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

Question

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.)

Explanation / Answer

Ans a) Value of equity today is given by Black - Scholes option pricing formula. It is similar to the value of call option:

E0 = V0*n(d1) - F*e^(-r*t)*n(d2)

where

d1 = (ln(V0/F) + (r + (sigmav^2)/2)*t)/(sigmav * root(t))

d2 = d1 - (sigmav * root(t))

Ans b) Value of the firm's zero coupon bond at time T is nothing but sum of safe claim payoff and short postion on put option written on firm's asset.

Bt = F + min(Vt - F , 0)

Ans c) Value of zero - coupon bond today = F * e^(-r*t)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.