17-1Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Chapter Seventeen

Cost of Capital

17-2Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

17.1 The Cost of Capital: Some Preliminaries

17.2 The Cost of Equity

17.3 The Costs of Debt and Preference Shares

17.4 The Weighted Average Cost of Capital

17.5 Divisional and Project Costs of Capital

17.6 Flotation Costs and the Weighted Average Cost of Capital

Summary and Conclusions

Chapter Organisation

17-3Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Chapter Objectives• Apply the dividend growth model approach and the

SML approach to determine the cost of equity.

• Estimate values for the costs of debt and preference shares.

• Calculate the WACC.

• Discuss alternative approaches to estimating a discount rate.

• Understand the effects of flotation costs on WACC and the NPV of a project.

17-4Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Cost of Capital: Preliminaries• Vocabulary→ the following all mean the same

thing:– required return– appropriate discount rate– cost of capital.

• The cost of capital depends primarily on the use of funds, not the source.

• The assumption is made that a firm’s capital structure is fixed—a firm’s cost of capital then reflects both the cost of debt and the cost of equity.

17-5Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Cost of Equity

• The cost of equity, RE , is the return required by equity investors given the risk of the cash flows from the firm.

• There are two major methods for determining the cost of equity:– Dividend growth model– SML or CAPM.

17-6Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The Dividend Growth Model Approach

• According to the constant growth model:

Rearranging:

gR

gDP

E

) (1 0

0

gP

DRE

0

1

17-7Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Cost of Equity: Dividend Growth Model Approach

Jumbo Co. recently paid a dividend of 20 cents per share. This dividend is expected to grow at a rate of 5 per cent per year into perpetuity. The current market price of Jumbo’s shares is $7.00 per share. Determine the cost of equity capital for Jumbo Co.

8%or 0.08

0.05 $7.00

1.05 $0.20

ER

17-8Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Estimating g

9.025%

/47.62 10.53 7.95 10.00 rategrowth Average

One method for estimating the growth rate is to use the historical average.

17-9Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The Dividend Growth Model Approach—Evaluation

• Advantages– Easy to use and understand.

• Disadvantages– Only applicable to companies paying dividends.– Assumes dividend growth is constant.– Cost of equity is very sensitive to growth estimate.– Ignores risk.

17-10Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The SML Approach• Required return on a risky investment is dependent on three

factors:

– the risk-free rate, Rf

– the market risk premium, E(RM) – Rf

– the systematic risk of the asset relative to the average, .

fMEfE RRRR

17-11Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Cost of Equity Capital: SML Approach

• Obtain the risk-free rate (Rf) from financial press—many use the 1-year Treasury note rate, say, 6 per cent.

• Obtain estimates of market risk premium and security beta:– historical risk premium = 7.94 per cent (Officer, 1989)– beta—historical

investment information services estimate from historical data

• Assume the beta is 1.40.

17-12Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Cost of Equity Capital: SML Approach (continued)

%.

%. . %

RRRR fMEfE

1217

9474016

17-13Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The SML Approach• Advantages

– Adjusts for risk.– Applicable in a wider range of circumstances (e.g. to

companies other than just those with constant dividend growth).

• Disadvantages– Requires two factors to be estimated: the market risk

premium and the beta co-efficient.– Uses the past to predict the future, which may not be

appropriate.

17-14Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The Cost of Debt

• The cost of debt, RD, is the interest rate on new borrowing.

• RD is observable:– yields on currently outstanding debt– yields on newly-issued similarly-rated bonds.

• The historic cost of debt is irrelevant—why?

17-15Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Cost of Debt

Ishta Co. sold a 20-year, 12 per cent bond 10 years ago at par ($100). The bond is currently priced at $86. What is our cost of debt?

14.4%

/2$86 $100

/10$86 $100 $12

/2NP PV

/NP PV

nI

RD

The yield to maturity is 14.4 per cent, so this is used as the cost of debt, not 12 per cent.

17-16Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The Cost of Preference Shares• Preference shares pay a constant dividend every

period.

• Preference shares are a perpetuity, so the cost is:

• Notice that the cost is simply the dividend yield.

0 P

DRP

17-17Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Cost of Preference Shares• A preference share issue paying an $8 dividend per

share was was sold 10 years ago for $60 per share. It sells for $100 per share today.

• The dividend yield today is $8.00/$100 = 8 per cent, so this is the cost of preference shares.

17-18Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The Weighted Average Cost of Capital

Let: E = the market value of equity = no. of outstanding shares × share price

D = the market value of debt = no. of outstanding bonds × price

V = the combined market value of debt and equity

Then: V = E + D

So: E/V + D/V = 100%

That is: The firm’s capital structure weightsare E/V and D/V.

17-19Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The Weighted Average Cost of Capital• Interest payments on debt are tax deductible, so

the after-tax cost of debt is:

• Dividends on preference shares and ordinary shares are not tax-deductible so tax does not affect their costs.

• The weighted average cost of capital is therefore:

CD TR 1 debt ofcost tax -After

CDE TRVDRV

E 1 WACC

17-20Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Weighted Average Cost of Capital

Gidget Ltd has 78.26 million ordinary shares on issue with a book value of $22.40 per share and a current market price of $58 per share. Gidget has an estimated beta of 0.90. Treasury bills currently yield 5 per cent and the market risk premium is assumed to be 7.94 per cent. Company tax is 30 per cent.

