Question

Milliken uses a digitally controlled dyer for placing intricate patterns on manufactured carpet squares for home and commercial use. It is purchased for $400,000. Its market value will be $310,000 at the end of the 1st year and drop by $48,000 per year thereafter to a minimum of $30,000. Operating costs are $20,000 the 1st year, increasing by 10% per year. Maintenance costs are only $8,000 the 1st year but will increase by 32% each year thereafter. Milliken’s MARR is 18%. Determine the optimum replacement interval for the dyer in years.

Answer 1

In optimum Replacement model one should replace the machine once the annual cost start increasing .

In the given problem the annual cost of operating the equipment in year 10 (i.e.144490.89) is more than as compared to WACC of year 9 ( i.e. 123288.86) so equipment should be replaced at the end of year 9 .

1	2	3	4	5	6	7	8	9	10	11	12
Year of service	Resale Value	Dep Cost = Purchase Price - Resale Value	Annual operating Cost	Annual Maint. Cost	Total running cost	Discounting Factor	Discounted running cost	Cumulative discounted Maint. Cost	Total Cost	Cumulative Dis. Factor	Weighted average annual cost
		Purchase Cost = 4,00,000			(4+5)				(3+9)		(10/11)
1	310,000.00	90,000.00	20,000.00	8,000.00	28,000.00	1.0000	28,000.00	28,000.00	118,000.00	1.00	118,000.00
2	262,000.00	138,000.00	22,000.00	10,560.00	32,560.00	0.8475	27,593.22	55,593.22	193,593.22	1.85	104,788.99
3	214,000.00	186,000.00	24,200.00	13,939.20	38,139.20	0.7182	27,390.98	82,984.20	268,984.20	2.57	104,840.89
4	166,000.00	234,000.00	26,620.00	18,399.74	45,019.74	0.6086	27,400.41	110,384.61	344,384.61	3.17	108,492.44
5	118,000.00	282,000.00	29,282.00	24,287.66	53,569.66	0.5158	27,630.64	138,015.24	420,015.24	3.69	113,823.36
6	70,000.00	330,000.00	32,210.20	32,059.71	64,269.91	0.4371	28,092.97	166,108.21	496,108.21	4.13	120,205.39
7	30,000.00	370,000.00	35,431.22	42,318.82	77,750.04	0.3704	28,801.07	194,909.28	564,909.28	4.50	125,602.31
8	30,000.00	370,000.00	38,974.34	55,860.85	94,835.19	0.3139	29,771.14	224,680.42	594,680.42	4.81	123,594.93
9	30,000.00	370,000.00	42,871.78	73,736.32	116,608.09	0.2660	31,022.20	255,702.62	625,702.62	5.08	123,228.86
10	30,000.00	370,000.00	47,158.95	97,331.94	144,490.89	0.2255	32,576.35	288,278.97	658,278.97	5.30	124,132.80

Note : 1. Computation of Discounting factor

Discount rate of money is 18% i.e. 0.18

Dicounting factor = ( V ^ r-1)

r = year

i = Rate of discount

2. It has been assumed that the useful life of machine is more than 10 years.