The White Swan Talc Company purchased $120,000 of mining equipment for a small t

Question

The White Swan Talc Company purchased $120,000 of mining equipment for a small talc mine. The mining engineer's report indicates the mine contains 40,000 cubic meters of commercial quality talc. The company plans to mine all the talc in the next 5 years as follows:

At the end of 5 years, the mine will be exhausted, and the mining equipment will be worthless. The company accountant must now decide whether to use sum-of- years' -digits depreciation or unit-of- production depreciation. The company considers 8% to be an appropriate time value of money. Compute the depreciation schedule for each of the two methods. Which method would you recommend that the company adopt? Show the computations to justify your decision.

Tale Production (m3) 15,000 11,000 4,000 6,000 4,000 Year 2 3

Explanation / Answer

In Sum of the year digits depreciation method,

Depreciation in year k = I* (n-k+1)/(n*(n+1)/2)

Here,

n = life of the asset

I = investment

In the given example,

n = 5 years

I = $120000

Hence, depreciation schedule is as follows:

Year

Investment

Depreciation factor (%) = (n-k+1)/(n*(n+1)/2)

Depreciation amount

1

120000

33.33%

40000

2

120000

26.67%

32000

3

120000

20.00%

24000

4

120000

13.33%

16000

5

120000

6.67%

8000

Discount rate = 8%

Present value of all the depreciation = 40000/1.08 + 32000/1.08^2 + 24000/1.08^3 + 16000/1.08^4 + 8000/1.08^5

Present value of all the depreciation = $100729

In unit of production depreciation method,

Depreciation in year K = ((Investment - salvage value)/(total activity))* activity in year K

Hence, depreciation schedule is as follows:

Year

Talc Production

Depreciation amount = (120000/total production)*talc production in the year

1

15000

45000

2

11000

33000

3

4000

12000

4

6000

18000

5

4000

12000

Present value of all the depreciation = 45000/1.08 + 33000/1.08^2 + 12000/1.08^3 + 18000/1.08^4 + 12000/1.08^5

Present value of all the depreciation = $100882.4

Since, the present value of depreciation is relatively higher in case of unit of production depreciation method that is $100882.4 in comparison to the value of depreciation ($100729) under the sum of the years digit depreciation method. Hence, the units of production depreciation method is recommended.

Year

Investment

Depreciation factor (%) = (n-k+1)/(n*(n+1)/2)

Depreciation amount

1

120000

33.33%

40000

2

120000

26.67%

32000

3

120000

20.00%

24000

4

120000

13.33%

16000

5

120000

6.67%

8000

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