© Prentice Hall, 2004

88

Corporate Financial Management 3e

Emery Finnerty Stowe

Cost of Capital

The Cost of Capital

The Cost of Capital::

is NOT the firm’s historical cost of funds.

The relevant cost is the opportunity cost.

The Cost of Capital

The Cost of Capital is the required return for whatever is being analyzed.

For example, it is the opportunity cost of funds tied up in a project.

It is the rate of return at which investors are willing to provide financing for the project today.

It reflects the risk of the project.

Corporate Valuation

The market value of the firm (or simply, the firm value) can be viewed in two ways:• Firm value equals the sum of the market

values of the claims on the firm’s assets (Ex., equity and debt securities issued by the firm).

• Firm value equals the sum of the market values of its assets.

This is simply the balance-sheet accounting identity, but in market value terms.

Financing Decisions and Firm Value

In a perfect capital market, the value of the firm does not depend on its capital structure - i.e. the way in which its assets are financed.

The mix of debt versus equity is irrelevant in determining firm value.

In imperfect capital markets, capital structure can affect the value of the firm.

Investment Decisions and Firm Value

The value of the firm does depend on the expected future cash flows to be generated by the firm’s assets, and on the required rate of return on these cash flows.

An asset will add value if its expected rate of return (the Internal Rate of Return or IRR) exceeds its required rate of return (i.e., its cost of capital).

The Market Line for Capital Budgeting Projects

The Capital Asset Pricing Model (CAPM) can be used to obtain the cost of capital for a capital budgeting project.

rj = rf + j(rm – rf)where

rj = cost of capital for project j

rf = riskless return

rm = required return on the market portfolio

j = beta of project j

Value and the Risk-Return Trade-Off

The value of a project depends on: the expected future cash flows the cost of capital

An increase in the expected future cash flows will increase value only if there is not a corresponding increase in risk.

The increase in risk will increase the project’s cost of capital.

If the increase in the cost of capital is sufficiently large, this will offset the positive effect of the increase in the expected future cash flows.

Graphical Representation of the SML

M

1.0

rf

Mr

)( fMifi rRrr

Riskless return

Market Risk

Premium

Risk Premium

for a stock twice as risky as

the market

2.0

)(2 fMfi rRrr

Risk Premium for a stock half as risky

as the market

0.5

)(2

1fMfi rRrr

Leverage

According to the CAPM, the required return depends only on the non-diversifiable risk.

The non-diversifiable risk borne by shareholders can be split into two parts: Business or Operating Risk Financial Risk

Operating risk results from operating leverage.

Financial risk results from financial leverage.

Operating Leverage

Operating leverage arises from the mix of fixed versus variable costs of production.Higher fixed costs (and correspondingly lower variable costs per unit) results in higher operating leverage. The firm’s profits are more sensitive to changes in

sales.

Conversely, lower fixed costs (and correspondingly higher variable costs per unit) result in lower operating leverage.

Operating Leverage

Jewel Plastics, Inc., plans to make plastic jewel cases for CD-ROM disks. Each packet of 10 cases can be sold for $5.00. Two alternative manufacturing technologies are available.

Ignoring taxes, compute the profits under each plan.

Plan A Plan BAnnual Fixed Costs

Variable Cost (per unit)

$60,000

$2.00

$100,000

$1.00

Operating Leverage

Profit = Sales – CostsUnit Sales × (Selling Price – Variable Costs) – Fixed Costs

At a sales level of 50,000 units, the profits under plan A are:50,000 ×($5.00 – $2.00) – $60,000 = $90,000.

Under Plan B, profits at a sales level of 50,000 units are $100,000.

Operating Leverage

-$100

-$50

$0

$50

$100

$150

$200

0 20 40 60 80Pro

fit

($ t

ho

usa

nd

s)

Units Sold(thousands)

Plan B

Plan A

Operating Leverage

Operating leverage affects the risk of the firm’s investments, and is unique for each investment.

