# Complete Guide To Corporate Finance

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

The internal rate of return (IRR) is frequently used by corporations to compare and decide between capital projects. The IRR is the interest rate (also known as the discount rate) that will bring a series of cash flows (positive and negative) to a net present value (NPV) of zero (or to the current value of cash invested). Using IRR to obtain net present value is known as the discounted cash flow method of financial analysis. (For more insight, read the

The simplest example of computing an IRR is a mortgage with even payments. Assume an initial mortgage amount of $200,000 and monthly payments of $1,050 for 30 years. The IRR (or implied interest rate) on this loan annually is 4.8%.

Because the stream of payments is equal and spaced at even intervals, an alternative approach is to discount these payments at a 4.8% interest rate, which will produce a net present value of $200,000. Alternatively, if the payments are raised to, say $1,100, the IRR of that loan will rise to 5.2%.

The formula for IRR, using this example, is as follows:

In other words, to get a future value of $7,764 with monthly payments of $50 per month for 10 years, the IRR that will bring that flow of payments to a net present value of zero is 5%.

Compare this investment strategy to investing a lump-sum amount; to get the same future value of $7,764 with an IRR of 5%, you would have to invest $4,714 today, in contrast to the $6,000 invested in the $50-per-month plan. So, one way of comparing lump-sum investments versus payments over time is to use the IRR.

What if you don't want to reinvest dividends, but need them as income when paid? And if dividends are not assumed to be reinvested, are they paid out or are they left in cash? What is the assumed return on the cash? IRR and other assumptions are particularly important on instruments like whole life insurance policies and annuities, where the cash flows can become complex. Recognizing the differences in the assumptions is the only way to compare products accurately. (Learn more about life insurance in

In capital budgeting, the IRR rule is as follows:

IRR > cost of capital = accept project

IRR < cost of capital = reject project

In the example below, the IRR is 15%. If the firm's actual discount rate for discounted cash flow models is less than 15%, the project should be accepted.

The primary advantage of implementing the internal rate of return as a decision-making tool is that it provides a benchmark figure for every project that can be assessed in reference to a company's capital structure. The IRR will usually produce the same types of decisions as net present value models, and it allows firms to compare projects on the basis of returns on invested capital.

Although IRR is easy to compute with either a financial calculator or computer software, there are some downfalls to using this metric. Similar to the PB method, the IRR does not give a true sense of the value that a project will add to a firm - it simply provides a benchmark figure for what projects should be accepted based on the firm's cost of capital. The internal rate of return does not allow for an appropriate comparison of mutually exclusive projects; therefore managers might be able to determine that project A and project B are both beneficial to the firm, but they would not be able to decide which one is better if only one may be accepted.

Another error arising with the use of IRR analysis presents itself when the cash flow streams from a project are unconventional, meaning that there are additional cash outflows following the initial investment. Unconventional cash flows are common in capital budgeting since many projects require future capital outlays for maintenance and repairs. In such a scenario, an IRR might not exist, or there might be multiple internal rates of return. In the example below two IRRs exist - 12.7% and 787.3%.

The IRR is a useful valuation measure when analyzing individual capital budgeting projects, not those which are mutually exclusive. It provides a better valuation alternative to the PB method, yet falls short on several key requirements.

*Discounted Cash Flow Analysis*tutorial.)**For example, a corporation will evaluate an investment in a new plant versus an extension of an existing plant based on the IRR of each project. In such a case, each new capital project must produce an IRR that is higher than the company's cost of capital. Once this hurdle is surpassed, the project with the highest IRR would be the wiser investment, all other factors (including risk) being equal.**

**Calculation Complexities****The IRR formula can be very complex depending on the timing and variances in cash flow amounts. Without a computer or financial calculator, IRR can only be computed by trial and error. One of the disadvantages of using IRR is that all cash flows are assumed to be reinvested at the same discount rate, although in the real world these rates will fluctuate, particularly with longer term projects. IRR can be useful, however, when comparing projects of equal risk, rather than as a fixed return projection.**

**Calculating IRR****Many accounting software programs now include an IRR calculator, as do Excel and other programs. A handy alternative for some is the good old HP 12c financial calculator, which will fit in a pocket or briefcase. (Check out the**

*Investopedia Calculators*.)The simplest example of computing an IRR is a mortgage with even payments. Assume an initial mortgage amount of $200,000 and monthly payments of $1,050 for 30 years. The IRR (or implied interest rate) on this loan annually is 4.8%.