17-21Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Weighted Average Cost of Capital (continued)

Gidget Ltd has four debt issues outstanding:

17-22Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Cost of Equity(SML Approach)

%.

%..%

RRRR fMEfE

1512

947 900 5

17-23Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Cost of Debt

The weighted average cost of debt is 7.15 per cent.

17-24Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Capital Structure Weights and WACC• Market value of equity = 78.26 million × $58 = $4.539 billion.• Market value of debt = $1.474 billion.

10.4%or 0.104

0.30 1 0.0715 0.245 0.1215 0.755 WACC

75.5%or 0.755 $6.013b$4.539b

24.5%or 0.245 $6.013b$1.474b

billion $6.013 billion $1.474 billion $4.539

VE

VD

V

17-25Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

WACC• The WACC for a firm reflects the risk and the target

capital structure to finance the firm’s existing assets as a whole.

• WACC is the return that the firm must earn on its existing assets to maintain the value of its shares.

• WACC is the appropriate discount rate to use for cash flows that are similar in risk to the firm.

17-26Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Divisional and Project Costs of Capital• When is the WACC the appropriate discount rate?

– When the project’s risk is about the same as the firm’s risk.

• Other approaches to estimating a discount rate:– divisional cost of capital—used if a company has more

than one division with different levels of risk– pure play approach—a WACC that is unique to a

particular project is used– subjective approach—projects are allocated to specific

risk classes which, in turn, have specified WACCs.

17-27Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The SML and the WACCExpectedreturn (%)

Beta

SML

WACC = 15%

= 8%

Incorrectacceptance

Incorrectrejection

B

A

161514

Rf =7

A = .60 firm = 1.0 B = 1.2

If a firm uses its WACC to make accept/reject decisions for all types of projects, it will have a tendency towards incorrectly accepting risky projects and incorrectly rejecting less risky projects.

17-28Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Using WACC for all Projects• What would happen if we use the WACC for all

projects regardless of risk?

• Assume the WACC = 15 per cent

Project Required Return IRR Decision

A 15% 14% Reject

B 15% 16% Accept

• Project A should be accepted because its risk is low (Beta = 0.60), whereas Project B should be rejected because its risk is high (Beta = 1.2).

17-29Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

The SML and the Subjective Approach

Expectedreturn (%)

Beta

SML

20

WACC = 14

10

Rf = 7

Low risk(–4%)

Moderate risk(+0%)

High risk(+6%)A

With the subjective approach, the firm places projects into one of several risk classes. The discount rate used to value the project is then determined by adding (for high risk) or subtracting (for low risk) an adjustment factor to or from the firm’s WACC.

= 8%

17-30Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Flotation Costs• The issue of debt or equity may incur flotation costs

such as underwriting fees, commissions, listing fees.• Flotation costs are relevant cash flows and need to

be included in project analysis.• To assist with this, a weighted average flotation cost

can be calculated:

DEA fVDfV

Ef

costflotation debt

costflotation equity

costflotation average weighted where

D

E

A

f

f

f

17-31Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Project Cost including Flotation CostsSaddle Co. Ltd has a target capital structure of 70 per cent equity and 30 per cent debt. The flotation costs for equity issues are 15 per cent of the amount raised and the flotation costs for debt issues are 7 per cent. If Saddle Co. Ltd needs $30 million for a new project, what is the ‘true cost’ of this project?

12.6%

0.07 0.30 0.15 0.70

Af

The weighted average flotation cost is 12.6 per cent.

17-32Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Project Cost including Flotation Costs (continued)

million $34.32

.1260 1

$30m

1

costs)flotation (ignoringcost Project project ofcost True

Af

• Saddle Co. needs to raise $30 million for the project after covering flotation costs.

17-33Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—Flotation Costs & NPV• Apollo Co. Ltd needs $1.5 million to finance a new

project expected to generate annual after-tax cash flows of $195 800 forever. The company has a target capital structure of 60 per cent equity and 40 per cent debt. The financing options available are:– An issue of new ordinary shares. Flotation costs of equity

are 12 per cent of capital raised. The return on new equity is 15 per cent.

– An issue of long-term debentures. Flotation costs of debt are 5 per cent of the capital raised. The return on new debt is 10 per cent.

• Assume a corporate tax rate of 30 per cent.

17-34Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—NPV (No Flotation Costs)

322 $159

000 500 $1 0.118

800 $195 NPV

11.8%or 0.118

0.30 1 0.1 0.4 15% 0.6 WACC

17-35Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example—NPV (With Flotation Costs)

$7340

982 651 $10.118

800 $195 NPV

982 651 $1 0.092 1

000 500 $1 cost True

9.2%or 0.092

0.05 0.4 0.12 0.6

Af

Flotation costs decrease a project’s NPV and could alter an investment decision.

Note: If the flotation costs are tax-deductible, we can calculate an after-tax weighted average flotation cost, fAT = fA(1-TC)

17-36Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Summary and Conclusions• The cost of equity is the return that equity investors

require on their investment in the firm.• There are two approaches to determine the cost of

equity: the dividend growth model approach and the SML approach.

• The cost of debt is the return that lenders require on the firm’s debt.

• WACC is both the required rate of return and the discount rate appropriate for cash flows that are similar in risk to the overall firm.

• Flotation costs can affect a project’s NPV and alter the investment decision.