Question

TI Inc. is considering a 4-year investment project. The project’s cash flows are summarized in the table below. Management is expecting at least a 8% annual return from this investment. What are the IRR and MIRR of the following cash flows? Which metric you would recommend to Truman’s CEO and why? (Explain briefly)

Year	0	1	2	3	4
Cash Flow	- $450,000	$9,000	$10,000	$15,000	$790,000

Answer 1

IRR:

IRR is the rate of return that makes NPV equal to 0

NPV = -450,000 + 9,000 / ( 1 + R)¹ + 10,000 / ( 1 + R)² + 15,000 / ( 1 + R)³ + 790,000 / ( 1 + R)⁴  

Using trial and error method, i.e, after trying various values for R, let's try R as 16.73%

NPV = -450,000 + 9,000 / ( 1 + 0.1673)¹ + 10,000 / ( 1 + 0.1673)² + 15,000 / ( 1 + 0.1673)³ + 790,000 / ( 1 + 0.1673)⁴  

NPV = 0

Therefore, IRR is 16.73%

MIRR:

Future value of year 1 cash flow = 9,000 ( 1 + 0.08)³ = 11,337.408

Future value of year 2 cash flow = 10,000 ( 1 + 0.08)² = 11,664

Future value of year 3 cash flow = 15,000 ( 1 + 0.08) = 16,200

Furure value of year 4 cash flow = 790,000 ( 1 + 0.08)⁰ = 790,000

Total future value = 790,000 + 16,200 + 11,664 + 11,337.408 = 829,201.408

829,201.408 = 450,000 ( 1 + R)⁴

1.84267 = ( 1 + R)⁴

1.165096 = 1 + R

R = 0.165096 or 16.51%

MIRR is 16.51%

I would recommend MIRR

Modified internal rate of return (MIRR) assumes that positive cash flows are reinvested at the firm's cost of capital, and the initial outlays are financed at the firm's financing cost. By contrast, the traditional internal rate of return (IRR) assumes the cash flows from a project are reinvested at the IRR. The MIRR more accurately reflects the cost and profitability of a project.

The MIRR is used to rank investments or projects of unequal size. The calculation is a solution to two major problems that exist with the popular IRR calculation. The first main problem with IRR is that multiple solutions can be found for the same project. The second problem is that the assumption that positive cash flows are reinvested at the IRR is considered impractical in practice. With the MIRR, only a single solution exists for a given project, and reinvestment rate of positive cash flows is much more valid in practice.