Book value method

The book value method is a business method for recording the depreciation of a good . It is a special case of geometric degressive depreciation . In this case, the decrease in value is reduced by a constant depreciation factor on the residual book value of the previous period.

Graphic for depreciation using the book value method

calculation

Formula for calculating the depreciation amount for a period: ${\displaystyle a_{t}}$

${\displaystyle a_{t}={\big (}1-{\sqrt[{T}]{\dfrac {R_{T}}{A}}}{\big )}*R_{t-1}\quad \Leftrightarrow \quad a_{t}=p*R_{t-1}}$

${\displaystyle p=1-{\sqrt[{T}]{\dfrac {R_{T}}{A}}}}$

Formula for calculating the book value of a period: ${\displaystyle R_{t}}$

${\displaystyle R_{t}=({\dfrac {R_{t}}{R_{t-1}}})*R_{t-1}\quad \Leftrightarrow \quad R_{t}=\alpha *R_{t-1}}$

${\displaystyle \alpha ={\dfrac {R_{t}}{R_{t-1}}}\quad \Leftrightarrow \quad {\sqrt[{T}]{\dfrac {R_{T}}{A}}}}$

${\displaystyle A}$ = Acquisition cost

${\displaystyle R_{T}}$ = Residual value

${\displaystyle R_{t}}$ = Book value at the end of the period ${\displaystyle t}$

${\displaystyle a_{t}}$ = Depreciation amount

${\displaystyle p}$ = Annual reduction in the depreciation amount

${\displaystyle \alpha }$ = Annual reduction in the residual book value

${\displaystyle T}$ = Period

${\displaystyle t}$ = Period

example

A machine with a value of 100,000 € should be written off over a period of 5 years. The residual value at the end of the last depreciation period is € 10,000

The degression amount is calculated as follows: ${\displaystyle p}$

The following applies: ${\displaystyle p=1-{\sqrt[{T}]{\dfrac {R_{T}}{A}}}}$

${\displaystyle p=1-{\sqrt[{5}]{\dfrac {10.000}{100.000}}}\approx 0{,}3690427}$

This results in the depreciation amounts as follows: ${\displaystyle a_{t}}$

The following applies: ${\displaystyle a_{t}=p*R_{t-1}}$

${\displaystyle a_{1}=p*R_{0}=0{,}3690427*100.000\approx 36.904{,}27}$

${\displaystyle a_{2}=p*(R_{1}-R_{0})=0{,}3690427*63.095{,}7344480193\approx 23.285{,}02}$

${\displaystyle a_{3}\approx 14.691{,}85}$

${\displaystyle a_{4}\approx 9.269{,}93}$

${\displaystyle a_{5}\approx 5.848{,}93}$

The degression amount is calculated as follows: ${\displaystyle \alpha }$

The following applies: ${\displaystyle \alpha ={\dfrac {R_{t}}{R_{t-1}}}}$

${\displaystyle \alpha ={\dfrac {R_{1}}{R_{0}}}\Leftrightarrow {\dfrac {R_{0}-a_{1}}{R_{0}}}={\dfrac {100.000-36.904{,}27}{100.000}}=0{,}6309573}$

The following applies: ${\displaystyle R_{t}=\alpha *R_{t-1}}$

${\displaystyle R_{1}=0{,}6309573*100.000=63.095{,}73}$

${\displaystyle R_{2}\approx 39.810{,}72}$

${\displaystyle R_{3}\approx 25.118{,}86}$

${\displaystyle R_{4}\approx 15.848{,}93}$

${\displaystyle R_{5}\approx 10.000}$

The depreciation plan is then as follows:

period	Depreciation amount ${\displaystyle a_{t}}$	Book value ${\displaystyle R_{t}}$
t = 0		€ 100,000
t = 1	€ 36,904.27	€ 63,095.73
t = 2	€ 23,285.02	€ 39,810.72
t = 3	€ 14,691.85	€ 25,118.86
t = 4	€ 9,269.93	€ 15,848.93
t = 5	€ 5,848.93	€ 10,000

literature

• Schildbach, Homburg, "Cost and Performance Accounting" 10th edition, Lucius & Lucius, Stuttgart, 2009, ISBN 978-3-8252-8312-4
• Freidach, "Kostenrechnung" 9th edition, Oldenburg Verlag, Munich, 2012, ISBN 978-3-4867-1645-0