You own a coal mining company and are considering opening a new mine. The mine w
ID: 2648991 • Letter: Y
Question
You own a coal mining company and are considering opening a new mine. The mine will cost $117.5 million to open. If this money is spent immediately, the mine will generate $20.4 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 $1.5 million per year in perpetuity. What does the IRR rule say about whether you should accept this opportunity? If the cost of capital is 8.1%, what does the NPV rule say?Explanation / Answer
Answer 1
From Graph given, it can be seen that NPV of the coal mine project becomes zero at 10.5%.
After 10 years, site must be cleaned and maintained. The cleaning and maintenance are expected to cost $ 1.5 million per year in perpetuity. So total cash outflow at year 10 end for the cleaning and maintenance will be $ 14.29 million ( $1.5 million/ 0.105).
IRR is the discount rate that makes the net present value of all cash flows from a particular project equal to zero. So we have to assume different discount rates by trail and error method. Suppose disc rate is 10.49%.
(Figures million $)
Year
Cash outflows
cash inflows
Net cashflows
Disc rate =10.49
Present value
A
B
A*B
0
-117.5
0
-117.5
1
-117.5
1
0
20.4
20.4
0.91
18.46
2
0
20.4
20.4
0.82
16.71
3
0
20.4
20.4
0.74
15.12
4
0
20.4
20.4
0.67
13.69
5
0
20.4
20.4
0.61
12.39
6
0
20.4
20.4
0.55
11.21
7
0
20.4
20.4
0.50
10.15
8
0
20.4
20.4
0.45
9.18
9
0
20.4
20.4
0.41
8.31
10
-14.29
20.4
6.11
0.37
2.25
NPV
0.0
So IRR of the project is 10.49%. So if cost of capital is less than 10.49% than Opportunity should be accepted.
Answer 2
The Cost of capital is 8.1%.
The cleaning and maintenance are expected to cost $ 1.5 million per year in perpetuity. So total cash outflow at year 10 end for the cleaning and maintenance will be $ 18.52 million ( $1.5 million/ 0.081).
Figures in million $
Year
Cash outflows
cash inflows
Net cashflows
Disc rate =8.1%
Present value
A
B
A*B
0
-117.5
0
-117.5
1
-117.5
1
0
20.4
20.4
0.93
18.87
2
0
20.4
20.4
0.86
17.46
3
0
20.4
20.4
0.79
16.15
4
0
20.4
20.4
0.73
14.94
5
0
20.4
20.4
0.68
13.82
6
0
20.4
20.4
0.63
12.78
7
0
20.4
20.4
0.58
11.83
8
0
20.4
20.4
0.54
10.94
9
0
20.4
20.4
0.50
10.12
10
-18.52
20.4
1.88
0.46
0.86
NPV
10.3
NPV of the project is $10.3 million. So Opportunity should be accepted.
Answer 3
IRR rule says we should accept the opportunity because IRR is greater than the cost of capital.
Year
Cash outflows
cash inflows
Net cashflows
Disc rate =10.49
Present value
A
B
A*B
0
-117.5
0
-117.5
1
-117.5
1
0
20.4
20.4
0.91
18.46
2
0
20.4
20.4
0.82
16.71
3
0
20.4
20.4
0.74
15.12
4
0
20.4
20.4
0.67
13.69
5
0
20.4
20.4
0.61
12.39
6
0
20.4
20.4
0.55
11.21
7
0
20.4
20.4
0.50
10.15
8
0
20.4
20.4
0.45
9.18
9
0
20.4
20.4
0.41
8.31
10
-14.29
20.4
6.11
0.37
2.25
NPV
0.0
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