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Corporate Finance:Capital Budgeting

Professor Scott Hoover

Management 221

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The Importance of Capital Budgeting definition: A “capital budget” is a long-term plan that

describes the use of long-term assets (capital) and details expected future cash inflows and outflows (budget).

How are projects created? someone identifies a potential market marketing personnel determine the market size (sales

projections, etc.) engineers, cost accountants, and management personnel

estimate production costs finance personnel take projected costs and revenues and

decide whether or not to accept the project

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verify that the projected cash flows are all the “incremental cash flows” for the project incremental cash flows include any impacts that the project

may have on firm cash flows identify cost of capital calculate NPV, IRR decide whether or not to accept the project.

finance personnel acquire financing for the project issue securities (stock, bonds, preferred stock) if necessary

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Project Evaluation Techniques Net Present Value (NPV)

NPV the present value of all cash flows (including the initial investment) evaluated at the company's cost of capital.

We will define cost of capital in more detail later. For now, think of it as the interest rate desired by company investors.

Example: A firm is considering a project with projected cash flows as follows.

Should the project be accepted?

Date 0 1 2 3 4 5

Cash Flow -$100,000 $20,000 $25,000 $30,000 $35,000 $35,000

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Suppose that the firm has a cost of capital of 10%. The NPV of the project is calculated as follows:NPV = - $100,000 + $20,000/1.1 + $25,000/1.12 + $30,000/1.13

+ $35,000/1.14 + $35,000/1.15

= $7,020 The NPV rule: Companies should accept any and all

projects that have positive NPVs and should reject any and all projects that have negative NPVs. Intuition: If the NPV is positive, then the project is expected to

pay more than enough money to give investors the return they desire.

Internal Rate of Return (IRR) IRR the implied interest rate on the project. Said

differently, the IRR is the interest rate that makes the NPV equal to zero.

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NPV = 0 = - $100,000 + $20,000/(1+IRR) + $25,000/(1+IRR)2 + $30,000/(1+IRR)3+ $35,000/(1+IRR)4 + $35,000/(1+IRR)5

Solving for the IRR (by trial and error or financial calculator) gives IRR = 12.4534%

The IRR rule: If a company's cost of capital is lower than the IRR, then the company should accept the project. If the cost of capital is higher than the IRR, then the project should be rejected. Note: This rule may not work if the project has unusual cash

flows. For example, if the sign (+ or -) of the expected cash flows changes more than once, there may be more than one IRR. In our example, there is one sign change, so there can only be one IRR.

In our example, the firm has a cost of capital of 10%. The project should be accepted because the project will create more profits than are needed to pay interest on the borrowing.

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Note that the NPV Rule and the IRR Rule are consistent as long as we have typical cash flow structures. To see this, consider the following.

We accept the project if and only if the cost of capital is below the IRR. Notice that this region corresponds to NPV>0.

Cost of Capital NPV IRR

8% $13,313 12.45%

10% $7,020 12.45%

12% $1,243 12.45%

12.4534% $0 12.45%

14% -$4,070 12.45%

16% -$8,966 12.45%

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Example: Suppose that two projects are mutually exclusive. This means that the firm may choose only one of the two projects. The expected cash flows are as follows.

If the cost of borrowing is 10%, which project should be chosen? NPVA = -$100,000,000 + $111,100,000 / 1.1 = $1,000,000

NPVB = -$1,000,000 + $2,200,000 / 1.1 = $999,999 The NPV of Project A is higher, so we should take it…

or should we?

Date CF for Project A CF for Project B

0 -$100,000,000 -$1,000,000

1 $111,100,000 $2,199,999

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Suppose our cash flow estimates turn out to be too high by, say, 2%. The cash flows would be.

NPVA = -$100,000,000 + $108,878,000 / 1.1 = -$1,020,000

NPVB = -$1,000,000 + $2,155,999 / 1.1 = $959,999

Date CF for Project A CF for Project B

0 -$100,000,000 -$1,000,000

1 $108,878,000 $2,155,999

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Notice that the NPV of A is now negative, while the NPV of B is still large and positive. This suggests that we should take Project B. Why? There is more room for error in our estimates with Project B.

Notice also that the IRR for Project B is much higher than the IRR for Project A: IRRA = ($111,100,000 - $100,000,000) / $100,000,000 =

11.1% IRRB = ($2,199,999 - $1,000,000) / $1,000,000

= 119.99% !!

