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192 Section 13: Investment Analysis
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 192 of 275
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm
Modified Internal Rate of Return
The traditional Internal Rate of Return (IRR) technique has several drawbacks which
hamper its usefulness in some investment applications. The technique implicitly
assumes that all cash flows are either reinvested or discounted at the computed
yield rate. This assumption is financially reasonable as long as the rate is within a
realistic borrowing and lending range (for example, 10% to 20%). When the IRR
becomes significantly greater or smaller, the assumption becomes less valid and
the resulting value less sound as an investment measure.
IRR also is limited by the number of times the sign of the cash flow changes
(positive to negative or vice versa). For every change of sign, the IRR solution has
the potential for an additional answer. The cash flow sequence in the example that
follows has three sign changes and hence up to three potential internal rates of
return. This particular example has three positive real answers: 1.86, 14.35, and
29. Although mathematically sound, multiple answers probably are meaningless
as an investment measure.
This Modified Internal Rate of Return procedure (MIRR) is one of several IRR
alternatives which avoids the drawbacks of the traditional IRR technique. The
procedure eliminates the sign change problem and the reinvestment (or
discounting) assumption by utilizing user stipulated reinvestment and borrowing
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 which reflects the return on
an investment of comparable risk. An average return rate on recent market
investments might be used.
The steps in the procedure are:
1. Calculate the future value of the positive cash flows (NFV) at the reinvestment
2. Calculate the present value of the negative cash flows (NPV) at the safe rate.
3. Knowing n, PV, and FV, solve for i.