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R = Discount rate (required rate of return)

The original capital investment is often called the cash flow at time 0 (or present time) and is represented by the symbol CF₀. The net present value (NPV) is equal to the sum of all the discounted cash flows minus the original payment made in order to receive the cash flows.

Positive / Negative NPV

A positive NPV means that the investor paid less than the present value for the stream of cash flows. A negative NPV means that the investor paid more than the present value for the stream of cash flows. An NPV equal to zero means that the investor paid the same amount as the present value for the stream of cash flows.

Finding NPV with a financial calculator

Most financial calculators may be used to calculate NPV. The basic idea is to input each cash flow in its proper order. Remember to input the original capital investment (CF₀) and any other cash outflows as negative numbers. After inputting the positive and negative cash flows, input the appropriate discount rate and then push the NPV key to find the solution. Check the owner's manual for specific details.

Analyzing a potential project

Companies often calculate NPV to evaluate potential projects. Analysts forecast the expected cash flows, discount the cash flows at the appropriate rate, and subtract the estimated initial capital

investment. A project with a positive NPV creates value for the shareholders of the company, whereas a project with a negative NPV destroys value for the shareholders.

Independent projects

Companies with limited funds to invest, and several potential

independent projects to evaluate, often rank the projects according to NPV and then invest in those projects with the highest NPV. The term "independent projects" means that a change in the cash flows in one project has no effect on the cash flows in any other project — each project is independent of all others being considered. The

concept of independence is important for making NPV decisions. For a more thorough discussion on independent events, consult a

probability textbook.

An example will illustrate the use of the net present value formula to evaluate a project.

Example Project A requires a capital investment of $2,000 and promises a payment of $1,000 at the end of Years One, Two, and Three. If the investor's required rate of return is 12%, what is the NPV of the investment? We can use the NPV formula with the values CF₁, CF₂, and CF₃ = $1,000, CF₀ = $2,000, T = 3, and R = 0.12. T NPV =

Σ

To solve for NPV with your financial calculator, enter each of the cash flows and capital investments in their proper order. Enter the discount rate of 12% and push the NPV key to get $401.83. Project A has a positive net present value.

Analyzing

opportunity cost for use of funds

Some analysts use net present value to determine if the cash flows are sufficient to repay the capital investment plus an amount for the opportunity cost of using the company's funds. A positive NPV means that the project is able to repay the initial investment, pay the

opportunity cost for the use of the funds, and generate additional funds that create value for the company; a negative NPV means that the project cannot generate enough funds to cover the original investment and the opportunity cost for the use of the funds.

Practice what you have learned about calculating the net present value of an investment by completing the Practice Exercise that begins on page 5-13; then continue to the section on "Internal Rate of Return."

PRACTICE EXERCISE 5.2

Directions: Calculate the answer to each question, then enter the correct answer. Check your solution with the Answer Key on the next page.

4. A project has an initial investment of $10,000 and a cash flow annuity of $5,000 for three years. If the required rate of return is 10%, what is the NPV of the project?

$_____________________

Should the project be accepted based on the NPV method of capital budgeting? _____ a) Yes

_____ b) No

5. A project has an initial investment of $20,000 and a cash flow annuity of $5,000 for four years. If the required rate of return is 12%, what is the NPV of the project?

$_____________________

Should the project be accepted based on the NPV method of capital budgeting? _____ a) Yes

ANSWER KEY

4. A project has an initial investment of $10,000 and a cash flow annuity of $5,000 for three years. If the required rate of return is 10%, what is the NPV of the project?

$2,434.26

Enter -$10,000 as CF₀ and three cash flows of $5,000 Enter 10% as the discount rate

Press the NPV key and you should get $2,434.26

Should the project be accepted based on the NPV method of capital budgeting?

Yes – The project should be accepted because its NPV is positive.

5. A project has an initial investment of $20,000 and a cash flow annuity of $5,000 for four years. If the required rate of return is 12%, what is the NPV of the project?

–$4,813.25

Enter -$20,000 as CF₀ and four cash flows of $5,000 Enter 12% as the discount rate

Press the NPV key and you should get -$4,813.25

Should the project be accepted based on the NPV method of capital budgeting?