Question

3. A large profitable corporation purchased a small plane for use by its executives. The plane cost $3,500,000. It is expected to have a service life of seven years and $0 salvage value. Develop the complete depreciation schedule for the plane showing year-by-year depreciation charges and book values, and determine the present worth of all the depreciation charges assuming an interest rate of 6% per year, using: (a) DDB method with switch to SL, (b) MACRS depreciation.

Answer 1

Answer:-

Given That:-

A large profitable corporation purchased a small plane for use by its executives. The plane cost $3,500,000. It is expected to have a service life of seven years and $0 salvage value. Develop the complete depreciation schedule for the plane showing year-by-year depreciation charges and book values, and determine the present worth of all the depreciation charges assuming an interest rate of 6% per year, using:

(a) DDB method with switch to SL,

With SLM, annual depreciation = $3,500,000 / 7 = $500,000

SLM depreciation rate = 1 / 7

DDB Depreciation rate = 2 x 1 / 7 = 2 / 7

Each year, comparison is made between DDB depreciation and SLM depreciation of remaining book value. A switch from DDB to SLM is made in the year when SLM depreciation is higher than DDB Depreciation. From table below, the switch happens in year 5.

Year	DDB	Remaining book value	SLM
1	3,500,000 x 2/7 = 1,000,000	25,00,000	3,500,000 / 7 = 500,000
2	2,500,000 x 2/7 = 714,286	17,85,714	2,500,000 / 6 = 416,667
3	1,785,714 x 2/7 = 510,204	12,75,510	1,785,714 / 5 = 357,143
4	1,275,501 x 2/7 = 364,431	9,11,070	1,275,501 / 4 = 318,875
5	911,070 x 2/7 = 260,306	6,50,764	911,070 / 3 = 303,690
6	650,764 x 2/7 = 185,933	4,64,831	650,764 / 2 = 325,382
7	464,831 x 2/7 = 132,809	3,32,022	464,831 / 1 = 464,831

So, Total depreciation schedule & Present worth (PW):

Year	Annual depreciation	Discount factor @6%	Discounted depreciation
1	10,00,000	0.9434	9,43,396
2	7,14,286	0.8900	6,35,712
3	5,10,204	0.8396	4,28,377
4	3,64,431	0.7921	2,88,663
5	3,03,690	0.7473	2,26,935
6	3,25,382	0.7050	2,29,381
7	4,64,831	0.6651	3,09,139
		Present worth =	30,61,604

(b) MACRS depreciation.

MACRS Depreciation schedule, assuming 7-year property class & mid-year convention

MACRS
Year	Depreciation %	Depreciation %	Discount factor @6%	Discounted depreciation
1	14.29	5,00,150	0.9434	4,71,840
2	24.49	8,57,150	0.8900	7,62,860
3	17.49	6,12,150	0.8396	5,13,973
4	12.49	4,37,150	0.7921	3,46,264
5	8.93	3,12,550	0.7473	2,33,556
6	8.92	3,12,200	0.7050	2,20,089
7	8.93	3,12,550	0.6651	2,07,864
			Present worth =	27,56,445

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