# You are offered three annuities (these make equal payments over a specific period).

Remember that when you use the perpetuity formula, the formula automatically present values the perpetuity one period, so if you use the perpetuity formula in year 15, the result is as of the beginning of year 15!

1. You are offered three annuities (these make equal payments over a specific period). Using an annual 5.5% discount rate, calculate each annuity’s price:

 # Price (\$) Payments (\$/month) Life (years) 1 ? 195 6 2 ? 200 (growing @ 1%/year) 5 3 ? 135 (growing @ 2.5%/year) Forever

2. You purchase a new machine for your firm. It costs \$84,000 and will expand your cash flow by \$13,500/year in year 1 growing by 2.5% per year after that. The system will work for 30 years before you have to replace it. What are the NPV (at a 5.5% discount rate) and IRR?

The vendor offers you another machine costing \$99,000 and lasting 35 years, with the same yearly cash flow and growth rate. What are the NPV and the IRR for it? Should you get it?

a. Use July 1, 2011, to calculate the future value of the \$5.9M owed on July 1, 2000.

b. Use July 1, 2011, to calculate the present value of the 25 yearly payments of

\$1,193,248.20. The first payment is made on July 1, 2011

c. Should Bobby take it? Why?

4. You are looking to lease a car. The dealer offers you the following: Car price = \$35,000

Monthly lease payments = \$499

Down payment = \$3,000

Lease term = 36 months

Purchase price at end of lease = \$18,000

What is the implicit interest rate on the lease?

5. The Airbus A220 has the following R&D costs (all negative cash flows):

 €400M (year 1) €300M (year 2) €200M (year 3) €100M (year 4)

Each plane will be sold for €48M – 15% down and the rest due on delivery one year later. The cost to produce each plane is €38M – these costs are recognized on delivery. The Sales and Marketing Department says that you will sell 30 planes (year 5) and sale will grow by 5 planes per year before they plateau at 60 planes. The last sale is made in year 16, when the A220 is replaced by a new model.

What are the NPV (as of the beginning of year 1) and the IRR of the plane using a 9% discount rate?