Question

3) Apex Silver Mines is considering whether to buy a new electrolytic refiner. The refiner costs $150,000, and will be depreciated using double declining-balance depreciation over its lifetime of seven years. The equipment is expected to generate $75,000 in increased silver production per year, in current dollars, and the company's tax rate is 40%. The company expects that silver prices will increase at an annual rate of 7%, while the general rate of inflation of other goods and services in the economy is estimated at 10% (a) Determine the before-tax cash flows for this investment for years 0 through 7, not considering inflation. ased silver prices. (b) Now, adjust the before-tax cash flows in years 1 through 7 to reflect (Note that these cash flows will be in nominal dollars.) (c) Compute the after-tax cash flows, and deflate them to show the after-tax cash flows in dollars of constant purchasing power. (d) Apex has stated that it wishes to earn a minimum acceptable rate of return of 20% after taxes, in real (constant) dollars. Under this criterion, is the new refiner a good investment?

Answer 1

		DEPRECIATION TAX SHIELD
	N	Year	1	2	3	4	5	6	7
	A	Book Value of asset at Year Beginning	$150,000	$107,143	$76,531	$54,665	$39,046	$27,890	$19,922
	B	Depreciation Rate =(1/7)*200%	28.57%	28.57%	28.57%	28.57%	28.57%	28.57%	28.57%
	C=A*B	Annual Depreciation	$42,857	$30,612	$21,866	$15,618	$11,156	$7,969	$5,692
	D=A-C	Book Value of asset at Year End	$107,143	$76,531	$54,665	$39,046	$27,890	$19,922	$14,230
	E=C*40%	Depreciation Tax Shield (Tax Rate=40%)	$17,143	$12,245	$8,746	$6,247	$4,462	$3,187	$2,277
	a)	Before tax cash flow , not considering inflation and increase in Silver Price
	N	Year	0	1	2	3	4	5	6	7
		Before tax Cash Flow	($150,000)	$75,000	$75,000	$75,000	$75,000	$75,000	$75,000	$75,000
	b)	BEFORE TAX CASH FLOW CONSIDERING INCREASE IN SILVER PRICE
		Silver Price in year (N+1)=1.07*(Silver Price in Year N)
	N	Year	0	1	2	3	4	5	6	7
		Before tax Cash Flow	($150,000)	$75,000	$80,250	$85,868	$91,878	$98,310	$105,191	$112,555
	c)	AFTER TAX CASH FLOW WITH INFLATION
	N	Year	0	1	2	3	4	5	6	7
	a	Before tax Cash Flow	($150,000)	$75,000	$80,250	$85,868	$91,878	$98,310	$105,191	$112,555
	b=a*40%	Taxes(Tax rate =40%)		($30,000)	($32,100)	($34,347)	($36,751)	($39,324)	($42,077)	($45,022)
	c	Depreciation Tax Shield		$17,143	$12,245	$8,746	$6,247	$4,462	$3,187	$2,277
	d=a+b+c	After tax cash flow (Nominal )	($150,000)	$62,143	$60,395	$60,267	$61,374	$63,448	$66,302	$69,810
	e=d/(1.1^N)	After tax cash flow at constant purchasing power (considering inflation)	($150,000)	$56,494	$49,913	$45,279	$41,919	$39,396	$37,426	$35,823	SUM
	PV=e/(1.2^N)	Present Value at discount rate of 20%	($150,000)	$47,078	$34,662	$26,203	$20,216	$15,833	$12,534	$9,998	$16,523
	NPV=Sum of PV	Net Present Value	$16,523
		Internal Rate of Return	24.34%	(Using IRR function of excel over After tax cash flow)
		The Refinery is a good investment
		Since, NPV is positive and IRR is greater than 20%
					Clipboard Font Allahment Number Styles Lens Editing F29 X f =IRR(F26:M26) M N O F $17,143 G $12,245 H $8,746 I $6,247 J $4,462 K $3,187 L $2,277 E=C*40% Depreciation Tax Shield (Tax Rate=40%) Before tax cash flow, not considering inflation and increase in Silver Price Year 0 1 2 Before tax Cash Flow ($150,000) $75,000 $75,000 3 $75,000 $75,000 $75,000 $75,000 $75,000 BEFORE TAX CASH FLOW CONSIDERING INCREASE IN SILVER PRICE Silver Price in year (N+1)=1.07*(Silver Price in Year N) Year 1 Before tax Cash Flow ($150,000) $75,000 0 2 $80,250 3 $85,868 4 $91,878 5 $98,310 6 7 $105,191 $112,555 AFTER TAX CASH FLOW WITH INFLATION 0 1 2 7 ($150,000) $75,000 $80,250 $85,868 $91,878 $98,310 $105,191 $112,555 ($30,000) ($32,100) ($34,347) ($36,751) ($39,324) ($42,077) ($45,022) $17,143 $12,245 $8,746 $6,247 $4,462 $3,187 $2,277 ($150,000) $62,143 $60,395 $60,267 $61,374 $63,448 $66,302 $69,810 Year Before tax Cash Flow b=a*40% Taxes(Tax rate -40%) Depreciation Tax Shield d=a+b+c After tax cash flow (Nominal) After tax cash flow at constant purchasing e=d/(1.1^N) power considering inflation) PV=e/(1.24N) Present Value at discount rate of 20% NPV=Sum of PV Net Present Value Internal Rate of Return $35,823 SUM $9,998 $16,523 ($150,000) $56,494 $49,913 $45,279 $41,919 $39,396 $37,426 ($150,000) $47,078 $34,662 $26,203 $20,216 $15,833 $12,534 $16,523 24.34% (Using IRR function of excel over After tax cash flow)