Last Study Topics

• Company and Project Costs of Capital• Beta As a Proxy

Today’s Study Topics

• Capital structure and COC• Measuring the Cost of Equity

The Expected Return on Union Pacific Corporation’s Common Stock

• Suppose that in mid-2001 you had been asked to estimate the company cost of capital of Union Pacific Corporation.

• Table 1 provides two clues about the true beta of Union Pacific’s stock: – The direct estimate of .40 and the average

estimate for the industry of .50. • Use the industry average of .50

Continue• In mid-2001 the risk-free rate of interest rf was

about 3.5%. • 8% for the risk premium on the market, • You would have concluded that the expected

return on Union Pacific’s stock was about 7.5%.

– Expected stock return= rf +Beta(rm – rf)

= 3.5 + .5(8.0) = 7.5%

CAPITAL STRUCTURE AND THE COMPANY COST OF CAPITAL

• we need to look at the relationship between the cost of capital and the mix of debt and equity used to finance the company.

• Think again of what the company cost of capital is and what it is used for.

• We define it as the opportunity cost of capital for the firm’s existing assets; – we use it to value new assets that have the same

risk as the old ones.

Company Cost of Capitalsimple approach

• Company Cost of Capital (COC) is based on the average beta of the assets.

• The average Beta of the assets is based on the % of funds in each assets.– Example– 1/3 New Ventures B=2.0– 1/3 Expand existing business B=1.3– 1/3 Plant efficiency B=0.6

• AVG Beta of assets = 1.3

Capital Structure

• Capital Structure - The mix of debt & equity within a company

• Expand CAPM to include Capital Structure

R = rf + B ( rm - rf )Becomes;

Requity = rf + B ( rm - rf )

Union Pacific Corp.Example

100 valueFirmAssets Total

70ueEquity val

30Debt value100Assets

%75.12%157030

70%5.7

7030

30

assets

equitydebtassets

R

requitydebt

equityr

equitydebt

debtR

Understanding

• If the firm is contemplating investment in a project that has the same risk as the firm’s existing business, the opportunity cost of capital for this project is the same as the firm’s cost of capital; in other words, it is 12.75%.– What would happen if the firm issued an

additional 10 of debt and used the cash to repurchase 10 of its equity?

Union Pacific Corp.Example

100 valueFirmAssets Total

60ueEquity val

40Debt value100Assets

%75.12%156040

60%875.7

6040

40

assets

equitydebtassets

R

requitydebt

equityr

equitydebt

debtR

Understanding

• The change in financial structure does not affect the amount or risk of the cash flows on the total package of debt and equity.

• Therefore, if investors required a return of 12.75% on the total package before the refinancing, they must require a 12.75% return on the firm’s assets afterward.

Solve for Equity

• Since the company has more debt than before, the debt holders are likely to demand a higher interest rate.

• We will suppose that the expected return on the debt rises to 7.875%. – Now you can write down the basic equation for

the return on assets and solve for return on Equity. i.e.

Continue

• Return on equity = 16%– Increasing the amount of debt increased debt

holder risk and led to a rise in the return that debt holders required (rdebt rose from 7.5 to 7.875%).

– The higher leverage also made the equity riskier and increased the return that shareholders required (requity rose from 15 to 16 %).

equitydebtassets rV

Er

V

DR

Continue

• The weighted average return on debt and equity remained at 12.75%.

• What happen to cost of capital and return on equity, – If Co. has paid all of its debt and replace it with

equity?

equitydebtassets rV

Er

V

DR

How Changing Capital Structure Affects Beta

• The stockholders and debtholders both receive a share of the firm’s cash flows, and both bear part of the risk. – For example, if the firm’s assets turn out to be

worthless, there will be no cash to pay stockholders or debtholders.

• But debtholders usually bear much less risk than stockholders. Debt betas of large blue-chip firms are typically in the range of .1 to .3.

Continue

• The firm’s asset beta is equal to the beta of a portfolio of all the firm’s debt and its equity.

• The beta of this hypothetical portfolio is just a weighted average of the debt and equity betas:

equitydebtassets BV

EB

V

DBB Portfolio

Continue

• If the debt before the refinancing has a beta of .1 and the equity has a beta of 1.1, then; – Beta assets = .8

equitydebtassets BV

EB

V

DB

Continue

• What happens after the refinancing? The risk of the total package is unaffected, but both the debt and the equity are now more risky.– Suppose that the debt beta increases to 0.2.– Beta Equity = 1.2

equitydebtassets BV

EB

V

DB

Understanding• Financial leverage does not affect the risk or

the expected return on the firm’s assets, but it does push up the risk of the common stock.

• Shareholders demand a correspondingly higher return because of this financial risk.

• Figure on the next slide shows the expected return and beta of the firm’s assets. – It also shows how expected return and risk are

shared between the debtholders and equity holders before the refinancing.

Capital Structure & COC

Expected return (%)

Bdebt Bassets Bequity

Rrdebt=7.5

Rassets=12.75

Requity=15

Expected Returns and Betas prior to refinancing

Understanding

• After the refinancing.– Both debt and equity are now more risky, and

therefore investors demand a higher return.– But equity accounts for a smaller proportion of

firm value than before. – As a result, the weighted average of both the

expected return and beta on the two components is unchanged.

0

20

0 0.2 0.8 1.2

Capital Structure & COC

Expected return (%)

Bdebt Bassets Bequity

Rrdebt=7.875

Rassets=12.75

Requity=16

Expected Returns and Betas prior to refinancing

Capital Structure and Discount Rates

• The company cost of capital is the opportunity cost of capital for the firm’s assets.

• That’s why we write it as rassets.

• If a firm encounters a project that has the same beta as the firm’s overall assets, then rassets is the right discount rate for the project cash flows.

Continue• When the firm uses debt financing, the

company cost of capital is not the same as requity the expected rate of return on the firm’s stock; requity is higher because of financial risk.

– When the firm changes its mix of debt and equity securities, the risk and expected returns of these securities change; however, the asset beta and the company cost of capital do not change.

Continue• When companies discount an average-risk

project, they do not use the company cost of capital as we have computed it.

• They use the after-tax cost of debt to compute the after-tax weighted-average cost of capital or WACC.

equitydebt rV

ErTc

V

DWACC )1(

Summary• Capital structure and COC• Measuring the Cost of Equity