Internal Rate of Return Formula
The internal rate of return (IRR), also referred to as the discounted cash flow of return (DCFROR), is the interest rate that makes the net present value zero. The internal rate of return formula calculates IRR, which is a very important component of capital budgeting and corporate finance which is used in determining which discount rate will make the initial cost of a capital investment equal to the current value of future cash flows posttax. The term internal here signifies the fact that the calculation of rate using this method does not include external factors, such as inflation, riskfree rate, the cost of capital, or any financial risks. Let us study the internal rate of return formula using solved examples.
What Is the Internal Rate of Return Formula?
The calculation of the Internal Rate of Return (IRR) includes the trial and error method with the formula of calculation of Net present value (NPV). The internal rate of return formula calculates IRR, which is the value of rate for which net present value equals zero. The internal rate of return formula can be expressed as,
\( 0 = \sum_{n = 1}^N \frac{ CF_n }{ (1 + IRR)^n } \)
 N = Total number of time periods
 n = Time period
 CF\(_n\) = Net cash flow at time period
 IRR = Internal rate of return
Let us see the applications of the internal rate of return formula in the following section.
Solved Examples Using Internal Rate of Return Formula

Example 1: An investor made an investment of $500 and got $570 next year. Calculate the internal rate of return on the investment.
Solution:
To find: Internal rate of return on investment
Given:
Invested amount, CFo = $500 (negative, because money went out)
Cash inflow after 1 year, CF_{1} = $570
Using internal rate of return formula,
0 = CF_{o }+ \(\dfrac{CF_1}{{(1 + IRR)}^1}\)
0 = $500 + \(\dfrac{570}{{(1 + IRR)}^1}\)
500 + 500 × IRR = 570
IRR = 0.14 = 14%
Answer: Internal rate of return on the investment = 14%.

Example 2: Sam bought a house for $250,000. He plans on selling the house 1 year later for $350,000, after deducting any realtor's fees and taxes. Calculate the internal rate of return on the complete transaction.
Solution:
To find: Internal rate of return on the complete transaction
Given:
Invested amount, CFo = $250,000 (negative, because money went out)
Cash inflow after 1 year, CF_{1} = $350,000
Using internal rate of return formula,
0 = CF_{o }+ \(\dfrac{CF_1}{{(1 + IRR)}^1}\)
0 = $250,000 + \(\dfrac{350,000}{{(1 + IRR)}^1}\)
250,000 + 250,000 × IRR = 350,000
IRR = 0.4 = 40%
Answer: Internal rate of return on the investment = 40%.