Principles of Corporate Finance
Richard A. Brealey and Stewart C. Myers
This is an equipment replacement decision. The objective is to minimize the present value of future costs. But there are a few real-life complications.
• Some cash flows are stated in real terms, some in nominal terms. We will use a real discount rate for the real cash flows, a nominal rate for the nominal flows. The alternative is to convert all cash flows to real terms (using a real discount rate) or all to nominal (using a nominal rate).
• The new boat lasts longer (20 years) than the rehabilitated Vital Spark (15 years). Thus we calculate equivalent annual costs. The alternative analysis looks at costs over 15 years for all options, but enters a terminal value at year 16 for the new boat.
• Assumptions about timing of cash flows have to be consistent and reasonable. See below.
• The present values of depreciation tax shields are an offset to required investment. Also, it may be possible to treat repairs as an immediate tax-deductible expense. We have assumed this in the following tables.
These calculations make use of the following assumptions (others could be equally valid):
1. NETCO must make a decision (rehabilitate or purchase) immediately (t = 0).
2. Marginal tax rate is 35%.
© 2002, R. A. Brealey and S. C. Myers
3. Forecasted operating costs are constant in real dollars.
4. Sale price for the Vital Spark and parts is $100,000 in real terms.
5. Investments qualify for the 7-year MACRS class.
6. NETCO’s revenues are unaffected by the investment decision, with the exception of the additional revenue from the new boat.
7. The new boat’s forecasted pre-tax value at t = 16 is $400,000. The pre-tax salvage value of the rehabilitated boat is $40,000.
8. Initial tax shields increase cash flow at t = 1.
9. Full operations with new or rehabilitated boat resume at t = 1.
10. Operating costs and additional revenues are taken at mid-year.
11. Long-term expected inflation is 3%.
12. Using a NETCO “risk premium” of 10% and the 6% T-bond rate, the nominal opportunity cost of capital for NETCO is 16%.
13. Using the assumed long-term inflation rate of 3%, the real opportunity cost of capital for NETCO is:
Table 1 tabulates cash flows based on these assumptions.
Table 2 shows equivalent annual cost. The rehabilitated Vital Spark wins, but its margin over the new boat is small. Perhaps the new boat's other attributes (better new accommodations, higher abandonment value) should carry the day.
Table 3 shows a present-value analysis with a terminal value for the new boat entered at year 16. The new boat is slightly more expensive than the rehabilitated Vital Spark.
The spreadsheet used to generate the tables is attached.
| | | | | |Table 1: NEW ECONOMY CASE. CASH FLOWS AND TIMING | | | | | | | | | | | | | | | | | |REHAB |REHAB PLUS...