Question

Calculate MIRR

Io or Co =$25,000
Saving rate=1.5%,
Loan rate=8%,
Discount rate is 7%

N Cash Flows
1 $8,000
2 12,000
3 <1,000>
5 15,000

Don't use excel

Answer 1

First, we will find out the present values of all negative cash flows, using the loan rate

PV of negative cash flow = - (initial outlay) + (negative cash flow in year n)/(1+ finance rate)ⁿ

In this case, we can use the loan rate as the finance rate

PV of negative cash flows = -$25,000 + ( - $1,000/(1 + 0.08)³

= - $25,000 - [$1,000/(1.2597)] = - $25,000 - $793.83

= - $25,793.83

Now, we have to find out the future value of positive cash flows using the saving rate, 1.5%. Given that cash flows occur for five years,

FV of positive cash flows = (Cash flow in year n) *(1.015)^{5 - n}

= {$8,000 * (1.015)^5-1} + {$12,000 * (1.015)^5-2} + {$15,000 * (1.015)^5-5}

= {$8,000 * (1.015)⁴} + {$12,000 * (1.015)³} + {$15,000 * (1.015)⁰}

= $8,490.91 + $12,548.14 + $15,000

= $36,039.05

The formula for calculating MIRR is

[{(Future value of positive cash flows) / (Present value of negative cash flows)}^(1/n)] -1,

where n is the life span of the project

Hence MIRR = ($36,039.05/{- (-$25,793.83)^(1/5) }-1= (1.39719)^(1/5) -1 = 1.06918 - 1

=0.06918 or 6.92%