FM for Actuaries

134 CHAPTER 4
Exercises
4.1 A project requires an initial cash outlay of $100 and an investment of $150
at the end of year 1, and is expected to generate $300 at the end of year 2, at
which time the project will terminate. Calculate the internal rate of return of
the project.
4.2 A project requires an initial cash outlay of $1,000 and a final investment of
$600 at the end of year 2, and is expected to generate $1,750 at the end of
the first year. Calculate the internal rate of return of the project.
4.3 Calculate the net present value of the cash flows in Exercise 4.1 by using:
(a) a constant interest rate of 6%,
(b) i S 1 =4%and iS 2 =5.5%.
4.4 Calculate the net present value of the cash flows in Exercise 4.2 by using:
(a) a constant interest rate of 6%,
(b) i F 1 =4%and iF 2 =5.5%.
4.5 You are given the following cash flows for an investment project. Calculate
the yield rate of the project, assuming that all cash flows occur at year end.
Year Contribution Investment income Withdrawal
0 10,000 1,550 0
1 1,000 500 0
2 1,000 500 3,000
3 0 200 7,000
4 0 200 7,000
4.6 Paul pays $5 million for a 7-year lease of a building and rented it out. He
will receive $1 million rental income at the end of the first and the second
year, and will receive $1.3 million at the end of the remaining years.
(a) Calculate the internal rate of return of his investment.
(b) Stock X is expected to generate a return of 14.5% per annum over the
next 7 years. Which investment should Paul choose? Explain why.