Question

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Acort Industries owns assets that will have an 80% probability of having a market value of $50 million in one year. There is a 20% chance that the assets will be worth only $20 million. The current risk-free rate is 5%, and Acort’s assets have a cost of capital of 10%. 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?

Answer 1

a.Current market value of its equity, If Acort is unlevered is calculated as follows,

Expected future value of firm =(0.8*50)+(0.2*20)

Expected future value of firm =44 million

Current market value of its equity = Expected future value of firm/(1+Cost of capital)

Current market value of its equity =44/(1+0.1)

Current market value of its equity = 40 million

b.Current market value of its equity, If Acort has debt with a face value of $20 million due in one year is calculated as follows,

Value of Debt = Face value of debt due in one year /(1+Risk free rate)

Value of Debt =20/(1+0.05)

Value of Debt =19.05 million

Value of equity = Value of unlevered firm- Value of Debt

Value of equity =40-19.05

Value of equity =20.95 million

c.Expected return of Acort’s equity without leverage is calculated as follows,

Expected return without leverage =(44/40)-1

Expected return without leverage =0.1 i.e.,10%

Expected return of Acort’s equity with leverage is calculated as follows,

Expected return with leverage =((44-20)/20.95)-1

Expected return with leverage =0.1456 i.e.,14.56%

d.Lowest possible realized return of Acort’s equity with and without leverage is calculated as follows,

Lowest possible realized return without leverage =(20/40)-1

Lowest possible realized return without leverage = (-0.5) i.e., (-50%)

Lowest possible realized return with leverage =(0/20.95)-1

Lowest possible realized return with leverage = 1 i.e., 100%