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# HP 10b Calculator - Calculating Modified Internal Rate of Return

Description
When there is more than one sign change (positive to negative or negative to positive) in a series of cash flows, there could potentially be more than one IRR percent. The Modified Internal Rate of Return (MIRR) is sometimes offered, particularly in the real estate profession, as a way to recognize imperfect capital markets, in which reinvestment rates and requirements of liquidity limit the more stringent assumptions of IRR and NPV. The MIRR may provide a unique solution in cases where IRR might have multiple solutions (where more than one sign change of cash flows occurs).
This procedure uses specified reinvestment and borrowing rates. Negative cash flows are discounted at a "safe" rate that reflects the return on an investment in a liquid account. The figure generally used is a short-term security (T-bill) or bank passbook rate. Positive cash flows are reinvested at a "reinvestment" rate that reflects the return on an investment of comparable risk. An average rate of return on recent market investments might be used.
Calculator symbol key
The procedures in this document use the following text to represent symbol keys:
 Key Description Text Representation colored key; shift key SHIFT
Calculating MIRR
Use the following steps to calculate the MIRR:
1. Use the cash flow application to calculate the present value of the negative cash flows at the safe rate. Key in 0 for any cash flow that is positive. Write down the result.
2. Use the cash flow application to calculate the future value of the positive cash flows at the reinvestment rate. Key in 0 for any cash flow that is negative.
3. Store the total number of periods in N, the present value of the negative cash flows in PV, and the future value of the positive cash flows in FV.
4. Press I/YR to calculate the annual interest rate.
Example of calculating MIRR
An investor is considering the investment summarized below. The safe rate is 9 percent and the investor expects to reinvest positive cash flows at 14 percent. What is the MIRR?
 Year Cash Flow (\$) 0 -75,000 1 -9,500 2 27.000 3 -11.000 4 50,000 5 83,000
What is the MIRR?
 Keys Display Description Press SHIFT, then CLEAR ALL 0.00 Clears all registers and stores periods per year Press 1, SHIFT, then P/YR 0.00 Sets to one payment per year Press 75000, [+/-], then CFj -75,000.00 Stores initial cash flow Press 9500, [+/-], then CFj -9,500.00 Stores flow 1 Press 0, then CFj 0.00 Stores 0 as flow 2 Press 11000, [+/-], then CFj -11,000.00 Stores flow 3 Press 9, then I/YR 9.00 Stores safe interest rate Press SHIFT, then NPV -92,209.61 Calculates PV of negative cash flow Press SHIFT, then CLEAR ALL 0.00 Clears all registers Press 0, then CFj 0.00 Stores 0 as initial cash flow Press 0, then CFj 0.00 Stores 0 as flow 1 Press 27000, then CFj 27,000.00 Stores flow 2 Press 0, then CFj 0.00 Stores 0 as flow 3 Press 50000, then CFj 50,000.00 Stores flow 4 Press 83000, then CFj 83,000.00 Stores flow 5 Press 14, then I/YR 14.00 Stores reinvestment rate Press SHIFT, then NPV 93,487.24 Calculates PV of positive cash flows Press [+/-], then PV -93,487.24 Changes sign and restores in PV Press 5, then N, then FV 180,001.69 Calculates FV of positive cash flows Press 92209.61,[+/-], then PV -92,209.61 Stores present value of negative flows in PV Press I/YR 14.31 Calculates annual MIRR

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