Question

You own a coal mining company and are considering opening a new mine. The mine itself will cost $120 million to open. If this money is spent immediately, the mine will generate $22 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 $1.8 million per year in perpetuity. What does the IRR rule say about whether you should accept this opportunity? (Hint: Consider the number of sign changes in the cash flows.) If the cost of capital is 7.6%, what does the NPV rule say?

Answer 1

SOLUTION:

THE VALUES PROVIDED IN THE QUESTION ARE AS FOLLOWS:

Initial investment = $120 million

Annual cash inflow for the 10 years = $22 million

10th year cash inflow = $ 22 million - $ 1.8 million = $ 20.2 million

AT IRR, NPV IS ZERO ,

AT IRR = PV OF CASH INFLOW – PV OF CASH OUTFLOW

HENCE , NPV OF THE PROJECT @ 12 %

Year	Total INFLOW / (Outflow)	Discounting Factor = (1/1+r)^n	P.V. (c ) = (axb)
	(A )	(B )	( C )= A * B
0	-120	1	-120.00
1	22	0.8929	19.64
2	22	0.7972	17.54
3	22	0.7118	15.66
4	22	0.6355	13.98
5	22	0.5674	12.48
6	22	0.5066	11.15
7	22	0.4523	9.95
8	22	0.4039	8.89
9	22	0.3606	7.93
10	20.2	0.3220	6.50
	SUM OF NPV		3.72

NPV OF THE PROJECT @ 13 %      

Year	Total INFLOW / (Outflow)	Discounting Factor = (1/1+r)^n	P.V. (c ) = (axb)
	(A )	(B )	( C )= A * B
0	-120	1	-120.00
1	22	0.8850	19.47
2	22	0.7831	17.23
3	22	0.6931	15.25
4	22	0.6133	13.49
5	22	0.5428	11.94
6	22	0.4803	10.57
7	22	0.4251	9.35
8	22	0.3762	8.28
9	22	0.3329	7.32
10	20.2	0.2946	5.95
	SUM OF NPV		-1.15

The formula is to calculate the IRR is as follows:

IRR = Lower Rate + Difference in lower rate /( Difference in lower rate + Difference in Higher Rate ) *(Higher Rate – Lower Rate )

IRR =12 +3.72/(3.72+1.15 )*(13-12 )

IRR =12+3.72*1/4.87

IRR =12+0.76

IRR=12.76

If the IRR is greater than cost of capital , accept the project

IF COST OF CAPITAL IS 7.6 % THEN NPV OF THE PROJECT ,

Year	Total INFLOW / (Outflow)	Discounting Factor = (1/1+r)^n	P.V. (c ) = (axb)
	(A )	(B )	( C )= A * B
0	-120	1	-120.00
1	22	0.9294	20.45
2	22	0.8637	19.00
3	22	0.8027	17.66
4	22	0.7460	16.41
5	22	0.6933	15.25
6	22	0.6444	14.18
7	22	0.5988	13.17
8	22	0.5565	12.24
9	22	0.5172	11.38
10	20.2	0.4807	9.71
	SUM OF NPV		29.45

As per the NPV rule , NPV is positive so the project should be accepted