Question

James is trying to figure out the optimal number of years to replace his machinery. The machinery will be replaced continously for the foreseeable future. The machinery costs

$35,000. The maintenance costs for each respective year are shown in the table below together with the salvage value of the machinery if it were to be sold in that year. James has decided to keep the machinery for at least 4 years but is uncertain whether a 4 or 5 year replacement period is most appropriate. The discount rate is 10% per annum and assume zero taxes.

Year 0 1 2 3 4 5

Initial cost -42,000   

Maintenance costs -2,800 -3,900 -5,000 -6,100 -7,200

Salvage value (if sold) 32,900 28,900 23,900 17,900 10,900

A. Using annuity equivalent method, determine the best replacement period for James (consider only 4 or 5 years).

B. Using perpetuity method, determine the best replacement period for James (consider only 4 or 5 years). Do you arrive with the same conclusion as part (a) above? Explain why?

C. If the salvage value of the machinery in year 5 turns out to be $14,000 rather than $10,900 as you initially expected, would you recommend James to replace the machinery in 4 or 5 years?

Answer 1

1) Annuity Equivalent Method

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	4 years	5 years
Compunding Factor @ 10%	1	0.9091	0.8264	0.7513	0.6830	0.6209
Initial Investment	(42,000.00)						(42,000.00)	(42,000.00)
Annual Maintenance Cost	-	(2,800.00)	(3,900.00)	(5,000.00)	(6,100.00)	(7,200.00)
PV of Annual Maintenance Cost	-	(2,545.45)	(3,223.14)	(3,756.57)	(4,166.38)	(4,470.63)	(13,691.54)	(18,162.17)
Salvage Value	-	-	-	-	17,900.00	10,900.00
PV of Salvage Value	-	-	-	-	12,225.94	6,768.04	12,225.94	6,768.04
Total							(43,465.60)	(53,394.13)

Best Replacement period for James is 4 years as outflow is lower than 5 years outflow

2) Perpetuity method

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	4 years	5 years
Compunding Factor @ 10% (CF)	1	0.9091	0.8264	0.7513	0.6830	0.6209
Initial Investment	(42,000.00)						(42,000.00)	(42,000.00)
Annual Maintenance Cost (AMC)	-	(2,800.00)	(3,900.00)	(5,000.00)	(6,100.00)	(7,200.00)
Perpetuity of AMC= AMC/CF	-	(3,080.00)	(4,719.00)	(6,655.00)	(8,931.01)	(11,595.67)	(23,385.01)	(34,980.68)
Salvage Value (SV)	-	-	-	-	17,900.00	10,900.00
Perpetuity of SV= SV/CF	-	-	-	-	26,207.39	17,554.56	26,207.39	17,554.56
Total							(39,177.62)	(59,426.12)

Best Replacement period for James is 4 years as outflow is lower than 5 years outflow

Answer for both method is same as it considers same outlfow, but only for perpectual period  

3) If the salvage value of the machinery in year 5 turns out to be $14,000

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	4 years	5 years
Compunding Factor @ 10%	1	0.9091	0.8264	0.7513	0.6830	0.6209
Initial Investment	(42,000.00)						(42,000.00)	(42,000.00)
Annual Maintenance Cost	-	(2,800.00)	(3,900.00)	(5,000.00)	(6,100.00)	(7,200.00)
PV of Annual Maintenance Cost	-	(2,545.45)	(3,223.14)	(3,756.57)	(4,166.38)	(4,470.63)	(13,691.54)	(18,162.17)
Salvage Value	-	-	-	-	17,900.00	14,000.00
PV of Salvage Value	-	-	-	-	12,225.94	8,692.90	12,225.94	8,692.90
Total							(43,465.60)	(51,469.27)

Best Replacement period for James is still 4 years as outflow is lower than 5 years outflow (increase in salvage value is lower than outflow)