1) If you invest $100 at an interest rate of 15%, how much will you have at the end of 8 years?
2) A new car is advertised to cost $10,000. If the interest rate is 5%, how much would you have to set aside now to provide this sum in 5 years?
3) The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 12-year annuity with payments of $50,000 per year. Calculate the PV for each of the following cases.
a. The annuity payments arrive at one-year intervals. The first payment arrives one year from now.
b. The first payment arrives in six months. Following payments arrive at one-year intervals (i.e., and 18 months, 30 months, etc)
4) You own a natural gas pipeline that will generate a $2 million cash return over the coming year. The pipeline's operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of gas shipped is declining, and cash flows are expected to decline by 4% per year. The discount rate is 10%
a. What is the PV of the pipeline's cash flows if its cash flows are assumed to last forever?
b. What is the PV of the cash flows if the pipeline is scrapped after 20 years?
5) You have just read an advertisement stating, "Pay us $100 per year for 10 years, and we will pay you $100 per year thereafter forever." If this is a fair deal, what is the rate of interest?
6) You work for a small widget-producing company. You're considering expanding the company's factory in Wichita. The expansion is projected to cost $400,000 this year. It will produce an inflow after operating costs of $100,000 in year 1, $200,000 in year 2, and $300,000 in year 3. The opportunity cost of capital is 12%. Calculate the NPV (Net Present Value) of the expansion. (Hint: NPV is the PV of the project's cash flows, including the original cost)