Question

Acort Industries owns assets that will have a 75% probability of having a market value of $52 million in one year. There is a 25% chance that the assets will be worth only $22 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 $18 million due in one year. According to MM (i.e. perfect market), 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

Solution :

a). The current market value of the unlevered equity

   $=\frac{75\% \times \ 52 \text{ million} + 25\% \times \ 22 \text{ million}}{1+10 \%}$

   = $ 40.45 million

b). The market value of the equity one year from now is

  $=(75\% \times \ 52 \text{ million} + 25\% \times \ 22 \text{ million})- \ 18 \ \text{million}$

  = $ 44.5 million - $ 18 million

  = $ 26.5 million

c). The expected return on the equity without the leverage = 10%

     The expected return on the equity with the leverage =   $=10\% +\frac{ \ 22 \text{ million}}{\ 26.5 \text{ million}}$

= 0.93 %

d). The lowest possible value of equity without the leverage = $20 million - $ 18 million

= $ 2 million

The lowest return on the equity without the leverage = 10%

The lowest return on the equity with the leverage = 2 % as the equity is eroded.