Question

-44 A pump in an ethylene production plant costs $15,000. After 9 years, the salvage value is declared at $0. (a) Determine depreciation charge and book value for Year 9 using straight-line, sum-of-years'- digits, and 7-year MACRS depreciation. (b) Find the PW of each depreciation schedule if the interest rate is 5%.

Answer 1

ANSWER :-

(a)

(i) SL Method

Annual depreciation ($) = Cost / Useful life = 15,000 / 9 = 1,666.67

Depreciation schedule as show:

SLM
Year	Beginning-of-year Book Value ($)	Annual Depreciation ($)	End-of-Year Book Value ($)
1	15,000.00	1,666.67	13,333.33
2	13,333.33	1,666.67	11,666.66
3	11,666.66	1,666.67	9,999.99
4	9,999.99	1,666.67	8,333.32
5	8,333.32	1,666.67	6,666.65
6	6,666.65	1,666.67	4,999.98
7	4,999.98	1,666.67	3,333.31
8	3,333.31	1,666.67	1,666.64
9	1,666.64	1,666.67	0.00

(ii) SOYD method

Sum-of-years-digit (SOYD) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Annual depreciation in year N = Cost x (Number of years remaining at beginning of year N / SOYD)

Depreciation schedule is as follows.

SOYD Year Asset Cost ($) Depreciation Rate Annual Depreciation ($) End-of-Year Book Value ($) 1 15,000 9/45 3,000.00 12,000.00 2 15,000 8/45 2,666.67 9,333.33 3 15,000 7/45 2,333.33 7,000.00 4 15,000 6/45 2,000.00 5,000.00 5 15,000 5/45 1,666.67 3,333.33 6 15,000 4/45 1,333.33 2,000.00 7 15,000 3/45 1,000.00 1,000.00 8 15,000 2/45 666.67 333.33 9 15,000 1/45 333.33 0.00

(iii) MACRS

Depreciation schedule as show

MACRS
Year	Asset Cost ($)	Depreciation Rate (%)	Annual Depreciation ($)	End-of-Year Book Value ($)
1	15,000	14.29	2,143.50	12,856.50
2	15,000	24.49	3,673.50	9,183.00
3	15,000	17.49	2,623.50	6,559.50
4	15,000	12.49	1,873.50	4,686.00
5	15,000	8.93	1,339.50	3,346.50
6	15,000	8.92	1,338.00	2,008.50
7	15,000	8.93	1,339.50	669.00
8	15,000	4.46	669.00	0.00

(b) Present Worth (PW) of depreciation are computed as follows

(i) SL Method

Year	SLM Depreciation ($)	PV Factor @5%	Discounted SLM Depreciation ($)
	(A)	(B)	(A) x (B)
1	1,666.67	0.9524	1,587.30
2	1,666.67	0.9070	1,511.72
3	1,666.67	0.8638	1,439.73
4	1,666.67	0.8227	1,371.17
5	1,666.67	0.7835	1,305.88
6	1,666.67	0.7462	1,243.69
7	1,666.67	0.7107	1,184.47
8	1,666.67	0.6768	1,128.07
9	1,666.67	0.6446	1,074.35
		PW of Depreciation ($) =	11,846.39

(ii) SOYD method as show

Year	SOYD Depreciation ($)	PV Factor @5%	Discounted SOYD Depreciation ($)
	(A)	(B)	(A) x (B)
1	3,000.00	0.9524	2,857.14
2	2,666.67	0.9070	2,418.75
3	2,333.33	0.8638	2,015.62
4	2,000.00	0.8227	1,645.40
5	1,666.67	0.7835	1,305.88
6	1,333.33	0.7462	994.95
7	1,000.00	0.7107	710.68
8	666.67	0.6768	451.23
9	333.33	0.6446	214.87
		PW of Depreciation ($) =	12,614.52

(iii) MACRS method as show

Year	MACRS Depreciation ($)	PV Factor @5%	Discounted MACRS Depreciation ($)
	(A)	(B)	(A) x (B)
1	2,143.50	0.9524	2,041.43
2	3,673.50	0.9070	3,331.97
3	2,623.50	0.8638	2,266.28
4	1,873.50	0.8227	1,541.33
5	1,339.50	0.7835	1,049.53
6	1,338.00	0.7462	998.44
7	1,339.50	0.7107	951.96
8	669.00	0.6768	452.81
9	0.00	0.6446	0.00
		PW of Depreciation ($) =	12,633.75

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