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Question:
Consider a firm that only has one type of debt. The face value of the debt is F. The market value of the firm's assets is 100 (= A(0)). The volatility of the rate of return on the firm's assets is 30%. The instantaneous risk free rate of interest is 3%.
Part A
If the maturity of the debt is one year, determine the market value of the firm's debt.
The yield to maturity, assuming continuous compounding is defined as
MV = F exp( - y * T)
where MV is the market value of debt, T the maturity measured in years and y the yield to maturity.
Part B
If the maturity of the debt is one month (0.083 years), determine the market value of the debt.
Part C
If the maturity of the debt is half a month (0.040 years), determine the market value of the debt.
Part D
What can you conclude from the above tables? Please explain your results.
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