Question

A construction company is purchasing a new Tractor for over the road use. The IRS classifies this as 3-year property. The truck costs $297000.
a) Determine the depreciation allowance for each year using SLN method.
Year 1 $  
Year 2 $  
Year 3 $  
Year 4 $  

b) Determine the depreciation allowance for each year using DDB method.
Year 1 $  
Year 2 $  
Year 3 $  
Year 4 $  

c) Determine the depreciation allowance for each year using MACRS.
Year 1 $  
Year 2 $  
Year 3 $  
Year 4 $  

d) Using a 10% MARR calculate the present worth of the depreciation for each of the 3 methods above.
PW_a = $  
PW_b = $  
PW_c = $

Answer 1

(a) SL Method

Annual depreciation ($) = Cost / Useful life = 297,000 / 3 = 99,000

Depreciation schedule is as follows.

SLM
Year	Beginning-of-year Book Value ($)	Annual Depreciation ($)	End-of-Year Book Value ($)
1	2,97,000	99,000	1,98,000
2	1,98,000	99,000	99,000
3	99,000	99,000	0
4	0	99,000	-99,000

(b) DDB Method

SL depreciation rate = 1/Useful life = 1/3

DDB Depreciation rate = 2 x SL rate = 2/3 = 0.67

Depreciation schedule is as follows.

DDB
Year	Asset Cost ($)	Depreciation Rate	Annual Depreciation ($)	End-of-Year Book Value ($)
1	2,97,000	0.67	1,98,000	99,000
2	99,000	0.67	66,000	33,000
3	33,000	0.67	22,000	11,000
4	11,000	0.67	7,333	3,667

(c) MACRS

Depreciation schedule is as follows.

MACRS
Year	Asset Cost ($)	Depreciation Rate (%)	Annual Depreciation ($)	End-of-Year Book Value ($)
1	2,97,000	33.33	98,990	1,98,010
2	2,97,000	44.45	1,32,017	65,993
3	2,97,000	14.81	43,986	22,008
4	2,97,000	7.41	22,008	0

(d) Present Worth (PW) of depreciation are computed as follows. Note that for SLM depreciation, book value becomes 0 at end of year 3, so PW is computed only for first 3 years.

PW OF DEPRECIATION
Year	SLM Depreciation ($)	PV Factor @10%	Discounted SLM Depreciation ($)
	(A)	(B)	(A) x (B)
1	99,000	0.9091	90,000
2	99,000	0.8264	81,818
3	99,000	0.7513	74,380
		PW of Depreciation ($) =	2,46,198
Year	DDB Depreciation ($)	PV Factor @10%	Discounted DDB Depreciation ($)
	(A)	(B)	(A) x (B)
1	1,98,000	0.9091	1,80,000
2	66,000	0.8264	54,545
3	22,000	0.7513	16,529
4	7,333	0.6830	5,009
		PW of Depreciation ($) =	2,56,083
Year	MACRS Depreciation ($)	PV Factor @10%	Discounted MACRS Depreciation ($)
	(A)	(B)	(A) x (B)
1	98,990	0.9091	89,991
2	1,32,017	0.8264	1,09,105
3	43,986	0.7513	33,047
4	22,008	0.6830	15,032
		PW of Depreciation ($) =	2,47,174