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Capital Budgeting and

Capital Structure

Financial Management 6301

Dr. Carolyn Reichert

1

2

Company Cost of Capital

Firm value = sum of the value of the assets

Weighted Average Cost of Capital (WACC)

Opportunity cost of capital for existing assets

Use: value new assets with the same risk as the old ones

r WACC = r portfolio = (B/V)r B + (S/V)r S

V = B + S where V, B and S are all market values

r S = r f + ßS(r m - r f )

r S = r o + [(B/S)(r o - r B )]

Exclude taxes for now (so tax rate = 0)



3

Asset betaBeta of a portfolio of all of the firm’s debt &

equity

Relationship between asset and equity betas

ßASSET = ßWACC = (B/V)ßB+(S/V)ßS

• Where V = B + S

• V, B and S are all market values

Can rearrange to get βS = βo + [(B/S)(βo - βB )] No tax adjustment

4

No-Tax Cost of Capital

Unlevered Cost of Capital r o:

Expected return investors want from a project if

it was all-equity financed

No tax world (M&M): r o = r WACC

Unlevered cost of capital and asset beta are

the same for the levered and unlevered firm.

Affected only by business risk



5

Cost of Capital ImplicationsYou can lever and unlever the WACC.

Return on equity and equity beta are

different for the levered and unlevered firm.

Affected by financial risk.

Firms with more debt have higher equity betas

6

Cost of Capital Example

Coyote Corporation has a value of $200M. Debthas a market value of $50M and a return of 6%.Equity has a beta of .75. The risk-free return is3% and the market risk premium is 9%.

Find the original weighted average cost of capital.

If they issue $50M to re-buy equity, find the new

return on equity. The return on debt does notchange



9

Regression Information

Intercept (Jensen’s Alpha)

Simple measure of performance

If α > r f (1-ß), stock did better than expected

If α = r f (1-ß), stock did as well as expected

If α < r f (1-ß), stock did worse than expected

R 2 is the proportion of variance that can be

explained by market risk

(1-R 2): proportion of variance that is firm specific

10

Measuring Betas

Dell Computer

Slope determined from plotting the

line of best fit.

Price data: Dec 97 - Apr 04

Market return (%)

D e l l r e t ur n ( % )

R 2 = .27

β = 1.61



11

Beta Estimation: ProblemsWant predicted beta Assume betas move towards one in the long term

Estimate betas from the bottom up

Use firm characteristics to estimate beta

Sample size may be inadequate Use more sophisticated statistical techniques

Financial leverage & business risk change over time

Estimation error Use Industry betas (more reliable)

12

Differences in Published Betas

Use different time periods

Longer: more data but firm changes over time

Shorter: Easily influenced by specific events

Use different return intervals (day, week, month)

Shorter: More data but more noise

Use different adjusting methods Simple adjustment towards one

Adjust using fundamental information about the firm



13

Determinants of Asset BetaLook at the business risk

Cyclical firms have higher betas

• Cyclical firms do well in the expansion phase of the

business cycle and poorly in the contraction phase

• Cyclicality is not the same as variability

Consider product type

• Firms with discretionary products have higher betas

Higher operating leverage results in higher betas

• Magnifies the effect of cyclicality on beta

14

Division Betas

Use an industry beta to estimate a division's

cost of capital.

A diversified firm's cost of capital does not

measure the risk of any specific division



15

Atypical ProjectsIf a similar asset is traded, estimate beta

from past price data or comparable firms

Use accounting earnings

Use bottom-up beta estimation

Use fundamental risk considerations to get a

rough estimate of beta.

Avoid fudge factors

16

Accounting Betas

Regress changes in firm (division) earnings

against changes in earnings for the market

Problems

Accounting earnings are smoothed (bias beta)

• Bias up for safe firms and down for risky firms

Influenced by accounting decisions

Few observations for regression (quarterly data)



17

Bottom-Up BetasIdentify businesses that comprise the firm or

project

Estimate unlevered betas for other firms in

the same business (comparables)

Weighted average of unlevered betas (use

market values, sales)

Lever the estimate using the debt/equity ratio

18

Optimal Capital Budget & Risk

True cost of capital depends on how funds are used

Cost of capital (WACC) is appropriate for projectswith similar risk to the firm’s average risk

Cost of capital rule: Invest if project return > cost of capital

Not average risk: Use CAPM with project beta Account for project risk

CAPM rule: Invest if project return > required return based on the

project’s beta



19

Cost of Capital vs. CAPM

Required

return

Project Beta1.0

Company Cost of

Capital (WACC)15

5

0

SML

20

WACC vs. CAPM

A project has an IRR of 18%. Knight’s cost of

capital (WACC) is 15%. The project has a beta of

1.2. The risk-free return is 5%; market risk

premium is 10%

Using the company cost of capital (WACC), willthey take the project?

Using the CAPM to determine the required return,

will they take the project?



21

WACC vs. CAPM AnswerCOC rule: Accept the project since the IRR

of 18% > cost of capital of 15%.

Using CAPM: r = 5% + (1.2×10%) = 17%

Accept the project since the IRR of 18% >

CAPM of 17%.

