Daniels,Inc.has assets valued at $2 million and 50,000 outstanding shares.A 5-year zero-coupon bond exists,which pays $400,000 at maturity.The bond is convertible into 10,000 shares.Assume σ = 0.30,r = 0.055,and no dividend is paid.What is the value of the bond?
A) $402,672
B) $452,172
C) $415,022
D) $385,172

Question

Quizplus · Accepted Answer

To value the convertible bond, we can use the Black-Scholes model, adjusted for the fact that the bond is convertible. The key inputs are the value of the underlying asset ($2 million), the conversion ratio (10,000 shares), the volatility (σ = 0.30), the risk-free rate (r = 0.055), and the time to maturity (5 years). The correct answer, A) $402,672, is obtained by inputting these values into the Black-Scholes formula or a similar option pricing model that accounts for the specifics of convertible bonds. This model considers the current value of the firm, the volatility of its assets, the risk-free rate, and the bond's terms to estimate its value.