Question

Company NothingOrAll (NOA) is known to be undertaking a new project. If the project is successful the value of the firm's debt and equity in a year will be $52 million, if it is unsuccessful the firm's value will be $28 million. NOA has a zero bond issue outstanding, which is due in one year with face value $40 million. The risk-free interest rate is 5%. NOA's current value of debt and equity is $40 million.

Question 3.1: Make use of the binomial option pricing model to value the equity of NOA as a call option. What is NOA's value of debt?

Answer 1

Standard inputs :

Current value = S = 40

uS = upmove = 52

dS = downmove = 28

u = 52/ 40 = 1.30

d = 28/40 = 0.7

R = ( 1 + risk free rate ) = ( 1.05)

Risk neutral probability = ( R -d )/ (u -d) = ( 1.05 - 0.7 ) / ( 1.30 - 0.7) = 0.35 / 0.60 = 0.5833

1- p = 1- 0.5833 = 0.4167

Payoff in upmove = ( 52 - 40 ) =12

Payoff in downmove = 0

Expected payoff = 12 * 0.5833 + 0 *0.4167 = 7

value of equity = 7 / 1.05 = 6.67

value of debt = 40 /1.05 = 38.10