1. GT10103 BUSINESS MATHEMATICS
DEPRECIATION
GT10103
BUSINESS MATHEMATICS
PREPARED BY:
SUHAILA BINTI MOHD ISMAIL (BG )
ROSMINDA AK PASANG (BG )
CHAN SAU CHANG(BG )

2. 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

3. 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.

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

5. 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

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

7. 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

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

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

10. 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

11. 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.

12. 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...

13. 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

14. 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

15. 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

16. 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, b) Accumulated depreciation = cost of asset – book value = RM180,000 – RM79, = RM100,133.04

17. 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

18. 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, = RM
For the third year = 33.13% x 6, = RM2,222.16

19. 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, = 12,000 – 10,514.76

20. 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

21. 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

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

23. 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

24. 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

25. 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

26. 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

27. THANK YOU