Question

The Lake Charles Chemicals LLC is considering investing in a new gas to liquids technology. R&D scientists and engineers are investigating a new liquid-based catalyst system that will enable to operate the reactor at lower temperature and pressure to achieve higher conversion efficiencies. The company expects a three-year R&D period before they start producing the product as a commercial commodity. The following financial information is presented for management review. • R&D Cost: $6.5 million over a three-year period: $1 million at the beginning of year; $2.5 million at the beginning of year 2; and $3 million at the beginning of year 3. For tax purposes, these R&D expenditures will be expensed rather than amortized. Capital investment: $5 million at the beginning of year 4. This investment consists of $2 million in a building and $3 million in plant equipment. The company already owns a piece of land as the building site. Financing: The company also borrowed $2 million from a national bank at 25% interest at the beginning of year 4. Depreciation method: The building is depreciated based on straight line depreciation method and the plant equipment is depreciated based on double-declining balance method. Project life: 10 years after a three-year R&D period. Salvage value: 10% of the initial capital investment for the equipment and 50% for the building (at the end of the project life) Total Sales: $50 million (at the end of year 4), with an annual sales growth rate of 10% per year (compound growth) during the next five years (year 5 through year 9) and - 10% (negative compound growth) per year for the remaining project life. Out-of-pocket expenditures: 80% of annual sales. Working Capital: $5 million is considered as an investment at the beginning of year 4 and fully recovered at the end of project life. • Marginal tax rate: 40% a) Determine the net after-tax cash flows over the project life b) Determine the IRR for this investment c) Determine the equivalent annual worth for the investment at MARR = 20%

