Acort industries o ns assets that will have a n 60% probability o having a marke

Question

Acort industries o ns assets that will have a n 60% probability o having a market value of $51 million in one year. There is a 40% chance t capital of 20%. atthe assets will be worth only $21 milion. The current nsk ree rate is 10 and Acort's assets have a cost o 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 $21 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 realzed return of Acort's equity with and without leverage?

Explanation / Answer

Probability to have a market value of $51 million (m1) is 60% (p1)

Probability to have the market value of $21 million(m2) is 40%(p2)

Risk-free rate (Rf)= 10%

Cost of capital(r) = 20%

(a) Calculation of market value of Equity if Acort is unlevered:

Current value of equity = [(p1*m1) + (p2 * m2)] / (1+r)

Current value of Equity = [(0.60 * $51 million) +(0.40* $21 million)] / (1 + 0.20)

Current value of Equity = ($30.6 million + $8.4 million) / 1.20

Current value of Equity = $39 million / 1.20 = $32.5 million

(b) If Acort has a debt with face value of $21 million due in one year,lets first calculate the current value of debt :

= Face value of Debt in one year/ (1+ Rf)

= $21 million / (1+ 0.10) = $19.09 million

Now the value of Acort's Equity shall be Current value of Equity - Debt ie. ($32.5 million - $19.09 million) = $12.96 million

(c) Expected Return of Acort's equity without leverage:

Current value of equity (without leverage) = $32.5 million

Value of equity in one year = $39 million

Expected Return = ($39 million /$32.5 million) -1 = 1.2 - 1 = 20%

Expected Return of Acort's equity with leverage:

Return =[( Value of equity in one year - Value of debt in one year)/ Current value of Debt ] -1

Return = ([$39 million - $21 million) / $12.96 million] - 1

Return = 1.3888 - 1 = 0.3888 = 38.89%

(d) Lowest Possible Return without leverage = ($21 million / $32.5 million) - 1 = - 35.38%

Lowest Possible Return with leverage = ( 0 / $32.5 million) -1 = -100%

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