Merton Model or Contingent Claims Analysis

Read the attached explanation of how to use the option pricing model to evaluate risky debt and equity. This is called the Merton Model or Contingent Claims Analysis. Answer the following questions:

1. What is the yield to maturity on Debtco's bonds?

The yeild to maturity on Debtco's bonds is equal to 10.87% when the riskfree interest rate is 8%.

The Mkt value of the firm is given as $100MM and the value of the equity of the firm is determined from the following equation:

E = N(d1)*V - N(d2)*Be^(rT)

d1 = [ln(V/B) + (r + sigma^2 / 2)*T] / [sigma*sqrt(T)]

d2 = d1 - sigma *sqrt(T)

where; V = value fo the firm

E = value of the equity in the firm

B = face value of the pure discount debt

r = riskless interest rate

T = time to maturity of the debt in years

sigma = standard deviation of the annualized continuously compounded rate of return on the firm's assets

ln = natural logarithm

e = the base of the natural log function (~ 2.71828)

N(d) = the probability that a random draw from a standard normal distribution will be less that d

Where the value of the debt = Mkt Value of the firm - value of the equity in the firm; i.e. $100MM - $28.24MM.

R = ln(face value of pure discount bond / value of the debt) / time to maturity of the debt; R = ln(80/71.76)/1 = 10.87%

2. Assume that the firm's management swaps its assets for riskier assets of the same total value. How would this asset swap affect the value of its debt and equity? Explain

The swap would increase the value of the equity and decrease the value of the debt.

Based on the equations used above, increasing sigma (standard deviation of the continuously compounded rate of return) for d1 would increase the numerator in the equation for d1. Since d1 has sigma to a higher power than the equation for d2, the value of Equity would increase. The value of the firm is unchanged, therefore, the value of the debt must decrease to balance the equation.