Answer 1

		Year	4	5	6	7	8	9	10	11	12	13
	A	Depreciation of Building($2million-$1million)/10	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000
		Depreciation of Equipment :
	B	Book Value at beginning of Year	$3,000,000	$2,400,000	$1,920,000	$1,536,000	$1,228,800	$983,040	$786,432	$629,146	$503,316	$402,653
	C	Depreciation Rate =(1/10)*200%	20%	20%	20%	20%	20%	20%	20%	20%	20%	20%
	D=B*C	Annual Depreciation	$600,000	$480,000	$384,000	$307,200	$245,760	$196,608	$157,286	$125,829	$100,663	$80,531
	E=B-D	Book Value at End of Year	$2,400,000	$1,920,000	$1,536,000	$1,228,800	$983,040	$786,432	$629,146	$503,316	$402,653	$322,123
	F=A+D	Total Annual Depreciation Expenses(Building+equipment)	$700,000	$580,000	$484,000	$407,200	$345,760	$296,608	$257,286	$225,829	$200,663	$180,531
		Salvage Cash Flows:
	G	After Tax Salvage Value of Building	$1,000,000
	H	Before tax Salvage Value of Equipment=10%*$3million)	$300,000
	I	Book Value at end of year13	$322,123
	J=I-H	Loss on Salvage	$22,123
	K=J*40%	Tax Saving on Loss(40%*22123)	$8,849
	L=H+K	After Tax Salvage Cash Flow from Equipment	$308,849
	M=G+L	Total Salvage Cash Flow at end of year 13	$1,308,849
				($1,000,000) ($2,500,000) ($3,000,000) ($5,000,000) $2,000,000 e=d*80% Year R & D Cash flows Capital Investment Financing (borrowed) Total Sales Out of pocket expenses Depreciation expenses Interest expenses(25%*$2million) Before tax Profit After Tax Profit (tax rate=40%) Add: Depreciation (Non cash expenses) After tax annual cash flow Working Capital Cash Flow Terminal Salvage Cash Flows: Return of Principal borrowed Net Cash Flow Present Value of Cash Floew Net Present Value Internal Rate of Return h=d+e+f+g p=g*(1-0.4) $50,000,000 ($40,000,000) ($ 700,000) ($500,000) $8,800,000 $5,280,000 $700,000 $5,980,000 ($5,000,000) $55,000,000 $60,500,01 ($44,000,000) ($48,400,00 ($580,000) ($484,0 ($500,000) ($500,00 $9,920,000 $11,116,01 $5,952,000 $6,669,6 $580,000 $484, $6,532,000 $7,153,6 j=p+i ($ 2,500,000) ($2,083,333) ($3,000,000) ($2,083,333) ($3,000,000) ($1,736,111) $980,000 $472,608 $6,532,000 $2,625,064 $7,153,6 $2,395,7 CF=a+b+c+j+k+l+m PV=CF/(1.2"n) NPV=Sum of PV IRR ($1,000,000) ($1,000,000) $8,761,499 37.76% (Using IRR function of excel over Net Cash Flow) Equivalent Annual Worth $1.932,962 (Using PMT function of excel with Rate=20%, Nper=13, Pv=NPV=-8761499) SUUD e=d*80% h=d+e+f+g prg*(1-0.4) Year 9 10 12 R&D Cash flows Capital Investment Financing (borrowed) Total Sales $60,500,000 $66,550,000 $73,205,000 $80,525,500 $72,472,950 $65,225,655 $58,703,090 $52,832,781 Out of pocket expenses ($48,400,000) ($53,240,000) ($58,564,000) ($ 64,420,400) ($57,978,360) ($52,180,524) ($46,962,472) ($42,266,224) Depreciation expenses ($ 484,000) ($407,200) ($345,760) ($296,608) ($257,286) ($225,829) ($ 200,663) ($180,531) Interest expenses(25%*$2 million) ($500,000) ($500,000) ($500,000)| ($500,000)! ($500,000) ($500,000) ($500,000) ($500,000) Before tax Profit $11,116,000 $12,402,800 $13,795,240 $15,308,492 $13,737,304 $12,319,302 $11,039,955 $9,886,025 After Tax Profit (tax rate=40%) $6,669,600 $7,441,680 $8,277,144 $9,185,095 $8,242,382 $7,391,581 $6,623,973 $5,931,615 Add: Depreciation (Non cash expense: $484,000 $407,200 $345,760 $296,608 $257,286 $225,829 $200,663 $180,531 After tax annual cash flow $7,153,600 $7,848,880 $8,622,904 $9,481,703 $8,499,669 $7,617,410 $6,824,636 $6,112,146 Working Capital Cash Flow $5,000,000 Terminal Salvage Cash Flows: $1,308,849 Return of Principal borrowed ($2,000,000) Net Cash Flow $7,153,600 $7,848,880 $8,622,904 $9,481,703 $8,499,669 $7,617,410 $6,824,636 $10,420,995 SUM Present Value of Cash Floew $2,395,726 $2,190,478 $2,005,412 $1,837,618 $1,372,744 $1,025,212 $765,428 $973,987 $8,761,499 Net Present Value Internal Rate of Return j=p+i CF=a+b+c+j+k+l+m PV=CF/(1.21n) NPV=Sum of PV IRR Equivalent Annual Worth Clipboard Font Alignment Number Styles Cells Editing H36 X F EIRR(H33:033) K L M HI $1,308,849 ($1,000,000) ($2,500,000) ($3,000,000) ($5,000,000) $2,000,000 17 M=G+L 18 n 19 a 20 b 21 C 22 d 23 e=d*80% 24 f 25 g 26 h=d+e+f+g 27 p=g*(1-0.4) 28 29 j=p+i Total Salvage Cash Flow at end of year 13 Year R&D Cash flows Capital Investment Financing (borrowed) Total Sales Out of pocket expenses Depreciation expenses Interest expenses(25%*$2million) Before tax Profit After Tax Profit (tax rate=40%) Add: Depreciation (Non cash expenses) After tax annual cash flow Working Capital Cash Flow Terminal Salvage Cash Flows: Return of Principal borrowed Net Cash Flow Present Value of Cash Floew Net Present Value Internal Rate of Return $50,000,000 ($40,000,000) ($700,000) ($500,000) $8,800,000 $5,280,000 $700,000 $5,980,000 ($5,000,000) $55,000,000 ($44,000,000) ($580,000) ($500,000) $9,920,000 $5,952,000 $580,000 $6,532,000 30 k 311 32 m 33 CF=a+b+c+j+k+l+m 34 PV=CF/(1.2^n) 35 NPV=Sum of PV 36 IRR $980,000 $472,608 $6,532,000 $2,625,064 ($1,000,000) ($2,500,000) ($3,000,000) ($3,000,000) ($1,000,000) ($2,083,333) ($2,083,333) ($1,736,111) $8,761,499 37.76% (Using IRR function of excel over Net Cash Flow) H38 X fc =PMT(20%,13,-H35) M=G+L $1,308,849 ($1,000,000) ($2,500,000) ($3,000,000) ($5,000,000) $2,000,000 $59 e=d*80% h=d+e+f+g p=g*(1-0.4) $ Total Salvage Cash Flow at end of year 13 Year R&D Cash flows Capital Investment Financing (borrowed) Total Sales Out of pocket expenses Depreciation expenses Interest expenses(25%*$2million) Before tax Profit After Tax Profit (tax rate=40%) Add: Depreciation (Non cash expenses) After tax annual cash flow Working Capital Cash Flow Terminal Salvage Cash Flows: Return of Principal borrowed Net Cash Flow Present Value of Cash Floew Net Present Value Internal Rate of Return $50,000,000 ($40,000,000) ($700,000) ($500,000) $8,800,000 $5,280,000 $700,000 $5,980,000 ($5,000,000) $ j=p+i S k m $980,000 $472,608 $ $: CF=a+b+c+j+k+l+m PV=CF/(1.2^n) NPV=Sum of PV IRR ($1,000,000) ($2,500,000) ($3,000,000) ($3,000,000) ($1,000,000) ($2,083,333) ($2,083,333) ($1,736,111) $8,761,499 37.76% (Using IRR function of excel over Net Cash Flow) 38 39 Equivalent Annual Worth $1,932,962 (Using PMT function of excel with Rate=20%, Nper=13, Pv=NPV=-876