Question

4. Modified internal rate of return (MIRR) 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 retun equal to the IRR. Thus, the modified IRR approach makes a more reasonable assumption other than the project's IRR Consider the following situation: Celestial Crane Cosmetics is analyzing a project that requires an initial investment of $600,000. The project's expected cash flows are: Year Cash Flow Year 1 $375,000 Year 2 -100,000 Year 3 450,000 Year 4 475,000 Celestial Crane Cosmetics'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) 19.80% 18.81 % 15.84% 20.79 %

Answer 1

Future value of cash inflows Year Inflow FVF @ 7% FV 1 375000 1.225 4,59,391.13 450000 1.070 4,81,500.00 1.000 4 475000 4,75,000.00 1415891.125 Hence, terminal Value 1415891.13 Present value of cash outflow Year PVF @ 7% |PV Outflow 600000 1 6,00,000.00 2. 100000 0.873 87,343.87 6,87,343.87 MIRR Computation MIRR=Terminal cash flow Outlay |=SQRT(SQRT(1415891.125/687343.87))-1 19.80%

How to find MIRR?

For computation of MIRR, unlike IRR we assume that the reinvestment of cashflows are made at cost of capital. Hence , we need to find the terminal value of positive cashflows(return) and the present value of negative cashflows(outlay).

For computation of terminal value, we need to find what will be the value of each cashflow at the end of 4th year if reinvested at 7%. For year 1 , it will be Cashflow of year 1 x (1.07)³ . Similarly for year 3 it will be cashflow of year 3 x (1.07) , since it will be reinvested only for a year. For year 4 the value will be cashflow itself, since we have to find value at end of year 4. The sum of these 3 figures will give you the terminal value.

For computation of Present value cashflows, in the given problem we have initial outlay and a negative cash flow in year2. Hence we need to find the PV factor and discount both these cashflows.

Now, by applying the formula given in the computation we can find the MIRR. Note: the n in formula refers to the no.of years. which in this case is 4.( hence the sort formula applied twice to arrive the answer using excel)

MIRR DECISION RULE

In case of MIRR, the project can be accepted if the MIRR is greater than the cost of capital.

Hence if Celestial Crane Cosmetics' managers select projects based on the MIRR criterion, they should select/accept this independent project.

Statement best describing difference between MIRR and IRR

Answer : statement 2: The IRR method assumes that the cashflows are reinvested at a rate of return equal to the IRR . The MIRR method assumes that the cashflows are reinvested at a rate of return equal to cost of capital.

Statement 1 is wrong because the basic principle of IRR is that it is the rate at which net present value of a project will be equal to zero.The NPV is the net present value of its cash inflows and outflows.

Statement 3 is partially wrong because in MIRR method also we need to calculate the present value of initial investment.