Question

You own a coal mining company and are considering opening a new mine. The mine itself will cost $ 116.6million to open. If this money is spent? immediately, the mine will generate $19.7million 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 $ 1.8million per year in perpetuity. What does the IRR rule say about whether you should accept this? opportunity? If the cost of capital is 8.5 %, what does the NPV rule? say?

Answer 1

From 11^th years onward the project needs $ 1,800,000 for environmental maintenance.

PV of this perpetuity at 10^th year = Annual expenses/discount rate

                                                       = $ 1,800,000/8.5%

                                                       = $ 1,800,000/0.085

                                                        = $ 21,176,470.59

Total cash flow at 10^th year = $19,700,000 - $ 21,176,470.59 = - $ (1,476,470.59)

Year	Cash flow (C)	Calculation of PV Factor	PV Factor @ 8.5 % (F)	PV (= C x F)
0	($116,600,000)	1/(1+0.085)^0	1	($116,600,000)
1	$19,700,000	1/(1+0.085)^1	0.921658986	$18,156,682.03
2	$19,700,000	1/(1+0.085)^2	0.849455287	$16,734,269.15
3	$19,700,000	1/(1+0.085)^3	0.782908098	$15,423,289.54
4	$19,700,000	1/(1+0.085)^4	0.721574284	$14,215,013.40
5	$19,700,000	1/(1+0.085)^5	0.665045423	$13,101,394.84
6	$19,700,000	1/(1+0.085)^6	0.612945091	$12,075,018.28
7	$19,700,000	1/(1+0.085)^7	0.564926351	$11,129,049.11
8	$19,700,000	1/(1+0.085)^8	0.520669448	$10,257,188.12
9	$19,700,000	1/(1+0.085)^9	0.479879675	$9,453,629.60
10	($1,476,470.59)	1/(1+0.085)^10	0.442285415	($653,021.41)
IRR	9.19%		NPV	$3,292,512.67

Excel formula for IRR is “=IRR(Cell No_: Cell No_)”

As IRR is higher than company’s cost of capital, project should be accepted.

Based on NPV rule, project should be accepted as NPV is positive.