Let the present value from production be equal to V = 100, and this value can...

Let the present value from production be equal to V = 100, and this value can move either up (with factor u = 1.4) or down (with factor d = 1/u) per period. Suppose that at t=3 management has the option to invest 130 million in order to double the value of production. The risk free rate is 2%.

What is the expanded present value of this production facility if management has the opportunity to expand at t = 3

Expert Solution

Note: Since there is no mention of how many months are there in between 2 periods. I have assumed it to be 1 month and the total maturity as 3 months and the risk-free rate is assumed to be continuously compounding per annum.

Value of Option = $14.04 millions

All the values in the below image are in $ millions

Value of Call Option at Expiry = Maximum of (Stock price - strike price) or 0
Value of Call Option at Node = [(Probability of up move * Value of Option at the upper node) + (Probability of Down Move * Value of Option at the lower node)] * e-rf * dT
where dT = Time period between 2 periods

jeff jeffy answered 1 year ago

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