Maths Made Easy Forums Standard Finance Interest & Depreciation Straight Line Depreciation

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Keymaster
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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%
= $2000 Use the straight line depreciation formula: S = V0 – Dn S = 20,000 – 2000 × 6 =$8000

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Keymaster
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 Jill 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 • Admin Keymaster Post count: 702 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 = 78,000 b. 9 months worth of depreciation 2,600 × 0.12 = 312 for the 9 months = 312 × 9/12 = 234 Taxable income = 78,000 – 234 = 77,766 c.  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) = 17,179.80 d. Value after first year = 2,600 – 234 = 2,366 e. tax deduction after another year = 2,366 × 0.12 = 283.92 • Admin Keymaster Post count: 702  Time Years 0 1 2 3 4 5 Value  9400 8460 7614 6853 6167 5551 The 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 • Admin Keymaster Post count: 702 In 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 = 8,000 b.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 =$32,000 V = 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