Question

Consider the following EOY cash flows for two mutually exclusive alternatives (one must be chosen). The MARR is 12% per year. Capital Investment Annual expenses Useful life Market value at end of useful life Lead Acid $8,000 $2,250 12 years $0 Lithium lon $13,000 $2,300 18 years $2,800 Click the icon to view the interest and annuity table for discrete compounding when /= 12% per year. (a) Determine which altemative should be selected based on the PW method. Assume repeatabllity and use a study period of 36 years. The PW of the Lead Acid is $ (Round to the nearest hundreds.) The PW of the Lithium Ion is $ (Round to the nearest hundreds.) Which alterative should be selected? Choose the correct answer below. O O Lithium Ion Lead Acid (b) Would the selected alternative remain the same if the MARR were 6%?. The PW of the Lead Acid is $ . (Round to the nearest hundreds.) The PW of the Lithium Ion is $ (Round to the nearest hundreds.) Which alternative should be selected? Choose the correct answer below. O A Lead Acid O B. Lithium Ion

Answer 1

	Present Value (PV) of Cash Flow=(Cash Flow)/((1+i)^N)
	i=discount rate=MARR=12%=0.12
	N=Year of Cash Flow
	ANALYSIS OF CASH FLOW FOR LEAD ACID
		N	A	B	C	CF	PV=CF/(1.12^N)
		Year	Cash outFlow first investment	Cash outflow for first repeat	Cash outflow for second repeat	Net Cash outFlow	Present Value of NetCash outFlow
		0	$8,000			$8,000	$8,000
		1	$2,250			$2,250	$2,009
		2	$2,250			$2,250	$1,794
		3	$2,250			$2,250	$1,602
		4	$2,250			$2,250	$1,430
		5	$2,250			$2,250	$1,277
		6	$2,250			$2,250	$1,140
		7	$2,250			$2,250	$1,018
		8	$2,250			$2,250	$909
		9	$2,250			$2,250	$811
		10	$2,250			$2,250	$724
		11	$2,250			$2,250	$647
		12	$2,250	$8,000		$10,250	$2,631
		13		$2,250		$2,250	$516
		14		$2,250		$2,250	$460
		15		$2,250		$2,250	$411
		16		$2,250		$2,250	$367
		17		$2,250		$2,250	$328
		18		$2,250		$2,250	$293
		19		$2,250		$2,250	$261
		20		$2,250		$2,250	$233
		21		$2,250		$2,250	$208
		22		$2,250		$2,250	$186
		23		$2,250		$2,250	$166
		24		$2,250	$8,000	$10,250	$675
		25			$2,250	$2,250	$132
		26			$2,250	$2,250	$118
		27			$2,250	$2,250	$106
		28			$2,250	$2,250	$94
		29			$2,250	$2,250	$84
		30			$2,250	$2,250	$75
		31			$2,250	$2,250	$67
		32			$2,250	$2,250	$60
		33			$2,250	$2,250	$53
		34			$2,250	$2,250	$48
		35			$2,250	$2,250	$43
		36			$2,250	$2,250	$38
						SUM	$29,013
	PW of LEAD ACID is	$29,013
								ANALYSIS OF CASH FLOW FOR LITHIUM ION Year CF P V=CF/(1.124N) Cash Cash Present outFlow outflow Net Value of first for first Cash NetCash investment repeat outFlow outFlow 0 $13,000 $13,000 $13,000 1 $2,300 $2,300 $2,054 2 $2,300 $2,300 $1,834 3 $2,300 $2,300 $1,637 $2,300 $2,300 $1,462 5 $2,300 $2,300 $1,305 $2,300 $2,300 $1,165 7 $2,300 $2,300 $1,040 8 $2,300 $2,300 $929 9 $2,300 $2,300 $829 10 $2,300 $2,300 $741 11 $2,300 $2,300 $661 12 $2,300 $2,300 $590 13 $2,300 $2,300 $527 14 $2,300 $2,300 $471 15 $2,300 $2,300 $420 16 $2,300 $2,300 $375 17 $2,300 $2,300 $335 ($500) $13,000 $12,500 $1,625 $2,300 $2,300 $267 $2,300 $2,300 $238 $2,300 $2,300 $213 $2,300 $2,300 $190 $2,300 $2,300 $170 $2,300 $2,300 $152 (2300-2800)=-500 (Market Value=2800) (2300-2800)=-500 (Market Value=2800) $2,300 $2,300 $2,300 $2,300 ($500) $13,000 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 ($500) ANALYSIS OF CASH FLOW FOR LITHIUM ION MARR=12% $2,300 $2,300 $2,300 $2,300 $12,500 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 ($500) SUM $471 $420 $375 $335 $1,625 $267 $238 $213 $190 $170 $152 $135 $121 $108 $96 $86 $77 $69 $61 $55 $49 $44 36 ($8) $33,122 PW of LITHIUM ION is $33,122 ALTERNATIVE LEAD ACID IS RECOMMENDED ANALYSIS OF CASH FLOW FOR LEAD ACID ABC CF PV=CF/(1.06^N) Cash Cash Cash outflow outFlow outflow for Present Value first for first second of NetCash Year investment repeat repeat Net Cash outFlow outFlow O $8,000 $8,000 $8,000 $2,250 $2,250 $2,123 $2,250 $2,250 $2,002 $2,250 $2,250 $1,889 $2,250 $2,250 $1,782 $2,250 $2,250 $1,681 $2,250 $2,250 $1,586 $2,250 $2,250 $1,496 $2,250 $2,250 $1,412 $2,250 $2,250 $1,332 $2,250 $2,250 $1,256 $2,250 $2,250 $1,185 $2,250 $8,000 $10,250 $5,094 $2,250 $2,250 $1,055 $2,250 $2,250 $995 $2,250 $2,250 $939 $2,250 $2,250 $886 $2,250 $2,250 $836 $2,250 $2,250 $788 $2,250 $2,250 $744 $2,250 $2,250 $702 $2,250 $2,250 $662 $2,250 $2,250 $624 $2,250 $2,250 $589 $2,250 $8,000 $10,250 $2,532 $2,250 $2,250 $524 ANALYSIS OF CASH FLOW FOR LEAD ACID $2,250 (Ctrl) $8,000 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $10,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,250 $2,532 $524 $495 $467 $440 $415 $392 $370 $349 $329 $310 $293 $276 $46,849 SUM PW of LEAD ACID is $46,849 ANALYSIS OF CASH FLOW FOR LITHIUM ION N A CFPV=CF/(1.06AN) Year 0 1 2 B Cash Cash outFlow outflow first for first investment repeat $13,000 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 Net Cash Present Value of outFlow NetCash outFlow $13,000 $13,000 $2,300 $2,170 $2,300 $2,047 $2,300 $1,931 $2,300 $1,822 $2,300 $1,719 $2,300 $1,621 $2,300 $1,530 $2,300 $1,443 $2,300 $1,361 $2,300 $1,284 10 9 10 11 ANALYSIS OF CASH FLOW FOR LITHIUM ION 12 (Ctrl) 15 16 17 18 (2300-2800)-500 (Market Value=2800) $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 ($500) $13,000 $12,500 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 $2,300 ($500) $500) SUM $1,361 $1,284 $1,212 $1,143 $1,078 $1,017 $960 $905 $854 $4,379 $760 $717 $677 638 $602 $568 $536 $506 $477 $450 $424 $400 $378 $356 $336 $317 $299 (561) $49,858 36 PW of LITHIUM ION is $49,858 ALTERNATIVE LEAD ACID IS RECOMMENDED