LECTURE 12

Depreciation

 

TEST 2: Lectures 7,8,9,10

5 questions, 45 minutes

Venue: K-Theater

Date:

Time: 1 – 1:45 – Groups 1, 2, 3

           2 – 2:45 – Groups 4,5,6

Follow tutorials

 

1.)    Straight Line method

 

Formula: Depreciation = (Book Value – Scrap Value *)/ useful life

 

*Salvage Value

 

Example 1:

AB Enterprises obtains a car for $55,000. This car will be used for 6 years, after which it will be sold for $25,000. Find the depreciation expense each year for the 6 years, calculated with the straight line method.

How much of depreciation has been taken after 2 years? After 4 years?

 

Answer:

 

Book Value = $55,000

Scrap value = $25,000

Useful life = 6 years

 

Depreciation expense per year = (55,000 – 25,000)/6 = $5000 per year.

 

 

Year	Depreciation Expense	Depreciated Value
1	$5000	$55,000 – 5000 = $50,000
2	$5000	$50,000 – 5000 = $45,000
3	$5000	$45,000 – 5000 = $40,000
4	$5000	$40,000 - 5000 = $35,000
5	$5000	$35,000 – 5,000 = $30,000
6	$5000	$30,000 – 5,000 = $25,000

 

*Depreciation taken after 2 years = $5000 + $5000 = $10,000

**Depreciation taken after 4 years = $5000 + $5000 + $5000 + $5000 = $20,000

 

Alternative formula approach:

At Year = 0, Book Value = 55,000; thus (b₁, t₁ = 55000, 0)

At year = 6, Book Value = 25,000, thus (b₂ , t₂ = 25000, 0)

 

(y – y₁) / (x – x₁) = (y₂ – y₁ )/ (x₂ – x₁ )

y is represented by book value, b and x is represented by time in years, t

(b – 55,000)/(t – 0) = (25000 – 55000)/(6-0)

(b – 55,000)/t  = -5000

b – 55,000 = -5000t

b = -5000t + 55,000

 

* In year 2, depreciated value = -5000 (2) + 55,000 = 45,000

Depreciation taken after 2 years = 55,000 – 45,000 = $10,000

 

** In year 4, depreciated value = -5000 (4) + 55,000 = 35,000

Depreciation taken after 4 years = 55,000 – 35,000 = $20,000

 

 

Exercise 1a:

AB Enterprises obtains a car for $37,000. This car will be used for 5 years, after which it will be sold for $2,000. Find the depreciation expense each year for the 5 years calculated with the straight line method.

How much of depreciation has been taken after 2 years? After 4 years?

 

Book Value = 

Scrap value = 

Useful life = 

 

Depreciation expense per year =

 

Year	Depreciation Expense	Depreciated Value
1
2
3
4
5

 

Depreciation taken after 2 years =

Depreciation taken after 4 years =

 

2.)    Declining balance:

 

This method records more depreciation expense in the earlier years.

 

Formula: D = B (1 – i) ⁿ

 

D = depreciated value at the end of the nth periond

B = Book value

i = depreciation rate

n = number of periods

 

Example 2a:

 

AB Enterprises obtains a car for $55,000. This car will be used for 6 years, after which it will be sold for $25,000. Find the depreciation expense each year for the 6 years, calculated with the double declining method.

How much of depreciation has been taken after 2 years? After 4 years?

How much more depreciation has been taken in the double declining method when compared with the straight line method after 2 years? After 4 years?

           

D = B (1 – i) ⁿ

            D = 25,000, B = $55,000, n = 6, i = ? 

            25,000 = 55,000 (1 - i) ⁶

            (1 - i) ⁶ =   25,000/55,000

            (1 - i) ⁶ =   0.4546

            (1 - i)  =  0.4546 ^1/6

            1 - i = 0.8769

            i = 0.1231

 

 

Year	Depreciation Expense: D	Depreciated Value***
1	55,000 X 0.1231 = 6770.5	55,000 - 6770.5 = 48,229.50
2	48229.50 X 0.1231 = 5937.051	48229.50– 5937.051 = 42,292.45
3	42,292.45 X 0.1231 = 5206.2	42,292.45- 5206.2 = 37,086.25
4	37,086.25 X 0.1231 = 4565.317	37,086.25 - 4565.317 = 32,520.93
5	32,520.93 X 0.1231 = 4003.327	32,520.93  - 4003.327 = 28,517.60
6	28,517.60X 0.1231 =  3510.51	28,517.60 – 3517.60# = 25,000

                       

                        #  The final depreciation is adjusted to get a deprecated value of $25,000

 

***These values are also given by the formula: B(1 +i) ⁿ

                        For example:

                        Year 1: D = 55,000 * (1 – 0.1231) ¹ = 48,229.50

                        Year 2: D = 55,000 * (1 – 0.1231) ² = 42,292.45       

Year 3: D = 55,000 * (1 – 0.1231) ³ = 37,086.25

Year 4: D = 55,000 * (1 – 0.1231) ⁴ = 32,520.93

Year 5: D = 55,000 * (1 – 0.1231) ⁵ = 28,517.60

Year 6: Depreciation is adjusted to 25,000

 

 

                        After 2 years, depreciation taken = 55,000 - 42,292.45 = 12,707.55

                        After 4 years, depreciation taken = 55,000 - 32,520.93 = 22,479.07

 

                        Compared with straight line method:

After 2 years, double declining method takes 12,707.55 – 10,000 = 2,707.55 more depreciation

After 4 years, double declining method takes 22,479.07 – 20,000 = 2,479.07 more depreciation

 

Notice that double declining method takes more depreciation in earlier years and less in later years compared with the straight line method. Over the useful life, both methods give same amount of overall depreciation.

Consider business implications: eg. Taxation, assets that have more value in the earlier years such as computer systems.

 

 

Exercise 2a:

 

AB Enterprises obtains a car for $37,000. This car will be used for 5 years, after which it will be sold for $2,000. Find the depreciation expense each year for the 5 years calculated with the double declining method.

How much of depreciation has been taken after 2 years? After 4 years?

 

How much more depreciation has been taken in the double declining method when compared with the straight line method after 2 years? After 4 years

 

 

           

            Independent Reading:

            FRA Chapter 21         

 

PREPARATION FOR FINAL EXAM : MAKE SURE YOU HAVE ALL THE TUTORIALS + ANSWERS + LECTURES FOR LECTURES 1 – 12. COMPREHENSIVE WITH GREATER EMPHASIS ON TOPICS COVERED AFTER THE MID-SEMESTER BECAUSE THESE HAVE NOT YET BEEN TESTED.