McLemore Industries has a zero coupon bond issue that matures in two years with
ID: 2779227 • Letter: M
Question
McLemore Industries has a zero coupon bond issue that matures in two years with a face value of $47,000. The current value of the company’s assets is $27,800, and the standard deviation of the return on assets is 58 percent per year.
Assume the risk-free rate is 5 percent per year, compounded continuously. What is the value of a risk-free bond with the same face value and maturity as the company’s bond? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What price would the bondholders have to pay for a put option on the firm’s assets with a strike price equal to the face value of the debt? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Using the answers from (a) and (b), what is the value of the firm’s debt? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Using the answers from (a) and (b), what is the continuously compounded yield on the company’s debt? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
From an examination of the value of the assets of McLemore Industries, and the fact that the debt must be repaid in two years, it seems likely that the company will default on its debt. Management has approached bondholders and proposed a plan whereby the company would repay the same face value of debt, but the repayment would not occur for five years. What is the value of the debt under the proposed plan? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the new continuously compounded yield on the debt? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
McLemore Industries has a zero coupon bond issue that matures in two years with a face value of $47,000. The current value of the company’s assets is $27,800, and the standard deviation of the return on assets is 58 percent per year.
Explanation / Answer
a. Using the equation for the PV of a continuously compounded lump sum, we get:
PV = $47,000 x e–.05(2) = $42505.96
b. Using Black-Scholes model to value the equity, we get:
d1 = [ln($27,800/$47,000) + (.05 + .582/2) x 2] / (.58 x sq root of 2 ) = –.10816
d2 = –.10816 – (.58 x square root of 2 ) = –.92828
N(d1) = .46017
N(d2) = .18141
Putting these values into Black-Scholes:
Equity = $27,800(.46017) – ($47,000e–.05(2))(.18141) = $12792.726 - $7711 = $5081.72
And using put-call parity, the price of the put option is:
Put = $47,000e–.05(2) + 5081.72 – 27800 = $19787.674
c. The value of a risky bond is the value of a risk-free bond minus the value of a put option on the
firm’s equity, so:
Value of risky bond = $42,505.96 – 19787.674 = $22718.286
Using the equation for the PV of a continuously compounded lump sum to find the return on debt,
we get:
$22718.286 = $47,000e–R(2)
.483367 = e–R2
RD = –(1/2)ln(.483367) = .36349 or 36.349%
d. The value of the debt with five years to maturity at the risk-free rate is:
PV = $47,000 x e–.05(5) = $36557.6
Using Black-Scholes model to value the equity, we get:
d1 = [ln($27800/$47,000) + (.05 + .582/2) x 5] / (.58 x sq root of 5 ) = -.0684
d2 = -.0684 – (.58x square root of 5 ) = –1.3653
N(d1) = .47608
N(d2) = .08691
Putting these values into Black-Scholes:
Equity = $27800(.47608) – ($47,000e–.05(5))(.08691) = $13235.024 - $3177.2210 = $10057.8
And using put-call parity, the price of the put option is:
Put = $47,000e–.05(5) + $10057.8 – $27800 = $18815.4
The value of a risky bond is the value of a risk-free bond minus the value of a put option on the
firm’s equity, so:
Value of risky bond = $36557.6 – 18815.4 = $17742.2
Using the equation for the PV of a continuously compounded lump sum to find the return on debt,
we get:
$17742.2 = $47000e–R(5)
.37749 = e–R5
RD = –(1/5)ln(.37749) = .19484 or 19.484%
The value of the debt declines because of the time value of money, i.e., it will be longer until
shareholders receive their payment. However, the required return on the debt declines. Under the
current situation, it is not likely the company will have the assets to pay off bondholders. Under
the new plan where the company operates for five more years, the probability of increasing the
value of assets to meet or exceed the face value of debt is higher than if the company only
operates for two more years.