Finance question

Your company can undertake an investment project today or next year. The cost of the investment is $100 regardless of when you invest. Currently, the expected value of cash ?ows from the project is $95 (so the current NPV of investing today is -$5). Next year the expected value of the project will increase by 25% or decrease by 20%. The risk-neutral probability of an increase in value is 1 2. The risk-free rate is 2.5%.

(a): Suppose you can delay investment for one year. This means in one year, you can observe whether the project value has increased or decreased and based on this information decide whether you want to invest $100 to "purchase" the project at it's current value.

(b): Assume that you invest at t=0. At t=1, you have the opportunity to scale up your investment. You can scale up by 40% by incurring an additional cost of $35. In other words, you have a call option to purchase 40% of the project value for a strike price of $35. What is the value of the option to scale up?

(c): Assume that you invest at t=0. At t =1, you have the opportunity to scale down your investment. You can scale down by 50% by selling a part of the project. You estimate the resale value to be $50. What is the value of the 1 option to scale down?

(d): Suppose you have the option to delay, to scale up, and to scale down. What value of having all three options?

(e): Note that the value of having all three options is less than the sum of value of each individual option (e.g. the answer for part d. is less than the sum of the answers to parts a-c). Why is this?