Question

Abort Industries owns assets that will have a (n)75% probability of having a market value of $47 million in one year. There is a 25% chance that the assets will be worth only $17 million. The current risk-free rate is 12%, and Abort's assets have a cost of capital of 24%.

a. If Abort is un-levered, what is the current market value of its equity?
b. Suppose instead that Abort has debt with a face value of $17 million due in one year. According to MM, what is the value of Abort's equity in this case?
c. What is the expected return of Abort's equity without leverage? What is the expected return of Abort's equity with leverage?
d. What is the lowest possible realized return of Abort's equity with and without leverage?

Answer 1

The current market value of Abort Industries' equity without leverage is approximately $31.85 million, while with leverage and $17 million in debt, the equity value is $22.5 million. Expected returns and lowest realized returns vary based on leverage, with the lowest realized return with leverage potentially being $0.

Step-by-step explanation:

The student has asked a question regarding evaluating the current market value of equity in an unleveraged and leveraged scenario using Modigliani-Miller (MM) theorem concepts, calculating expected returns, and determining the lowest possible realized return.

a. Current Market Value of Unleveraged Equity

To find the current market value of Abort Industries' equity without leverage, we discount the expected market value of the assets back at the cost of capital. The expected market value is calculated by taking the probability-weighted average of the possible future values.

Expected Market Value = (0.75 * $47 million) + (0.25 * $17 million) = $35.25 million + $4.25 million = $39.5 million.
Discounting this at the cost of capital of 24%:

Current Market Value = Expected Market Value / (1 + Cost of Capital)
Current Market Value = $39.5 million / (1 + 0.24) = $31.85 million (approximately).
b. Current Market Value with Debt

If Abort Industries has $17 million in debt due in one year, according to MM, the value of equity is the market value of the assets less the value of the debt.

Equity Value = Current Market Value - Debt
Equity Value = $39.5 million - $17 million = $22.5 million (assuming the debt is risk-free and certain to be paid).
c. Expected Returns

The expected return of equity without leverage is based on the average outcome, discounted at the cost of capital. The expected return of equity with leverage would also account for the cost of the debt being serviced.

d. Lowest Possible Realized Return

The lowest possible realized return of Abort's equity without leverage would be the worst-case scenario, which is the asset value at $17 million. With leverage, it would be $0 since the equity is wiped out if the asset value equals the debt value.