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Ct is not known for certain. It is a random variable. It has a probability distribution with a mean and standard deviation. Ct = E(Ct) = expected cash flow

“r” is the appropriate cost of capital. It should have the same riskiness as Ct

If Ct is a normal extension of the firm’s operations, and the firm is entirely equity financed, we use the stockholders’ required return as found through the CAPM for the appropriate value of ‘r’.

E(Ri) = Rf + (i (Rm – Rf)

Remember: the Beta of security i is the standardized covariance of its returns with the returns on the market portfolio.

(i = Covi,Mkt

(2Mkt

Determinants of Beta

1. Cyclicality of revenues – How responsive are revenues to changes in the business cycle? Does the firm produce normal goods or inferior goods?

Highly cyclical ( high covariance with the market ( high beta.

2. Operating Leverage (Degree of Operating Leverage) – Degree to which costs are fixed. High FC relative to VC ( high operating leverage

Contribution margin = Price – VC = incremental profit from an additional sale

Low Contribution margin = low FC & high VC = low DOL – example is grocery store High Contribution margin = high FC & low VC = high DOL – example is airline High Operating Leverage ( profits are more responsive to changes in sales ( higher beta

3. Financial Leverage – similar to operating leverage if we think of debt as a FC

(Equity = Equity beta = beta of a firm’s stock. This is what we have been measuring and looking at thus far. It is a measure of both the firm’s business risk and its financial risk.

(Asset = Asset beta = weighted average of the betas of all a firm’s securities (common stock, debt and preferred stock). This is a measure of the firm’s business risk only.

(Asset = Debt ((D) + Equity ((E)

D+E D+E

If a firm has no debt, (Asset = (Equity

So, we can think of (Asset as what (Equity would be if the firm had no debt – if it is an unlevered firm.

(Equity is observable and is the beta of the levered firm

(Asset is unobservable and is the beta of the unlevered firm

(D = standardized covariance between the return on a firm’s debt and the market return. We can calculate (D just as we calculated (E. (D = CovD,Mkt (2Mkt

If the debt is risk-free, (D = 0.0 because the covariance of a risk-free asset with anything is zero. Even if the debt is risky, its covariance with the market (and its its beta) will be very low. As a result (and for simplicity), we usually choose to assume that (D = 0.

If (D = 0.0, then (Asset = Equity ((E)

D+E

And,

(Equity = D+E (Asset

E

(Equity = [pic]

This is called the Hamada Equation and it allows us to find the unobservable (Asset if we know the observable (Equity and its debt-to-equity ratio.

If (Asset = Beta of an unlevered firm, it doesn’t change as leverage changes, but of course (Equity does.

( debt ( ( (Equity

The beta of a levered firm equals the beta of an unlevered firm times one plus the D/E ratio. This means that whenever a firm increases its debt, it increases its (observable) beta, increases its risk, and thus increases the return that shareholders require.

If we want to compare the riskiness of two firms that have different amounts of debt, we can’t just look at their observable betas ((Equity) and compare them. We have to ‘unlever’ each firm to find their unobservable betas ((Asset) which can be compared.

Also, if we want to find out what effect a change in the level of debt will have on a firm, we need to first ‘unlever’ the firm to find its unlevered beta, then ‘relever’ the firm using the new level of debt to calculate its new (observable) beta and then use that to calculate the new required rate of...