Discounted Cash Flow Valuations and Net Present Value

1. You are offered three annuities (these make equal payments over a specific period). Using an annual 3.5% discount rate, calculate each annuity’s price:

#

price

Payments ($/month)

Life (yrs.)

1

?

95

4

2

?

100 (growing @1.5%/yr.)

4

3

?

55 (growing @1.5%/yr.)

Forever

2. You purchase a machine. It costs $75,000 and will expand cash flow by $1,000 /month in year 1 growing by 2% per year after that. The system will work for 10 years before you have to replace it. What are the NPV (at a 3.3% discount rate) and IRR? The vendor offers you another machine costing $100,000 and lasting 12 years, with the same cash flow gains and a 3% growth rate. What are the NPV and the IRR for it? Should you get it?

3. Read Why the Mets Pay Bobby Bonilla $1.19 Million Every July 1

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 and the dealer offers you: Car price = $30,000 Monthly payments = $499 Down payment = $2,000 Lease term = 48 months Purchase price at end of lease = $12,000 What is the implicit interest rate on the lease?

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

€600M (year 1) €500M (year 2) €400M (year 3)

Each plane will be sold for €50M – 25% down and the rest due on delivery one year later. The cost to produce each plane is €44M – these costs are recognized on delivery. Sales says that you will sell 30 planes (year 4), growing by 15 planes per year. The last sale is made in year 12, when it 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?