Question

Quantitative Problem: Bellinger Industries is considering two projects for inclusion in its capital budget, and you have been asked to do the analysis. Both projects' after-tax cash flows are shown on the time line below. Depreciation, salvage values, net operating working capital requirements, and tax effects are all included in these cash flows. Both projects have 4-year lives, and they have risk characteristics similar to the firm's average project. Bellinger's WACC is 7%.

Years	0	1	2	3	4
Project A	-1250	700	410	200	250
Project B	-1250	300	345	350	700

What is Project A's MIRR? Round your answer to two decimal places. Do not round your intermediate calculations. %

What is Project B's MIRR? Round your answer to two decimal places. Do not round your intermediate calculations. %

If the projects were independent, which project(s) would be accepted according to the MIRR method?

If the projects were mutually exclusive, which project(s) would be accepted according to the MIRR method?

Answer 1

MIRR assumes that the cash inflows of the project are reinvested at the cost of capital or WACC of the project. For computing MIRR, we need to compute one single future value or terminal value of the cash inflows of the project.

Terminal of a cash inflow = Cash inflows x (1 + r)ⁿ , where r is the wacc and n being the no. of years remaining.

Terminal value of cash inflows

Year	Project A	Project B
1	700 x (1 + 0.07)3 = 857.5301	300 x (1 + 0.07)3 = 367.5129
2	410 x (1 + 0.07)2 = 469.4090	345 x (1 + 0.07)2 = 394.9905
3	200 x (1 + 0.07)1 = 214	350 x (1 + 0.07)1 = 374.5
4	250	700
Terminal value	1790.9391	1837.0034

Project A

Now, MIRR is the rate at which present value of the terminal value is equal to the initial investment or year 0 cash outflow.

Terminal value / (1 + r)⁴ = Initial outflow

or, 1790.9391 / (1 + r)⁴ = 1250

or, (1 + r)⁴ = 1.43275128

or, (1 + r) = (1.43275128)^{1 / 4}

or, (1 + r) = 1.0941

or, r = 0.0941 or 9.41%

Therefore, MIRR for Project A is 9.41%.

Project B

Terminal value / (1 + r)⁴ = Initial outflow

or, 1837.0034 / (1 + r)⁴ = 1250

or, (1 + r)⁴ = 1.46960272

or, (1 + r)= (1.46960272)^{1 / 4}

or, (1 + r) = 1.1010

or, r = 0.1010 or 10.10%

Therefore, MIRR for Project B is 10.10%.

If projects were independent

Independent projects means accepting one project does not reject the other. As per MIRR criteria, like IRR, those projects should be accepted whose MIRR > WACC.

In our case, both Projects A & B should be accpeted.

If projects were mutually exclusive

Mutually exclusive projects mean that accepting one project rejects the other. In this case, we should accept that project that has the highest MIRR.

Therefore, Project B should be accepted.