1) A new machine tool costs $500,000, and has a useful life of 10 years. Its est
ID: 1105863 • Letter: 1
Question
1) A new machine tool costs $500,000, and has a useful life of 10 years. Its estimated salvage value at the end of year 10 is $50,000.
(a) Determine the depreciation for years 1-10 using the straight-line method (with the assumed salvage value), and also using double declining balance.
(b) Compute the present worth of the two series of depreciation amounts, assuming that you have a minimum acceptable rate of return of 12% per year.
(c) What does your answer to part (b) above tell you about which depreciation method would be preferable for you? Explain.
Explanation / Answer
1.
A.
Straight line depreciation = (initial cost – salvage value)/useful life = (500000-50000)/10
Straight line depreciation = $45000 per year
Double Declining balance depreciation = 200%*Book value*annual depreciation rate
Initial book value = $500000
Annual depreciation rate = 1/useful life = 1/10 = 10%
Year
Book Value ($)
Double Declining Depreciation (200%*Book value*10%)
Book value at the year end
1
500000
100000
400000
2
400000
80000
320000
3
320000
64000
256000
4
256000
51200
204800
5
204800
40960
163840
6
163840
32768
131072
7
131072
26214.40
104857.60
8
104857.60
20971.52
83886.08
9
83886.08
16777.22
67108.86
10
67108.86
17108.86
50000
B.
R = 12%
Present value of straight line depreciation amount = 45000*(1-1/1.12^10)/.12
Present value of straight line depreciation amount = $254260.04
Present value of the double declining depreciation amount = 100000/1.12^1 + 80000/1.12^2 +64000/1.12^3 +51200/1.12^4 + 40960/1.12^5 + 32768/1.12^6 + 26214.4/1.12^7 + 20971.52/1.12^8 + 16777.22/1.12^9 + 17108.86/1.12^10
Present value of the double declining depreciation amount = $302883.5
C.
The double declining depreciation method will be preferred because the present value of depreciation amount is higher. Then, it will cause the saving of taxes whose present value will also be higher. As a result, the organization will save more with this method. Hence, the double declining depreciation method is preferred in comparison to the straight line depreciation.
Year
Book Value ($)
Double Declining Depreciation (200%*Book value*10%)
Book value at the year end
1
500000
100000
400000
2
400000
80000
320000
3
320000
64000
256000
4
256000
51200
204800
5
204800
40960
163840
6
163840
32768
131072
7
131072
26214.40
104857.60
8
104857.60
20971.52
83886.08
9
83886.08
16777.22
67108.86
10
67108.86
17108.86
50000
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