A project has cash inflows of Y1 = $30,000, Y2 = $50,000, and Y3 = $70,000. The project costs $100,000 in year 0. Selecting a test MIRR1 of 20%, we can apply the algorithm for finding the “actual” MIRR.
a. What is the terminal date of the project?
b. Assume an MIRR1 of 20%. What is the future value of all cash inflows and outflows at project completion in year 3 (not including the initial investment)?

Question

c. Discount the terminal value to the present.

This amount is higher than the original investment of $100,000, which implies the discount rate is not “wearing down” the cash flow enough. The implication is to try a discount rate that is higher. Let MIRR2 24%, and compute another test value.

a. What is the terminal date of the project?

b. Assume an MIRR2 = 24%. What is the terminal value of the project?

c. Discount the terminal value to the present value.

Accepted Answer

a. Three years.

b. Table (1)

c. [latex] ext { test1 }=\$ 173,200 imes PV (20 \%, 3)=\$ 173,200 imes 0.5787=\$ 100,230.84[/latex]

a. Three years.

b. Table (2)

c. [latex] ext { test2 }=\$ 178,128 imes \operatorname{PV}(24 \%, 3)=\$ 178,128 imes 0.52449=\$ 93,426.35[/latex]

Since test1 and test2 bracket the initial investment of $100,000, we can infer MIRR1 and MIRR2 bracket the “actual” MIRR. We now have enough information to use the interpolation formula, Eq. 10–7, which is a modified version of the IRR interpolation formula.

[latex]\cfrac{ ext { test2 }- ext { test1 }}{ ext { MIRR2 }- ext { MIRR1 }}=\cfrac{ ext { Cash outflow }- ext { test1 }}{ ext { MIRR }- ext { MIRR1 }}[/latex] (Eq. 10–7)

[latex]\begin{aligned}\cfrac{\$ 93,426.35-\$ 100,230.84}{24 \%-} & =\cfrac{\$ 100,000-\$ 100,230.84}{ ext { MIRR }-20 \%} \\cfrac{-\$ 6,804.49}{4 \%} & =\cfrac{-\$ 230.84}{ ext { MIRR }-20 \%}\end{aligned}[/latex]

Multiplying both sides by -1, then multiplying both sides by (MIRR 20%) first, then by 4% gives

[latex]\begin{aligned}( ext { MIRR }-20 \%) imes \$ 6,804.49 & =\$ 230.84 imes 4 \% \ ext { MIRR }-20 \% & =(\$ 230.84 / \$ 6,804.49) imes 4 \% \ ext { MIRR } & =0.136 \%+20 \%=20.136 \%\end{aligned}[/latex]

Projects with the highest MIRR rank higher than projects with lower MIRR. Projects with an MIRR greater than the cost of capital can be profitably funded. Those with an MIRR equal to or less than the cost of capital should not be funded.
One advantage of MIRR is that it is directly comparable to the yield on other investments. MIRR can be used in place of IRR to find the optimal capital budget. The highest ranking projects should be funded first, using the capital with the lowest marginal cost of capital (MCC). When MCC equals or exceeds MIRR, the optimal capital budget has been reached. MIRR also provides some indication of the amount of “cushion” in a project. For example, if the cost of capital is 12%, and the IRR on a project is 15%, there is a 3% “cushion” in the project. The major drawback to MIRR is that it is somewhat complex.

Question 10.5: A project has cash inflows of Y1 = $30,000, Y2 = $50,000, a...

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