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1. The current price of a tradable (non-dividend) security S is 100 and its future prices follow a binomial lattice with u = 1.5 and d = u¹, i.e., if the market is up next year the securitys price will be 150; if the market is down next year the securitys price will be 66.6. A project under consideration has a present value (of discounted expected subsequent future) cash flow of 1500 if the market is up next year, and has a present value (of discounted expected subsequent future) cash flow of 666.6 if the market is down next year. The risk-free rate is 5%.

Questions:

1. (a) What is the projects PV ?
   2. What are the objective probabilities if the required expected rate of return is 25%?
   3. What is the expected rate of return if the objective probability the market will go up is 0.6?
2. (a) The projects initial investment I₀ (at time 0) is 1050. What is the projects NPV ? Should the project be undertaken?
   2. Suppose it is possible to delay the project 1 year. To do so will cost you 175 today, and the required investment next year will increase by 10%. Should you acquire this delay option?
   3. Let p denote the premium cost today to delay the project, and let 100% denote the percentage increase in the required investment. Determine the acceptance region for the project.
3. Suppose in year 1 you can spend an additional 25 to delay the project 1 more year. The required investment will increase by another 10%. What is the projects NPV ? Should the project be undertaken, and how should the delay option be optimally implemented?

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