It affects both the diversifiable as well as the non-diversifiable risk of the investment.

Through its effect on non-diversifiable risk, it also affects the investment’s cost of capital.

The firm’s choice of operating leverage may be limited by the number of alternative production methods.

Financial Leverage

The presence of fixed costs associated with debt financing results in financial leverage.

As financial leverage increases, the variability of shareholder returns increases. This increases shareholder’s risk.

Financial Leverage

Clubs & Stuff is currently all-equity financed. Club’s expected future cash flows are $300 per year in perpetuity, with a minimum annual cash flow of $150. Club’s shareholders currently require a 15% return.Analyze the impact on shareholder returns if Club issues $1,000 of risk-free debt with an interest rate of 10%, and uses the funds to pay dividends to the shareholders.Assume perfect markets.

Financial Leverage

Currently, the value of Clubs & Stuff is$300 / 0.15 = $2,000

With $1,000 in debt at 10%, Club’s annual interest expense will be $100. Since Club’s minimum annual cash flow is more than $100, the debt will be risk free.Issuing $1,000 of debt and paying the proceeds to the shareholders will result in Club being 50% debt financed. In perfect markets, firm value is independent of

capital structure.

Financial Leverage

With 50% debt financing, shareholders will demand a higher rate of return since their risk will increase.

As the firm’s returns vary, the returns to shareholders will vary more with debt financing than without. The firm has to pay out a fixed cost of $100

per year to the debtholders.

The Weighted Average Cost of Capital

The Weighted Average Cost of Capital, WACC, is the weighted average rate of return required by the suppliers of capital for the firm’s investment project.

The suppliers of capital will demand a rate of return that compensates them for the proportional risk they bear by investing in the project.

Components of a Financing Package

Consider the case where a project will be financed with 40% debt and 60% equity.

Suppose the project requires an initial investment of $8,000 and has a NPV of $2,000. The TOTAL value of the project is thus $10,000.

How much debt should the firm use? (0.40) × $10,000 = $4,000.

Components of a Financing Package

Since the project requires an initial investment of $8,000, the firm will raise the remaining $4,000 by selling stock.

Since the total value of the project is $10,000, the stock will be worth $6,000. In perfect markets, ALL of the benefits from a

project (i.e., the project’s NPV) goes to the shareholders.

WACC Calculation

Let L = the ratio of debt financing to total financing,

re = required return for equity,

rd = required return on debt, and

T = marginal corporate tax rate on income from the project.

Then,

de

de

rTLrL

rTED

Dr

ED

E

)1()1(WACC

)1(WACC

WACC Calculation

Compute the WACC for the Nikko Co. given the following information:

Nikko has 8 million common shares outstanding priced at $14.625 each. Next year’s dividend on these shares is expected to be $2.71, and will grow at 5% per year forever. Nikko has 60,000 bonds outstanding, each with a coupon rate of 12% and are priced at $1,050 each to yield 8% to bondholders. Nikko’s marginal corporate income tax rate is 34%.

WACC Calculation

Market value of Nikko’s equity = 8 million × $14.625 per share = $117 million.

Market value of Nikko’s debt = 60,000 × $1,050 per bond = $63 million.

Total market value of Nikko = $117 million + $63 million = $180 million.

Proportion of debt financing used by Nikko = L = $63 M / $180 ML = 35%

WACC Calculation

To compute the rate of return required by Nikko’s stockholders, we use the constant growth model of stock valuation.

rDP

ge = + = + =1

0

71625

0 05 23 53%$2.

$14.. .

WACC Calculation

Since we are interested in measuring the firm’s current cost of capital, we use the bond yield (not the coupon rate) currently demanded by the bondholders.

Thus, rd = 8%.

Also, the tax rate, T, is 34%.

WACC Calculation

de rTLrL )1()1(WACC

%8)34.01(35.0%53.23)65.0(WACC

%14.17WACC

How Not to Use the WACC

Assume that a firm’s existing operations have a risk equal to the average risk of new projects being considered for adoption with different risk levels and hence different required returns.

