Question

Question: BETHESDA MINING COMPANY Bethesda Mining is a midsized coal mining company with 20 mines located i... BETHESDA MINING COMPANY Bethesda Mining is a midsized coal mining company with 20 mines located in Ohio, Pennsylvania, West Virginia, and Kentucky. The company operates deep mines as well as strip mines. Most of the coal mined is sold under contract, with excess production sold on the spot market. The coal mining industry, especially high-sulfur coal operations such as Bethesda, has been hard-hit by environmental regulations. Recently, however, a combination of increased demand for coal and new pollution reduction technologies has led to an improved market demand for high-sulfur coal. Bethesda has just been approached by Mid-Ohio Electric Company with a request to supply coal for its electric generators for the next four years. Bethesda Mining does not have enough excess capacity at its existing mines to guarantee the contract. The company is considering opening a strip mine in Ohio on 5,000 acres of land purchased 10 years ago for $5 million. Based on a recent appraisal, the company feels it could receive $5.5 million on an aftertax basis if it sold the land today. Strip mining is a process where the layers of topsoil above a coal vein are removed and the exposed coal is removed. Some time ago, the company would simply remove the coal and leave the land in an unusable condition. Changes in mining regulations now force a company to reclaim the land; that is, when the mining is completed, the land must be restored to near its original condition. The land can then be used for other purposes. Because it is currently operating at full capacity, Bethesda will need to purchase additional necessary equipment, which will cost $85 million. The equipment will be depreciated on a seven-year MACRS schedule. The contract runs for only four years. At that time the coal from the site will be entirely mined. The company feels that the equipment can be sold for 60 percent of its initial purchase price in four years. However, Bethesda plans to open another strip mine at that time and will use the equipment at the new mine. The contract calls for the delivery of 500,000 tons of coal per year at a price of $82 per ton. Bethesda Mining feels that coal production will be 620,000 tons, 680,000 tons, 730,000 tons, and 590,000 tons, respectively, over the next four years. The excess production will be sold in the spot market at an average of $76 per ton. Variable costs amount to $31 per ton, and fixed costs are $4,100,000 per year. The mine will require a net working capital investment of 5 percent of sales. The NWC will be built up in the year prior to the sales. Bethesda will be responsible for reclaiming the land at termination of the mining. This will occur in Year 5. The company uses an outside company for reclamation of all the company's strip mines. It is estimated the cost of reclamation will be $2.7 million. In order to get the necessary permits for the strip mine, the company agreed to donate the land after reclamation to the state for use as a public park and recreation area. This will occur in Year 6 and result in a charitable expense deduction of $6 million. Bethesda faces a 38 percent tax rate and has a 12 percent required return on new strip mine projects. Assume that a loss in any year will result in a tax credit. You have been approached by the president of the company with a request to analyze the project. Calculate the payback period, profitability index, net present value, and internal rate of return for the new strip mine. Should Bethesda Mining take the contract and open the mine? no need for excel i need calculations and show your work please

Answer 1

Revenue calculation:

Formula	Year (n)	1	2	3	4
	Total production (P)	620,000	680,000	730,000	590,000
	Contract price/ton ('c)	82	82	82	82
	Contract delivery (tons) (CD)	500,000	500,000	500,000	500,000
(c*CD)	Total contract revenue (a)	41,000,000	41,000,000	41,000,000	41,000,000
	Spot price/ton (s)	76	76	76	76
(P - CD)	Excess production (in tons) (EP)	120,000	180,000	230,000	90,000
(s*EP)	Total spot market revenue (b)	9,120,000	13,680,000	17,480,000	6,840,000
(a+b)	Total revenue ('R)	50,120,000	54,680,000	58,480,000	47,840,000

Initial outlay = cost of equipment + opportunity cost of not selling the land + build-up of Net Working Capital (NWC)

= 85,000,000 + 5,500,000 + (5%*Year 1 revenue)

= 90,500,000 + (5%*50,120,000) = 90,500,000 + 2,506,000 = 93,006,000

Operating Cash Flow Calculation:

