Question

4. (5 pts) You have purchased a piece of depreciable equipment and have decided to use the double declining-balance depreciation method for depreciation charges. Use the following table to conduct and determine:

a. Annual depreciation and annual book value through the useful life of the equipment.

b. Determine the value of the capital gain or loss.

Cost Basis: $100,000

Market Value: $10,000

Useful Life: 5 years

MARR: 5%

Answer 1

Solution

1.   Double Declining balance method

Here beginning book value = 100000

Now in this case the asset will be depreciated 200% of normal rate of straight line depreciation method and the declining balance of book value will be used

Now the Time period of useful life = 5 years

Straight line depreciation rate= 100%/5= 20%

Therefore Double declining balance method depreciation rate= 2*20% =40%

Book value Year 1 beginning= 100000

Depreciation Year 1= 100000*.4= 40000

Book value at the end of year= Book value Year 1 beginning- Depreciation Year 1= 100000- 40000= 60000

Book value Year 2 beginning= 60000

Depreciation for Year 2= 60000*.4= 24000

Similarly we can get depreciation for all years till we reach a salvage value =10000

Year	Book value at beginning of year(a)	Depreciation Allowance(b)	Depreciation rate	Book Value end of year a-b
1	100000	40000	40%	60000
2	60000	24000	40%	36000
3	36000	14400	40%	21600
4	21600	8640	40%	12960
5	12960	2960	Book value at beginning of year -Salvage value(10000)	10000

Note since the salvage value is 10000 so in the final year the depreciation is calculated as Book value at beginning of 5th Year- Salvage value

B. Now in the 5th Year

Book value at beginning of 5th Year – 12960

Actual Depreciation in value=12960*.4= 5184

Therefore Actual value of asset at end of 5th year = 12960-5184= 7776

But the market value being shown =10000

Therefore capital gain= 10000-7776 =2224

As MARR= 5%

Present value of capital gain = 2224/ (1+.05)^5

= 1742.562