Question

The Charvon oil company is planning to make a large investment in coal-to-liquids (CTL) gasoline. The end product will be a perfect substitute for gasoline made from petroleum, but the feedstock will be coal instead of oil. Two technologies are available to the Charvon company. The first is called indirect CTL, where the coal is gasified prior to being liquefied. The second is called direct CTL, where the coal is dissolved in a solvent, and the resulting liquid is processed into gasoline. The Charvon company has hired you as a consultant to help them decide which technology they should choose. Charvon expects to produce 1.5 million gallons of CTL gasoline in each of the next twenty years, and they can sell the gasoline for S2.5 per gallon. The capital cost of indirect CTL is S10 million and operating costs for indirect CTL (labor, fuel, and maintenance) are $400,000 per year. The capital cost of direct CTL is S12 million and operating costs for direct CTL are $300,000 per year. One problem with indirect CTL is that the coal gasification process releases large amounts of CO2 into the atmosphere. Assume that for every gallon of gasoline produced with indirect CTL, 0.02 tons of CO2 are released. You have learned that starting in Year 1 the government will implement a tax of S15 per ton of CO2, which is applied as increase in the operating cost. Assume that ifyou choose direct CTL you will not be subject to the tax on CO2. Assume capital cost for both technologies can be depreciated using straight line with project life time of 20 years, starting from year 1 to year 20. Consider income tax rate of 40%for the taxable income nd discount rate of 12% for all costs and revenues

Answer 1

	CALCULATION OF NPV OF DIRECT CTL
					A	Initial Investment	$12,000,000
					B	Annual Sales quantity in gallons	1500000
					C	Sales price per gallon	$2.50
					D=B*C	Annual sales in dollars	$3,750,000
					E	Annual Operating cost	$300,000
					F=D-E	Annual Pre tax cash flow	$3,450,000
					G	Income tax rate	0.40
					H=F*(1-G)	After tax cash flow(without considering depreciation)	$                  2,070,000
					I=A/20	Depreciation per year	$600,000
					J=I*G	Depreciation tax shield	$                      240,000
					K=H+J	Annual after tax cash flow	$                  2,310,000
					L	Discount rate	12%
					M	Present Value(PV) of annual cash flow	$17,254,415	(Using PV function of excel with Rate=12%,Nper=20, Pmt=2310000)
					N=M-A	Net Present value(NPV)	$5,254,415
					CALCULATION OF NPV OF INDIRECT CTL
					A	Cost of capital	$10,000,000
					B	Annual sales in dollars	$3,750,000
					C	Annual Operating cost	$400,000
					D=B-C	Annual Pre tax cash flow	$3,350,000
					E	Income tax rate	0.40
					F=D8(1-E)	After tax cash flow(without considering depreciation)	$                  2,010,000
					G=A/20	Depreciation per year	$500,000
					H=G*E	Depreciation tax shield	$                      200,000
					I=F+H	Annual after tax cash flow	$                  2,210,000
						Discount rate	12%
						Present Value(PV) of annual cash flow	$16,507,470	(Using PV function of excel with Rate=12%,Nper=20, Pmt=2210000)
						EFFECT OF TAX ON CO2
					J	Amount of CO2 generated(Ton)	30000	(1500000*0.02)
