Npv And Irr Rules

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

1

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3

(600) 100% (600) (600) 123

200 91% 182 (418)

200 83% 165 (253)

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

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IRR RULE

For a standard project, IRR Rule:

NPV > 0

Choose a project

if and only if

IRR > Cost of Capital

if and only if

IRR > Cost of Capital

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

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

12%

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

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

10%

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

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D 1 2 960,000 (572,000)

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Main title 3000 2000 1000 0 -1000 -2000 -3000

Discount Rate NPV

-4000 -5000 -6000 -7000 -8000 -9000 R RRR RRR RRR RRR RRR RRR RR o ooo ooo ooo ooo ooo ooo oo w www www www www www www ww

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NPV AND IRR RULES

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A B C D E AN EXAMPLE OF MUTUALLY EXCLUSIVE PROJECTS Cost of capital

10% Year

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Project A

Cash flow PV factor PV of cash flow NPV IRR

(10,000) 100% (10,000) 8,182 100%

20,000 91% 18,182

Project B

Cash flow PV factor PV of cash flow NPV IRR

(20,000) 100% (20,000) 11,818 75%

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

Cost of capital

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10% Year

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Project A

Cash flow PV factor PV of cash flow NPV

(10,000) 100% (10,000) 8,182

20,000 91% 18,182

Project B-A

Cash flow PV factor PV of cash flow NPV

(10,000) 100% (10,000) 3,636

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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