Question

Tropical Sweets is considering a project that will cost $80 million and the cost of capital for this type of project is 10 percent and the risk-free rate is 6 percent. After discussions with the marketing department, you learn that there is a 30 percent chance of high demand, with future after-tax cash flows of $50 million per year for three years. There is a 40 percent chance of average demand, with after-tax cash flows of $40 million per year for three years. If demand is low (a 30 percent chance), after-tax cash flows will be only $10 million per year for three years. The project cannot be delayed. But if Tropical Sweets implements the project, then Tropical Sweets will have a growth option. It will have the opportunity to replicate the original project at the end of its life and Tropical knows the cost will be the same $80 million (100% sure). Done in Excel.

1) What is the expected NPV without growth option?​

2) What is the expected NPV with growth option?​

Answer 1

Expected NPV without growth = Sumproduct( PV of Cashflow, Probability of demand)

So, PV of after tax cashflow should be found out and then

NPV is computed based on the below formula

NPV = PV of Cash Inflow - Project outlay at year 0

Then Expected NPV can be calculated by multiplying NPV with probability for each state of demand.

The sum of Expected NPV will be the NPV without Growth option.

NPV with Growth option:

The project will be replicated at year 3 after the life of 3 years.

NPV = NPV of 1st project + PV of NPV of repeat project(at Year 3)

= NPV of 1st Project + NPV/(1 + WACC)³

The following excel screenshot provides the solution:

NPV without Growth = $4.55

NPV with Growth option = $7.97