Acort Industries owns assets that will have a n 60% probability of having a mark

Question

Acort Industries owns assets that will have a n 60% probability of having a market value of $41 million in one year. There is a 40% chance that the assets will be worth only $11 million. The current risk-free rate is 2%, and Acort's assets have a cost of capital of 4%. 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 $6 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? a. If Acort is unlevered, what is the current market value of its equity? The current market value of the unlevered equity is (Round to three decimal places.)

Explanation / Answer

a). Solution :- Current market value of equity = (0.60 * 41 Million + 0.40 * 11 Million) / (1 + 0.04)

= (24.60 Million + 4.40 Million) / 1.04

= 29 Million / 1.04

= $ 27.885 Million.

Conclusion :- Current market value of equity = $ 27.885 Million.

b). Solution :- Current market value of debt = 6 Million / (1 + 0.02)

= 6 Million / 1.02

= $ 5.882 Million

Current market value of equity = 27.885 Million - 5.882 Million

= $ 22.003 Million (Rounded off to $ 22 Million)

Conclusion :- Current market value of equity = $ 22 Million.

c). Solution :- Expected return without leverage =  (29 Million / 27.885 Million) - 1

= (1.04 - 1)

= 0.04 i.e., 4 %

Expected return with leverage = [ (29 Million - 6 Million) / 22 Million ] - 1

= (23 Million / 22 Million) - 1

= 1.0455 - 1

= 0.0455 i.e., 4.55 % (approx).

Conclusion :-

d). Solution :- Lowest possible return without leverage = (6 Million / 27.885 Million) - 1

= 0.2152 - 1

= (-) 0.7848 i.e., (-) 78.48 %

Lowest possible return with leverage = [ (6 Million - 6 Million) / 22 Million ] - 1

= (0 Million / 22 Million) - 1

= 0 - 1

= (-) 1 i.e., (-) 100 %

Conclusion :-

Expected return without leverage 4.00 % Expected return with leverage 4.55 %

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