# Complete Guide To Corporate Finance

## Net Present Value And Internal Rate Of Return - Introduction To Net Present Value And Internal Rate Of Return

Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows. NPV compares the value of a dollar today to the value of that same dollar in the future, taking inflation and returns into account. NPV analysis is sensitive to the reliability of future cash inflows that an investment or project will yield and is used in capital budgeting to assess the profitability of an investment or project.

NPV is calculated using the following formula:

If the NPV of a prospective project is positive, the project should be accepted. However, if NPV is negative, the project should probably be rejected because cash flows will also be negative.

For example, if a retail clothing business wants to purchase an existing store, it would first estimate the future cash flows that store would generate, then discount those cash flows into one lump-sum present value amount, say $565,000. If the owner of the store was willing to sell his business for less than $565,000, the purchasing company would likely accept the offer as it presents a positive NPV investment. Conversely, if the owner would not sell for less than $565,000, the purchaser would not buy the store, as the investment would present a negative NPV. (Sometimes losing investments aren't what they seem. Learn more in

Internal rate of return (IRR) is the discount rate often used in capital budgeting that makes the net present value of all cash flows from a particular project equal to zero. Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake the project. As such, IRR can be used to rank several prospective projects a firm is considering. Assuming all other factors are equal among the various projects, the project with the highest IRR would probably be considered the best and undertaken first.

You can think of IRR as the rate of growth a project is expected to generate. While the actual rate of return that a given project ends up generating will often differ from its estimated IRR rate, a project with a substantially higher IRR value than other available options would still provide a much better chance of strong growth.

IRRs can also be compared against prevailing rates of return in the securities market. If a firm can't find any projects with IRRs greater than the returns that can be generated in the financial markets, it may simply choose to invest its retained earnings into the market. (For related reading, see

To do this, the firm estimates the future cash flows of the project and discounts them into present value amounts using a discount rate that represents the project's cost of capital and its risk. Next, all of the investment's future positive cash flows are reduced into one present value number. Subtracting this number from the initial cash outlay required for the investment provides the net present value (NPV) of the investment.

Let's illustrate with an example: suppose JKL Media wants to buy a small publishing company. JKL determines that the future cash flows generated by the publisher, when discounted at a 12% annual rate, yield a present value of $23.5 million. If the publishing company's owner is willing to sell for $20 million, then the NPV of the project would be $3.5 million ($23.5 - $20 = $3.5). The $3.5 million dollar NPV represents the intrinsic value that will be added to JKL Media if it undertakes this acquisition.

So, JKL Media's project has a positive NPV, but from a business perspective, the firm should also know what rate of return will be generated by this investment. To do this, the firm would simply recalculate the NPV equation, this time setting the NPV factor to zero, and solve for the now-unknown discount rate. The rate that is produced by the solution is the project's internal rate of return (IRR).

For this example, the project's IRR could, depending on the timing and proportions of cash flow distributions, be equal to 17.15%. Thus, JKL Media, given its projected cash flows, has a project with a 17.15% return. If there were a project that JKL could undertake with a higher IRR, it would probably pursue the higher-yielding project instead. Thus, you can see that the usefulness of the IRR measurement lies in its ability to represent any investment opportunity's return and to compare it with other possible investments. (Learn about industry-specific investment options in

NPV is calculated using the following formula:

For example, if a retail clothing business wants to purchase an existing store, it would first estimate the future cash flows that store would generate, then discount those cash flows into one lump-sum present value amount, say $565,000. If the owner of the store was willing to sell his business for less than $565,000, the purchasing company would likely accept the offer as it presents a positive NPV investment. Conversely, if the owner would not sell for less than $565,000, the purchaser would not buy the store, as the investment would present a negative NPV. (Sometimes losing investments aren't what they seem. Learn more in

*How To Profit From Investment "Losers"*.)Internal rate of return (IRR) is the discount rate often used in capital budgeting that makes the net present value of all cash flows from a particular project equal to zero. Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake the project. As such, IRR can be used to rank several prospective projects a firm is considering. Assuming all other factors are equal among the various projects, the project with the highest IRR would probably be considered the best and undertaken first.

You can think of IRR as the rate of growth a project is expected to generate. While the actual rate of return that a given project ends up generating will often differ from its estimated IRR rate, a project with a substantially higher IRR value than other available options would still provide a much better chance of strong growth.

*The Top New Investment: Doing Nothing*.)**Differences between NPV and IRR and Their Uses**

Both NPV and IRR are primarily used in capital budgeting, the process by which companies determine whether a new investment or expansion opportunity is worthwhile. Given an investment opportunity, a firm needs to decide whether undertaking the investment will generate net economic profits or losses for the company.To do this, the firm estimates the future cash flows of the project and discounts them into present value amounts using a discount rate that represents the project's cost of capital and its risk. Next, all of the investment's future positive cash flows are reduced into one present value number. Subtracting this number from the initial cash outlay required for the investment provides the net present value (NPV) of the investment.

Let's illustrate with an example: suppose JKL Media wants to buy a small publishing company. JKL determines that the future cash flows generated by the publisher, when discounted at a 12% annual rate, yield a present value of $23.5 million. If the publishing company's owner is willing to sell for $20 million, then the NPV of the project would be $3.5 million ($23.5 - $20 = $3.5). The $3.5 million dollar NPV represents the intrinsic value that will be added to JKL Media if it undertakes this acquisition.

So, JKL Media's project has a positive NPV, but from a business perspective, the firm should also know what rate of return will be generated by this investment. To do this, the firm would simply recalculate the NPV equation, this time setting the NPV factor to zero, and solve for the now-unknown discount rate. The rate that is produced by the solution is the project's internal rate of return (IRR).

For this example, the project's IRR could, depending on the timing and proportions of cash flow distributions, be equal to 17.15%. Thus, JKL Media, given its projected cash flows, has a project with a 17.15% return. If there were a project that JKL could undertake with a higher IRR, it would probably pursue the higher-yielding project instead. Thus, you can see that the usefulness of the IRR measurement lies in its ability to represent any investment opportunity's return and to compare it with other possible investments. (Learn about industry-specific investment options in

*Fine Art Funds: A Beautiful Investment*,*The Perfect Investment For Chocolate-Lovers*and*The Shoe-Lover's Investment Portfolio*.)