Question

A mining company is deciding whether to open a strip mine, which costs $2.5 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 of $12 million, payable at the end of Year 2.

What is the project's MIRR at WACC = 10%?

What is the project's MIRR at WACC = 20%?

Answer 1

• Modified internal rate of return (MIRR) assumes that positive cash flows are reinvested at the firm's cost of capital, and the initial outflows are financed at the firm's financing cost.
• so it means that we will assume that the cash inflows of $13.50 million at end of year 1 will be reinvested for 1 year at the WACC. So the Cash Inflows for the Company is $13.50*WACC.
• Now let us take up the cost parts, the initial outflow is $2.50 million and there is also a cost of $12 million at the end of year 2. Now since we are calculating the MIRR of the project we have to calculate the Present Value of Costs. So the cost will be Initial Cost+PV of cost after 2 years at WACC.

Now let us look up the formulae of MIRR and get the answer:-

MIRR=[(FV of Cash Inflows/PV of cash Outflows) ^ (1/n)]-1= answer

1. MIRR at WACC=10%

Let us write all the variables:-

Initial Cost=$2.50 million

Cash Inflow=$13.50 milllion

Cost to be incurred at the end of 2nd year=$12 million

WACC=10%

MIRR=[(13.50*1.10/2.50+12/1.10*1.10) ^ (1/2)]-1

MIRR=[(14.85/12.4174) ^ (1/2)]-1

MIRR=Square root of 1.1959=1.0936-1=9.36%

2. MIRR at WACC=20%

Let us write all the variables:-

Initial Cost=$2.50 million

Cash Inflow=$13.50 milllion

Cost to be incurred at the end of 2nd year=$12 million

WACC=20%

MIRR=[(13.50*1.20/2.50+12/1.20*1.20) ^ (1/2)]-1

MIRR=[(16.20/10.8333) ^ (1/2)]-1

MIRR=Square root of 1.4954=1.2229-1=22.29%.