session 1

Application of CAPM



Main textbook for the course : Brealey and Myers, Principles of corporate finance, McGraw-Hill


1. Summary of what we've recently learned on risk and portfolios selection (chapters 7 and 8) :

Expected risk premium of the security = beta of the security x market risk premium

That is for each security the point (beta, expected return) stands on the same straight line called the security market line,

that line start at (0, interest rate) and goes through the point for the market portfolio (1, r0 + 8.4%)


1.5 Remember the usefulness and the limits of DCF and CAPM


2. Capital budgeting (chapter 9 of the text book) :


The question treated in this session is : "What discount rate a company should apply to a new project under consideration ?"


As we know : "the true cost of capital of a new project depends on the project to which the capital is put, and more specifically on its risk". It is called the opportunity cost of capital for the project. It is the cost of capital of shares of firms with a comparable overall risk to the risk of the project.


The overall "company cost of capital" is defined as the rate of return of a portfolio made of all the securities - shares and bonds - issued by the company.

It is also, necessarily (see below), the overall company assets return.


Some people tend to use the overall "company cost of capital" to use as a discount rate for any new project.

This is not correct in general : here is an example.

Microsoft has a "beta" of 1.23.

That is when the market (of Standard & Poor's stocks) moves 10%, on average (in the past) Microsoft moves in the same in same direction 12.3%.

Since Microsoft company has no debt (1995), Microsoft company cost of capital is 16.5% (like its equity return - we shall see why below)

Does that mean Microsoft (created in 1975, by two young men respectively around 19 and 24) should request any new investment to yield


Of course not. Microsoft, in the past did produce that rate of return, and more. But we are concerned with is the future, and with a particular project.

For Microsoft, like for any other firm, some projects are on the safe side, and some projects are very risky.


The rule of thumb used by some firms :

Some firms then use the following rule of thumb :

Category Discount rate
Speculative venture 30%
New products 20%
Expansion of existing business 15% (or even better : "company cost of capital")
Cost improvement (known technology) 10%


What the CAPM has to say :

The CAPM is widely used by large corporations to estimate the discount rate that is to be applied. It states :

r -r0 = project beta x (rm -r0)


To calculate this you have to figure out the beta of the project (its sensibility to market variations).

The best is to get it from "firms with the same sensibility".


A simplification :

The "company cost of capital" is the correct discount rate for those projects that have the same risk as the overall company's existing business, but not for those projects that are safer or riskier.

Henceforth we shall consider a project with the same risk as the company overall risk.


And we are following the CAPM theory, which has the advantage of offering a framework of thinking, and the drawback of being approximate.

Our problem, among other things, are the betas.

Can we get them from some sort of a directory?

Well, we can (with some faith...)

(hand-out pp 208-210 : betas of AT&T and of HP, and Merrill Lynch's "beta book")


A little more on betas :

We can measure the beta of a given security by plotting the market returns and the security returns over several years (market in abscissa, security in ordinate). We obtain a scattergram (a cloud of points).

The best fitting line across the cloud of points (called the regression line) has a slope which is the beta of the security.


Some examples using the CAPM equation :

Share beta expected return
AT&T 0.92 13.7%
Biogen 2.20 24.5%
Bristol Myers 0.97 14.1%
Coca Cola 1.12 15.4%
Compaq 1.18 15.9%
Exxon 0.51 10.3%
Ford Motor 1.12 15.4%
General Electric 1.22 16.2%
McDonald's 1.07 15.0%
Microsoft 1.23 16.3%


r0=6% (zero risk discount rate, around 1995)

rm - r0 = 8.4% (market premium)



Our problem : capital budgeting, i.e. allocating money to a project (if it is selected), and how to select it :

Which opportunity cost of capital to use ?

If we know projects of the same kind, and their return, then we know which cost of capital to use.


We said that we will consider a project with the same overall risk as the whole firm (for instance an expansion of the core business).


We also defined the cost of capital for the whole firm as the expected return of all its assets.

And we have

assets (at market value) of the firm = debt of the firm + equity (at market value) of the firm



return of assets = (D/(D+E)) x debt return + (E/(D+E)) x stock return


Indeed if you owned entirely the firm, you would have a portfolio with these returns, and they have to be equal.


This simple equation has an important consequence :

When a firm reduces its debt, its stock return decreases.


Let's see why :

Debtors incur much less risk than shareholders. Typically debt return = (say) 8%, and equity return = (for instance) 15%

Then if D/(D+E) = 40% and E/(D+E) = 60%, we get

return of assets = 40% x 8% + 60% x 15% = 12.2%


Since the rate of return of the assets does not change with the capital structure we readily see that if the ratio of debt increases then the equity return must go up too, to maintain a weighted average of 12.2%.

Or equivalently if the debt decreases, the equity return will decrease too.

Suppose D goes to 30% and E goes to 70% (of D+E)

Suppose the new debt return decreases a bit and goes to 7.3% (less debt, less risk on the debt...)

Then we must have

30% x 7.3% + 70% x equity return = 12.2%


This yields : new equity rate of return = 14.3% !


The betas also change : a little calculation shows in comparable hypotheses, an initial beta of 1.2 goes down to 1.1.


Points to remember :

1. A project must be evaluated on its own, with the appropriate opportunity cost of capital


2. If the project has the same risk as the whole company, then the correct discount rate is the rate of return of the assets of the company


3. The rate of return of the assets of the company is not the same as the rate of return of its stock on the stock market


4. The rate of return of the assets of the company is the weighted average of its equity return and debt return.


5. If the capital structure changes, for instance if the debt ratio decreases, then the equity return will decrease too.


6. The rate of return of a portfolio of all the shares + bonds of the company is called the company cost of capital. It is mathematically equal to the rate of return of its assets.


(7. debt have a small or zero beta, and they are uncorrelated to stocks, therefore the beta of a company average project is the weighted average of the beta of its stocks and the beta of its debt (about zero). Therefore the higher the debt, the higher the beta of the share.)


Example : calculation of the company cost of capital for Duke Power :

Once again, what discount rate should be applied to an average project of expansion at Duke Power ?

Answer : the company cost of capital.

This can be calculated from its equity return and debt structure.

Around 1995, for Duke Power we had, beta=.47, market risk premium=(as usual) 8.4% and r0=(at that time) 6%

therefore equity return = 6% + 0.47 x 8.4% = (about) 10%,

and debt return = 8%, and equity % was 65% of total capital structure.

Then company cost of capital for Duke Power was about 9.3%.