# Digital depreciation

Digital depreciation is a business method for recording the depreciation of a good . It is a special case of the arithmetic-degressive depreciation . With this, the decrease in value decreases year after year by a constant amount. The special thing about digital depreciation is that this amount has to match the decrease in value in the last year.

The digital depreciation is calculated as follows:

${\ displaystyle a_ {T} = d = {\ frac {2 \ cdot AB} {T \ cdot (T + 1)}} = {\ frac {AB} {1 + 2 + \ dots + T}}}$ AB = depreciation basis = acquisition costs + incidental acquisition costs - residual value
${\ displaystyle a_ {T} =}$ Depreciation amount for the last period of the depreciation period
d = Annual reduction in the depreciation amount
T = period
t = period

## example

A machine with a value of 15,000 is to be digitally written off over a period of 4 years. Incidental acquisition costs and residual value are zero.

Then d is calculated as follows:

d = 2 x 15,000 / (4 x (4 + 1)) = 30,000 / 20 = 1,500

However, this is only the depreciation amount for the last period. The depreciation amount of the previous periods increases by this amount and can be determined for periods 1–3 as follows:

${\ displaystyle a_ {t} = (T-t + 1) \ cdot d}$ • Period 1: (4 - 1 + 1) 1,500 = 6,000
• Period 2: (4 - 2 + 1) 1,500 = 4,500
• Period 3: (4 - 3 + 1) 1,500 = 3,000

The depreciation plan is then as follows:

 period Depreciation amount Book value t = 0 15,000 t = 1 6,000 9,000 t = 2 4,500 4,500 t = 3 3,000 1,500 t = 4 1,500 0