This illustrates why that we should always look at the IRR on projects in addition to the NPV.

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The NPV always gives the correct decision when projects are independent (meaning that we can take any or all of them).

When projects are mutually exclusive, the NPV rule may give an incorrect decision. In those cases, we need to come to some subjective conclusion based on all the evidence.

Why might projects be mutually exclusive? capital constraints management constraints resource constraints

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What cash flows are relevant to the project decision? example: Suppose that you have spent $1,000,000 on a

project already. If you abandon the project right now, you will get nothing. If you spend an additional $200,000, you will get a payoff on the project of $1,100,000. The cost of capital is 10%. What should you do? Argument #1: NPV = -$1,200,000 + $1,100,000/1.1 = -

$200,000 Reject (abandon) the project.

Argument #2: NPV = -$200,000 + $1,100,000/1.1 = $800,000 Continue the project

Which is correct? Intuitively, we know that we should continue. Implication:

Any cost that has already been spent/committed should be ignored in NPV analysis.

These costs are irrelevant and are called “sunk costs”.

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The bottom line on relevant cash flows is the following. Any cash flow that is different if the firm takes the project than

if the firm rejects the project is a relevant cash flow. These cash flows are called the incremental cash flows for the

project. example: Suppose that a firm is considering a project. If

the project is accepted, the firm will sell some of its old equipment for $2,500,000. The equipment has a book value of $1,400,000. If the firm’s marginal tax rate is 30%, what is the cash flow for the sale? Is the cash flow relevant? … yes. Cash flow = Sale Price - Profits Tax Rate

= Market Value - (Market Value - Book Value) Tax Rate = $2,500,000 - ($2,500,000 - $1,400,000) 0.3 = $2,170,000

This type of cash flow is called a “salvage cash flow.”

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example: Suppose that a firm owns land that has a market value of $5,000,000. The firm is considering a project that will require the use of the land. What is the relevant cash flow for the land? Is the cash flow relevant? … YES! If the firm accepts the projects, it gives up the ability to sell the

land or do something else with it. The incremental cash flow here is the value of the best

alternative use of the land. Assuming the best use is to sell it, the firm incurs an

incremental cash flow of -$5,000,000 if the project is accepted. Note: we would also include any tax effect on the sale.

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example: Suppose that your firm is considering a project. If the project is accepted, the firm will have to create a cash account of $200,000 to handle “net working capital” requirements. The project will last for 6 years. Are there relevant cash flows here? …yes The firm will have to "deposit" $200,000 at the beginning of the

project, so there will be a cash outflow of $200,000 at that time. At the end of the project, the firm will be able to close the

account, so there will be a cash inflow of $200,000 at that time.

Any impacts on net working capital accounts (current assets and current liabilities) are considered relevant cash flows.

Notice that we “recover” the net working capital at the end of the project. When the project is over, we will no longer need the net working capital, so we are able to use the funds for other purposes

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example: Suppose that Dell Computer is considering a project in which it will introduce a new line of computers. These computers will be in direct competition with Dell's current line of Pentium computers. As a result, Dell expects decreased profits (after-tax) of $54,000,000 per year. Are there relevant cash flows here? …yes If Dell introduces the new line, it will have decreased sales of

Pentium computers. If it doesn't introduce the line, sales of Pentium computers will not decrease.

Relevant cash flow = -$54,000,000 per year. This type of cash flow is called an externality. If an externality

results in decreased sales for other products, the externality is called cannibalization.

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Accounting Numbers vs. Relevant Cash Flows example: Suppose that a company has the following

income statement.

What is the relevant cash flow?

Income Statement

Sales $400,000

Costs $275,000

Depreciation $100,000

Operating Income $25,000

Taxes (40%) $10,000

Net Income $15,000

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What are the relevant cash flows?

Income Statement Cash Flow

Sales $400,000 $400,000

Costs $275,000 $275,000

Depreciation $100,000

Operating Income $25,000

Taxes (40%) $10,000 $10,000

Net Income $15,000 $115,000

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Total Cash flow = $400,000 - $275,000 - $10,000 = $115,000 The taxes are calculated as (Sales - Costs - Depreciation)

Tax Rate, so we calculated the total cash flow as CF = S - C - (S - C - D) T. Rearranging this, we get

CF = (S - C) (1-T) + D T

This cash flow called the “operating cash flow.”

Notes: Sales do not, in general, equal receipts from sales (since

some sales are made on accounts receivable). Cost of Goods Sold does not, in general, equal the

disbursement for projects (since some purchases are made on accounts payable).

