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Problem 4 Consider a simple firm value model (known as the Merton model) Suppose that...

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Problem 4 Consider a simple firm value model (known as the Merton model) Suppose that a firm has market value V consisting of equity and debt with the debt being in the form of a zero-coupon bond with face value K and maturity T. Define: o: Firm value today VT: Firm value at time T' Eo:Value of the firm's equity today ET:Value of the firm's equity at time T F: Face value of the firm's zero-coupon bond :Volatility of firm value r: Risk-free interest rate. If VT F, the firm should make the debt repayment at time T and the value of equity at this time becomes VT - F.Therefore the value of the firm's equity at time T is given by ET max(VT - F, 0) (a) What is the value of equity today (Eo)? (Hint: Use the Black-Scholes option pricing formula.) (b) Define: Bo:Value of the firm's zero coupon bond today Br:Value of the firm's zero coupon bond at time T. If VT F, the firm can repay the promised amount F and the value of the bond at this time isF Then what is the value of the firm's zero-coupon bond at time T (Br)? (c) What is the value of the zero-coupon bond today (Bo)? (Hint: Use the Black-Scholes option pricing formula.)

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