Question

The IRR evaluation method assumes that cash flows from the project are reinvested at the same rate equal to the IRR. However, in reality the reinvested cash flows may not necessarily generate a return equal to the IRR. Thus, the modified IRR approach makes a more reasonable assumption other than the project’s IRR. Consider the following situation: Green Caterpillar Garden Supplies Inc. is analyzing a project that requires an initial investment of $2,500,000. The project’s expected cash flows are: Year Cash Flow Year 1 $275,000 Year 2 –125,000 Year 3 450,000 Year 4 450,000 Green Caterpillar Garden Supplies Inc.’s WACC is 7%, and the project has the same risk as the firm’s average project. Calculate this project’s modified internal rate of return (MIRR): 21.58% 19.31% -16.50% 23.86% If Green Caterpillar Garden Supplies Inc.’s managers select projects based on the MIRR criterion, they should this independent project. Which of the following statements about the relationship between the IRR and the MIRR is correct? A typical firm’s IRR will be equal to its MIRR. A typical firm’s IRR will be greater than its MIRR. A typical firm’s IRR will be less than its MIRR.

Answer 1

Answer:

MIRR -16.50%

They should reject the project is it destroys capital it do not meet to pay up the cost of the investment.

A typical firm’s IRR will be greater than its MIR

If the project yields higher than the cost of capital the IRR will be higher than the MIRR as reinvest the cashflow at the project yield rather than copany's cost of capital, thus it overstate the return.

Explanation:

$MIRR = \sqrt{\frac{FV \: inflow}{PV \: outflow}} -1$

WACC (cost of capital, reinvestment and financiation rate) = 7%

Cash inflow:

$Inflow \: (1+ r)^{time} = Amount$

Year 1 275000    336,886.825

Year 3 450000     481500

Year 4 450000    450000

Total                        1,268,386.825

Cash outflow:

F=                           -2,500,000

Year 2 -125000 -    109, 179.841

$\frac{125,000}{(1 + 0.07)^{2} } = PV$  

Total                    2,609,179.841

Now we can solve for MIRR:

$MIRR = \sqrt[n]{\frac{FV \: inflow}{PV \: outflow}} -1$

$MIRR = \sqrt[4]{\frac{1,268,386.82}{2,609,179.84}} -1$

MIRR - 16.49991% = -16.50%