Question

Calculate the MIRR of the cash flows of the project below. Assume both the finance rate and the reinvestment rate are 5%

Time Period                Cash Flow

         0                             -100

         1                                20

         2                                80

         3                                90

Answer 1

Under the MIRR method, all cash flows, except initial investment, are brought to a terminal value using the appropriate discount rate. This results in a single stream of cash inflow in the terminal year. The MIRR is obtaineed by assuming a single outflow in the zeroth year and the terminal cash inflow. The discount rate which equates the single outflow and the terminal cash inflow is called the MIRR.

So, the first step would be to compute the terminal cash inflow which is computed just like future value is computed. The year 1 cash flow will be invested @ 5% for two more years. Similarly, year 2 cash flow will be invested @5% for 1 more year and year 3 cash flow would not be reinvested.

Terminal Cash Inflow

Year	Cash inflow	Terminal value
1	20	20 x (1.05)2 = 22.05
2	80	80 x (1.05)1 = 84
3	90	90 x (1.05)0 = 90
Terminal Cash Inflow		196.05

Now, to compute the MIRR, the present value of the terminal cash flow when discounted @MIRR should be equal to the initial investment -

Terminal Cash Inflow x PVF (MIRR, 3) = Initial Investment

or, 196.05 x PVF (MIRR, 3) = 100

or, PVF (MIRR, 3) = 0.51007396072

We search for this value in the Present value factor table in year 3. So, we have -

at 25%, PVF = 0.512

at 26%, PVF = 0.49990601766

Our value lies in between these two values, so we need to interpolate.

Difference required (from 25%) = 0.512 - 0.51007396072 = 0.00192603928

Total Difference (Between 25% and 26%) = 0.512 - 0.49990601766 = 0.01209398234

MIRR = Lower rate + Difference in rates x (Difference required / Total Difference)

or, MIRR = 25% + 1% x (0.00192603928 / 0.01209398234) = 25.1592560023% or 25.16%