Fortunately, the adjustments for those discrepancies are taken care of when we include the change in net working capital as a cash flow.

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The Weighted Average Cost of Capital (WACC) definition: the “cost of capital” is the firm's marginal cost (as

a percentage) of acquiring capital, given that the firm maintains its current debt/equity/preferred stock distribution.

Cost of Equity (or….the Cost of Retained Earnings) Suppose that a firm is all-equity and that the firm intends to

stay that way. What is the firm's cost of borrowing money? Investors will demand an interest rate (in expectation) that

compensates them for the non-diversifiable risk they face.

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Diversifiable (unsystematic or irrelevant) risk vs. Non-diversifiable (market or systematic or relevant) risk

Important point: Investors will only be compensated for the risk that they would face given that they reduce it as much as possible. If they do not choose to diversify, they will not be compensated for the extra risk they have voluntarily chosen to take.

The risk that remains after it has been reduced as much as possible is called “non-diversifiable risk.” …risk associated with macroeconomic conditions such as

inflation, changes in taxation, changes in trade policies, etc. The risk that has been taken away is called “diversifiable risk.”

…risk associated with only the firm, such as chance of a manufacturing plant fire, chance of e coli in food products, etc.

Why is this diversifiable risk?

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The Capital Asset Pricing Model (CAPM): KE = Rf +(Rm-Rf) = measure of the non-diversifiable risk of the stock.

= 1…..investment has the same non-diversifiable risk as the market.

= 0….investment has no non-diversifiable risk (Treasury bills, for instance).

< 0….investment is negatively correlated with the market (gold perhaps). These can be very useful for diversification.

0 < < 1….investment has less non-diversifiable risk than the market.

> 1….investment has more non-diversifiable risk than the market.

returnmarket return,stockwhere

,,

mi

m

mi

RR

RVar

RRCov

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Cost of Debt What is the firm's interest rate on debt?

easy to measure because we can readily observe the yield on existing debt

must adjust the cost for the interest tax deduction cost of debt KD

after-tax cost of debt = KD(1-t), where t is the company's tax rate

Example: Suppose a company has bonds outstanding with 5 years to maturity, 10% annual coupons, and a market price of $980. The company's marginal tax rate is 40%. What is the cost of debt? KD = 10.53%

What is the after-tax cost of debt? KD (1-t) = 10.53% (1-0.4) = 6.32%

Notice that because of the tax advantage, it is typically fairly cheap to borrow by issuing debt.

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Cost of Preferred Stock There is no tax advantage (typically) on preferred stock. easy to calculate because preferred stock is really just a

perpetual bond Example: Suppose that a company has preferred stock that

currently sells (on the open market) for $34 per share. The promised dividend is $4 per year. What is the cost of the company's preferred stock? KPS = DPS / P = 4/34 = 0.1176 = 11.76%

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Weighted Average Cost of Capital

Notice that D, E, PS, and TA (which is D+E+PS) should be included as market values.

Why? The WACC is the appropriate discount rate to use for

projects because it gives us the firm's average cost of borrowing.

Said differently, it is the amount of money that must be paid out of firm profits to satisfy all the firm’s investors.

PSED KTA

PSK

TA

EtK

TA

DWACC 1

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example: Suppose that a firm is financed with $40M debt, $10M preferred stock, and $50M common equity. What is the WACC? Further information: debt: currently, the firm has an 8% annual coupon, 10 year

bond that sells for $1000. preferred stock: currently the firm has preferred shares

outstanding that sell for $27.50. The promised dividend is $3.

common equity: The company has a beta of 1 and the expected market return is 11.25%.

marginal tax rate: 38% What is the firm's WACC if the firm plans to finance with

new issues? KD = 8% (since the bonds sell at par) KPS = D1/P = 3/27.50 = 10.909% KE = 11.25% (since the beta is 1) WACC = 0.4 (8%) (1-0.38) + 0.1(10.909%) + 0.5 (11.25%) =

8.7%

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Questions What if the company is not publicly-traded? What is the project under consideration differs from the

company’s current projects? In theory, the WACC should be the interest rate that

compensates investors for the level of non-diversifiable risk associated with the project. We can use the company’s WACC only if the project under consideration is similar in risk to the rest of the company. If not, we use what is called the “pure play approach.”

