4. [60 points] A firm is considering a simple investment project. If it goes forward, then the firm must pay $900 now, but it receives a payment of $400 in each of the following three years. Except as noted, each part of the problem is worth 5 points.

(a) [16 points] You should calculate, to the nearest dollar, the present value of this project for four different scenarios. Assume that the firms opportunity cost of capital is simply the (risk-adjusted) market interest rate. Scenario A: The interest rate is 14%. Scenario B: The interest rate is 17%. For the second two scenarios, assume that the OCC is 20%, but there is also inflation. The effect of inflation is to increase the value of the payment received by the inflation rate, with each year that passes. The payment that would have been $400 initially exceeds $400 by the time it occurs a year later, and each years payment will be larger than the previous years payment. Scenario C: The inflation rate is 2%. Scenario D: The inflation rate is 5%.

(b) In which scenarios is the project profitable? (You should briefly justify your answers.)

(c) Can you find two scenarios such that the scenario with the higher interest rate also produces less investment? Can you find two scenarios such that the scenario with the higher interest rate also produces more investment?

(d) Can you find two scenarios such that the scenario with the higher inflation rate also produces less investment? Can you find two (different) scenarios such that the scenario with the higher inflation rate also produces more investment?

(e) Calculate the real interest rate for each scenario.

(f) Can you find two scenarios such that the scenario with the higher real interest rate also produces less investment? Can you find two scenarios such that the scenario with the higher real interest rate also produces more investment?

(g) Based on your answers to (d)-(f), which single variable is most useful for predicting changes in investment: the interest rate, the inflation rate, or the real interest rate?

(h) [9 points] Calculate, by numerical approximation, the internal rate of return of this investment project, to the nearest hundredth of a percent, assuming that there is no inflation.

(i) Given your previous answers, what is a good and simple rule for determining whether an investment project is profitable, based on the projects internal rate of return? You should show that this rule provides correct guidance in each of the four scenarios.

Optional bonus question [5 points]: Assuming no inflation, what is the internal rate of return on this project if the $400 annual payments continue forever? Justify your answer.