Question

A roller conveyor system used to transport cardboard boxes along an order filling line costs $100 000 plus $20 000 to install. It is estimated to depreciate at a declining-balance rate of 25% per year over its 15-year useful life. Annual maintenance costs are estimated to be $6000 for the first year, increasing by 20% each year thereafter. In addition, every third year, the rollers must be replaced at a cost of $7000. Interest is at 10% (a) Construct a spreadsheet which has the following headings: Year, Salvage Value, Maintenance Costs, EAC(Capital Costs), EAC(Maintenance Costs), and EAC(Total Costs). Compute the EAC(Total Costs) if the conveyor were to be kept for years, n = 1,...,15. (6) Construct a chart showing the EAC(Capital Costs), EAC(Maintenance Costs), and EAC(Total Costs) if the conveyor were to be kept for years, = 1,...,15. (e) What is the economic life of the roller conveyor system?

Answer 1

Solution :

In the given question , there is no information of salvage value , however if we consider by definition the salvage value, which is the value of the asset at the end of the useful life in consideration of what the company expects to achieve. Assuming the company expects to receive in full the written down value at the end of 15th year, therefore we must make a depreciation calculation.

Salvage Value Calculation

Year	Opening Balance	Depreciation Rate	Depreciation	Closing Balance
1	120,000	25	30,000	90,000
2	90,000	25	22,500	67,500
3	67,500	25	16,875	50,625
4	55,875	25	13,698.75	41,906.25
5	42,176.25	25	10,544.06	31,632.19
6	31,632.19	25	7,908.06	23,724.14
7	23,724.14	25	5,931.04	17,793.11
8	17,793.11	25	4448.28	13,344.83
9	13,344.83	25	3,336.21	10,008.62
10	10,008.62	25	2,502.16	7,506.47
11	7,506.47	25	1,876.62	5,629.85
12	5,629.85	25	1,407.46	4,222.39
13	4,222.39	25	1,055.60	3,166.79
14	3,166.79	25	791.70	2,375.09
15	2,375.09	25	593.77	1,781.32

Now taking the Written down value of Roller system at 15th year of $ 1,781.32 as the salvage value.

Now let us construct the spread sheet having the mentioned headings given in the question

Year	Capital Cost of Roller System (a)		Maintenance Cost	Replacement cost at every third year	Total Cost	Salvage Value	Discounting factor @10% (e)	Present Value of salvage Value (f)	Net Cash Outlay g (a)-(f)	Annuity factor (Capital Cost) (Note) (h)	EAC (capital cost) i= g*h	EAC (maintenance cost) j= total of b * h	EAC (Total Cost)
0	120,000								119,573.81	0.1314	15,712	56,822	61,423
1			6000				0.9090
2			7200				0.8264
3			8640	7000	15640		0.7513
4			10368				0.6830
5			12441				0.6209
6			14293	7000	21293		0.5644
7			17916				0.5131
8			21499				0.4665
9			25799	7000	32799		0.4240
10			30959				0.3855
11			37150				0.3504
12			44581	7000	51581		0.3186
13			53497				0.2896
14			64196				0.2633
15			77035	7000	84035	1781	0.2393	426.19
		Total Maintenance Cost	432,211	Total Cost	467,211		7.6060

Note for Capital recovery factor formula:

Capitalrecovery factor = i(1+i)n/(1+i)n - 1

here i = interest rate ; 10%

n = no of years ;15 years

Calculating the figures based on the above formula, we get Capital recover factor, annuity of $1 is 0.1314

The above table is the answer for question a and b.

c) The economic life is 15 years as based on the assumption there is a salvage value at the end of 15th year, after that the asset would be nil.