Explanation:
Collectively, shareholders and subordinated debt holders receive the excess of firm value over the face value of the senior debt, F, if that excess is positive. Therefore, they have a call option on V with strike price equal to F. This implies that the value of the senior debt is the value of the firm V minus the value of the option held by equity and subordinated debt holders:
D(V,F,T,t) = V − c(V,F,T,t)
The call option is worth $63.56 million. This is the value of equity and subordinated debt combined. Therefore, the value of senior debt is $36.44 million (= 100M − 63.56M).
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Q.4359 A publicly traded firm valued at $100 million has subordinate debt (SD) with face value of $20 million, and senior debt (D) with face value of $60 million, both maturing in 5 years. The interest rate is 10 percent, and the volatility is 20 percent. This information is summarized in the figure below:
Figure 1 - Summary of Data
| Firm value V | $100m |
|---|---|
| Face value of senior debt, F | $60m |
| Face value of junior debt, U | $20m |
| Time to maturity, T | 5 years |
| Volatility of firm value, σ | 20% |
| Interest rate, r | 10% |
An analyst has uses the Merton model to work out the value of a call option on the value of the firm with exercise price equal to F [c(V,F,T,t)]. He obtains the following figures.
Figure 2 - Option with strike at F
| Face value of debt | $60m |
|---|---|
| d₁ | 2.039 |
| N(d₁) | 0.9793 |
| d₂ | 1.592 |
| N(d₂) | 0.9443 |
| c(V,F,T,t) | 63.56 |
Determine the value of senior debt.
A
$3.56 million
B
$16.44 million
C
$20 million
D
$36.44 million
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