Modified internal rate of return (MIRR) is a financial Finance is the science of funds management. The general areas of finance are business finance, personal finance, and public finance. Finance includes saving money and often includes lending money. The field of finance deals with the concepts of time, money, and risk and how they are interrelated. It also deals with how money is spent and budgeted measure of an investment Investment is the commitment of money or capital to purchase financial instruments or other assets in order to gain profitable returns in the form of interest, income, or appreciation of the value of the instrument. It is related to saving or deferring consumption. Investment is involved in many areas of the economy, such as business management's attractiveness. It is used in capital budgeting Capital budgeting is the planning process used to determine whether a firm's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing. It is budget for major capital, or investment, expenditures to rank alternative investments. As the name implies, MIRR is a modification of the internal rate of return The internal rate of return is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return (DCFROR) or simply the rate of return (ROR). In the context of savings and loans the IRR is also called the effective interest rate. The term internal refers to (IRR) and as such aims to resolve some problems with the IRR.
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Problems with the IRR
While there are several problems with the IRR The internal rate of return is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return (DCFROR) or simply the rate of return (ROR). In the context of savings and loans the IRR is also called the effective interest rate. The term internal refers to, MIRR resolves two of them.
First, IRR assumes that interim positive cash flows are reinvested at the same rate of return as that of the project that generated them[1]. This is usually an unrealistic scenario and a more likely situation is that the funds will be reinvested at a rate closer to the firm's cost of capital. The IRR therefore often gives an unduly optimistic picture of the projects under study. Generally for judging the projects more fairly, the weighted average cost of capital The WACC is the minimum return that a company must earn on existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere. Companies raise money from a number of sources: common equity, preferred equity, straight debt, convertible debt, exchangeable debt, warrants, options, pension liabilities, should be used for reinvesting the interim cash flows.
Second, more than one IRRs can be found for projects with alternating positive and negative cash flows, which leads to confusion.
Calculation
MIRR is calculated as follows:
where n is the number of equal periods at the end of which the cash flows occur (not the number of cash flows), PV is present value Present value is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk. Present value calculations are widely used in business and economics to provide a means to compare cash flows at different times on a meaningful "like to like& (at the beginning of the first period), FV is future value Future value measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function[citation needed] (at the end of the last period).
The formula adds up the negative cash flows after discounting them to time zero, adds up the positive cash flows after factoring in the proceeds of reinvestment at the final period, then works out what rate of return would equate the discounted negative cash flows at time zero to the future value of the positive cash flows at the final time period[2].
Spreadsheet applications A spreadsheet is a computer application that simulates a paper, accounting worksheet. It displays multiple cells that together make up a grid consisting of rows and columns, each cell containing alphanumeric text, numeric values or formulas. A formula defines how the content of that cell is to be calculated from the contents of any other cell each, such as Microsoft Excel Microsoft Excel is a spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot tables and a macro programming language called VBA (Visual Basic for Applications). It has been the most widely used spreadsheet application available for these platforms since version, have inbuilt functions to calculate the MIRR. In Microsoft Excel this function is "=MIRR".
Example
If an investment project is described by the sequence of cash flows:
| Year | Cash flow |
|---|---|
| 0 | -1000 |
| 1 | -4000 |
| 2 | 5000 |
| 3 | 2000 |
then the IRR r is given by
In this case, the answer is 25.48% (the other solutions to this equation are -593.16% and -132.32%, but they will not be considered meaningful IRRs).
To calculate the MIRR, we will assume a finance rate of 10% and a reinvestment rate of 12%. First, we calculate the present value of the negative cash flows (discounted at the finance rate):
Second, we calculate the future value of the positive cash flows (reinvested at the reinvestment rate):
Third, we find the MIRR:
The calculated MIRR (17.91%) is significantly different from the IRR (25.48%).
References
Categories: Mathematical finance Categories: Applied mathematics | Fields of application of statistics | Fields of finance | Investment
