You are evaluating whether to invest in a car production facility that will pay a perpetual stream of cash flows once the assets are fully in place. You have no abandonment option, and you have no option to wait and see. You do have the option to expand production once, at t=1. This expansion option entails building a second, identical assembly line in the same facility. If you choose to expand production, your perpetual cash flows double in size starting the period following expansion (after the cost of initial investment and expansion has been realized) and remain doubled forever thereafter. Additionally, you immediately incur the full expansion cost at t=1. Your expansion option entails halting all production at the existing assembly line. This means that choosing the expansion option at t=1 results in no cash inflows during that period. If you choose to remain at the initial production level, your cash flows are unchanged and begin in the period following when you incur the initial cost.

You expect one of two states of the world to be realized next year: Up or Down. You can further assume that it is impossible to switch states from year to year. This means once you are in a state, you remain in that state forever. You have the following additional information:

The total initial cost is $100 million

The total expansion cost is $100 million, incurred only if you expand

Cash flows once the assets are fully in place (once all investment costs have been realized) are as follows

o Up state: $12 million in the first year after assets are fully in place, and $20 million per year forever thereafter

o Down state: $12 million in the first year after assets are fully in place, and $2 million per year forever thereafter

A candidate for a tracking portfolio risky asset is an ETF on the S&P 500 index. It is expected to exhibit the following cash flow realizations for $1 invested today:

o Up state: $1.35

o Down state: $0.90

The risk free rate is expected to be 6% per year forever.

1.

a) Find the PV of the investment without accounting for the option

b) Find the PV of the investment accounting for the expansion option

c) Compute the value of the option