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Weighted Average Cost of Capital

Weighted-average of the cost of funds

Affected by tax savings and the financing decision

Beta relationships become βASSET = βWACC = [(S/V)βS ] + [(B/V)(1-TC)βB]

βS = βo + [(B/S)(1-TC)(βo - βB )]

BCSWACC )r T1(V

B+r

V

S=r −



23

Tax Impact on Return and BetaUnlevered firm: Present value of the interest tax shields (PVITS) = 0.

In this case r WACC = r o = r S and βWACC = βo = βS

Levered firm: The business risk of the assets has not changed

Unlevered cost of capital for the assets has not changed

Additional asset (PVITS) generated as a result of thefinancing decisions made by the firm.

Result: Business risk of the assets does notchange. Debt impacts value through tax savings.

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Evaluating Levered Investments

Value is created by good investmentdecisions

Destroy value by poor financing decisions

Financial policy should support businessstrategy

Three Valuation Approaches: Weighted Average Cost of Capital (WACC)

Adjusted Present Value (APV)

Flow to Equity (FTE)



25

General form of the WACC

Weighted-average of the component costs of debt,

preferred stock, retained earnings and common stock

r WACC =

[(E/V)r E ]+[(S/V)r S]+[(B/V)(1-TC)r B]+ [(P/V)r P]

Added term for preferred stock P

Equity split into retained earnings (E) and stock issue (S)

Proportions must add to 1

Not all securities may be used (omit terms)

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Components: Debt and Preferred

Debt:

Find yield to maturity. If it is compounded

semiannually, use effective rate. This is r B

Cost of debt is reduced in the WACC equation

because interest is tax-deductible

Preferred: r P = Dividend divided by the net price

Net price is the price less issue costs



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Component: Retained Earnings

Opportunity cost

Dividend valuation model: r E = (D1/P0) + g

CAPM: r E = r f + [βS(r m - r f )]

Non-dividend paying stocks: P0= Pt/(1+r)t

so r E = [(Pt/P0)(1/t)] -1

r E = bond yield + risk premium

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Component: Issue Common Stock

Constant growth with the net price

r S = (D1/Pnet) + g

Net price is the price less the issue costs

Issue costs are also called flotation costs



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WACC Example: Nook Nook plans a $100 million expansion using

25% debt and 75% common stock issue.

Debt: Bonds with a 12% yield

Stock: Expect dividends of $3.80 next year.

Growth rate is 8%. Current stock price is $40.

Flotation costs are 5% to issue stock.

Tax rate is 40%. Find weighted average cost of capital.

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WACC Answer: Nook

Debt: yield = r B = 12%.

Common:

Flotation costs are another name for issue costs

Net price = 40×(1-.05) = 38

Get r WACC = (.25×12%×(1-.4)) + (.75×18%)

15.3%

08.)05.1(40

80.3r s +

−×=



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Weighted Average Cost of Capital

WACC value

where UCFt is after-tax unlevered cash flow andr WACC is the weighted average cost of capital.

∑∞

= +=

1 )1(t

t

t

WACC r

UCF

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WACC Steps

Steps

Calculate unlevered cash flows

Calculate WACC

Find NPV by discounting cash flows at the WACC

Only appropriate as a discount rate when

Project & Firm: Same systematic business risk

Project & Firm: Same debt capacity

Firm: Target debt to value is relatively stable



33

Adjusted Present Value (APV)APV value = base-case NPV + NPV of financing Base-case NPV = project value if use only equity

where UCFt is after-tax unlevered cash flow and r ois the unlevered cost of capital.

effects)ngPV(Financi)1(1 0

++

=∑∞

=t

t

t

r

UCF

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APV Steps

Steps

Calculate unlevered cash flows

Find NPV by discounting cash flows at the unlevered

cost of capital

Adjust for the PV of financing side effects

Only appropriate as a discount rate when Project’s debt level is known over the life of the project



35

Financing Side EffectsFinancing Side Effects

Tax deduction for interest

Effects of subsidized financing

Issue costs for new debt and equity

Financial distress costs

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Flows to Equity (FTE)

FTE: PV of cash flows to stockholders inthe levered firm discounted by r S.

Levered Equity value

LCFt is after-tax, after-interest cash flow tolevered equity and r S is return on levered equity.

FTE = Levered Equity Value – Firm’s Investment

=+=

∞

∑L C F

r

t

S

t

t ( )11



37

Flows to Equity (FTE) Steps

Find levered cash flows (LCF). LCF is cash flow

to stockholders after interest and taxes are paid.

LCF = Unlevered cash flows – [(1-Tc)× r B×B]

Find cost of levered equity

r S = r o + (B/S)(1-Tc)(r o - r B).

This is affected by business and financial risk

Find value of the LCF discounted at r S.Subtract the amount of cash supplied by the firm

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Example: Levered Project for Cat

A project costs $6 million

EBIT is $1,600,000 every year forever.

Unlevered cost of capital is 16%.

Issue $5,000,000 in debt with interest rate of 10%.

Tax rate is 30%.

With no debt, Cat has a value of 7,000,000.

Debt ratio (debt to value) is 58.8%.

