Making Investment Decisions with the Net Present Value

Rule

Principles of Corporate Finance

Seventh Edition

Richard A. Brealey

Stewart C. Myers

Chapter 6

McGraw Hill/Irwin

Topics Covered

• What To Discount• IM&C Project• Project Analysis

What To Discount

Only Cash Flow is Relevant

Cash flows• This information has to be checked for

completeness, consistency, and accuracy. • The financial manager has to ferret out hidden

cash flows and take care to reject accounting entries that look like cash flows but truly are not.

• Second, how does the financial manager pull everything together into a forecast of overall, “bottom-line” cash flows?

Continue• This requires careful tracking of taxes;

changes in working capital; inflation; and the end-of-project “salvage values” of plant, property, and equipment.

• Third, how should a financial manager apply the net present value rule when choosing between investments in plant or equipment with different economic lives?

Cash Flows1. Only cash flow is relevant:• Net present value depends on future cash

flows. • Cash flow is the simplest possible concept; it

is just the difference between dollars received and dollars paid out.– Always estimate cash flows on an after-tax basis.– Make sure that cash flows are recorded only when

they occur and not when work is undertaken or a liability is incurred.

Continue• 2. Estimate CF’s on an Incremental Basis: The value of a project depends on all the

additional cash flows that follow from project acceptance.– Do Not Confuse Average with Incremental

Payoffs; • Does it always make sense to throw good money after

good?• E.g., Railroad bridge repair project.

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– Include All Incidental Effects; • It is important to include all incidental effects on the

remainder of the business. • For example, a branch line for a railroad may have a

negative NPV when considered in isolation, but still be a worthwhile investment when one allows for the additional traffic that it brings to the main line.

– Do Not Forget Working Capital Requirements;• Most projects entail an additional investment in

working capital. • This investment should, therefore, be recognized in

your cash-flow forecasts.

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– Include Opportunity Costs;• The cost of a resource may be relevant to the

investment decision even when no cash changes hands. • For example, suppose a new manufacturing operation

uses land which could otherwise be sold for $100,000.• This example prompts us to warn you against judging

projects on the basis of “before versus after.” • The proper comparison is “with or without.”• however, where the resource can be freely traded, its

opportunity cost is simply equal to the market price.

Continue– Forget Sunk Costs;

• Sunk costs are like spilled milk. • They are past and irreversible outflows. • Sunk costs are bygones, they cannot be affected by the

decision to accept or reject the project, and so they should be ignored.

– Beware of Allocated Overhead Costs;• A project may generate extra overhead expenses; then

again, it may not. • We should be cautious about assuming that the

accountant’s allocation of overheads represents the true extra expenses that would be incurred.

Case: Simon North• In 1898 Simon North announced plans to construct a

funeral home on land he owned and rented out as a storage area for railway carts. (A local newspaper commended Mr. North for not putting the cart before the hearse.) Rental income from the site barely covered real estate taxes, but the site was valued at $45,000. However, Mr. North had refused several offers for the land and planned to continue renting it out if for some reason the funeral home was not built. Therefore he did not include the value of the land as an outlay in his NPV analysis of the funeral home. Was this the correct procedure? Explain.

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• Solution: No, this is not the correct procedure. The opportunity cost of the land is its value in its best use, so Mr. North should consider the $45,000 value of the land as an outlay in his NPV analysis of the funeral home.

• Be consistent in how you handle inflation!!

• Use nominal interest rates to discount nominal cash flows.

• Use real interest rates to discount real cash flows.

• You will get the same results, whether you use nominal or real figures

InflationINFLATION RULEINFLATION RULE

Inflation

ExampleYou own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

1 real interest rate = 1+nominal interest rate1+inflation rate

InflationExample - nominal figures

Year Cash Flow PV @ 10%

1 8000

2 8000x1.03 = 8240

8000x1.03 = 8240

8000x1.03 = 8487.20

80001.10

2

3

7272 73

6809 92

3 6376 56

4 5970 78

429 99

82401 108487 20

1 108741 82

1 10

2

3

4

.

.

.

.

$26, .

..

..

.

InflationExample - real figures

Year Cash Flow PV@6.7961%

1 = 7766.99

2 = 7766.99

= 7766.99

= 7766.99

80001.03

7766.991.068

82401.03

8487.201.03

8741.821.03

2

3

4

7272 73

6809 92

3 6376 56

4 5970 78

26 429 99

7766 991 068

7766 991 068

7766 991 068

2

3

4

.

.

.

.

..

..

..

= $ , .

