Problem: You are contemplating an investment project that has two phases. As currently planned, the first phase of the project requires an investment of $100,000 today. One year from now, the project will deliver either $120,000 or $80,000, with equal probabilities. When these Phase I payouts occur, you will be able to invest an additional $100,000 in Phase II One year later, Phase II will pay out either 20 percent more than Phase 1 Actually delivered or else 20 percent less, again with equal probabilities.
You may commit to both phases at the start, or you may commit to Phase 1 (and postpone a decision on Phase II) or you may invest in neither. If you commit to both phases at the start, there is really no reason to delay. Suppose that you can choose in that case to implement both phases virtually simultaneously, so that both investments are made today and all payouts occur one year from now. (Note however that the size of the Phase II payout still depends on the size of the Phase 1 Payout. Conceptually, you can think of the Phase II payout as occurring immediately after Phase 1 Payouts.)
Q1. Using an expected payoff criterion, and discounting at 10 percent, which of the alternatives (First, Both or Neither) is the optimal decision?
Q2. What is the breakeven discount rate at which neither is a better decision than first?
Q3. Suppose you have access to an additional, similar investment that resembles the original but is more volatile: for the same initial investment, it delivers a Phase I return of + 40 percent (that is, either $140,000 or $60,000) with equal probabilities. Similarly, it delivers a Phase II return of +40 percent of the Phase I payouts, again with equal probabilities. Show that this new investment is preferable to the original, with a discount rate of 10 percent
Q4. Evidently, the higher volatility of the investment (+40 percent as opposed to + 20 percent) makes the potential cash flows attractive. With the discount rate at 10 percent, what levels of volatility would lead to an expected value above zero?