Question

The value of a company's equity is $138 million and the volatility of its equity is 28%. The debt that will have to be repaid in 6 years is $65 million. The risk-free interest rate is 2.8% per annum. Use Merton's model to estimate the expected loss from default, the probability of default, and the recovery rate in the event of default. Explain why Merton's model gives a high recovery rate.

Answer 1

Solution Using Black Scholes Step 1: Calculate d1 and d2 d1 = d2 1.641 0.955 Step 2: Find N(d1) and N(d2) N(d1) Delta0.9496 N(d2) - Proba NoDefault0.8302 (in a risk-neutral world) Step 3: Find E using Black-Scholes Market value of equity 85.42 Characteristic of risky debt Market value of debt Yield to maturity Spread (bp) 52.58 3.54% 74. Decomposition of risky debt Riskless debt Put 54.95 2.37 Another decomposition Face value Default probability Loss if no recovery Expected recovery Exp.Loss|Default Exp Recovery Rate Value of risky debt 65 16.98% 65 48.47 16.53 74.57% 52.58 Cost of capital (using CAPM) Beta equity 1.534