Question

A company purchased 20 new automobiles at a cost of $20,000 each. The useful life of the cars is 6 years. The salvage value of the car is $3000. A) Compute the depreciation for these two methods over the years under Double declining balance method (DDB) and MACRS. B) Draw CFD for the depreciation cost for each method. C) If interest rate is 3% find the PW of each CFD. D) Which method should be selected?

Answer 1

Initial Cost = 20 * 20,000 = 400,000

Salvage Value = 20 * 3000 = 60,000

(a) Depreciation:

Under Double Declining Balance Method:

Straight-Line Depreciation Percent = 100% / Useful Life = 100% / 6 = 16.66%

Double Declining Depreciation Rate = 2 x Straight-Line Depreciation Percent = 16.66 * 2 = 33.33%

Depreciation for a Period = Depreciation Rate x Book Value at Beginning of the Period

Under DDB:

Double Declining Balance Method
Year	Book Value (Beginning Year)	Depreciation	Book Value (End Year) (Beginning BV-Depreciation)
1	$4,00,000.00	$1,33,333.33	$2,66,666.67
2	$2,66,666.67	$88,888.89	$1,77,777.78
3	$1,77,777.78	$59,259.26	$1,18,518.52
4	$1,18,518.52	$39,506.17	$79,012.35
5	$79,012.35	$19,012.35	$60,000.00
6	$60,000.00	$0.00	$60,000.00

Under MACRS:

MACRS
Year	Asset Cost ($)	Depreciation Rate (%)	Annual Depreciation ($)	End-of-Year Book Value ($)
1	$4,00,000.00	20.00	$80,000.00	$3,20,000.00
2	$4,00,000.00	32.00	$1,28,000.00	$2,72,000.00
3	$4,00,000.00	19.20	$76,800.00	$3,23,200.00
4	$4,00,000.00	11.52	$46,080.00	$3,53,920.00
5	$4,00,000.00	11.52	$46,080.00	$3,53,920.00
6	$4,00,000.00	5.76	$23,040.00	$3,76,960.00

(b) CFD for the depreciation cost for each method:

(c) PW under Double Declining Method:
= -400000 + 133333.33/1.03^1 + 88888.89/1.03^2 + 59259.26/1.03^3 + 39506.17/1.03^4 + 19012.35/1.03^5 + 0/1.03^6
= -$81032.30

PW under MACRS Method:
= -400000 + 80000/1.03^1 + 128000/1.03^2 + 76800/1.03^3 + 46080/1.03^4 + 46080/1.03^5 + 23040/1.03^6
= -$31408.80

(d) Thus, MACRS should be selected as it's PW is higher than DDB.