Engineering Economy. Engineering Economy, Engineering, Economy, Business and Economy, Business, Economics, Finance, Accounting,

1. Depreciation
Depreciation Methods
1. Straight Line / 2. Declining Balance / 3. Sum-of-the-year’s-digits / 4. Unit of Production
It is a process of allocating Costs
Cost to be allocated = Acquisition Cost (Purchase Price) – Salvage Value
Depreciation is a systematic and rational process of distributing the
cost of tangible assets over the life of assets

2. 1. Straight Line Depreciation Method
Illustration Question:
On June, 2011, a Company purchased an equipment at a cost of SAR
140,000, having a life span of 5 years. At the end of the 5th year the salvage
value will be SAR 20,000. Calculate the depreciation for 2011 & 2012 using
straight line depreciation method.
Depreciation = (Cost – Residual/ Salvage Value)
Useful Life
Depreciate at equal rate throughout the life

3. Answer
Cost = 140,000
Salvage Value = 20,000
Life = 5
Depreciation = (Cost – Residual/ Salvage Value)
Useful Life
Depreciation for 2011 = (140,000 – 20,000) 6
5 12
120,000 1 = 24,000 = SR 12,000
5 2 2
Depreciation for 2012 = (140,000 – 20,000)
5
= 120,000 = SR 24,000
5

4. 2. Declining Balance Method
Book Value of the Asset depreciate every year
Depreciation Rate = (100)/(Life in Years)
Depreciation = Book Value x Depreciation Rate
Book Value = Cost – Accumulated Depreciation
Double (200%) Declining Balance Method 40%
Triple (300%) Declining Balance Method 60%
150% Declining Balance Method 30%
50% Declining Balance Method 10%
If the Asset Value depreciation is 20% in the Straight Line Method:

5. Illustration Question:
On January, 2011, a Company purchased an equipment at a cost of SAR
140,000, having a life span of 5 years. The depreciation rate is 20%.
a) Calculate the depreciation from 2011 to 2015 using Declining Balance
Depreciation method. Also calculate the salvage value of the equipment at
the end of the year 2015.
b) Calculate the depreciation from 2011 to 2015 using Double Declining
Balance Depreciation method. Also calculate the salvage value of the
equipment at the end of the year 2015.

6. Answer (a)
Year Book Value (SAR) in the
beginning
Depreciation
2011 140,000 (140,000) (20/100) = 28,000
2012 140,000 – 28,000 = 112,000 (112,000) (20/100) = 22,400
2013 112,000 – 22,400 = 89,600 (89,600) (20/100) = 17,920
2014 89,600 – 17,920 = 71,680 (71680) (20/100) = 14,336
2015 71,680 – 14,336 = 57,344 (57,344) (20/100) = 11,469
At the end of the year 2015, the SALVAGE VALUE = 57,344 – 11,469 =
SR45,875
Depreciation = Book Value x Depreciation Rate
Book Value = Cost – Accumulated Depreciation

7. Answer (b) Double Declining (40%)
Year Book Value (SAR) in the
beginning
Depreciation
2011 140,000 (140,000) (40/100) = 56,000
2012 140,000 – 56,000 = 84,000 (84,000) (40/100) = 33,600
2013 84,000 – 33,600 = 50,400 (50,400) (40/100) = 20,160
2014 50,400 – 20,160 = 30,240 (30,240) (40/100) = 12,096
2015 30,240 – 12,096 = 18,144 (18,144) (40/100) = 7258
At the end of the year 2015, the SALVAGE VALUE = 18,144 – 7258 = SR10886
Depreciation = Book Value x Depreciation Rate
Book Value = Cost – Accumulated Depreciation

8. 3. Sum-of-the-year’s-digits method
1st Year = n/(1+2+3+ ……. + n)
2nd Year =(n – 1)/(1+2+3+ ……. + n)
3rd Year = (n – 2)/(1+2+3+ ……. + n)
Last Year = 1/(1+2+3+ ……. + n)
Depreciation= (Cost – Salvage Value) (Fraction of the Year)
If ‘n’ is number of years;
Fraction for the years is given by:
This is done to reduce tax payments. Depreciation expense is a non-cash expense so
must be used to reduce tax payments and get higher net cash inflows

9. Illustration Question
A company purchased an Asset on January,
2011. The Cost of the Asset is SR 100,000 and
its life is 5 years. The Salvage Value at the end
of useful life will be SR 10,000. Using Sum-of-
the-years-digits method calculate the
depreciation from 2011 to 2015.

10. Answer
Sum of the Years = 1+2+3+4+5 =15
Depreciation for 2011 = (100,000 – 10,000) (5/15) = SR 30,000
Depreciation for 2012 = (100,000 – 10,000) (4/15) = SR 24,000
Depreciation for 2013 = (100,000 – 10,000) (3/15) = SR 18,000
Depreciation for 2014 = (100,000 – 10,000) (2/15) = SR 12,000
Depreciation for 2015 = (100,000 – 10,000) (1/15) = SR 6,000

11. Short-Cut to Measure Sum of the Years
For n’ years:
Sum of the Years = (n+1) (n/2)
ILLUSTRATION:
For 500 Years = (500+1) (500/2)
= (501) (250)
= 125,250

12. 4. Units of Production Method
Illustration Question: A company purchased a car at a Cost of SR 52,000. Its estimated
running (Units of Output) for 5 years is 10,000 miles, distributed as follows.
1st Year = 4000; 2nd Year = 2500; 3rd Year = 1500; 4th Year = 1000; 5th Year = 1000
The Residual Value after 5 years is SR 2000. Calculate the Depreciation Expenses and
Book Value for each year (for 5 years)
Depreciation = Cost – Residual Value
Estimated Units of Output

13. Answer
Cost of the Asset (vehicle) = SR 52,000
Residual Value = SR 2,000
Estimated Units of Output (Miles) = 10,000
Depreciation Expense = Cost – Residual Value
Estimated Units of Output
= (52,000 – 2,000)/10,000 = SR 5 per mile
Years Depreciation Expense (SR)
Book Value (SR) at the year
end
0 52,000
1 4,000 x 5 = 20,000 52000 – 20000 = 32,000
2 2,500 x 5 = 12,500 32000 – 12500 = 19,500
3 1,500 x 5 = 7,500 19500 – 7500 = 12,000
4 1,000 x 5 = 5,000 12000 – 5000 = 7,000
5 1,000 x 5 = 5,000 7000 – 5000 = 2,000