Pure Play Approach 1. Identify public companies that work in the line of business

we are considering. 2. Estimate the WACCs for those companies. 3. Use those estimates to find the appropriate discount rate

for the project.

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Equivalent Annual Annuities Example: A company is considering two projects, but may only

choose one of them. The company’s WACC is 9%. The expected cash flows of those projects are as follows.

Which project should the company choose? NPVA = $749,806 ; NPVB = $1,058,561

Date E(CF) for Project A E(CF) for Project B

0 -$1,000,000 -$1,000,000

1 $500,000 $300,000

2 $800,000 $600,000

3 $800,000 $600,000

4 $600,000

5 $600,000

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It appears that B is the better project, but notice that B ties up the firm for 5 years, while A ties it up for 3 years. An advantage of A is that the firm might be able to earn additional profits in years 4 and 5. How can we take that into account?

Equivalent Annual Annuity the annuity payment over the life of the project that would give the same NPV as the project itself. Project A: C/1.09 + C/1.092 + C/1.093 = $749,806 C = $296,215 Project B: C/1.09 + C/1.092 + C/1.093 + C/1.094 + C/1.095 =

$1,058,561 C = $272,148 So, project A provides more value per year and therefore is

preferred to project B.

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Other measures of value payback discounted payback adjusted net present value economic value added (EVA)

The Importance of Sensitivity Analysis

Examples see handout

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#1: A company is considering a project that requires an initial investment of $24M to build a new plant and purchase equipment. The investment will be depreciated as a MACRS 7-year class (see p. 21 in the text) asset. The new plant will be built on some of the company's land which has a current, after-tax market value of $4.3M. The company will produce units at a cost of $130 each and will sell them for $420 each. There are annual fixed costs of $0.5M. Unit sales are expected to be 150,000 each year for the next 6 years, at which time the project will be abandoned. At that time, the plant and equipment is expected to be worth $8M (before tax) and the land is expected to be worth $5.4M (after tax). To supplement the production process, the company will need to purchase $1M worth of inventory. That inventory will be depleted during the final year of the project. The company has $100M of debt outstanding with a yield-to-maturity of 8%, and has $150M of equity outstanding with a beta of 0.9. The expected market return is 13% and the risk-free rate is 5%. The company's marginal tax rate is 40%. Should the project be accepted?

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Solution to #1 WACC:

wD = $100M / $250M = 0.4

kD = 8%wE = $150M / $250M = 0.6

kE = 5% + 0.9(13% - 5%) = 12.2% WACC = 0.48%(1-0.4) + 0.612.2% = 9.24%

Capital Expenditure: -$24M at date 0

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Date MACRS % Depreciation Book Value

0 $24.000

1 14.29% $3.430 $20.570

2 24.49% $5.878 $14.692

3 17.49% $4.198 $10.494

4 12.49% $2.998 $7.496

5 8.93% $2.143 $5.353

6 8.92% $2.141 $3.212

7 8.93% $2.143 $1.070

8 4.46% $1.070 $0.000

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Salvage cash flow of new equipment in 6 years: Salvage CF = $8M - 0.4($8M - $3.212M) = $6.085M

Change in Net Working Capital: -$1M at date 0; +$1M at date 6

Operating Cash Flows: Sales = 150,000 $420 = $63,000,000 Costs = 150,000 $130 + $0.5M = $20,000,000 OCF = (S - C) (1-0.4) + D 0.4 = 25,800,000+D0.4

Date Depreciation OCF

0

1 $3.430 $27.172

2 $5.878 $28.151

3 $4.198 $27.479

4 $2.998 $26.999

5 $2.143 $26.657

6 $2.141 $26.656

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Other Relevant Cash Flows: Land The $4.3M is an opportunity cost and must be included at date

0. If the project is accepted, however, the land can be sold in 6

years for $5.4M. Is this an incremental cash flow? Yes, because we wouldn't be selling it then if we reject the project.

Putting all this together gives us the total expected incremental cash flows for the project

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Date Cap. Exp. NWC Salvage OCF Other (Land) Total

0 -$24M -$1M -$4.3M -$29.300M

1 $27.172M $27.172M

2 $28.151M $28.151M

3 $27.479M $27.479M

4 $26.999M $26.999M

5 $26.657M $26.657M

6 $1M $6.085M $26.656M $5.4M $39.141M

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NPV = -29.3 + 27.172/ 1.0924 + … + 39.141/1.09246 = $99.37M > 0IRR = 92.53% > 9.24%

Accept the project