Question

I have had some trouble understanding the IRR formula. Can you guy break it down.

Answer 1

Ans- The internal rate of return (IRR) is a measure of an investment’s rate of return. The term internal refers to the fact that the calculation excludes external factors, such as the risk-free rate, inflation, the cost of capital, or various financial risks.

It is also called the discounted cash flow rate of return (DCFROR).

Definition:

The internal rate of return on an investment or project is the "annualized effective compounded return rate" or rate of return that sets the net present value of all cash flows (both positive and negative) from the investment equal to zero. Equivalently, it is the discount rate at which the net present value of the future cash flows is equal to the initial investment, and it is also the discount rate at which the total present value of costs (negative cash flows) equals the total present value of the benefits (positive cash flows).

Calculation:

Given a collection of pairs (time, cash flow) representing a project, the net present value is a function of the rate of return. The internal rate of return is a rate for which this function is zero, i.e. the internal rate of return is a solution to the equation NPV = 0.

Given the (period, cash flow) pairs ({\displaystyle n}, {\displaystyle C_{n}}) where {\displaystyle n} is a non-negative integer, the total number of periods {\displaystyle N}, and the {\displaystyle \operatorname {NPV} }, (net present value); the internal rate of return is given by by in:

Note that in this formula, {\displaystyle C_{0}} (≤0) is the initial investment at the start of the project. The period {\displaystyle n} is usually given in years, but the calculation may be made simpler if {\displaystyle r} is calculated using the period in which the majority of the problem is defined (e.g., using months if most of the cash flows occur at monthly intervals) and converted to a yearly period thereafter.

Any fixed time can be used in place of the present (e.g., the end of one interval of an annuity); the value obtained is zero if and only if the NPV is zero.

In the case that the cash flows are random variables, such as in the case of a life annuity, the expected values are put into the above formula.

Often, the value of {\displaystyle r} that satisfies the above equation cannot be found analytically. In this case, numerical methods or graphical methods must be used.

Example:

If an investment may be given by the sequence of cash flows then the IRR is given by:

Year ({\displaystyle n})	Cash flow ({\displaystyle C_{n}})
0	-123400
1	36200
2	54800
3	48100

In this case, the answer is 5.96% (in the calculation, that is, r = .0596).