					K=15*J	Carbon tax	$                      450,000
						SENSITIVITY ANALYSIS
						P	T=450000*P	K=3350000-T	L=K*(1-0.4)	M=L+200000	N=PV(12%,20,-M)	N-10000000
	Probability of Carbon tax	Rxpected NPV of Indirect CTL	Expected NPV of Direct CTL			Probability of $15 per ton carbon tax	Expected carbon tax	Pretax cash flow	After tax Cash flow	Annual Cash flow with depreciation	Present Value of Cash flow	Net Present Value
	1	$4,490,721	$5,254,415			1	$                      450,000	$2,900,000	$   1,740,000	$1,940,000	$14,490,721	$4,490,721
	0.9	$4,692,396	$5,254,415			0.9	$                      405,000	$2,945,000	$   1,767,000	$1,967,000	$14,692,396	$4,692,396
	0.8	$4,894,071	$5,254,415			0.8	$                      360,000	$2,990,000	$   1,794,000	$1,994,000	$14,894,071	$4,894,071
	0.7	$5,095,746	$5,254,415			0.7	$                      315,000	$3,035,000	$   1,821,000	$2,021,000	$15,095,746	$5,095,746
	0.6215	$5,254,060	$5,254,415			0.6215	$                      279,675	$3,070,325	$   1,842,195	$2,042,195	$15,254,060	$5,254,060
	0.6	$5,297,421	$5,254,415			0.6	$                      270,000	$3,080,000	$   1,848,000	$2,048,000	$15,297,421	$5,297,421
	0.5	$5,499,096	$5,254,415			0.5	$                      225,000	$3,125,000	$   1,875,000	$2,075,000	$15,499,096	$5,499,096
	0.4	$5,700,770	$5,254,415			0.4	$                      180,000	$3,170,000	$   1,902,000	$2,102,000	$15,700,770	$5,700,770
	0.3	$5,902,445	$5,254,415			0.3	$                      135,000	$3,215,000	$   1,929,000	$2,129,000	$15,902,445	$5,902,445
	0.2	$6,104,120	$5,254,415			0.2	$                        90,000	$3,260,000	$   1,956,000	$2,156,000	$16,104,120	$6,104,120
	0.1	$6,305,795	$5,254,415			0.1	$                        45,000	$3,305,000	$   1,983,000	$2,183,000	$16,305,795	$6,305,795
	0	$6,507,470	$5,254,415			0	$                                  -	$3,350,000	$   2,010,000	$2,210,000	$16,507,470	$6,507,470
						THRESHOLD PROBABILITY OF TAX	0.6215
	Probability of Carbon tax	Expected NPV of Indirect CTL	Expected NPV of Direct CTL
	0	$6,507,470	$5,254,415
	0.1	$6,305,795	$5,254,415
	0.2	$6,104,120	$5,254,415
	0.3	$5,902,445	$5,254,415
	0.4	$5,700,770	$5,254,415
	0.5	$5,499,096	$5,254,415
	0.6	$5,297,421	$5,254,415
	0.6215	$5,254,060	$5,254,415
	0.7	$5,095,746	$5,254,415
	0.8	$4,894,071	$5,254,415
	0.9	$4,692,396	$5,254,415
	1	$4,490,721	$5,254,415
												Book1 Microsoft Excel Home Insert Page Layout Formulas Dats Review View Developer Cut Σ AutoSum)" A Inherit Copy Fill 2T 스미 Merge & Center-s-% , Paste JFormat Painter B l' #글 逞 Conditional Format Cell Insert Delete Format Sort & Find & ler Filter Select Editing Formatting-as Table-styles Clipboard Font Alignment Number Sbyles Cells . G x Y g-PV(12%,20,-2310000) Annual Sales quantity in callons Sales price per gallon Annual sales in dollars Annual Operating cost 1500000 $2.50 $3,750,000 $300,000 Function Arquments Py Rate Nper 20 Pmt -2310000 -0.12 蔨 Annual Pre tax cash flo $3,450,000 20 -2310000 Income tax rate 0.40 Fy considering depreciabo 2,070,000 Depreciation per year Depreciation tax shield 240,000 Annual after tax cash flow 2,310,000 Discount rate - number $600,000 17254414.7 Returns the present value of an investment: the botal amourt that o series of future payments is worth now Rate stthe nterest rate per pered For exampie, use 6%/4 for quortety payments 6% APR . 