1. Suppose you have the following historical data on the market return, and the cash flows generated by a private firm.

2. Year	Market Return	Private Firm Cash Flow
   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20	9.12% 42.01% 86.60% 8.62% 37.35% 0.81% 23.74% 31.88% 27.42% 4.44% 22.84% 20.29% 12.03% 0.03% 6.43% 24.13% 1.42% 15.43% 6.60% 41.49%	$43.60 $219.65 $633.50 $30.65 $199.95 $43.55 $119.55 $156.15 $85.60 $64.75 $67.05 $62.45 $85.70 $200.00 $81.95 $258.20 $137.70 $357.50 $26.45 $390.6

3. Assume the statistical properties of the market return and the private firm cash flow do not change over time. The risk-free rate of return is 2.00%, and also does not change over time. Throughout, assume the CAPM gives the correct expected rate of return of assets.

   3(a). [5 points] Estimate the expected value of the market return, and the variance of the market return, using the historical data. What are the estimated values?

   3(b). [5 points] Estimate the expected value of the annual cash flow of the private firm. Also estimate the covariance of the cash flow with the market return. What are the estimated values?

   3(c). [10 points] Assume that the private firm is a perpetuty, that generates a cash flow, drawn from the same prob- ability distribution,. every year, forever. Using your estimated quantities from 3(a) and 3(b) (and any other estimated quantities you need), estimate, by any valid method, the value of the private firm. What value do you find?

   3(d). [5 points] Suppose the private firm can be purchased for $250. (Noteyou should not use this assumption when answering any of the earlier questions!) What is the NPV of purchasing the private firm?

   3(e). [5 points] Assume the private firm can always be purchased/sold for $250. What is the return on the private firm each year? (Twenty numbers in all/) That is, each year, assume you can purchase the private form for

   $250, hold it for one year, receive the cash flow for that year (at the end of the year), and then sell the private firm back for $250. What is the return in each of the twenty years of this strategy?

   3(f). [5 points] Estimate the beta coefficient (with respect to the market return) of the return of the private firm, using the values you calculated in 3(e).

   3(g). [5 points] Find a discount rate for the private firm, using the beta coefficient estimated from 3(f), and the expected return of the market estimated in 3(a).

   3(h). [5 points] Use the perpetuity formula to discount the expected cash flows, estimated in 3(b), at the discount

   found in 3(g). What present value do you find?

   3(i). [5 points] Is the present value found in 3(h) the same as the one found in 3(c)? Should the two values be the same? Why or why not? If they are not the same, which one is the correct present value of the private firm? Explain briefly.