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MIRR Calculator
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See Also Internal Rate of Return Modified Internal Rate of Return

Regardless of an academic preference for NPV, surveys suggest that many executives prefer IRR over NPV. Obviously, managers find it intuitively more appealing to evaluate investments in terms of percentage rates of return than dollars of NPV. Based on this fact, we can devise a percentage evaluator that is better than the regular IRR - we can modify the IRR and make it a better indicator of relative profitability, thus better for use in capital budgeting. This new measure is called the Modified IRR or MIRR, and is defined as follows:

MIRR Formula 1

MIRR Formula 2

MIRR Formula 3

Here COF refers to cash outflows or the cost of the project, and CIF refers to cash inflows . The left term is simply the present value of the investment outlays when discounted at the cost of capital, and the numerator of the right term is the compounded value of the inflows assuming that the cash inflows are reinvested at the cost of capital. The compounded value of the cash inflows is also called the terminal value or TV. The discount rate that forces the Present Value of the TV to equal the PV of the costs is defined as the MIRR

If the investment costs are all incurred at t=0, and if the first operating inflow occurs at t=1, then the equation may be used

Formula for MIRR

EXAMPLE 1

An investment with an initial cash out flow of $1,000 pays back $500 in the first year, $400 in the second year, $300 in the third year, and $100 in the fourth year. If the cost of capital is 10%, find the Modified Internal Rate of Return (MIRR)

SOLUTION

MIRR Example 1 a

MIRR Example 1 b

MIRR Example 1 c

We could use linear interpolation to find the MIRR, say we choose a rate of 15% for the above equation this results in a value of 

MIRR Example 1 d

Since PV of TV at 15% is below PV of Costs ($1000), we will choose a rate lower than 15 say 10%

At 10% , PV of TV is above PV of Costs ($1000).

MIRR Example 1 e

Now we will interpolate to find an approximation of MIRR at which PV of TV equals PV costs

MIRR Interpolate 1

MIRR Interpolate 2

MIRR Interpolate 3

Using MS Excel to compute MIRR

Returns the modified internal rate of return for a series of periodic cash flows. MIRR considers both the cost of the investment and the interest received on reinvestment of cash.

Syntax

MIRR(values,finance_rate,reinvest_rate)

Values   is an array or a reference to cells that contain numbers. These numbers represent a series of payments (negative values) and income (positive values) occurring at regular periods.

  • Values must contain at least one positive value and one negative value to calculate the modified internal rate of return. Otherwise, MIRR returns the #DIV/0! error value.
  • If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.

Finance_rate   is the interest rate you pay on the money used in the cash flows.

Reinvest_rate   is the interest rate you receive on the cash flows as you reinvest them.

Remarks

  • MIRR 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 and with the correct signs (positive values for cash received, negative values for cash paid).
  • If n is the number of cash flows in values, frate is the finance_rate, and rrate is the reinvest_rate, then the formula for MIRR is:

Examples

Suppose you're a commercial fisherman just completing your fifth year of operation. Five years ago, you borrowed $120,000 at 10 percent annual interest to purchase a boat. Your catches have yielded $39,000, $30,000, $21,000, $37,000, and $46,000. During these years you reinvested your profits, earning 12 percent annually. On a worksheet, your loan amount is entered as -$120,000 in B1, and your five annual profits are entered in B2:B6.

To calculate the investment's modified rate of return after five years:

MIRR(B1:B6, 10%, 12%) equals 12.61 percent

To calculate the modified rate of return after three years:

MIRR(B1:B4, 10%, 12%) equals -4.80 percent

To calculate the five-year modified rate of return based on a reinvest_rate of 14 percent

MIRR(B1:B6, 10%, 14%) equals 13.48 percent