Martha B's has total assets of $1,810.These assets are expected to increase in value to either $1,900 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,U.S.Treasury bills are yielding 5.5 percent.What is the value of the equity in this firm?

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To value the equity in the firm, we can use the concept of risk-neutral valuation. First, calculate the expected value of the assets at the end of the year, then determine the value of the equity by subtracting the bond's face value and discounting back at the risk-free rate.1. Expected value of assets at the end of the year:$$ \text{Expected value} = 0.5 \times \$1,900 + 0.5 \times \$2,400 = \$2,150 $$2. Value of equity:The equity value is the excess of the asset value over the bond's face value if the assets are worth more than the bond's face value. Otherwise, it's worth zero because the bondholders get paid first.- If assets increase to $1,900, equity = max($1,900 - $2,000, 0) = $0- If assets increase to $2,400, equity = max($2,400 - $2,000, 0) = $4003. Expected value of equity:$$ \text{Expected equity} = 0.5 \times \$0 + 0.5 \times \$400 = \$200 $$4. Discount the expected equity back at the risk-free rate (5.5%):$$ \text{Value of equity} = \frac{\$200}{1 + 0.055} = \$189.57 $$It appears there was a mistake in my calculations, as the final answer does not match any of the provided options. The correct approach involves calculating the expected payoff to equity holders and then discounting that amount back at the risk-free rate. However, the initial calculation of the expected value of the assets and the subsequent steps seem to have been misinterpreted. Let's correct this by focusing on the correct method to find the value of the equity:1. Calculate the payoff to equity in each state:   - If assets are $1,900, equity gets nothing since it's less than the bond value.   - If assets are $2,400, equity gets $400 ($2,400 - $2,000).2. Calculate the probability-weighted payoff to equity:   - Since there are only two states considered equally likely, the expected payoff to equity is $200 (half of $400, since there's a 50% chance of getting nothing and a 50% chance of getting $400).3. Discount the expected payoff to equity back at the risk-free rate to find its present value:   - This involves using the formula for present value, $PV = \frac{FV}{(1 + r)^n}$, where $FV$ is the future value, $r$ is the interest rate, and $n$ is the number of periods.Given the mistake in the initial explanation and the mismatch with the provided options, the correct approach involves understanding that the value of equity is derived from the expected payoff in the future, discounted at the risk-free rate. However, without the correct calculations aligning with the options provided, the initial answer cannot be directly corrected to match an option. The key steps involve calculating the expected payoff to equity (considering the bond's face value and the possible asset values), and then discounting that expected payoff at the given risk-free rate to find the present value of the equity. The provided options suggest a specific numerical answer is expected, which requires precise calculations based on the given scenario.

Martha B's Has Total Assets of $1,810