Inflation

Example• You are given project cash flows estimated in real

terms, that is, current dollars and nominal interest rate is 15%:

Real Cash Flows ($ 000)• C0 C1 C2 C3• -100 35 50 30• It would be inconsistent to discount these real cash

flows at 15 percent.

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• Two alternatives: – Either restate the cash flows in nominal terms and

discount at 15 %,– or restate the discount rate in real terms and use

it to discount the real cash flows.• Assume that inflation is projected at 10 percent a year.

• Cash flow for year 1;• 35,000 X 1.10 = $38,500

Continue• Cash flow for year 2;

• 50,000 X (1.10)2 = $60,500

• Cash flow for year 3;• 30,000 X (1.10)3 = $39,930

• NPV = 5.5, or $5,500.

IM&C’s Guano Project

• You are given the forecasts shown in Table 1.– The project requires an investment of $10 million

in plant and machinery (line 1). – This machinery can be dismantled and sold for net

proceeds estimated at $1.949 million in year 7 (line 1, column 7).

– This amount is your forecast of the plant’s salvage value.

IM&C’s Guano ProjectRevised projections ($1000s) reflecting inflation

IM&C’s Guano Project

• NPV using nominal cash flows

$3,519,000or 519,3

20.1

444,3

20.1

110,6

20.1

136,10

20.1

685,10

20.1

205,6

20.1

381,2

20.1

630,1000,12

76

5432

NPV

IM&C’s Guano ProjectCash flow analysis ($1000s)

A Further Note on Estimating Cash Flow

• Working capital increases in the early and middle years of the project.

• What is working capital?• you may ask, and why does it increase?• Its most important components are inventory,

accounts receivable, and accounts payable.• i.e.,

– WC = inventory + AR - AP– $1,289 = 635 + 1,030 - 376

Continue• Why does working capital increase? There are

several possibilities:– 1. Sales recorded on the income statement overstate

actual cash receipts from guano shipments because sales are increasing and customers are slow to pay their bills. Therefore, accounts receivable increase.

– 2. It takes several months for processed guano to age properly. Thus, as projected sales increase, larger inventories have to be held in the aging sheds.

– 3. An offsetting effect occurs if payments for materials and services used in guano production are delayed. In this case accounts payable will increase.

IM&C’s Guano Project

Details of cash flow forecast in year 3 ($1000s)

A Further Note on Depreciation• It provides an annual tax shield equal to the

product of depreciation and the marginal tax rate:– Tax shield = depreciation x tax rate– = 1,583 x .35 – =554, or $554,000

• The present value of the tax shields ($554,000 for six years) is $1,842,000 at a 20 % discount rate.

IM&C’s Guano ProjectTax depreciation allowed under the modified accelerated cost recovery system (MACRS)

IM&C’s Guano Project

Tax Payments ($1000s)

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• Next slide Shows revised after-tax cash flows and present value.

• This time we have incorporated realistic assumptions about taxes as well as inflation.

• We of course arrive at a higher NPV than previous calculations.

IM&C’s Guano ProjectRevised cash flow analysis ($1000s)

Case: Firm’s Tax Position

• Discuss the following statement: “We don’t want individual plant managers to get involved in the firm’s tax position. So instead of telling them to discount after-tax cash flows at 10 percent, we just tell them to take the pretax cash flows and discount at 15 percent. With a 35 percent tax rate, 15 percent pretax generates approximately 10 percent after tax.”

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• Unfortunately, there is no simple adjustment to the discount rate that will resolve the issue of taxes. Mathematically: C 1 ≠ C 1 /(1 - 0.35)

1.10 1.15 C 2 ≠ C2 /(1 - 0.35)

(1.10)2 (1.15)2

Case: Mrs. T. Potts• Mrs. T. Potts, the treasurer of Ideal China, has a

problem. The company has just ordered a new kiln for $400,000. Of this sum, $50,000 is described by the supplier as an installation cost. Mrs. Potts does not know whether the Internal Revenue Service (IRS) will permit the company to treat this cost as a tax-deductible current expense or as a capital investment. In the latter case, the company could depreciate the $50,000 using the five-year MACRS tax depreciation schedule. How will the IRS’s decision affect the after-tax cost of the kiln? The tax rate is 35 % and the opportunity cost of capital is 5 %.

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• If the $50,000 is expensed at the end of year 1, the value of the tax shield is:– 0.35 x $50,000 = $16,667

1.05• If the $50,000 expenditure is capitalized and

then depreciated using a five-year MACRS depreciation schedule, the value of the tax shield is:

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• If the cost can be expensed, then the tax shield is larger, so that the after-tax cost is smaller.

Summary

• What To Discount• IM&C Project