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# CORPORATE FINANCE: - page 4 / 11

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Just as the total market value of the assets must equal the total market value of the equity, the risk on the right-hand side of the balance sheet must equal the risk on the left-hand side of the balance sheet.  Does this risk equivalency make sense?

Since the value of financial assets is derived from the cash flows of the real assets, the risk of these financial securities must likewise be derived from the risk of the cash flows of the real assets.  Hence, the beta of the (only) financial security, βS, must equal the beta of the real asset, βA1.  The real asset "determines" the value and the risk of the financial security.

In the "real world," the risk of real assets usually is not directly observable.  It is difficult to obtain real asset betas since "used" real assets do not routinely trade on organized secondary markets.  Since they don't trade regularly, real asset prices in a secondary market are not readily observable.  Accordingly, the returns of real assets cannot routinely be calculated.  Therefore, regressions of real asset returns on market returns are not possible to determine asset betas.

However, financial securities often trade regularly in the secondary financial markets.  Therefore, prices are observable and returns can easily be calculated.  Using these returns, betas can be determined by regressing security returns upon the market portfolio returns.

Since the risk (βS) of the financial security (equity in our all-equity firm) equals the risk of the firm's real assets, βA, we can "infer" real asset risk by observing the risk of the financial security.  However, remember that the "true causation" of the security's risk is due to the risk of the real asset, not vice-versa.  However, since security risk equals asset risk, and we can observe security risk, we use this procedure to estimate asset risk.  Accordingly, we find the appropriate discount rate for the asset as:

E(rA1) = rf + (Erm) - rfS, where βS is the stock's beta.

Using the stock's beta we can infer the required return for the real asset.  For our one-asset firm with all-equity financing, this return is the required return, or the discount rate in NPV calculations.

III.   The Multi-Asset Firm:

Assume that the above firm was contemplating an expansion and buying a second asset, A2, which is just like the first asset, A1.  In this case, the managers could use the required rate for A1 to calculate the NPV for A2.  Since the basic business risk of the firm would not change, i.e., the firm is just expanding its size in the same line of business, the same discount rate would be appropriate for the second asset.  In general, you can use the firm's equity beta to evaluate the risk of a project if

· The project is in the same risk-class as the rest of the firm's assets, and

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