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# Equity as an option: calculate value of equity and value of debt

A corporation's assets are currently worth \$1,030. In one year, they will be worth either \$1,000 or \$1,300. The risk-free interest rate is 4%. Suppose they have an outstanding debt issue with a face value of \$1,000. This debt is due in one year.

a. The value of the equity is \$____?. (Rounded to 2 decimal places.)

b. The value of the debt is \$____?. (Round to 2 decimal places) and the interest rate on the debt is____%(Input answer as a whole percent).

c. The value of the equity would either go up or go down____? if the risk-free rate were 7 percent.
Why?

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the same problem with these numbers:

assets currently worth \$1,040
in one year will be either 1,000 or 1,340
risk free interest rate is 3%
supposethey have an outstanding debt issue with a face value of \$1,000. The debt is due in one year.

a,b are the same and for c the risk free rate is 8%

#### Solution Preview

When viewing equity as a call option, the value of the "underlying asset" becomes the value of the assets of the firm, and the "strike price" of the option becomes the face-value of the debt. In order to see this, let's start with the value of an option. Let's call S to the price of the underlying asset and K to the strike price. The value of a call option at the time of exercise is:

S - K if S > K -- i.e., if you should exercise it
0 if S <= K -- i.e., if you should choose not to exercise it.

Now let's think of S as the value of the assets and K to the face-value of debt. The value of equity in one year will be:

S - K if S>K ...

#### Solution Summary

The solution is very understandable when using call option strategy as a framework. All the formulas and calculations are included to reach the answers.

\$2.19