If the firm uses its current WACC, it will accept projects of above average risk and reject projects of below average risk.

Thus, the risk of the firm will rise.

Misapplication of the WACC

Risk ()

Rat

e of

Ret

urn

WACC

How to use the WACC

The correct procedure is to use a cost of capital for each project that reflects the risk of that project.

Correct Application of the WACC

Risk ()

Rat

e of

Ret

urn

WACC

)( fMifi rRrr

Potentially inappropriate project rejection

Region of potentially inappropriate project

acceptance

Financial Risk

Financial risk is due to the presence of debt financing used by the firm. An all-equity financed firm has no financial

risk (only business or operating risk).

A firm can control its financial risk by its choice of capital structure and the maturities of its obligations.

Financial Leverage and the Cost of Capital

In perfect capital markets, financial leverage has no effect on the WACC. WACC is independent of the capital structure.

Thus, a project’s value is not affected by the way in which it is financed.

However, financial leverage does alter how the risk of the project is borne by the debtholders and the shareholders.

Financial Leverage and the Cost of Capital

As financial leverage increases, the risk borne by both the debtholders and the shareholders increases.

Required Return

Financial Leverage and the Cost of Capital

L0.0 1.0

WACC

re

rf rd

Financial Leverage and Beta

Consider a firm with J different assets, each with a beta of j.

Let wj denote the proportion of firm value invested in asset j.

The beta of all the assets of the firm, A, is then given by:

A j jj

Jw

1

Financial Leverage and Beta

Using the CAPM, we get

WACC = rf + A(rm – rf)

Thus, we can see that WACC is independent of the capital structure since A is unaffected by capital structure.

Financial Leverage and Beta

How does financial leverage affect the stock’s beta?

Let d denote the beta of the debt and denote the beta of the stock.

rd= rf + d(rm – rf) and re= rf + (rm –

rf)

Financial Leverage and Beta

Recall that

WACC = (1 – L) re +L (1 – T) rd

WACC = rf + A (rm – rf)

Plugging in the CAPM specifications for re and rd and rearranging the terms, we get:

(1 – LT) A = Ld + (1 – L)

Financial Leverage and Beta

(1 – LT) A = Ld + (1 – L)

Suppose that debt is risk-free. Then d = 0. Then,

)1(

)1(

TL

LA

WACC for a Capital Budgeting Project

The Evergreen Sprinkler Corp. (ESC) is considering expanding its current operations, and you are asked to estimate the WACC to be used for this project. ESC’s outstanding stock is valued at $16.8 million, while its debt has a market value of $7.2 million. ESC’s stock has a beta of 1.80 and its debt is risk free. ESC’s marginal tax rate is 37%. The risk-free rate is 5% and the required return on the market portfolio is 13%.

WACC for a Capital Budgeting Project

Since ESC’s debt is worth $7.2 million and its equity is worth $16.8 million, the value of L is $7.2/($7.2 + $16.8) or 0.30.

Further, = 1.80 and T = 0.37.

Thus, the beta of the assets of ESC is:

4173.1)30.037.01(

80.1)30.01(

)1(

)1(

TL

LA

WACC for a Capital Budgeting Project

WACC = rf + A (rm – rf)

=5% + 1.42×(13% – 5%)

= 16.36%

WACC for a New Line of Business

Consider a firm that intends to expand into a new line of business. What WACC should it use for evaluating this proposal?If the new line of business is of different risk than the firm’s existing assets, the firm’s WACC cannot (should not) be used.

Estimate A for other firms in this line of business.

Use the average A and the CAPM to get the WACC.

Operating Leverage and the WACC

Unlike financial leverage, operating leverage affects A, the beta of the assets.

Higher operating leverage leads to higher asset betas.

This in turn leads to higher WACC.

Given the choices of production, a firm may not have much choice over operating leverage, and thus the WACC.