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See Also Net Present Value Modified Internal Rate of Return
Discounted cash flow methods provide a more objective basis for evaluating and selecting investment projects. These methods take account of both the magnitude and the timing of expected cash flows in each period of a project's life. Stockholders, for example, place a higher value on an investment project that promises cash returns over the next five years tahn on a project that promises identical cash flows for years 6 to 10. Thus, the timing of expected cash flows is extremely important in the investment decision.

Discounted cash flow methods enable us to capture differences in the timing of cash flows for various projects through the discounting process. In addition, through our choices of discount rate, we can also account for project risk. One of the discounted cash flow methods is the Internal Rate of Return (IRR).

The Internal Rate of Return (IRR) for an investment proposal is the discount rate that equates the present value of the expected net cash flows (CFs) with the initial cash outflow (ICO). If the initial cash outflow or cost occurs at time t0, it is represented by that rate, IRR, such that

 
present value

Remember, the actual rate of return on an investment is one which results in an NPV of 0

EXAMPLE 1

An investment with an initial cash out flow of $50,000 pays back $15,000 per year for the next four years. Find the IRR

SOLUTION

present value

We use linear interpolation to estimate the actual rates of return for the four investment alternatives. Linear interpolation is a trial and error method of estimating actual rates of return when such rates are different from tables or calculators. If we start off with a rate of return of 8%, then present value of cash inflows is $49,681 and NPV is $-318.20.

present value

As the actual rate of return is one where NPV is 0, we try to look for a rate lower than 8%, thus we choose 7% which produces present value of cash flows of $50,808.15 and NPV of $808.15. Thus the actual rate of return is somewhere between 7% and 8%.

irr

Using MS Excel to compute Internal Rate of Return  
Syntax

Returns the internal rate of return for a series of cash flows represented by the numbers in values. These cash flows do not have to be even, as they would be for an annuity. However, the cash flows must occur at regular intervals, such as monthly or annually. The internal rate of return is the interest rate received for an investment consisting of payments (negative values) and income (positive values) that occur at regular periods.

IRR(values,guess)

Values   is an array or a reference to cells that contain numbers for which you want to calculate the internal rate of return.

  • Values must contain at least one positive value and one negative value to calculate the internal rate of return.
  • IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want.
  • If an array or reference argument contains text, logical values, or empty cells, those values are ignored.

Guess   is a number that you guess is close to the result of IRR.

  • Microsoft Excel uses an iterative technique for calculating IRR. Starting with guess, IRR cycles through the calculation until the result is accurate within 0.00001 percent. If IRR can't find a result that works after 20 tries, the #NUM! error value is returned.
  • In most cases you do not need to provide guess for the IRR calculation. If guess is omitted, it is assumed to be 0.1 (10 percent).
  • If IRR gives the #NUM! error value, or if the result is not close to what you expected, try again with a different value for guess.