Question

Exercise II (Depreciation)

An asset will cost $1,750 when purchased this year. It is further expected to have a salvage value of $250 at the end of its five year depreciable life. Calculate complete depreciation schedules giving the depreciation charge, D(n), and end-of-year book value, B(n), for straight-line (SL), Declining Balance (DB) with a rate of d=0.25, double declining balance (DDB), and modified accelerated cost recovery (MACRS) depreciation methods. Assume a MACRS recovery period of 5 years with the following depreciation rates.

Year

1

2

3

4

5

6

d (MACRS)

0.2

0.32

0.192

0.1152

0.1152

0.0576

B. check which of the four methods provides the maximum present worth?

C. If the owner starts the depreciation process using DDB depreciation method at which year the owner should switch to straight line method? Justify your response.

Answer 1

(A)

(a) SL Method

Annual depreciation ($) = (Cost - Salvage value) / Useful life = (1,750 - 250) / 5 = 1,500 / 5 = 300

Depreciation schedule is as follows.

SLM
Year	Beginning-of-year Book Value ($)	Annual Depreciation (Dn) ($)	End-of-Year Book Value (Bn) ($)
1	1,750	300	1,450
2	1,450	300	1,150
3	1,150	300	850
4	850	300	550
5	850	300	250

(b) Declining balance (DB) at 0.25 (25%) (This method ignores salvage value)

Depreciation schedule is as follows.

DB
Year	Asset Cost ($)	Depreciation Rate	Annual Depreciation (Dn) ($)	End-of-Year Book Value (Bn) ($)
1	1,750	0.25	438	1,313
2	1,313	0.25	328	984
3	984	0.25	246	738
4	738	0.25	185	554
5	554	0.25	138	415

(c) Double Declining balance (DDB) (This method ignores salvage value)

SLM depreciate rate = 1/Useful life = 1/5 = 0.2

DDB Depreciation rate = 2 x SLM rate = 2 x 0.2 = 0.4

Depreciation schedule is as follows.

DDB
Year	Asset Cost ($)	Depreciation Rate	Annual Depreciation (Dn) ($)	End-of-Year Book Value (Bn) ($)
1	1,750	0.40	700	1,050
2	1,050	0.40	420	630
3	630	0.40	252	378
4	378	0.40	151	227
5	227	0.40	91	136

(d) MACRS (This method ignores salvage value)

Depreciation schedule is as follows.

MACRS
Year	Asset Cost ($)	Depreciation Rate	Annual Depreciation (Dn) ($)	End-of-Year Book Value (Bn) ($)
1	1,750	0.2	350	1,400
2	1,750	0.32	560	840
3	1,750	0.192	336	504
4	1,750	0.1152	202	302
5	1,750	0.1152	202	101
6	1,750	0.0576	101	0

(B) Present Worth (PW) of depreciation cannot be computed unless discount rate (interest rate) is provided.

(C) Swtching to Straight line method (SLM) is made in the year when DDB Annual depreciation is less than SLM Annual depreciation. From above schedules, DDB depreciation < SLM depreciation in year 3 ($252 < $300), so switching should be done in year 3.