
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 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%
Using the numbers from this example, the formula for calculating IRR is as follows:
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 10year period, that money would turn into $7,764 at the end of the 10 years with a 5% IRR.
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 lumpsum 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 $50permonth plan. So, one way of comparing lumpsum 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 
The primary advantage of implementing the internal rate of return as a decisionmaking 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%.
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 
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.
Advantages And Disadvantages Of NPV and IRR


Fundamental Analysis
Examining Mexico's TrillionDollar GDP
Examining the gross domestic product growth and composition of Mexico, the second largest economy in Latin America 
Economics
Explaining Accounting Conservatism
Accounting conservatism is a principal that requires accounting rules be applied with high degrees of verification. 
Fundamental Analysis
What Causes Inflation in the United States
Inflation is the main catalyst behind U.S monetary policy. But what causes this phenomenon of sustained rising prices? Read on to find out. 
Term
What are NonGAAP Earnings?
NonGAAP earnings are a company’s earnings that are not reported according to Generally Accepted Accounting Principles. 
Fundamental Analysis
Calculating Return on Net Assets
Return on net assets measures a company’s financial performance. 
Economics
Understanding Cost of Revenue
The cost of revenue is the total costs a business incurs to manufacture and deliver a product or service. 
Economics
Explaining Carrying Cost of Inventory
The carrying cost of inventory is the cost a business pays for holding goods in stock. 
Fundamental Analysis
Is India the Next Emerging Markets Superstar?
With a shift towards manufacturing and services, India could be the next emerging market superstar. Here, we provide a detailed breakdown of its GDP. 
Investing
How To Calculate Minority Interest
Minority interest calculations require the use of minority shareholders’ percentage ownership of a subsidiary, after controlling interest is acquired. 
Term
Estimating with Subjective Probability
Subjective probability is someone’s estimation that an event will occur.

Operating Cost
Expenses associated with the maintenance and administration of ... 
Trade Credit
An agreement where a customer can purchase goods on account (without ... 
Normal Profit
An economic condition occurring when the difference between a ... 
Cost Accounting
A type of accounting process that aims to capture a company's ... 
ZeroSum Game
A situation in which one person’s gain is equivalent to another’s ... 
Supply
A fundamental economic concept that describes the total amount ...

What should I study in school to prepare for a career in corporate finance?
Depending on which area you want to specialize in, corporate finance can be one of the most competitive fields in business. ... Read Full Answer >> 
Why would a company issue preference shares instead of common shares?
Preference shares, or preferred stock, act as a hybrid between common shares and bond issues. As with any produced good or ... Read Full Answer >> 
What is the difference between cost of debt capital and cost of equity?
In corporate finance, capital – the money a business uses to fund operations – comes from two sources: debt and equity. While ... Read Full Answer >> 
What is the difference between gross profit, operating profit and net income?
The terms profit and income are often used interchangeably in daytoday life. In corporate finance, however, these terms ... Read Full Answer >> 
Can I use my IRA to pay for my college loans?
If you are older than 59.5 and have been contributing to your IRA for more than five years, you may withdraw funds to pay ... Read Full Answer >> 
Can I use my 401(k) to pay for my college loans?
If you are over 59.5, or separate from your plansponsoring employer after age 55, you are free to use your 401(k) to pay ... Read Full Answer >>