Question

A company is considering replacing an existing machine (defender) with newer machine (challenger). If repaired, the defender can be used for another 5 years. The current market value of the defender is $8,200 (i.e., it can be sold now for $8,200). The operating cost of the defender is $2,200 during the first year which will increase 40% per year every year after the overhaul. Future market values are expected to decline by 35% per year. The new machine (challenger) has a service life of 7 years. It will cost $9,900 to purchase now. Its annual operation and maintenance cost is $1,850 per year in the first year. This annual operation and maintenance cost will increase by 35% per year for subsequent years. The market value of the challenger will decline by 31% every year over its service life. Use MARR equals 8%.

a] Create table showing the market value and annual operation and maintenance costs for the defender and the challenger for the next seven years.

[b] Find the economic lives of: [i] the defender and [ii] the challenger.

[c] Determine when the defender should be replaced (if any).

Write out the related equation

Answer 1

	a)
		Current Market Value	$8,200
		Defender
		Year	1	2	3	4	5	6	7
		Market Value(at the year end)-35% decline in each year	$5,330	$3,464.50	$2,251.93	$1,463.75	$951.44	$618.43	$401.98
		Operation and Maintenance Cost(Yearly)(increases by 40% every year)	$2,200	$3,080	$4,312	$6,037	$8,452	$11,832	$16,565
		Current Market Value	$9,900
		Challenger
		Year	1	2	3	4	5	6	7
		Market Value	$6,831	$4,713.39	$3,252.24	$2,244.04	$1,548.39	$1,068.39	$737.19
		Operation and Maintenance Cost(Yearly)(increases by 35% every year)	$1,850	$2,497.50	$3,371.63	$4,551.69	$6,144.79	$8,295.46	$11,198.87

b)

b)	Economic life is the period over which an entity expects to be able to use an asset, assuming a normal level of usage and preventive maintenance.
	i=0.08
	Defender
		a	b	c=a*b	d	e	f	g	h	i
	End of year	Maintenance cost at year end	Discounting rate at 8%	Present worth of Maintenance cost	Summation of present worth	Present worth of cumulative maintenance cost and first cost	i(1+i)^n	(1+i)^n-1	coloum f/coloum g	Annual equivalent total cost through year given
	1					8200			1.080	$            8,856.00
	2	$     2,200.00	0.926	$     2,037.04	$     2,037.04	$                10,237.04	0.093	0.166	0.561	$            5,740.62
	3	$     3,080.00	0.857	$     2,640.60	$     4,677.64	$                14,914.68	0.101	0.260	0.388	$            5,787.39
	4	$     4,312.00	0.794	$     3,423.00	$     8,100.65	$                23,015.32	0.109	0.360	0.302	$            6,948.80
	5	$     6,036.80	0.735	$     4,437.23	$   12,537.87	$                35,553.20	0.118	0.469	0.250	$            8,904.53
	6	$     8,451.00	0.681	$     5,751.61	$   18,289.48	$                53,842.68	0.127	0.587	0.216	$          11,647.00
	7	$   11,832.13	0.630	$     7,456.25	$   25,745.73	$                79,588.41	0.137	0.714	0.192	$          15,286.74
	8	$   16,564.98	0.583	$     9,665.51	$   35,411.24	$              114,999.65	0.148	0.851	0.174	$          20,011.64
	The economic life of machine is for 2 years since the annual equivalent total cost is minimum at the end of year 2
	Challenger
		a	b	c=a*b	d	e	f	g	h	i
	End of year	Maintenance cost at year end	Discounting rate at 8%	Present worth of Maintenance cost	Summation of present worth	Present worth of cumulative maintenance cost and first cost	i(1+i)^n	(1+i)^n-1	coloum f/coloum g	Annual equivalent total cost through year given
	1					$9,900.00			1.080	$          10,692.00
	2	$     1,850.00	0.926	$1,712.96	$1,712.96	$11,612.96	0.093	0.166	0.561	$            6,512.19
	3	$     2,497.50	0.857	$2,141.20	$3,854.17	$15,467.13	0.101	0.260	0.388	$            6,001.76
	4	$     3,371.63	0.794	$2,676.51	$6,530.68	$21,997.80	0.109	0.360	0.302	$            6,641.59
	5	$     4,551.69	0.735	$3,345.63	$9,876.30	$31,874.11	0.118	0.469	0.250	$            7,983.08
	6	$     6,144.79	0.681	$4,182.04	$14,058.34	$45,932.45	0.127	0.587	0.216	$            9,935.90
	7	$     8,295.46	0.630	$5,227.55	$19,285.89	$65,218.34	0.137	0.714	0.192	$          12,526.64
	8	$   11,198.87	0.583	$6,534.43	$25,820.32	$91,038.67	0.148	0.851	0.174	$          15,842.07
	The economic life of machine is for 3 years since the annual equivalent total cost is minimum at the end of year 3

c)

The defender can be replaced by the year end of 2 since the cost of maintenance is very high after the year end.