Formula	Year (n)	1	2	3	4	5	6
	Total production (P)	620,000	680,000	730,000	590,000
	Total revenue ('R)	50,120,000	54,680,000	58,480,000	47,840,000
	Variable cost/ton (vc)	31	31	31	31
(vc*P)	Variable cost (VC)	19,220,000	21,080,000	22,630,000	18,290,000
	Fixed cost (FC)	4,100,000	4,100,000	4,100,000	4,100,000
	Reclamation cost (RC)					2,700,000
	Charitable expense deduction (CED)						6,000,000
MACRS 7-year schedule	Depreciation rate (d)	14.29%	24.49%	17.49%	12.49%
Equipment cost of 85mn*d	Depreciation (D)	12,146,500	20,816,500	14,866,500	10,616,500
(R-VC-FC-RC-CED-D)	EBIT	14,653,500	8,683,500	16,883,500	14,833,500	(2,700,000)	(6,000,000)
(EBIT*38%)	Tax @ 38%	5,568,330	3,299,730	6,415,730	5,636,730	(1,026,000)	(2,280,000)
(EBIT - Tax)	Unlevered net income (NI)	9,085,170	5,383,770	10,467,770	9,196,770	(1,674,000)	(3,720,000)
	Add: Depreciation (D)	1,21,46,500	2,08,16,500	14,866,500	10,616,500
(NI + D)	Operating Cash Flow (OCF)	21,2,31,670	26,200,270	25,334,270	19,813,270	(1,674,000)	(3,720,000)

NWC calculation:

Formula	Year (n)	1	2	3	4
(5% of Year n revenue)	Beginning NWC (a)	2,506,000	2,734,000	2,924,000	2,392,000
(5% of Year n+1 revenue)	Ending NWC (b)	2,734,000	2,924,000	2,392,000	0
(a-b)	Change in NWC	(228,000)	(190,000)	532,000	2,392,000

After-tax salvage calculation:

Book value (BV) after 4 years = purchase price - accumulated depreciation over 4 years

= 85,000,000 - 12,146,500 - 20,816,500 - 14,866,500 - 10,616,500 = 26,554,000

Salvage value (SV) = 60%*purchase price = 60%*85,000,000 = 51,000,000

Gain (G) = SV - BV = 51,000,000 - 26,554,000 = 24,446,000

Tax on gains = 38%*G = 38%*24,446,000 = 9,289,480

After-tax salvage value = SV - tax on gains = 51,000,000 - 9,289,480 = 41,710,520

Formula	Year (n)	0	1	2	3	4	5	6
	Initial outlay (IO)	(93,006,000)
	OCF		21,231,670	26,200,270	25,334,270	19,813,270	(1,674,000)	(3,720,000)
	Change in NWC		(228,000)	(190,000)	532,000	2,392,000	-	-
	After-tax salvage value (ATSV)					41,710,520
(IO + OCF + Change in NWC + ATSV)	Free Cash Flow (FCF)	(93,006,000)	21,003,670	26,010,270	25,866,270	63,915,790	(1,674,000)	(3,720,000)
1/(1+d)^n	Discount factor @ 12%	1.000	0.893	0.797	0.712	0.636	0.567	0.507
(FCF*Discount factor)	PV of FCF	(9,30,06,000.00)	18,753,276.79	20,735,228.00	18,411,100.07	40,619,640.04	(949,872.56)	(1,884,667.77)
Sum of all PVs	NPV	26,78,704.57
Using FCF &IRR function	IRR	13.17%
(NPV-IO)/-IO	Profitability Index (PI)	1.03

Payback period calculation:

Formula	Year (n)	0	1	2	3	4	5	6
	Free Cash Flow (FCF)	(93,006,000)	21,003,670	26,010,270	25,866,270	63,915,790	(1,674,000)	(3,720,000)
CFCFn-1 + FCFn	Cumulative FCF (CFCF)	(93,006,000)	(72,002,330)	(45,992,060)	(20,125,790)	43,790,000	42,116,000	38,396,000
(CFCF3/FCF4)	Fraction of break-even year (F)					0.31
(3 + F)	Payback period					3.31

Payback period = 3.31 years.