Question

MULTIPLE IRRS AND MIRR A mining company is deciding whether to open a strip mine, which costs $1.5 million. Cash inflows of $13.5 million would occur at the end of Year 1. The land must be returned to its natural state at a cost $11 million, payable at the end of Year 2. a. Plot the project's NPV profile. NPV i Millions of Dollas) NPV (Millions of Dollas) | *** ****** NPV Millions of Dollar) | ********* * *** non to ON to ou NO O Ion un ********* ******** toooon ******* ** +++ + 100 200 300 400 WACC(% 100 200 300 400 WACC%) 100 200 300 400 WACC(%) NPV (Milons of Dollar) | ********** ou non ************* - 0.5 ** 100 200 300 400 WACC) The correct sketch is -Select-

Answer 1

a). Graph C is correct as it shows NPV = 1.00 at WACC = 0% and NPV tending to zero at WACC ~ 500%.

NPV (at WACC = 0%) = -1.5 + 13.5 -11 = 1 million

NPV (at WACC = 500%) = - 1.5 + 13.5/(1+500%) - 11/(1+500%)^2 = 0.44 million

b). NPV (at WACC of 10%) = -1.5 + 13.5/(1+10%) -11/(1+10%)^2 = 1.68 million, so project can be accepted.

NPV (at WACC of 20%) = -1.5 + 13.5/(1+20%) -11/(1+20%)^2 = 2.11 million, so project can be accepted.

c). Multiple IRRs occur when projects have negative cash flows in between or at the end of the project. One example where this can happen is in the case of road construction project where maintenance work will be required to be carried out every few years. Another example is the case of nuclear power plants where a negative cash flow will happen at the end of the project.

d). MIRR (at WACC = 10%) = 18.41%

MIRR (at WACC = 20%) = 33.14%

(MIRR is calculated using the MIRR function in excel with the given cash flows and respective WACC.)

Yes, MIRR leads to the same decision for this project as the NPV method as the calculated MIRR is greater than WACC.

MIRR will not always lead to the same decision as NPV. In case of mutually exclusive projects having crossing NPV profiles and a WACC less than the crossover rate, MIRR will not give the same result as NPV.