Problem 1: PV of uncertain cash flows
A project with a 3-year life has the following probability distributions for possible end-of-year cash flows in each of the next three years:
Year 1 Year 2 Year 3
Prob Cash Flow Prob Cash Flow Prob Cash Flow
0.30 $300 0.15 $100 0.25 $200
0.40 500 0.35 200 0.75 800
0.30 700 0.35 600
0.15 900
Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the expected cash flow in each year, then evaluate those cash flows.)
Problem 2: Solving for N for an annuity
You are currently investing your money in a bank account which has a nominal annual rate of 9 percent, compounded monthly. If you invest $900 at the end of each month, how many months will it take for your account to grow to $301,066.27 (rounded to the nearest month)?
Problem 3: Interest rate of an annuity
South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying?
Problem 4: Number of periods for an annuity
Your subscription to Jogger's World Monthly is about to run out and you have the choice of renewing it by sending in the $10 a year regular rate or of getting a lifetime subscription to the magazine by paying $100. Your cost of capital is 7 percent. How many years would you have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year. (Round up if necessary to obtain a whole number of years.)
Problem 5: Effective annual rate
You have just taken out a 10-year, $12,000 loan to purchase a new car. This loan is to be repaid in 120 equal end-of-month installments. If each of the monthly installments is $150, what is the effective annual interest rate on this car loan?
Problem 6: FV of annuity due
To save money for a new house, you want to begin contributing money to a brokerage account. Your plan is to make ten contributions to the brokerage account. Each contribution will be for $1,500. The con-tributions will come at the beginning of each of the next 10 years, i.e., the first contribution will be made at t = 0 and the final contribution will be made at t = 9. Assume that the brokerage account pays a 9 percent return with quarterly compounding. How much money do you expect to have in the brokerage account nine years from now (t = 9)?