Question

You own a coal mining company and are considering opening a new mine. The mine itself will cost

$118.5

million to open. If this money is spent​ immediately, the mine will generate

$19.9

million for the next 10 years. After​ that, the coal will run out and the site must be cleaned and maintained at environmental standards. The cleaning and maintenance are expected to cost

$1.7

million per year in perpetuity. What does the IRR rule say about whether you should accept this​ opportunity? If the cost of capital is

8.3%​,

what does the NPV rule​ say?

Answer 1

IRR is the internal rate of return at which present value of cash inflows are equal to initial investment. If IRR is higher than cost of capital then project should be accepted.

Initial investment = Year 1 cash flow/(1+IRR) + Year 2 cash flow/(1+IRR)² + Year 3 cash flow/(1+IRR)³ ... + Year 10 cash flow/(1+IRR)¹⁰

NPV is the difference between present value of cash inflows and initial investment. if NPV is positive then project should be accepted.

present value of cash inflows = Year 1 cash flow/(1+cost of capital) + Year 2 cash flow/(1+cost of capital)² + Year 3 cash flow/(1+cost of capital)³ ... + Year 10 cash flow/(1+cost of capital)¹⁰

after year 10, cleaning and maintenance are expected to cost $1.7 million per year in perpetuity. so we need to calculate present value of this perpetuity at the end of year 10.

present value of perpetuity = cash flow/cost of capital = $1.7/0.083 = $20.48 million

year 10 cash inflow will be $19.9 - $20.48 = -$0.58 million

both IRR and NPV rule say you should accept this​ opportunity because IRR of 9.12% is higher than the cost of capital of 8.3% and NPV is positive.

Years	Cash flows
0	-$118.50
1	$19.90
2	$19.90
3	$19.90
4	$19.90
5	$19.90
6	$19.90
7	$19.90
8	$19.90
9	$19.90
10	-$0.58
Cost of capital	8.30%
IRR	9.12%
NPV	$4.02

Calculations