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INTRODUCTION TO RISK, RETURN, AND THE OPPORTUNITY COST OF CAPITAL

We have thus far skirted the issue of project risk; now it is time to confront it head-on. We can no longer be satisfied with vague statements like The opportunity cost of capital depends on the risk of the project. We need to know how to measure risk and we need to understand the relationship between risk and the cost of capital.

Think for a moment what the cost of capital for a project means. It is the rate of return that shareholders could expect to earn if they invested in equally risky securities. So one way to estimate the cost of capital is to find securities that have the same risk as the project and then estimate the expected rate of return on these securities.

We start our analysis by looking at the rates of return earned in the past from different investments, concentrating on the extra return that investors have received for investing in risky rather than safe securities. We then show how to measure the risk of a portfolio by calculating its standard deviation and we look again at past history to find out how risky it is to invest in the stock market.

Finally, we explore the concept of diversification. Most investors do not put all their eggs into one basket they diversify. Thus investors are not concerned with the risk of each security in isolation; instead they are concerned with how much it contributes to the risk of a diversified portfolio. We therefore need to distinguish between the risk that can be eliminated by diversification and the risk that cannot be eliminated.

After studying this material you should be able to

_ Estimate the opportunity cost of capital for an average-risk project.

_ Calculate the standard deviation of returns for individual common stocks or for a stock portfolio.

_ Understand why diversification reduces risk.

_ Distinguish between unique risk, which can be diversified away, and market risk, which cannot.

Rates of Return: A Review

When investors buy a stock or a bond, their return comes in two forms: (1) a dividend or interest payment, and (2) a capital gain or a capital loss. For example, suppose you were lucky enough to buy the stock of General Electric at the beginning of 1999 when its price was about $102 a share. By the end of the year the value of that investment had appreciated to $155, giving a capital gain of $155 $102 = $53. In addition, in 1999 General Electric paid a dividend of $1.46 a share. The percentage return on your investment was therefore

The percentage return can also be expressed as the sum of the dividend yield and percentage capital gain. The dividend yield is the dividend expressed as a percentage of the stock price at the beginning of the year:

Thus the total return is the sum of 1.4% + 52.0% = 53.4%. Remember we made a distinction between the nominal rate of return and the real rate of return. The nominal return measures how much more money you will have at the end of the year if you invest today. The return that we just calculated for General Electric stock is therefore a nominal return. The real rate of return tells you how much more you will be able to buy with your money at the end of the year. To convert from a nominal to a real rate of return, we use the following relationship:

In 1999 inflation was only 2.7 percent. So we calculate the real rate of return on General Electric stock as follows:

Therefore, the real rate of return equals .494, or 49.4 percent. Fortunately inflation in 1999 was low; the real return was only slightly less than the nominal return.

Seventy-Three Years of Capital Market History

When you invest in a stock, you can t be sure that your return is going to be as high a that of General Electric in 1999. But by looking at the history of security returns, you can get some idea of the return that investors might reasonably expect from investments in different types of securities and of the risks that they face. Let us look, therefore, at the risks and returns that investors have experienced in the past.