Consider the following cash flows. All market interest rates are 12% right now.
Year 0 1 2 3 4
Cash Flow 160 170 180 230
(a) What price would you pay for these cash flows? What total wealth do you expect after 2.5 years if you sell the rights to the remaining cash flows? Assume interest rates remain constant. (Hint: Assume that you can continuously compound. For example, a cash flow expected in a half year would be discounted with (1 +i)^-0.5)
(b) What is the duration of these cash flows?
(c) Immediately after buying these cash flows, all market interest rates drop to 11%. What is the approximate impact on your total wealth right now?
(d) Again, consider the drop to 11% interest rates. What is the expected wealth you will have after 2.5 years, with these new lower interest rates? How does that compare to your answer in (a)? How does this compare to your answer in (c)? Why do you think there is this difference?