Because the stream of payments is equal and spaced at even intervals, an alternative approach is to discount these payments at a 4.8% interest rate, which will produce a net present value of $200,000. Alternatively, if the payments are raised to, say $1,100, the IRR of that loan will rise to 5.2%.

The formula for IRR, using this example, is as follows:

- Where the initial payment (CF
_{1}) is $200,000 (a positive inflow) - Subsequent cash flows (CF
_{ 2}, CF_{ 3}, CF N) are negative $1,050 (negative because it is being paid out) - Number of payments (N) is 30 years times 12 = 360 monthly payments
- Initial Investment is $200,000
- IRR is 4.8% divided by 12 (to equate to monthly payments) = 0.400%

IRR = .400% |

**Power of Compounding****IRR is also useful in demonstrating the power of compounding. For example, if you invest $50 every month in the stock market over a 10-year period, that money would turn into $7,764 at the end of the 10 years with a 5% IRR.**

Compare this investment strategy to investing a lump-sum amount; to get the same future value of $7,764 with an IRR of 5%, you would have to invest $4,714 today, in contrast to the $6,000 invested in the $50-per-month plan. So, one way of comparing lump-sum investments versus payments over time is to use the IRR.

**Other IRR Uses****Another common use of IRR is in the computation of portfolio, mutual fund or individual stock returns. In most cases, the advertised return will include the assumption that any cash dividends are reinvested in the portfolio or stock. Therefore, it is important to scrutinize the assumptions when comparing returns of various investments.**

What if you don't want to reinvest dividends, but need them as income when paid? And if dividends are not assumed to be reinvested, are they paid out or are they left in cash? What is the assumed return on the cash? IRR and other assumptions are particularly important on instruments like whole life insurance policies and annuities, where the cash flows can become complex. Recognizing the differences in the assumptions is the only way to compare products accurately. (Learn more about life insurance in

*5 Things You Didn't Know About Life Insurance*and*Does Spiderman Need Life Insurance?*)In capital budgeting, the IRR rule is as follows:

IRR > cost of capital = accept project

IRR < cost of capital = reject project

In the example below, the IRR is 15%. If the firm's actual discount rate for discounted cash flow models is less than 15%, the project should be accepted.

Investment |
Inflows |
||||

Year 0 |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |

-1,000,000 |
300,00 |
300,000 |
300,000 |
300,000 |
300,000 |

Although IRR is easy to compute with either a financial calculator or computer software, there are some downfalls to using this metric. Similar to the PB method, the IRR does not give a true sense of the value that a project will add to a firm - it simply provides a benchmark figure for what projects should be accepted based on the firm's cost of capital. The internal rate of return does not allow for an appropriate comparison of mutually exclusive projects; therefore managers might be able to determine that project A and project B are both beneficial to the firm, but they would not be able to decide which one is better if only one may be accepted.

Another error arising with the use of IRR analysis presents itself when the cash flow streams from a project are unconventional, meaning that there are additional cash outflows following the initial investment. Unconventional cash flows are common in capital budgeting since many projects require future capital outlays for maintenance and repairs. In such a scenario, an IRR might not exist, or there might be multiple internal rates of return. In the example below two IRRs exist - 12.7% and 787.3%.

Investment |
Inflows |
||||

Year 0 |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |

-1,000,000 |
10,000,000 |
-10,000,000 |
0 |
0 |
0 |