12% Formula resut $17,254,415 Hee on this furctizn | οκ IĮ cancel Present Value(P) of annual cash flow (Using PV function of excel with Rate: 1296,Nper-20 Pmt-2310000) 20-23 100001 N=M-A Net Present value(NPV) $5,254415 Sheet1 Sheet2 , Sheet3 Edit 11:25 AM O Type here to search ENG 2/6/2018 Book1 Microsoft Excel Home Insert Page Layout Formulas Dats Review View Developer Cut Σ AutoSum)" A Ea Copy Fill 2T 스미 Merge & Center-s-% , Paste JFormat Painter B l' #글 逞 Conditional Format Cell Insert Delete Format Sort & Find & ler Filter Select Editing Formatting as Table Styles Clipboard Font Alignment Number Sbyles Cells x IAI| =PV(12%,20,-2210000) PV 29 H-G E Depreciation tax shield 200,000 Function Arquments Py Annual after tax cashflow 2,210,000 Discount rate Present Value(PV) of annual cash floy -0.12 Rate 112% Nper 20 Pmt -221000 蔨 20 Using PV function of excel with Rate-12%. Nper-20, Pmt:221 0000) -2210000 20-2210000 Fy = number -16507470.41 Returns the present value of on investment: the botal amounk that a series of future paymenks is worth now. EFFECT OF TAX ON CO2 Pmt is the payment made each period and cannot change over the lfe of the Amount of CO2 generated(Ton) Formua resut-$16,507,470 30000 (1500000 002) Hee on this furctizn 36 K 15J Carbon tax 450,000 37 トト Sheet1 /Sheet2 Sheet3 Edit O Type here to search ENG 1129AM 2/6/2018 Book1 Microsoft Excel Dats Review V Home Insert % Cut Ea Copy Page Layout Formulas ew Developer Σ AutoSum)" A Inhenit 11A A Paste Format Painter B 1 u. OrT스' =ミ读孛 Merge acenter, $ % , a-o Conditional as Tant Styles, Insert Delete Format Formatting 〒 as Table. Styles-I 2Clear〒 Clear Filter, Select- Editing 〒 Clipboard Font Alignment Number Cells K40 -FA/(12%, 20,-1940000) Amount of CO2 generated(Ton) 30000 1500000 0.02) 36 K15J Carbon tax 450,000 Pretax cash flow After tax cash flowithout considering depreciation) Annual cash floww with depreciation Present Value of Cash flovw (3350000-450000) 1,740,000 1,940,000 14490 (1740000+200000) 39 40 41 42 Using PV function of excel with Rate-12%,Nper-20, Pmt=1940000 SENSITVITY ANALYSIS L-K (1 N=PV(12%,20-11000000 43 T-450000*P K 3350000T 0.4) MEL+200000M) Probabili ty of Carbon NPV After tax Annual Cash Cash low with Present Value of Present Net of NPV of Direct ndirect CTL CTL Probability of $15 per ton carbon tax Expected carbon 44 tax Pretax cash flow flow depreciaton Cash flow Value 1、740,00 $4.490,721 $5,254,415 1450,000 $2,900,000o 45 Ready O Type here to search ^候DENG 12:01 PM 2/6/2018 Bookl Microsoft Excel Chart Tools Home InsertPage Layout Formulas Data Review iewDeveloper Designayout Format Change Save As Chart Type Template RowColumn Data Switch Select Chart Location Data Chart Layouts Chart Sbyles Chart 1 ected Probability of NPV of xpected NPV 59 60 61 62 63 64 65 $7,000,00o $6,000,000 $5,000,000 68 69 70 71 72 73 74 75 76 $4,000,000 Expected NPV of Indirect CTL Expected NPV of Direct CTL $3,000,000 $2,000,000 $1,000,000 80 81 0.2 0.4 0.6 0.8 1.2 Average: 3577697.142 Count: 39 Sum: 128797097,1-豳。凹-100% Ready O Type here to search ^ ヨENG 3:14 PM 2/6/2018