Step $1$: Concept Clip: Modified Internal Rate of Return

Modified Internal Rate of Return is a fundamental concept in finance.

Watch the video and answer the question that follows.

According to the video, the calculations of the IRR is based on the assumption that cash flows can be reinvested at:

the IRR.

the MIRR.

the NPV$.$

the WACC.

Follow these steps describing how the MIRR is calculated to complete the table for Project X$.$

$$ The Project X has just one outflow: $$$$1,000$ at t$=0$

$,$ this means that it is not discounted and its PV $=$$$1,000$

$.($Note: If the project has more than one outflow, you need to find the PV at t$=0$

for each one and sum them to arrive at the PV of total costs for use in the MIRR calculation.$)$

$$ You need to find the future value of each inflow compounded at the WACC out to the terminal year, which is the year the last inflow is received. $($Hint: Assume that cash flows are reinvested at the WACC.$)$

$$ You have the cost at t $=0,$$$1,000$

$,$ and the FV

$.$ There is some discount rate that will cause the PV of the terminal value to equal the cost. That interest rate is defined as the MIRR. $($Note: Using your financial calculator, enter N$=4$

$,$ PV$=1,000$

$,$ PMT$=0$

$,$ and FV

$.$ Then when you press the I$/$YR

key, you get the MIRR. Some calculators have a built$-$in MIRR function that streamlines the process. In Excel, you can use either the RATE function or MIRR function to calculate the MIRR.$)$

Project X

$0$

$1$

$2$

$3$

$4$

WACC $=15\%$

Inflow $-$$$1,000$ $$800$ $$750$ $$650$ $$500$

Complete the following table.

NPV $=$

FV $=$

MIRR $=$

Step $2$: Learn: Modified Internal Rate of Return

Watch the following video for an example, then answer the questions that follow.

Suppose a firm is considering two mutually exclusive equally risky projects with WACC $=15\%$ and the following cash flows:

$0$

$1$

$2$

$3$

$4$

Project X $-$$$1,000$ $$800$ $$750$ $$650$ $$500$

Project Y $-$$$1,000$ $$1,050$ $$700$ $$600$ $$450$

How can you calculate the MIRR for the project that maximizes shareholder value?

Assuming that your professional financial calculator is able to calculate the MIRR, use the following table to indicate which values you should enter to compute the MIRR for Project X$.$

CF$0$

CF$1$

CF$2$

CF$3$

CF$4$

Input

Keystroke Arrow down Arrow down Arrow down Arrow down Arrow down IRR I MIRR

Output

Suppose that your calculator does not have the ability to compute the MIRR. Here are the steps you need to take to calculate the MIRR for Project Y$.$

$1.$ Use the following table to indicate which values you should enter to compute the net present value $($NPV$)$ of all cash inflows.

CF$0$

CF$1$

CF$2$

CF$3$

CF$4$

Input

Keystroke Arrow down Arrow down Arrow down Arrow down Arrow down I$/$Y NPV

Output

$2.$ Use the following table to indicate which values you should enter to compute the future value of the NPV$.$

Input

Keystroke N I$/$Y PV PMT FV

Output

$3.$ Use the following table to indicate which values you should enter to compute the MIRR.

Input

Keystroke N PV PMT FV I$/$Y

Output

Finally, you can answer the question: The MIRR for the project maximizes shareholder value.

Step $3$: Practice: Modified Internal Rate of Return

Now it$$s time for you to practice what you$$ve learned.

Suppose a firm is considering two mutually exclusive equally risky projects with WACC $=15\%$ and the following cash flows:

$0$

$1$

$2$

$3$

$4$

$5$

Project A $-$$$1,000$ $$800$ $$750$ $$650$ $$500$ $$425$

Project B $-$$$1,000$ $$1,050$ $$700$ $$600$ $$450$ $$545$

What is the MIRR of the project that maximizes the shareholder return?

$28\mathrm{.}15\%$

$36\mathrm{.}61\%$

$38\mathrm{.}34\%$

$85\mathrm{.}91\%$