Mostly Right, Inc. has assets that are currently valued at $1,500. One year from now, the assets are expected to be worth either $1,300 or $1,900. The company also has a zero coupon bond issue with a face value of $1,400 that is due in one year. The risk-free rate of return is 4%. What is the value of the equity in Mostly Right, Inc.?
A) $0
B) $48.33
C) $166.67
D) $208.33
E) $250.00

Question

Quizplus · Accepted Answer

The value of the equity in Mostly Right, Inc. can be calculated using the option pricing approach, treating the equity as a call option on the firm's assets with a strike price equal to the face value of the debt. The expected value of the assets in one year is the average of the two possible outcomes: (1300 + 1900) / 2 = 1600. If the assets are worth $1,300, the equity is worthless since the asset value is less than the debt value. If the assets are worth $1,900, the equity value is $1,900 - $1,400 = $500. The expected equity value before discounting is the probability-weighted average of these outcomes, but since both outcomes are equally likely, we consider the positive outcome: $500. To find the present value, we discount this back at the risk-free rate: $500 / (1 + 0.04) = $480.77. However, this calculation assumes the equity value in the negative scenario is also considered, which it should not be since equity cannot have a negative value. The correct approach is to recognize that the equity has value only in the scenario where the firm's assets exceed the debt value. Therefore, the correct calculation for the present value of the equity, considering the positive outcome and the 50% probability, is: ($500 * 0.5) / 1.04 = $240.38. This answer is not listed because of a mistake in the calculation process. The correct process involves calculating the value of the equity as an option, but the provided options do not match the corrected calculation. The mistake was in the final step of the calculation, not accounting for the probability correctly or misinterpreting the options. The correct answer should reflect the value of the equity as an option on the firm's assets, given the debt obligation and the risk-free rate for discounting.