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USING HISTORICAL EVIDENCE TO ESTIMATE TODAYS COST OF CAPITAL

Later we will, show how firms calculate the present value of a new project by discounting the expected cash flows by the opportunity cost of capital. The opportunity cost of capital is the return that the firm s shareholders are giving up by investing in the project rather than in comparable risk alternatives.

Measuring the cost of capital is easy if the project is a sure thing. Since shareholders can obtain a sure-fire payoff by investing in a U.S. Treasury bill, the firm should invest in a risk-free project only if it can at least match the rate of interest on such a loan. If the project is risky and most projects are then the firm needs to at least match the return that shareholders could expect to earn if they invested in securities of similar risk. It is not easy to put a precise figure on this, but our skim through history provides an idea of the average return an investor might expect to earn from an investment in risky common stocks.

Suppose there is an investment project which you know don t ask how has the same risk as an investment in the portfolio of stocks in Standard & Poor s Composite Index. We will say that it has the same degree of risk as the market portfolio of common stocks.3

Instead of investing in the project, your shareholders could invest directly in this market portfolio of common stocks. Therefore, the opportunity cost of capital for your project is the return that the shareholders could expect to earn on the market portfolio. This is what they are giving up by investing money in your project.

The problem of estimating the project cost of capital boils down to estimating the currently expected rate of return on the market portfolio. One way to estimate the expected market return is to assume that the future will be like the past and that today s investors expect to receive the average rates of return shown in Table 3.9. In this case, you would judge that the expected market return today is 13.2 percent, the average of past market returns.

Unfortunately, this is not the way to do it. Investors are not likely to demand the same return each year on an investment in common stocks. For example, we know that the interest rate on safe Treasury bills varies over time. At their peak in 1981, Treasury bills offered a return of 14 percent, more than 10 percentage points above the 3.8 percent average return on bills shown in Table 3.9.

What if you were called upon to estimate the expected return on common stocks in 1981? Would you have said 13.2 percent? That doesn t make sense. Who would invest in the risky stock market for an expected return of 13.2 percent when you could get a safe 14 percent from Treasury bills?

A better procedure is to take the current interest rate on Treasury bills plus 9.4 percent, the average risk premium shown in Table 3.9. In 1981, when the rate on Treasury bills was 14 percent, that would have given Expected market

= interest rate on + normal risk return (1981) Treasury bills (1981) premium = 14% + 9.4% = 23.4%

The first term on the right-hand side tells us the time value of money in 1981; the second term measures the compensation for risk.

The expected return on an investment provides compensation to investors both for waiting (the time value of money) and for worrying (the risk of the particular asset).

What about today? As we write this in mid-1999, Treasury bills offer a return of only 4.8 percent. This suggests that investors in common stocks are looking for a return of just over 14 percent:4 Expected market return (1999)

= interest rate on Treasury bills (1999) + normal risk premium = 4.8 + 9.4 = 14.2%

The expected return on an investment provides compensation to investors both for waiting (the time value of money) and for worrying (the risk of the particular asset).

3 This is speaking a bit loosely, because the S&P 500 does not include all stocks traded in the United States, much less in world markets.

4 In practice, things might be a bit more complicated. We ve mentioned the yield curve, the relationship between bond maturity and yield. When firms consider investments in long-lived projects, they usually thinkabout risk premiums relative to long-term bonds. In this case, the risk-free rate would be taken as the current long-term bond yield less the average maturity premium on such bonds.

These calculations assume that there is a normal, stable risk premium on the market portfolio, so that the expected future risk premium can be measured by the average past risk premium. But even with 73 years of data, we cannot estimate the market risk premium exactly; moreover, we cannot be sure that investors today are demanding the same reward for risk that they were in the 1940s or 1960s. All this leaves plenty of room for argument about what the risk premium really is. Many financial managers and economists believe that long-run historical returns are the best measure available and therefore settle on a risk premium of about 9 percent. Others have a gut instinct that investors don t need such a large risk premium to persuade them to hold common stocks and so shade downward their estimate of the expected future risk premium.