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NPV Rule for Capital Budgeting

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					NPV AND IRR RULES

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A B C NPV RULE FOR CAPITAL BUDGETING

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Choose a project if it costs less than the PV of its cash flows. More generally: take a project if its Net Present Value is positive. EXAMPLE Interest rate Year Cash flow PV factor PV of cash flow Cumulative PV Net Present Value 10% 0 (600) 100% (600) (600) 123 1 200 91% 182 (418) 2 200 83% 165 (253) 3 500 75% 376 123

Investors would have to invest 123 more (a total of 723) to get the cash flows of 200, 200, and 500 at an interest rate of 10%. Therefore the project has a value of 123 for investors. The interest rate is called the cost of capital, because it is the opportunity cost of funds - the rate investors can earn on alternative investments.

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NPV AND IRR RULES

A 1 2 3 4 5 6 7 8 9 10 IRR RULE

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For a standard project, IRR Rule:

NPV > 0

if and only if if and only if

IRR > Cost of Capital IRR > Cost of Capital

Choose a project

Standard means - cash outflows occur in early years and cash inflows in later years. - the alternative to the project is the status quo.

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NPV AND IRR RULES

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A B C D E F G NONSTANDARD PROJECTS MAY HAVE MORE THAN ONE INTERNAL RATE OF RETURN

Cost of capital

12%

Year Net cash flow PV factor PV of net cash flow Cumulative PV Net present value IRR (Internal Rate of Return)

0 (400,000) 100% (400,000) (400,000) 1,148 10%

1

2

960,000 (572,000) 89% 80% 857,143 (455,995) 457,143 1,148

For this project, varying the initial guess in the IRR function can cause the IRR to change. This is a good project (positive NPV), but you can't tell it from the IRR function. The following chart shows that there are two break-even costs of capital or IRR's. The NPV is positive at the actual cost of capital (12%), so it is a good project.

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NPV AND IRR RULES

A B 1 Year 0 2 Net cash flow (400,000) 3 4 Discount Rate NPV 5 6 2% (8,612) 7 4% (5,769) 8 6% (3,418) 9 8% (1,509) 10 10% 11 12% 1,148 12 14% 1,970 13 16% 2,497 14 18% 2,758 15 20% 2,778 16 22% 2,580 17 24% 2,185 18 26% 1,612 19 28% 879 20 30% 21 32% (1,010) 22 34% (2,139) 23 36% (3,374) 24 38% (4,705) 25 40% (6,122)

D 1 2 960,000 (572,000)

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4,000 2,000 Net Present Value (2,000) (4,000) (6,000) 0% 20% 40% 60%

(8,000)
(10,000) Discount Rate

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NPV AND IRR RULES

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A B C D AN EXAMPLE OF MUTUALLY EXCLUSIVE PROJECTS Cost of capital 10% Year Project A Cash flow PV factor PV of cash flow NPV IRR Cash flow PV factor PV of cash flow NPV IRR 0 (10,000) 100% (10,000) 8,182 100% (20,000) 100% (20,000) 11,818 75%

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1 20,000 91% 18,182

Project B

35,000 91% 31,818

Project B is best, even though its IRR is lower.

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NPV AND IRR RULES

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A B C D E PROJECTS CAN BE VALUED ON AN INCREMENTAL BASIS

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Cost of capital

10% Year 0 (10,000) 100% (10,000) 8,182 (10,000) 100% (10,000) 3,636 1 20,000 91% 18,182

Project A

Cash flow PV factor PV of cash flow NPV Cash flow PV factor PV of cash flow NPV

Project B-A

15,000 91% 13,636

Project B has a positive NPV relative to A (on an incremental basis) so should be taken.

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Jeff Sperry Jeff Sperry
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