In many jurisdiction the annual depreciation rate for specific asset classes is specified in taxation law, or at least that is the case in Australia. As such for a calculation to be at all usable it must achieve that, not some Manager invented approximation.
The maths to achieve it is not difficult, but for clarity lets start with the simplest case and the OP example ie $5000 initial value and 20% annual depreciation
Straight line depreciation
This is identical to simple interest with a negative interest rate. The formula to calculate multi-year depreciation is
Substituting into this formula the asset book value can be calculate, shown below at yearly intervals for the next 5 years
Time in Years | Book Value | Interval depreciation |
---|---|---|
0 | 5000 | |
1 | 4000 | 1000 |
2 | 3000 | 1000 |
3 | 2000 | 1000 |
4 | 1000 | 1000 |
5 | 0 | 1000 |
As well as calculating deprecation for multiple years it can also be used to calculate the straight line depreciation for a fraction of a year. Shown below is for 1/12 of a year intervals.
Time in Years | Book Value | Interval depreciation |
---|---|---|
0.0000 | $5,000.00 | |
0.0833 | $4,916.67 | $83.33 |
0.1667 | $4,833.33 | $83.33 |
0.2500 | $4,750.00 | $83.33 |
0.3333 | $4,666.67 | $83.33 |
0.4167 | $4,583.33 | $83.33 |
0.5000 | $4,500.00 | $83.33 |
0.5833 | $4,416.67 | $83.33 |
0.6667 | $4,333.33 | $83.33 |
0.7500 | $4,250.00 | $83.33 |
0.8333 | $4,166.67 | $83.33 |
0.9167 | $4,083.33 | $83.33 |
1.0000 | $4,000.00 | $83.33 |
Of particular note, the value at 1 year is exactly 20% independent of interval it is calculated over. Now moving on to:
Declining Value
This is identical to compound interest with a negative interest rate. The formula to calculate multi-year depreciation is:
Substituting into this formula the asset book value can be calculate, shown below at yearly intervals for the next 5 years
Time in Years | Book Value | Interval depreciation |
---|---|---|
0 | $5,000.00 | |
1 | $4,000.00 | $1,000.00 |
2 | $3,200.00 | $800.00 |
3 | $2,560.00 | $640.00 |
4 | $2,048.00 | $512.00 |
5 | $1,638.40 | $409.60 |
As well as calculating deprecation for multiple years it can also be used to calculate the declining value depreciation for a fraction of a year. Shown below is for 1/12 of a year intervals.
Time in Years | Book Value | Interval depreciation |
---|---|---|
0.0000 | $5,000.00 | |
0.0833 | $4,907.88 | $92.12 |
0.1667 | $4,817.46 | $90.42 |
0.2500 | $4,728.71 | $88.75 |
0.3333 | $4,641.59 | $87.12 |
0.4167 | $4,556.07 | $85.51 |
0.5000 | $4,472.14 | $83.94 |
0.5833 | $4,389.74 | $82.39 |
0.6667 | $4,308.87 | $80.87 |
0.7500 | $4,229.49 | $79.38 |
0.8333 | $4,151.56 | $77.92 |
0.9167 | $4,075.08 | $76.49 |
1.0000 | $4,000.00 | $75.08 |
Of particular note, the value at 1 year is exactly 20% independent of interval it is calculated over. Any calculation method which does not achieve this does not meet taxation regulation requirements.