You can invest in just one of four projects on a lot of land you own. For simplicity, you have modeled the payoffs (as net present value in today’s dollars) of the projects as discrete distributions. By selling the land, you can make $60,000 for sure. If you build an apartment, you estimate a payoff of $130,000 if things go well (with probability 0.60) and $70,000 otherwise. If you build a single-family house, the payoff is $100,000 (with probability 0.60) and $60,000 otherwise. Finally, you could build a gambling casino which would pay very well—$500,000—but with a probability of just 0.10 since the final government permits are not likely to be granted; all will be lost otherwise.
a. Find the expected payoff for each of these four projects. In terms of just the expected payoff, rank these projects in order from best to worst.
b. Find the standard deviation for each of these four projects. In terms of risk only, rank the projects from best to worst.
c. Considering both the expected payoff and the risk involved, can any project or projects be eliminated from consideration entirely?
d. How would you decide among the remaining projects? In particular, does any single project dominate the others completely?