## Thursday, October 20, 2011

### Net Present Value (NPV) and the Internal Rate of Return (IRR)

CFA Level 1 - Corporate Finance

Net Present Value
Using the company's cost of capital, the net present value (NPV) is the sum of the discounted cash flows minus the original investment.

Formula 11.11

 Look Out!Projects with NPV > 0 increase stockholders returnProjects with NPV < 0 decrease stockholders return

Example: Net Present Value
Using the cash flows in the previous examples, calculate the NPV for each machine and decide which project Newco should accept. As calculated previously, Newco's cost of capital is 8.4%.

Answer: NPVA = -5,000 + 500 + 1,000 + 1,000 + 1,500 + 2,500 + 1,000 = \$469

(1.084)1 (1.084)2 (1.084)3 (1.084)4 (1.084)5 (1.084)6
NPVB = -2,000 + 500 + 1,500 + 1,500 + 1,500 + 1,500 + 1,500 = \$3,929

(1.084)1 (1.084)2 (1.084)3 (1.084)4 (1.084)5 (1.084)6

Given that both machines have NPV > 0, both projects are acceptable. However, for mutually exclusive projects, the decision rule is to choose the project with the greatest NPV. Since the NPVB > NPVA, Newco should choose the project for Machine B
Internal Rate of Return
The internal rate of return (IRR)on a project is the rate of return at which the projects NPV equals zero. At this point, a project's cash flows are equal to the project's costs. Similar to how management must establish a maximum payback period, management must also set what is known as a "hurdle rate", the minimum rate of return a company will accept for a project.

When a project is reviewed with a hurdle rate in mind, the greater the IRR is above the hurdle rate, the greater the NPV, and conversely, the further the IRR is below the hurdle rate, the lower the NPV.
 Look Out!For the IRR, the decision rules are as follows:If IRR > hurdle rate, accept the projectIf IRR< hurdle rate, reject the project
For a project to be accepted, the IRR must be greater than or equal to the hurdle rate. If a company is deciding between two projects, the project with the highest IRR is the project to be accepted.

Formula 11.12

The IRR formula is quite difficult to calculate without the use of a financial calculator. Thus, a financial calculator is highly recommended to solve for a project's IRR. Otherwise trial and error must be used.
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