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# P2.T6.404. Valuation of subordinated debt (Stulz applying Merton model)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
AIMs: Explain the differences between valuing senior and subordinated debt using a contingent claim approach. Explain, from a contingent claim perspective, the impact of [stochastic] interest rates on the valuation of risky bonds, equity, and the risk of default.

Questions:

404.1. Consider the following assumptions about a firm with two classes of debt (senior and subordinated) both of which are five year zero-coupon bonds:
• Firm value (V) = $100.0 million with volatility of 20.0% per annum • Face value of senior debt (F) maturity in five (5) years =$60.0 million
• Face value of subordinated debt (U) maturity in five (5) years = $40.0 million • Riskless rate = 3.0% • c(V,F,T) = c(100,60,5) =$49.33
• c(V,F+U,T) = c(100,100,5) = $24.33 Which is nearest to the value of the subordinated debt? a.$10.67
b. $25.00 c.$31.00
d. $35.67 404.2. Assume a firm with only two classes of debt: senior debt consisting of a zero-coupon bond with face value of$100.0 million; and subordinated debt consisting of a zero-coupon bond with face value of $50.0 million. Consider the following two statements: I. An increase in firm (asset) volatility necessarily implies a decrease in the value of the subordinated debt II. As time to maturity decreases, the value of the subordinated debt necessarily increases (pulls to par) Under the Merton model for credit risk, which is (are) true statements? a. Neither b. I. only c. II. only d. Both are true 404.3. Assume the following assumptions (Stulz's initial assumptions) of a "high-value" firm which include a currently unrealistic, high risk-free rate: • Firm value (V) =$100.0 million with volatility of 20.0% per annum
• Face value of senior debt (F) maturity in five (5) years = $100.0 million • Face value of subordinated debt (U) maturity in five (5) years =$50.0 million
• Riskless rate = 10.0%
• c(V,F,T) = c(200,100,5) = $139.40 • c(V,F+U,T) = c(200,150,5) =$109.95
If the risk-free rate decreases to 2.0%, what is the impact?

a. Increase in value of equity
b. Decrease in value of senior debt
c. Increase in value of subordinated debt
d. None of the above