# 1.36 The Reinvestment Rate and the MIRR (The Idea)

What if the reinvestment rate assumption were not the same as the IRR, e.g., 10%, which is less than the IRR? Then:

FV = \$1,000 × 6.105

PV (cost) = \$2,532

FV ÷ PV = \$6,105 ÷ \$2,532 = 2.411×

For every dollar invested, I will have at the horizon, \$2.411, and using the formula:

(FV / PV) 1/ (n x p) – 1 =

[(2.411) 1/5 – 1] = 0.1924.

This implies a rate of return of about 19.24%, i.e., lower than the IRR. This new, 19.24% return is called the Modified IRR, or MIRR. This is a more accurate measure of return, given the input of a more realistic reinvestment assumption, than our having arbitrarily assumed a reinvestment rate for the future cash flows at the already calculated IRR.

Another way of looking at this (not mentioned above), is by equating the present value of the future inflows with the project’s cost, i.e., by setting the NPV to equal zero:

\$6,105 ÷ (1.1924)5 = \$2,532

In summary, when the reinvestment rate (“REIN”) is the same as the IRR, the IRR and the MIRR will be the same. In most instances, the reinvestment rate will be less than the IRR, because the firm will have less attractive opportunities, as compared to the project at hand, which was accepted due to its high expected return; this need not always be true however. The important relationships are summarized below:

if REIN = IRR then IRR = MIRR
if REIN < IRR then MIRR < IRR (and vice versa)

MIRR Rule

As with the IRR, accept all independent projects whose MIRR > k (where k is the hurdle rate, cost of capital); amongst competing, mutually exclusive projects, accept that which has the highest MIRR. Neither the IRR nor the MIRR addresses the issue of project size.

Notes:

• To make matters worse, the reinvestment rate does not have to be the same each year; it may be a variable.  We have not presented that possibility here.
• The IRR will be the same as the MIRR when there are no interim cash flows, thus requiring no reinvestment. This would be the corporate project equivalent to a zero-coupon bond, i.e., one outflow and inflow each.
• One reason the MIRR method is so attractive is that it does not have the “multiple solutions” issue that the IRR has, as will be illustrated below.