Question

ABC Corporation makes it a policy that for any new equipment purchased, the annual depreciation cost should not exceed 25% of the first cost at any time with no salvage value. Determine the length of service life necessary if the depreciation used is the SYDmethod.

Answer 1

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ABC Corporation

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.