Question

Let the present value from production be equal to V = 100, and this value can move either up or down in the next period (t=1) to V = 150 and V = 67. Suppose that at t=1 management has the option to invest 90 million in order to double the value of production. The risk free rate is 2%. You only have to consider the given periods. What is the value of this option?

Answer 1

We can use the binomial method to calculate the value of option.

First we find the probability of upward movement.

Let Upward movement be X. hence downward movement is (1-X)

We know that value of the firm today is the present value of expected price at end of year 1

Value today = PV (Weighted Average value after 1 year)

100 = 1/ 1.02 (X * 150 + (1-X)* 67)

102 = 150X + 67 -67X

X = 35 / 83

X = 42.17%

We will invest 90 million only when the value moves upwards, as that would result in additional value of 150 million. Hence we will earn 60 million on expansion.

Probability to earn 60 million on expansion is 42.17.

Expected value of expansion after 1 year = 25.30

Hence Present Value of option = 25.30 / (1+ Risk Free Rate) = 25.30 / 1.02 = 24.81

Value of option is 24.81