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NPV AND IRR RULES
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A B C D E F G H
NPV RULE FOR CAPITAL BUDGETING
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 10%
Year 0 1 2 3
Cash flow (600) 200 200 500
PV factor 100% 91% 83% 75%
PV of cash flow (600) 182 165 376
Cumulative PV (600) (418) (253) 123
Net Present Value 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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A B C D E F G
IRR RULE
For a standard project, NPV > 0 if and only if IRR > Cost of Capital
IRR Rule: Choose a project 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 12%
Year 0 1 2
Net cash flow (400,000) 960,000 (572,000)
PV factor 100% 89% 80%
PV of net cash flow (400,000) 857,143 (455,995)
Cumulative PV (400,000) 457,143 1,148
Net present value 1,148
IRR (Internal Rate of Return) 10%
For this project , varying the ini t ia l guess in th e IRR funct ion can cause the IRR to change.
This is a good project (posi t ive NPV), but you can't tel l i t from th e IRR funct ion . The fol lowing
chart show s that there are two break-even costs of capita l or IRR's. The NPV is posi t ive at the
actual cost of capita l (12%), so it is a good project .
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NPV AND IRR RULES
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A B C D E F G H
Year 0 1 2
Net cash flow (400,000) 960,000 (572,000)
Discount Rate NPV
2% (8,612)
4% (5,769)
6% (3,418)
8% (1,509)
10% -
12% 1,148
14% 1,970
16% 2,497
18% 2,758
20% 2,778
22% 2,580
24% 2,185
26% 1,612
28% 87930% -
32% (1,010)
34% (2,139)
36% (3,374)
38% (4,705)
40% (6,122)
(10,000)
(8,000)
(6,000)
(4,000)
(2,000)
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2,000
4,000
0% 20% 40% 60%
NetPresentValue
Discount Rate
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A B C D E
AN EXAMPLE OF MUTUALLY EXCLUSIVE PROJECTS
Cost of capital 10%
Year 0 1
Project A Cash flow (10,000) 20,000
PV factor 100% 91%
PV of cash flow (10,000) 18,182
NPV 8,182
IRR 100%
Project B Cash flow (20,000) 35,000
PV factor 100% 91%
PV of cash flow (20,000) 31,818
NPV 11,818
IRR 75%
Project B is best, even though its IRR is lower.
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A B C D E F G H
PROJECTS CAN BE VALUED ON AN INCREMENTAL BASIS
Cost of capital 10%
Year 0 1
Project A Cash flow (10,000) 20,000
PV factor 100% 91%
PV of cash flow (10,000) 18,182
NPV 8,182
Project B-A Cash flow (10,000) 15,000
PV factor 100% 91%
PV of cash flow (10,000) 13,636
NPV 3,636
Project B has a positive NPV relative to A (on an incremental basis) so should be taken.
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