1. Making investment decisions with the Net Present Value rule This town's full of money grabbers Go ahead-Bite the Big Apple, don't mind the maggots, huh Shadoobie, My brain's been battered My friends they come around they Flatter, flatter, flatter, flatter, flatter Pile it up, pile it high on the platter- Jagger, Richards

2. What to discount 1. Only cash flow is relevant. 2. Estimate incremental cash flows. 3. Be consistent in treatment of inflation. 4. Recognize project interactions.

3. Only cash flow is relevant 1. Depreciation is not a cash flow. 2. Remember investment in working capital. Dec Jun Sales 500 0 Less investment in receivables -500 +500 Cash flow 0 500 Receivables paid off in June

4. What To Discount  Estimate Cash Flows on an Incremental Basis  Do not confuse average with incremental payoffs  Include all incidental effects  Do not forget working capital requirements  Include opportunity costs  Forget sunk costs  Beware of allocated overhead costs  Treat inflation consistently Points to “Watch Out For”

5.  Be consistent in how you handle inflation!!  Use nominal interest rates to discount nominal cash flows.  Use real interest rates to discount real cash flows.  You will get the same results, whether you use nominal or real figures INFLATION RULE

6. Inflation Example You own a lease that had cost you $7,7666.99 last year, but your lease cost will grow to $8,000 next year, and the cost will increase at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

7. Inflation Example - nominal figures

8. Inflation Example - real figures

9. Be consistent in handling inflation Another example (for you to check at home): 1. Discount nominal flows (growing at 10%) at nominal 20% rate 55 60.5 66.7 NPV = -100 + + + = 26.5 1.20 1.20 2 1.20 3 2. Discount real flows at real rate Without 10% inflation: 50 50 50 NPV = -100 + + + = 26.5 1.09 1.09 2 1.09 3 Note: Real rate = 1.20/1.10 - 1 =.09

10. Do not assume all cash flows rise in line with inflation Differential price changes, e.g. wages and prices Some cash flows are fixed

11. Cost of capital is likely to be more stable in real terms But even if you work in real terms: You need to estimate inflation to calculate taxes to calculate working capital to calculate real discount rate

12. Should you measure returns before or after tax 1.The cost of capital is the return required by investors after tax. 2.Discount cash flows after corporate tax.

13. Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.

14. Project interactions - 1 investment timing The cost of computers is steadily falling. The savings from a new computer are constant. When should the firm buy the computer? NPV in Year year of of Cost of PV purchase NPV purchase computer savings (r = 10%) today 0 $50 $70 $20 $20.0 1 45 70 25 22.7 2 40 70 30 24.8 3 36 70 34 25.5 4 33 70 37 25.3 5 31 70 39 24.2 MORAL: NPV is maximized by investing in Year 3

15. Project interactions - 2 long- versus short-lived equipment COSTS Year: 0 1 2 3 PV @ 10% A 15 4 4 4 25 B 10 6 6 20 Equivalent annual cost of A = 25/(3-year annuity factor) = 25/2.5 = 10.05 Equivalent annual cost of B = 20/(2-year annuity factor) = 20/1.7 = 11.52 MORAL: Annual cost of A is LESS than that of B

16. Project interactions - 3 machine replacement Annual operating cost of old machine = 8 Cost of new machine Year: 0 1 2 3 PV @ 10% 15 5 5 5 27.4 Equivalent annual cost of new machine = 27.4/(3-year annuity factor) = 27.4/2.5 = 11.0179 MORAL: Do not replace until operating cost of old machine exceeds 11.018