS

Questions 1 to 5 refer to the following information. You are an analyst with Smith Securities.

One of the companies that you follow is Mac Company. Mac Company is considering the

purchase of a new 400-ton stamping press. The press costs $400,000. The press will depre-

ciate straight line to 0 over a five-year life. The press will generate $200,000 in revenues

and $60,000 in operating expenses. The press will be sold for $120,000 after five years. An

inventory investment of $60,000 is required during the life of the investment. Mac is in the

40 percent tax bracket. The cost of capital is 10%.

1. What is Mac’s net investment outlay?

2. What is Mac’s annual after-tax operating cash flow?

3. What is the terminal year’s after-tax nonoperating cash flow at the end of year 5?

4. What is the NPV?

5. Invest or Not?

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6. Your supervisor tells you that you are relying too heavily on the NPV approach in

order to value the investment decision. She thinks that you should use an IRR ap-

proach because of the mutually exclusive problem. How should you respond to your

supervisor?

7. Quick computing installed equipment 3 years ago. This equipment becomes obsolete

in 5 years. It originally cost 40 million and they use straight-line depreciation. It can

be sold now for 18 million. The tax rate is 35%. What is the after-tax cash flow from

the sale?

8. Your boss tells you they want to replace old equipment with new equipment. She gives

you the following numbers to calculate the initial outlay and operating cash flows. The

tax rate is 40%.

Table 4: Replacement

Variable Old New

BV 400

MV 500 1000

Sales 200 300

Expenses 100 130

Depreciation 30 50

7 Chapter 10 Questions

1. A project generates sales of $10 million, variable costs equal to 50% of sales, and fixed

costs of $2 million. The firms tax rate is 35%. What are the effects of the following

changes on after-tax profits and cash flow?

A. Sales increase from 10 to 11 million.

B. Variable costs increase to 65% of sales.

2. The project in the review question 1 will last for 10 years and the discount rate is 12%.

What is the effect on project NPV of each of the changes considered in the problem?

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3. Explain why options to expand or contract production are most valuable when forecasts

about future business conditions are uncertain?

4. • The initial outlay is $200,000.

• Project Life is 5 years.

• Cash flow is $60,000.

• Salvage value is zero.

• The required rate of return is 10 percent.

• In one year, after realizing first-year cash flow, the company has the option to

abandon the project and receive the salvage value of $200,000.

Should the Company Abandon?

5. A farm estimates the NPV for a new plant to be -2 million. The farm is evaluating

an incremental investment of 6 million that would give management the flexibility to

switch between coal, natural gas, and oil as an energy source. The original plant relied

only on coal. The switch has an estimated value of 10 million. What is the value of

the new plant?

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8 Chapter 8 Answers

1.

NPV = −50, 000 + 13, 889 + 12, 860 + 15, 876 + 7350 + 3, 402 = 3, 378.83 (5)

2. The IRR is 10.88% With the TI calculator the IRR can be calculated with:

• 50,000 +/- Enter

• ↓ 13, 889 Enter ↓

•• ↓ 12, 860 Enter ↓

•• ↓ 15, 876 Enter ↓

•• ↓ 7, 350 Enter ↓

•• ↓ 3, 402 Enter ↓

•• IRR CPT

3. NPV is positive and IRR is greater than the cost of capital so invest.

4. You break even in the third year. So the payback is 3 years.

Table 5: Payback

Year 0 1 2 3 4 5

Discounted Cash flow -50,000 15,000 15,000 20,000 10,000 5,000

Cumulative -50,000 -35,000 -20,000 0 10,000 15,000

5. The discounted payback uses discounted cash flows.

Table 6: Discounted Payback

Year 0 1 2 3 4 5

Discounted Cash flow -50,000 13,889 12,860 15,876 7350 3,402

Cumulative -50,000 -36,111 -23,251 -7,374 -24 3,378

The discounted payback is 4 years plus 24.09/3402=.007 or 4.01 years.

6.

PI =PV

InitialInvestment=

53, 378

50, 000= 1.067 (6)

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7. Independent projects accept all with positive NPV or IRR greater than cost of capital.

Project A NPV is 3,024 and Project B NPV is 2,780. So accept both.

8. Accept the project with highest NPV which is Project A.

9. Calculate NPV and choose one with the highest NPV. Project A has a NPV of 58.49

and project B has a NPV of 139. Project B is the better of the two.

10. The NPV today is 1150-950=$200

The NPV next year is 1150−9001.1

=$227

Wait until next year.

9 Chapter 9 Answers

1. The investment outlay is

Outlay = FCInv + NWCInv − Sal0 + T (SAL0 −B0) (7)

(400, 000) + 60, 000− 0 + 0 = $460, 000 (8)

2. Depreciation is $400,000/5=$80,000 per year. The after-tax operating cash flow:

CF = (S − C −D)(1− T ) + D (9)

= [200, 000− 60, 000− 80, 000](1− .40) + 80, 000 = $116, 000 (10)

3. The terminal year nonoperating cash flow is

TNOCF = Sal5 + NWCInv − T (Sal5 −B5) (11)

= 120, 000 + 60, 000− .4(120, 000− 0) = $132, 000 (12)

4. The NPV

NPV = −460, 000 + 116, 000[1

.1− 1

.1(1.1)5] +

132, 000

1.105= $61, 700 (13)

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5. Yes, invest. NPV is positive.

6. I would tell my supervisor that there is only one project and therefore IRR and NPV

will give us the same answer.

7. Depreciation expense per year = $40/5 = $8 million

Book value of old equipment = $40 (3 x $8) = $16 million

After-tax cash flow = $18 [0.35 x ($18 $16)] = $17.3 million

8. Initial Outlay = 1000-500 + .4(500-400)=540

Operating Cash Flow = [(300-200) - (130-100) - (50-30)](1-.40) + (50-30)=50

10 Chapter 10 Answers

1. a. (Revenue expenses) changes by: $1 million $0.5 million = $0.5 million

After-tax profits increase by: $0.5 million x (1 0.35) = $0.325 million

b. Expenses increase from $5 million to $6.5 million.

After-tax income and cash flow decrease by: $1.5 million x (1 0.35) = $0.975 million

2. The 12%, 10-year annuity factor is=5.65022

The effect on NPV equals the change in CF x 5.65022

a. $0.325 million x 5.65022 = $1.836 million

b. $0.975 million x 5.65022 = $5.509 million

3. Options give one the ability to change your actions is most important when the ultimate

best course of action is most difficult to forecast.

4. Four years of $60,000 cash flow has a PV of $190,191. This is lower than the $200,00.

Do Abandon

5. The NPV includes the real option. NPV = NPV(original)-cost of option-value of option

= -2-6+10 =$2 million

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