Question

Hindelang Inc. is considering a project that has the following cash flow and WACC data. What is the project's MIRR? Note that a project's MIRR can be less than the WACC (and even negative), in which case it will be rejected. WACC: 12.25% Year 0 1 2 3 4 Cash flows -$850 $300 $320 $340 $360

Answer 1

Answer:

MIRR = 16.6%

Explanation:

We have the formula to calculate the MIRR of the project:

+) $MIRR =\sqrt[n]{\frac{FV}{PV} } - 1$

In which:

• FV - terminal value, the future value of net cash inflow which is assumed to be re-invested at the rate of cost of capital = WACC = 12.25%
• PV - the present value of the net cash outflows during the investment at the rate of cost of capital = WACC
• n: numbers of years (n=4)

The future value of net cash inflow Year i = Cash inflow × (1 + Cost of capital)^(number of years reinvested)

= Cash inflow × 1.1225^(n - i)

+) $FV1 = 300 * 1.1225^{3}$ = $424.327

+) $FV2 = 320 * 1.1225^{2}$ = $403.202

+) $FV3 = 340 * 1.1225^{1}$ = $381.65

+) $FV4 = 360 * 1.1225^{0}$ = $360

=> Terminal Value = 424.327 + 403.202 + 381.65 + 360 = $1569.179

Present Value Year i = $\frac{Cash flow}{(1+WACC)^{i} } = \frac{Cash flow}{1.1225^{i} }$

The project requires the initial investment = - $850 and there are no cash outflows during 4 years of the project

=> PV of the project = PV Year 0 = $\frac{850}{1.1225^{0} }$ = 850

=> MIRR = $\sqrt[4]{\frac{1569.179}{850}} - 1$ =  0.166 = 16.6%

Answer 2

Using the modified IRR formula, the MIRR on the investment with the cash flow stated is 16.56%

The Modified Internal Rate of Return is calculated thus :

• $MIRR = [\frac{Terminal\:value}{PV}]^{\frac{1}{n}} - 1$

• Period, n = 4
• Present Value, PV = cash flow at year 0 = 850
• WACC = 12.25% = 0.1225

Terminal value = Summation of the cash flows from year 1 to year 4 :

• (300×1.1225)³ + (320×1.1225)² + (340×1.1225)¹ + (360×1.1225)^0 = $1569.18

We can then calculate the MIRR thus :

$MIRR = [\frac{1.569.18}{850}]^{\frac{1}{4}} - 1$

$MIRR = [\frac{1.569.18}{850}]^{\frac{1}{4}} - 1$

$MIRR = 1.1656 - 1$

$MIRR = 0.1656$

$MIRR = 0.1656 \times 100 = 16.56$%

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