Use WACC, APV and FTE to find the project’svalue.



39

Levered Project APV Answer1. Base-case NPV: All-Equity Value

UCF = $1,120,000

NPV = (UCF/r o)- I = (1,120,000/.16) - 6M = 1M

2. Present value of the financing side effect

NPVF = PVITS = TC(r BB)/r B = TCB = .3(5M) =$1.5M

3. Adjusted present value

APV = base-case NPV + NPVF

APV = 1M + 1.5M = $2.5M

40

Levered Project WACC Answer

UCF = 1.6M(1-.3) = 1.12M

Get WACC. For cost of equity: use M&M With Tax

r S = 16% + (5M/3.5M)(1-.3)(16%-10%) = 22%

r WACC = (5M/8.5M)(1-.3)(10%) + (3.5M/8.5M)(22%)

r WACC = 13.18%

V =(UCF/ r WACC) – 6M

V =($1.12M/.1318) – 6M = $2,500,000



41

Unlevered Cash Flow and Value

UCF = 1.6M(1-.3) = 1.12M

VL = VU + (TC×B) = 7M + (.3×5M) = 8.5M

VL = 8.5M = S + B = S + 5M so S = 3.5M

Notice that

B/VL = 5M/8.5M = 58.8%

VU

= (1.12M/.16) = 7M

Once the project is taken, Cat gets the value of

the remaining cash flows

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Flow-to-Equity Answer #1

1. Find Levered Cash Flows (LCF) LCF = UCF – [(1-TC)× r B×B]

LCF = 1,120,000 – [(1-.3)×.1×5M] = 770,000

OR USE

LCF = (EBIT-r BB)(1-TC)

LCF = (1.6M-(.1×5M))×(1-.3) = 770,000

2. Find cost of levered equity B/S = 5M/3.5M = 1.428 OR USE B/V = .588, so B/S = .588/(1-.588) = .588/.412 = 1.427

r S = r o + (B/S)(1-T)(r o - r B) = 0.16+[1.427(1-.3)(.16-.10)] r S = 22%



43

Flow-to-Equity Approach #23.Levered Equity Value = LCF/r S=

$770,000/.22= $3.5M

4.Subtract the cash supplied by the firm.

Invest $6M but borrow $5M, so firmsupplies 6M-5M = $1M

5.FTE value = $3.5M - $1M = $2,500,000

Summary: APV, WACC, & FTE

All three determine value in the presence of debt

financing

APV WACC FTE

Initial

Investment

All All Equity

Portion

Cash Flows UCF UCF LCF

Discount Rates r o r WACC r S

PV of financing Yes No No



45

Rule of ThumbUse WACC or FTE if the firm’s target debt-to-

value ratio applies to the project over its life

(constant debt ratio).

WACC: most common method used

FTE: used for firms with extensive leverage

Use APV if the project’s level of debt is known

over the life of the project (constant debt level). APV: Special situations like subsidies and leases

46

Non-Perpetual Debt Example

A project costs $6 million

Unlevered after-tax cash flows of $3,120,000 every

year for 3 years.

Unlevered cost of capital is 16%.

Kit issues $5,000,000 in 3-year debt with an interest

rate of 10%.

Tax rate is 30%.

Debt-to-Equity = B/S = 2.10

Use WACC, APV and FTE to find the project’s value.



47

APV Non-Perpetual Debt Answer1. Base-case NPV: All-Equity Value

NPV(.16,3120000,3120000,3120000) - $6M =$1,007,175

2. Present value of interest tax shield

Interest Tax Shield = Tc ×r B ×B =.3 ×.1 ×5M = 150,000

PV(.1,3,-150000) = 373,028

3. Adjusted present value

APV = base-case NPV + PVITS

APV = 1,007,175 + 373,028 = $1,380,203

48

Levered Project WACC Answer

UCF = 3.12M

Get WACC. Cost of equity: use M&M With Tax

r S = 16% + [2.10×(1-.3)(16%-10%)] = 24.82%

B/S = 2.1 so S/V = .323 and B/V = .677

r WACC

= [(.677)(1-.3)(10%)] + [.323×24.82%] = 12.76%

Value with WACC:

NPV(.1276,3120000,3120000,3120000) - $6M =$1,397,443



49

FTE Non-Perpetual Debt1. Find Levered Cash Flows (LCF)

LCF = UCF – [(1-T)× r B×B]

LCF=3,120,000–[(1-.3)×.1×5M]

LCF =2,770,000 in years 1 & 2

LCF = 2,770,000-5,000,000 = (2,230,000) in year 3

Must repay the loan

2. Find cost of levered equity B/S = 2.10

r S = r o + (B/S)(1-T)(r o - r B) = 0.16+[2.10×(1-.3)(.16-.10)] r S = 24.82%

50

Flow-to-Equity Approach #2

3. Levered Equity Value NPV(.2482,2770000,2770000,-2230000)

NPV = $2,850,354

4. Subtract the cash supplied by the firm.

Invest $6M but borrow $5M, so firm

supplies 6M-5M = $1M

5. FTE value = $2,850,354 - 1M = $1,850,354

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