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# Valuation Models

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Acort Industries owns assets that will have an 60% probability of having a market value of \$55 million in one year. There is a 40% chance that the assets will be worth only \$25 million. The current risk-free rate is 4%, and Acort's assets have a cost of capital of 8%.

a. If Acort is unlevered, what is the current market value of its equity?
b. Suppose instead that Acort has debt with a face value of \$20 million due in one year. According to MM, what is the value of Acort's equity in this case?
c. What is the expected return of Acort's equity without leverage? What is the expected return of Acort's equity with leverage?
d. What is the lowest possible realized return of Acort's equity with and without leverage?

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#### Solution Preview

a. If Acort is unlevered, what is the current market value of its equity?

Expected asset value in one year=55*60%+25*40%=\$43 M
Current value of its equity=Expected value of equity in one year/(1+cost of capital)^1
= 43/(1+8%)^1=\$39.81481 M

b. Suppose instead that Acort has debt with a face value of \$20 million due in one year. ...

#### Solution Summary

Solution describes the steps to determine unlevered and levered value of equity. It also calculates expected rate of return of equity in the given cases.

\$2.19