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A manufacturing company makes it a policy that for every new equipment purchased, the annual depreciation...

A manufacturing company makes it a policy that for every new equipment purchased, the annual depreciation cost should not exceed 25% of the first cost at any time without salvage value. Determine the length of service life if the depreciation used is the SYD method

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A manufacturing company
We know, In SYD the largest depreciation charges is in first year.
So, d1= (C0-Cn)*(n/sum of years)
Where, d1= Depreciation in first year. C0= Cost of asset. Cn= Salvage value of asset.
As the annual depreciation cost should not exceed 25% of the first cost at any time without salvage value so the equation will reduce to:
.25C0= (C0-Cn)*(n/sum of years)
Or, 25C0/100= (C0-0)*(n/sum of years) because salvage value is zero.
Or, 25C0/100= C0*(n/sum of years)
Or, C0/4= C0*(n/sum of years)
Or, Sum of years= 4n
Now, using the A.P. formula for summation we know summation= n*(n+1)/2
Or, 4n= n*(n+1)/2
Or, 8n= n^2+n
Or, 8n-n= n^2
Or, 7n= n^2
Therefore n= 7 years.
So the length of service life if the depreciation used is the SYD method is 7 years.

ekkarill92 answered 1 year ago
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