Question

Acort Industries owns assets that will have​ a(n) 70 % probability of having a market value of $ 43 million in one year. There is a 30 % chance that the assets will be worth only $ 13 million. The current​ risk-free rate is 8 %​, and​ Acort's assets have a cost of capital of 16 %. 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? a. If Acort is​ unlevered, what is the current market value of its​ equity? The current market value of the unlevered equity is ​$ nothing million

Answer 1

Answer :

a) Expected value of assets = 0.70 * 43 + 0.30 * 13 = $ 34 million

Value of unlevered firm = 34 / ( 1 + 0.16 ) = 29.31

Value of equity assuming Acort is unlevered = $ 29.31 million

b) Debt due in one year = $ 8 million

Risk-free rate = 8%

Value of debt = 8 / ( 1 + 0.08 ) = $ 7.41 million

Value of equity = Value of unlevered firm - Value of debt

= 29.31 - 7.41

Value of equity = $ 21.90 million

c) Expected return of equity ( without leverage ) = 34 / 29.31 - 1 = 16.00%

Expected return of equity ( with leverage ) = ( 34 - 8 ) / 21.90 - 1 = 18.72%

d) Lowest possible realized return:

Here, worst possible return = 13

Therefore,

Expected return of equity ( without leverage ) = ( 13 - 0) / 29.31 - 1 = - 55.65%

Expected return of equity ( with leverage ) = ( 13 - 8 ) / 21.90 - 1 = - 77.17%