Depreciation
Depreciation
Depreciation is an allowable tax deduction for people in many occupations. On MT
Pockets’ next tax return she will be able to claim depreciation on her new computer.
Consider the following my young apprentice.
Depreciation is the loss in value of assets. Depreciation can be calculated in two ways.
- Straight line depreciation occurs when the value of an asset decreases by a constant
amount each year.
- Declining balance depreciation occurs when the salvage value of an item is a
percentage of the previous year's value.
For straight line depreciation: S = V0 – Dn
Where S = salvage (current) value of the asset
D = amount of depreciation apportioned per period
V0 = purchase price of the asset
n = total number of periods
For declining balance depreciation: S = V0(1 - r)n
where S = the salvage value after n periods
V0 = purchase price of the asset
r = the percentage interest rate per period, expressed as a decimal
In the activities that follow, you will compare the value of an asset when depreciated
by the reducing balance method. You will also calculate the tax deductions allowed for
certain items as they depreciate in value.
Go to depreciation.xls (Excel 148kB)
Depreciation
Comparing depreciation: Questions
MT Pockets has recently purchased a new car for $30 000. Use the depreciation
schedule to investigate the declining value of MT's new asset and to compare the
methods of depreciation.
1. MT Pockets recently purchased a new car for $30 000. Using the straight line
method with a depreciation rate of 20%, what would be the value of MT’s car after
3 years?
2. Using the declining balance method and a depreciation rate of 35%, find by how
much MT Pockets’ car depreciates in the 2nd year.
3. Using the straight line method, in how many years will MT Pockets’ car be ‘written
off’ (ie depreciate to a value of zero)?
4. Will the value of MT Pockets’ car ever actually reach zero using the declining
balance method? Explain.
5. An item is depreciated by the straight line method, with a depreciation rate of 20%.
How does changing the purchase price affect the salvage value of the item after 5
years? Why is this so? In how many years would an item depreciating at 10% pa
be ‘written off’?
6. What is the minimum straight line depreciation rate that would reduce an item’s
salvage value to zero within 4 years?
7. A luxury car has a purchase price of $100 000 and is depreciated at the rate of 20%
pa. Find the difference in the salvage value after 5 years, obtained by each
method?
8. Study the formula for cell E13. Explain how the spreadsheet calculates the values
that appear in this cell.
9. Using the declining balance method, what is the minimum rate of depreciation that
would reduce the salvage value of MT Pockets’ car to less than $1000 in 5 years?
Give your answer to 1 decimal place.
10. In reality, the value of assets such as a motor vehicle has greatest depreciation in
the first years and becomes less in later years. Which method of depreciation best
models this situation? Explain.
Depreciation
Comparing depreciation: Answers
1. $12 000
2. $6825
3. Using the straight line method, MT Pockets’ car will be ‘written off’ in 5 years.
4. Under declining balance depreciation, the value of an asset never actually reaches
zero. This is so because this type of depreciation is an example of exponential
decay. The horizontal axis is called an ‘asymptote’ because the curve approaches
but never touches it. For a rate of 95.6% or greater, the spreadsheet returns a
salvage value in the 5th year of $0.00 because values in this column are rounded to
2 decimal places. Whilst all values in the spreadsheet are given correct to the
nearest cent, it is usual practice in accounting to round off to the nearest dollar.
For a rate of 89% or greater the spreadsheet returns a salvage value of $0, rounded
to the nearest dollar. In a practical sense it would also be unrealistic to expect the
salvage value of an item to be calculated to the nearest dollar, let alone to the
nearest cent.
5. The salvage value is $0 for all values of the purchase price. This is so because the
value of the item depreciates by 20% of the purchase price each year, for 5 years
(ie 5 x 20% = 100%). An item depreciating at 10% pa would be ‘written off’ in 10
years.
6. 25%
7. $32 768
8. The spreadsheet multiplies the value of the item in the previous year (F12) by the
rate of depreciation (E6).
9. A rate of 49.4% pa will reduce the value of MT Pockets’ car to $995.12 by the end
of the 5th year.
10. The straight line method assumes that an asset depreciates by the same amount
each year, whereas the declining balance method reduces the value of the asset by
a constant percentage each year. Consequently, the declining balance method
best models what happens to this kind of asset in the real world.
Depreciation
Tax deductions: Questions
Go to the ‘Tax deductions’ spreadsheet. This table will list the value of (1-r)n to 4
decimal places for different values of r and n and can be used to calculate the salvage
value of an item. By first following the instructions below we will examine the tax
deductions that can be made for certain items as they depreciate in value.
Complete the table above by following these steps:
i. In cell C6 enter the formula: =(1-C$5)^$B6
ii. Highlight the row C6 to L6 then go to the Edit menu and click on the Fill Right
command.
iii. Highlight the block C6 to L15 then go to the Edit menu and click on the Fill
Down command.
[If you have opened this spreadsheet with Excel 2007, drag the fill handle in cell
C6 across to cell L6 and then down to cell L15.]
Answer the questions below.
1. An item is purchased for $500 and depreciates at a rate of 25% pa. Use the table
to calculate the value of the item after 6 years.
2. Assuming a depreciation rate of 15% pa, how long would it take for an item with a
purchase price of $1000 to depreciate to less than a quarter of its original value?
3. The company that MT Pockets works for purchases a new delivery van on the 1st
July for $40 000 and uses the declining balance method of depreciation with a
depreciation rate of 30% pa. Calculate the amount that the delivery van will
depreciate by in the first year.
4. If the delivery van in question (3) was replaced after 3 years, what would be its
trade-in value?
5. What tax deduction could the company in question (3) make for depreciation of
the delivery van for the 3rd year?
6. On the first day of the current financial year MT Pockets purchased a new
computer for $4000. A tax deduction for depreciation of the computer is allowed
at the rate of 35% pa. Use the table to determine what would be the value of the
computer after 5 years? Return to the Comparing Depreciation spreadsheet and
enter the same data. How do you account for the difference?
Depreciation
7. When the value of MT Pockets’ computer falls below $1000, the computer can be
‘written off’. After how many years will this occur?
8. How much can MT Pockets claim on her tax return for the current financial year for
depreciation of her computer? [Key Question]
9. If the effective life of MT Pockets’ computer is considered to be 4 years with no
salvage value, what would be the yearly tax deduction using the straight line
method of depreciation?
10. What is the total amount that MT Pockets could claim as a tax deduction for
depreciation in 4 years using the declining balance method?
Tax deductions: Answers
1. 0.1780 x $500 = $89.
2. In 9 years the item would have a value of $231.60
3. 0.3 x $40 000 = $12 000.
4. 0.3430 x $40 000 = $13 720.
5. 0.490 x $40 000 – 0.3430 x $40 000 = $5880.
6. 0.1160 x $4000 = $464. There is a difference of 12 cents. This is a ‘rounding error’
which occurs because of the rounding (to 4 decimal places) of the values in the
table.
7. After 4 years. The computer will then be worth $714.
8. MT Pockets can claim 0.35 x $4000 = $1400.
9. $4000 ÷ 4 = $1000.