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Calculating Required Rates of Return

To calculate Big Oil`s weighted-average cost of capital, you also need the rate of return that investors require from each security.

THE EXPECTED RETURN ON BONDS

We know that Big Oil`s bonds offer a yield to maturity of 9 percent. As long as the company does not go belly-up, that is the rate of return investors can expect to earn from holding Big Oil`s bonds. If there is any chance that the firm may be unable to repay the debt, however, the yield to maturity of 9 percent represents the most favorable outcome and the expected return is lower than 9 percent.

For most large and healthy firms, the probability of bankruptcy is sufficiently low that financial managers are content to take the promised yield to maturity on the bonds as a measure of the expected return. But beware of assuming that the yield offered on the bonds of Fly-by-Night Corporation is the return that investors could expect to receive.

THE EXPECTED RETURN ON COMMON STOCK

Estimates Based on the Capital Asset Pricing Model. Earlier we showed you how to use the capital asset pricing model to estimate the expected rate of return on common stock. The capital asset pricing model tells us that investors demand a higher rate of return from stocks with high betas. The formula is Expected return

= risk-free + (stock`s АГАз expected market ) on stock interest rate beta risk premium

Financial managers and economists measure the risk-free rate of interest by the yield on Treasury bills. To measure the expected market risk premium, they usually look back at capital market history, which suggests that investors have received an extra 8 to 9 percent a year from investing in common stocks rather than Treasury bills. Yet wise financial managers use this evidence with considerable humility, for who is to say whether investors in the past received more or less than they expected, or whether investors today require a higher or lower reward for risk than their parents did?

Let`s suppose Big Oil`s common stock beta is estimated at .85, the risk-free interest rate of rf is 6 percent, and the expected market risk premium (rm rf) is 9 percent. Then the CAPM would put Big Oil`s cost of equity at

Of course no one can estimate expected rates of return to two decimal places, so we`ll just round to 13.5 percent.

Dividend Discount Model Cost of Equity Estimates. Whenever you are given an estimate of the expected return on a common stock, always look for ways to check whether it is reasonable. One check on the estimates provided by the CAPM can be obtained from the dividend discount model (DDM). Earlier we showed you how to use the constant-growth DDM formula to estimate the return that investors expect from different common stocks. Remember the formula: if dividends are expected to grow indefinitely at a constant rate g, then the price of the stock is equal to: where P0 is the current stock price, DIV1 is the forecast dividend at the end of the year, and requity is the expected return from the stock. We can rearrange this formula to provide an estimate of requity:

In other words, the expected return on equity is equal to the dividend yield (DIV1/P0) plus the expected perpetual growth rate in dividends (g).

This constant-growth dividend discount model is widely used in estimating expected rates of return on common stocks of public utilities. Utility stocks have a fairly stable growth pattern and are therefore tailor-made for the constant-growth formula.

Remember that the constant-growth formula will get you into trouble if you apply it to firms with very high current rates of growth. Such growth cannot be sustained indefinitely.

Using the formula in these circumstances will lead to an overestimate of the expected return.

Beware of False Precision. Do not expect estimates of the cost of equity to be precise. In practice you can`t know whether the capital asset pricing model fully explains expected returns or whether the assumptions of the dividend discount model hold exactly. Even if your formulas were right, the required inputs would be noisy and subject to error. Thus a financial analyst who can confidently locate the cost of equity in a band of two or three percentage points is doing pretty well. In this endeavor it is perfectly OK to conclude that the cost of equity is, say, БІАААмabout 15 percentБІАААн or БІАААмsomewhere between 14 and 16 percent.БІАААн6

Sometimes accuracy can be improved by estimating the cost of equity or WACC for an industry or a group of comparable companies. This cuts down the БІАААмnoiseБІАААн that plagues single-company estimates. Suppose, for example, that Jo Ann Cox is able to identify three companies with investments and operations similar to Geothermal`s. The average WACC for these three companies would be a valuable check on her estimate of WACC for Geothermal alone.

Or suppose that Geothermal is contemplating investment in oil refining. For this venture Geothermal`s existing WACC is probably not right; it needs a discount rate reflecting the risks of the refining business. It could therefore try to estimate WACC for a sample of oil refining companies. If too few БІАААмpure-playБІАААн refining companies were availableБІАААдmost oil companies invest in production and marketing as well as refiningБІАААд an industry WACC for a sample of large oil companies could be a useful check or benchmark. (We report estimates of oil industry WACCs at the end of the next section.)