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 batteredMy friends they come around they Flatter, flatter, flatter, flatter, flatterPile it up, pile it high on the platter- Jagger, Richards

What to discount1. Only cash flow is relevant.

2. Estimate incremental cash flows.

3. Be consistent in treatment of inflation.

4. Recognize project interactions.

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

Receivablespaid offin June

What To Discount

Estimate Cash Flows on an Incremental BasisDo not confuse average with incremental payoffsInclude all incidental effectsDo not forget working capital requirementsInclude opportunity costs Forget sunk costsBeware of allocated overhead costsTreat inflation consistently

Points to “Watch Out For”

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 RULEINFLATION RULE

InflationExample

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?

rate)inflation +(1rate)interest nominal+(1

=rate)interest real1(

InflationExample - nominal figures

99.429,26$

78.59708741.82=8000x1.034

56.63768487.20=8000x1.033

92.68098240=8000x1.032

73.727280001

10% @ PVFlowCash Year

4

3

2

10.182.87413

10.120.84872

10.18240

1.108000

InflationExample - real figures

Year Cash Flow PV@6.7961%

1 = 7766.99

2 = 7766.99

= 7766.99

= 7766.99

80001.03

7766.991.068

82401.03

8487.201.03

8741.821.03

2

3

4

7272 73

6809 92

3 6376 56

4 5970 78

26 429 99

7766 991 068

7766 991 068

7766 991 068

2

3

4

.

.

.

.

..

..

..

= $ , .

Be consistent in handling inflationAnother example (for you to check at home):1. Discount nominal flows (growing at 10%) at nominal 20% rate

55 60.5 66.7NPV = -100 + + + = 26.5 1.20 1.202 1.203

2. Discount real flows at real rate

Without 10% inflation:

50 50 50NPV = -100 + + + = 26.5 1.09 1.092 1.093

Note: Real rate = 1.20/1.10 - 1 = .09

Do not assume all cash flows rise in line with inflation

• Differential price changes, e.g. wages and prices

• Some cash flows are fixed

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

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.

Equivalent Annual Cost

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

Project interactions - 1investment 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

Project interactions - 2long- 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

Project interactions - 3machine 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