GT10103 BUSINESS MATHEMATICS DEPRECIATION GT10103 BUSINESS MATHEMATICS PREPARED BY: SUHAILA BINTI MOHD ISMAIL (BG08110376) ROSMINDA AK PASANG (BG08110445) CHAN SAU CHANG(BG09110303)

LEARNING OBJECTIVES Explain the meaning of depreciation Explain the difference in the various depreciation methods Compute annual depreciation, accumulated depreciation and book value Construct a depreciation schedule

Description of depreciation Depreciation is an accounting procedure for allocating the cost of capital assets. Example are such as buildings, machinery tools, and vehicles over their useful life. Depreciation expenses allow firms to recapture the amount of money needed for replacement of the assets and to recover the original investment. Depreciation can also be viewed as a decline in the value of assets due to age, wear, and tear or decreasing efficiency.

Methods Straight Line Method Declining Balance Method Sum-of-Year Digits Method

1. Straight line method The simplest and the most common method used. The total amount of depreciation is spread evenly to each accounting period throughout the useful life of the asset. To finding : - the annual depreciation - annual rate of depreciation - book value

Formula Annual depreciation: = cost – salvage value useful life = total depreciation Annual Rate of Depreciation: = annual depreciation x100% OR total depreciation = 1 x100% Book Value: cost – accumulated depreciation

Example 1 Faber Castell bought a lorry for RM38,000. The lorry is expected to last 5 years and its salvage value at the end of 5 years is RM8,000. Straight line method: Here, Cost = RM38,000 Salvage value = RM8,000 Total depreciation = RM38,000-RM8,000 = RM 30,000 Useful life = 5 years

Annual Rate of Depreciation: Annual description: = cost – salvage value useful life = RM38,000 – RM8,000 5 = RM6,000 Annual Rate of Depreciation: = RM6,000 x100% = 1 x100% RM30,000 or useful life = 20% = 1 x100% = 20%

Book value at the end of the third year = cost – accumulated depreciation = RM38,000 – (3 x RM6,000) = RM20,000

Example 2: The book value of an asset after the third year and fifth year using the straight line method are RM7, 000 and RM5, 000 respectively. What is the annual depreciation of the asset? Solution: Decline value from third year to fifth year = RM7, 000 – RM5, 000 = RM2, 000 This decline occurs within 2 years. Hence, annual depreciation of the asset = RM1, 000

2. Declining balance method This method is an accelerated method in which higher depreciation charges are deducted in the early life of the asset. If the original cost of the asset is C and the rate of depreciation is r%, then the depreciation values (book values) of the asset are calculated as follows.

Depreciation for year 1 = Cr Book value at the end of the year 1 = Cost of asset = C Depreciation for year 1 = Cr Book value at the end of the year 1 = C – Cr= C(1–r) Depreciation for year 2 = C(1 - r)r Book value at the end of year 2 = C(1-r)- C(1-r)r= C(1-r) ² Depreciation for year 3 = C(1-r)² r Book value at the end of year 3 = C(1 – r) ² - C(1 – r) ² r = C(1 – r)³ Continuing with the formula...

formula BV = C (1 – r)ⁿ Where, BV = book value C = cost of asset r = rate of depreciation n = number of years From the formula BV = C (1 – r)ⁿ , we get (1 – r)ⁿ = BV C ____ 1 – r = ⁿ√BV r = 1 - ⁿ√BV

The book value at the end of the useful life is the salvage value, S. Hence, Annual Rate of Depreciation ______ r = 1 - ⁿ√ S C where, r = annual rate of depreciation n = useful life in years The accumulated depreciation D up to n years is given by D = C – C (1 – r )ⁿ

Example 3 The cost of fishing boat is RM180,000. The declining balance method is used for computing depreciation. If the depreciation rate is 15%, compute the book value and accumulated depreciation of the boat at the end of 5 years. Solution: C = RM180,000 r = 15% n = 5years

a) Book value at the end of 5 years = C (1 – r ) ⁿ = RM180,000 (1 – 0 a) Book value at the end of 5 years = C (1 – r ) ⁿ = RM180,000 (1 – 0.15) = RM79,866.96 b) Accumulated depreciation = cost of asset – book value = RM180,000 – RM79,866.96 = RM100,133.04

Example 4 Cost of asset = RM15,000 Useful life = 4years Scrap value = RM3,000 (a) Find the annual rate of depreciation, C = RM15,000 S = RM3,000 t = 4 years

For the first year = 33.13% x 15,000 = RM4,969.50 ______ r = 1 - ⁿ√ S C , we get ____________ r = 1 - ⁿ√ RM3,000 RM15,000 = 33.15% b) Construct the depreciation schedule, using the declining balance method. Solution: For the first year = 33.13% x 15,000 = RM4,969.50 For the second year = 33.13% x 10,030.50 = RM3323.10 For the third year = 33.13% x 6,707.40 = RM2,222.16

Year Annual description (RM) Accumulated depreciation (RM) Book Value (RM) 15,000.00 1 4,969.50 10,030.50 2 3,323.10 8,292.60 6,707.40 3 2,222.16 10,514.76 4,485.24 4 1,485.24* 12,000.00 3,000.00 *1,485.24 = 12,000 – 10,514.76

SUM-OF-YEAR DIGITS METHOD The sum-of-year digits method is another accelerated method. In this method, the rate of depreciation is based on sum of the digits representing the number of years of the asset’s useful life. Formula: S = n(n+1) 2 Where S = sum of years’ digits n = useful life

The amount of depreciation in first year is n/S of the depreciable value of the asset, the second year is n-1/S, the third n-2/S and so on. A machine is purchase for RM45,000. Its life expectancy is five years with a zero trade-in value. Prepare a depreciation schedule using the sum-of-year digits method. Example

Solution: Useful life, n = 5 Sum of year digits, S = 1+2+3+4+5=15 Or, S = n(n+1) 2 = 5(5+1) = 15

Amount of depreciation for each year is calculated below as follows. Years Annual depreciation 1 5/15 X 45,000 = RM15,000 2 4/15 X 45,000 = RM12,000 3 3/15 X 45,000 = RM9,000 4 2/15 X 45,000 = RM6,000 5 1/15 X 45,000 = RM3,000

The depreciation schedule is as follows Year Annual depreciation (RM) Accumulated depreciation (RM) Book value at the end of year (RM) - 45,000 1 15,000 30,000 2 12,000 27,000 18,000 3 9,000 36,000 4 6,000 42,000 3,000 5

Example A computer is purchase for RM3,600. It is estimated that its salvage value (value of asset at the end of useful life) at the end of eight years will be RM600. Find the depreciation and the book value of the computer for the third year using sum-of- year digits method. Solution: S = n(n+1) 2 = 8(8+1) = 36

Depreciation value = original cost – salvage value = RM3,600 – RM600 = RM3,000 Depreciation for the third year = = 6/36 X 3,000 = RM500 Accumulated depreciation for the first three years = (8/36 + 7/36 + 6/36) X 3,000 = RM1,780 So, Book value = RM3,600-RM1,780 = RM1,850

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