Acort Industries owns assets that will have a(n) 75% probability of having a mar

Question

Acort Industries owns assets that will have a(n) 75% probability of having a market value of $53 million in one year. There is a 25% chance that the assets will be worth only $23 million. The current risk-free rate is 3%, and Acort's assets have a cost of capital of 6%.

a. If Acort is unlevered, what is the current market value of its equity? ____ million (round to 3 decimal places)

b. Suppose instead that Acort has debt with a face value of $19 million due in one year. According to MM, what is the value of Acort's equity in this case? ____ million (round to 3 decimal places)

c. What is the expected return of Acort's equity without leverage? What is the expected return of Acort's equity with leverage? ____% (round to 2 decimal places)

d. What is the lowest possible realized return of Acort's equity with and without leverage? ____% (round to 2 decimal places)

Please show all work. Thank you!

Explanation / Answer

a.) Current market value of Equity = (0.75x53 + 0.25x23)/(1+0.06)

                                                 = (39.75 + 5.75)/1.06

                                                 =45.50/1.06

                                                 =42.92 million

b.) Debt Present Value =$19/(1+0.03) =$19/1.03 =$18.45 million

Market Value of Equity =$42.92 - 18.45 =$24.47 million

c.) Expected Return without Leverage = (39.75 + 5.75)/42.92 -1 =45.50/42.92 -1 =1.0601-1 =0.0601 or 6.01%

Expected Return with Leverage = (45.50 - 19)/24.47 -1 =26.50/24.47 -1 =1.0829 -1 =0.0829 or 8.29%

d.) Lowest Possible Return without leverage = 23/42.92 -1 =0.5358-1 = -0.4641 or -46.41%

Lowest Possible Return with leverage = (23-19)/24.47 -1 =0.1635-1 = -0.8365 or -83.65%

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