# 1.39 MIRR Solution

 Period Nominal Net Cash Inflow FVF @ 10% Future Values 1 \$500 1.331 \$665.50 2 \$400 1.210 484.00 3 \$300 1.100 330.00 4 \$100 1.000 100.00 Terminal Value= \$1,579.50

(1,579 ÷ 10001/4 – 1 12.11%

Question:  What if the cash flows occurred at the start (rather than the end) of each period?

Solution In reality, we spread projections using end-of-period assumption – even though the flows are received over the course of the period and not discretely, in one fell swoop at the end alone. Still this exercise has some interesting numerical implications, as you shall see. In order to solve this, we may employ the same method used in converting an ordinary annuity to an annuity due.  Specifically,

{[(1,579.50) (1.10)1÷ 1,000}1/4 ≅15%

This “short-cut approach” may seem counter-intuitive, or just incorrect, because this example is clearly not an annuity. To prove out the validity of the short-cut used, let’s do it the long way. If we get the same answer, the short-cut was correct.

 Period Nominal Net Cash Inflow FVF @ 10% Future Values 1 \$500 1.4641 \$732.05 2 \$400 1.331 532.40 3 \$300 1.2100 363.00 4 \$100 1.1000 110.00 Terminal Value = \$1,737.45

We get the same terminal value, multiplier, and return!

Note the MIRR is a.k.a. External Rate of Return (ERR)!