Martha B's has total assets of $1,750. These assets are expected to increase in value to either $1,800 or $2,400 by next year. The company has a pure discount bond outstanding with a face value of $2,000. This bond matures in one year. Currently, Treasury bills are yielding 6 percent. What is the value of the equity in this firm?
A) $16.98
B) $34.59
C) $36.67
D) $37.08
E) $51.89

Question

Quizplus · Accepted Answer

The value of the equity in the firm can be calculated using the option pricing approach, considering the company's assets as the underlying asset and the bond's face value as the strike price. The equity value is essentially the call option value on the firm's assets with the strike price equal to the bond's face value.1. Calculate the expected asset values in each scenario:   - If assets increase to $1,800, the equity value is $0 because the assets are less than the bond's face value ($2,000).   - If assets increase to $2,400, the equity value is $400 ($2,400 - $2,000).2. Calculate the expected equity value:   - The probability of each outcome is 50% (assuming a simplified scenario).   - Expected equity value = 0.5 * $0 + 0.5 * $400 = $200.3. Discount the expected equity value back to present value:   - Using the Treasury bill yield of 6% as the discount rate:    - Present value = $200 / (1 + 0.06) = $200 / 1.06 ≈ $188.68.However, the correct calculation involves recognizing that the equity value is contingent on the firm's assets being greater than the bond's face value at maturity. The correct approach involves calculating the expected payoff of the equity (as a call option) and discounting it back at the risk-free rate. Given the choices provided and the correct approach to value the equity as an option, none of the calculations directly lead to the numbers provided in the options. The correct answer involves understanding the option-like nature of equity in a levered firm and applying option pricing principles, but the precise calculation seems to have been misunderstood in the explanation process.Given the misunderstanding in the calculation process, the correct approach to find the equity value involves using the Black-Scholes model or a similar option pricing model that accounts for the probability-weighted outcomes of the asset values exceeding the bond's face value, and then discounting those outcomes by the risk-free rate. However, without the explicit probabilities, volatilities, and a direct application of such a model, the precise equity value calculation as per the options provided cannot be accurately determined based on the initial explanation.Revisiting the calculation with the correct approach and the information provided:- The value of the equity is the value of the option to repay the bond at maturity if the firm's assets exceed the bond's face value.- Since the bond's face value is $2,000, the firm's equity holders will only choose to repay the bond if the firm's assets are worth more than $2,000 at maturity.- In the scenario where the assets are worth $1,800, the bond is not repaid, and the equity is worth $0.- In the scenario where the assets are worth $2,400, the bond is repaid, and the equity holders keep the residual value of $400.- The expected value of the equity before discounting is not directly calculated as $200, but rather, the value should be calculated based on the probability of the firm's assets being above the bond's face value and the payoff in that scenario, then discounted back at the risk-free rate.Given the error in the initial explanation and calculation, the correct answer should involve a proper option pricing approach, but the provided choices and explanation do not align with the standard methodologies for valuing equity as an option in a leveraged firm. The correct answer, based on the simplified approach provided, should reflect the value of the equity as an option on the firm's assets, but the detailed calculation to arrive at one of the specific choices provided (A, B, C, D, E) was not accurately described in the initial explanation.

Martha B's Has Total Assets of $1,750