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Straight Line Depreciation
S = Vo – Dn
where S = salvage value
Vo = original value
D = amount of depreciation per period
n = number of periodsDeclining Balance
$$S=V_o(1-r)^n$$
S = Salvage value
Vo = Original value
r = reducible interest rate per period
n = number of periodsIn January 2004, the Coco Dog Food Company purchased a new packaging machine which cost $36500. After 3 years the salvage value of the machine was $12500.
a. If the straight line method is used, find the annual amount of depreciation.
b. If the declining balance method is used, find the annual depreciation rate, correct to 1 decimal place.
c. The company decides to sell the machine after 4 years. Which method of depreciation would you suggest the company use in order to gain the greatest tax benefit? Support your answer with mathematical calculations.a. Depreciation = $36,500 – $12,500
= $24,000 annually
= $24,000 ÷ 3
= $8,000b.12,500 = 36,500(1 – r)3
$$\frac{12,500}{36,500}=(1-r)^3$$
$$\sqrt[3]{{\frac{{25}}{{73}}}} = 1 – r$$
0.699636 = 1 – r
-0.30036 = -r
r = 0.300
∴ 30.0%c. after 4 years
Straight Line Method Declining Balance Method V = 36,500 – 4 × 8,000 = $4500
Total depreciation = $36,500 – $4,500
= $32,000V = 36,500(1 – 0.3)4 = $8763.65
Total depreciation = $36,500 – $8763.65
= $27,736.35∴ Greatest tax benefit will be with the straight line method as there is more tax deductions to claim
Time Years
0
1
2
3
4
5Value $
9400
8460
7614
6853
6167
5551The table shows the value of the Big Red carpet cleaning machine over 5 years.
What is the rate of the depreciation of the machine?look at any year’s drop – you only need to do one, but we have done a few to illustrate that it makes no difference which ones you pick
8460/9400 × 100 = 90% ie, it is 90% of what it used to be, so it depreciated by 10%
6853/7614 × 100 = 90.005%
5551/6167 × 100 = 90.01%
it won’t matter which two you pick, as long as they are consecutive, will always give you 90%
so if 90% is left, it depreciated by 10%pa
Ryan is a tradesman who receives a weekly salary of $1500. He bought new tools for $2600 on 30 September and calculates depreciation using the declining balance method at a rate of 12% per annum.
a. What is Ryan’s gross annual income?
b.Calculate Ryan’s taxable income for this financial year if the only tax deduction is the depreciation for his tools.
c. Use the tax table (below) to calculate Ryan’s tax payable.
d.What is the salvage value of the tools after the first financial year?
e. What is the allowable tax deduction in the next financial year?a. Income = $1,500 × 52
= $78,000b. 9 months worth of depreciation
$2,600 × 0.12 = $312
for the 9 months = $312 × 9/12
= $234
Taxable income = $78,000 – $234
= $77,766c.
TAXABLE INCOME TAX $0 – $6000 Nil Nil $6001 – $35,000 Nil 15c for each $1 in excess of $6000 $35,001 – $80,000 $4350 30c for each $1 in excess of $35,000 $80,001 – $180,000 $17,850 38c for each $1 in excess of $80,000 $180,001 and over $55,850 45c for each $1 in excess of $180,000 tax = $4,350 + 0.30(77,766 – 35,000)
= $17,179.80d. Value after first year = $2,600 – $234
= $2,366e. tax deduction after another year = $2,366 × 0.12
= $283.92Jill bought a new car for $55,000. In the first year the value of the car depreciated by 20%. In the second year, the car depreciated by 15%. In the third year, the value depreciated by 10%. What is the percentage value of the car now of its original price? = 55,000 × 80% × 85% × 90%
= $33,660
If the car went down by 20% – this means it is now only 80% of its original value (100% – 20% = 80%)
then it went down by 15%: 100% – 15% = 85%
then it went down by a further 10%: 100% – 10% = 90%
to find the value of the car now we can just multiply by each percent (rather than finding out individual values and subtracting) – this method is called ‘successive dicsounts’$$=\frac{33660}{55000}\times100
= 61.2%
now we need to find the value of the original as a percent, so the new value over the old value, times 100 A car was purchased for $20,000. It depreciates at a rate of 10% of its purchase price each year. What is the value of the car after 6 years?
Find 10% of the purchase price of $20,000
= 20 000 × 10%
= $2000Use the straight line depreciation formula: S = V0 – Dn
S = 20 000 – 2000 × 6
= $8000
A new piece of machinery is purchased for $245 000 and depreciates by 12% each year using the declining balance method. What is the value of the machine at the end of 4 years? S = 245 0000(1 – 0.12)4
= $146 925.36
use the depreciation formula S = V0(1 – r)n
V0 = 245 000 r = 0.15 n = 487 000 – 73 950 = $13 050 Originally $87 000 and now $73 950, so subtract to find the amount of depreciation, which is what can be claimed as a tax deduction A computer was worth $3700 and depreciates at 40%. Find:
a. the tax deduction for depreciation for the financial year
b. the value of the asset at the end of the financial year.a. 3700 × 40%
= $1480tax deduction = 40% of the original value b. S = 3700 × (1 – 0.4)1
= $2220Salvage Value
S = V0(1 – r)nA truck was bought for $87 000 on April 1. If it depreciates using the declining balance method at 15% p.a. find the amount of depreciation that can be claimed as a tax deduction that financial year. S = 87 000(1 – 0.15)1
= $73 950
15% = 15 ÷ 100
= 0.15 as a decimal
use the declining balance formula S = V0(1 – r)n
87 000 – 73 950
= $13 050
Originally $87 000 and now $73 950, so subtract to find the amount of depreciation, which is what can be claimed as a tax deduction A baker’s oven cost $8000 plus delivery and installation of $500. It is estimated to have a scrap value of $500 after a useful life of 5 years. What is the annual depreciation. 500 = 8500 – 5D S = V0 – Dn
s = scrap (salvage) value = 500
V0 = original value = 8500
D = depreciation amount = ?
n = number of years = 5500 = 8500 – 5D
-8000 = -5D
D = 1600
solve the equation for D – 8500 both sides divide both sides by -5 ∴ depreciates annually by $1600 A car is originally purchased for $39 900. 5 years later the car is valued at $20,400. What is the annual amount of depreciation? 20 400 = 39 900 – D × 5 Use the formula S = Vo – Dn
where S = 20,400, Vo = 39 990, n = 4-19 500 = – 5D subtract 39,900 from both sides
D = $3900
∴ $3900 per yeardivide both sides by -5
Furniture was purchased for $32 000 and had a salvage value of $4000 after 7 years. <br />
a. Find the amount of depreciation apportioned per year if the straight line method was used.<br />
4000 = 32000 – 7d
-32000-28000 = -7d
d = 4000
∴ $4000 per year
S = V0 – dn
S = salvage value = $4000
V0 = original value = $32 000
d = depreciation amount = ?
n = number of years = 7
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