Acort Industries owns assets that will have a(n) 80% probability of having a mar

Question

Acort Industries owns assets that will have a(n) 80% probability of having a market value of $45 million in one year. There is a 20% chance that the assets will be worth only $15 million. The current risk-free rate is 9%, and Acor's assets have a cost of capital of 18%. 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 $8 million due in one year. According to M&M;, 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?

Explanation / Answer

a) Value of assets (=equity) after one year = 80% x 45 + 20% x 15 = $39.00

Value of equity today = 39 / (1 + 18%) = $33.05 million

b) If there is debt, then value of asset after one year = 80% x 45 + 20% x 15 = $39.00

Current Value of debt = 8 / (1 + 9%) = $7.34 million

Value of equity today = 39 / 1.18 - 7.34 = $25.71 million

c) Without leverage, Expected Return = 39 / 33.05 - 1 = 18%

With leverage, Expected Return = (39 - 8) / 25.71 = 20.6%

d) Without leverage, Lowest possible return = 15 / 33.05 - 1 = -54.6%

With leverage, Lowest possible return = (15 - 8) / 25.71 - 1 = -72.8%

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