Question

Depreciation scenario Your organisation has decided to purchase an item of equipment expected to work 1700 hours per year (average) for a 12 year working life. (a) Discuss, in about 200 words, two methods you could use to compare alternative options when buying this equipment. (b) Assume that the item of equipment you decided to purchase had a purchase price of $2,900,000 and a residual value at the end of 12 years of $260,000. Tabulate the depreciation and book value for the life of the item by each of the following methods: 1) straight line 2) declining balance 3) sum of digits. (c) Tabulate details of a sinking fund to accumulate to the original purchase price less residual value assuming an interest rate of 6%. (d) Draw a graph showing the book values in each of the above (plotted on the same graph for comparison). (e) Comment on the factors that an equipment owner might consider when selecting one of these methods. (f) Assume now that you have purchased this equipment. What is the Total Annual payment required for operating the equipment? You have the following additional data: • Maintenance costs are $60,000 in the first year • Operator wages are $100,000 in the first year • Storage, transport and other miscellaneous costs are $15,000 in the first year • Money costs 8% per year Hint: Start by calculating the Capital Recovery Factor (g) Maintenance, operator and miscellaneous costs are expected to increase at a flat rate of 4% per year over the life of the machine. Based on a Profit margin of 32%, create a table that calculates the hourly charge out rate, including profit, you would need for its hire during each year of the working life of the equipment. (h) Also based on this hourly charge and expected operating hours, what is the expected annual income over the working life of the equipment?

Answer 1

a)

Method 1

When comparing alternative options, a Project NPV analysis could be used to decide on the use of the asset. If there are multiple uses for an asset, using a discounted cash flow, the company can determine which of the 2 options is likely to generate better cash flow for the Company. Project NPV is the sum of the discounted cash flows generated by using the asset.

Method 2

Project IRR is another method to analyse which option to choose. The IRR is the rate of return at which the Company's NPV is 0. It gives a reference point for breaking even on the project. Hence higher the IRR, the larger the margin of safety for the Company and hence this can be used to analyse the better option.

b)

Purchase Price = 290000

Salvage Value = 260000

Straight Line Method
Year	Opening Book Value	Depreciation	Closing Book Value
1	2,900,000	220,000	2,680,000
2	2,680,000	220,000	2,460,000
3	2,460,000	220,000	2,240,000
4	2,240,000	220,000	2,020,000
5	2,020,000	220,000	1,800,000
6	1,800,000	220,000	1,580,000
7	1,580,000	220,000	1,360,000
8	1,360,000	220,000	1,140,000
9	1,140,000	220,000	920,000
10	920,000	220,000	700,000
11	700,000	220,000	480,000
12	480,000	220,000	260,000

Depreciation Rate of Double Declining Balance Method = 1/12 * 2 = 1/6 = 16.67%

Double Declining Balance
Year	Opening Book Value	Depreciation	Closing Book Value
1	2,900,000	483,333	2,416,667
2	2,416,667	402,778	2,013,889
3	2,013,889	335,648	1,678,241
4	1,678,241	279,707	1,398,534
5	1,398,534	233,089	1,165,445
6	1,165,445	194,241	971,204
7	971,204	161,867	809,337
8	809,337	134,889	674,447
9	674,447	112,408	562,039
10	562,039	93,673	468,366
11	468,366	78,061	390,305
12	390,305	65,051	325,254

Total of digits of a year = 1+2+3+4+5+6+7+8+9+10+11+12 = 78

Sum of Digits
Year	Opening Book Value	Depreciation	Closing Book Value	Remaining useful life
1	2,900,000	406,154	2,493,846	12
2	2,493,846	372,308	2,121,538	11
3	2,121,538	338,462	1,783,077	10
4	1,783,077	304,615	1,478,462	9
5	1,478,462	270,769	1,207,692	8
6	1,207,692	236,923	970,769	7
7	970,769	203,077	767,692	6
8	767,692	169,231	598,462	5
9	598,462	135,385	463,077	4
10	463,077	101,538	361,538	3
11	361,538	67,692	293,846	2
12	293,846	33,846	260,000	1

Under the sum of digits method, each years depreciation is calculated as follows:

(Purchase Price - Salvage Value) X Remaining Useful Life/Sum of Digits

c)

Amount to be accumalated = $2,640,000

Year	Opening Balance	Interest	Transfer to sinking fund	Closing Balance
1	0	0	156,491	156,491
2	156,491	9,389	156,491	322,372
3	322,372	19,342	156,491	498,206
4	498,206	29,892	156,491	684,589
5	684,589	41,075	156,491	882,156
6	882,156	52,929	156,491	1,091,577
7	1,091,577	65,495	156,491	1,313,563
8	1,313,563	78,814	156,491	1,548,868
9	1,548,868	92,932	156,491	1,798,291
10	1,798,291	107,897	156,491	2,062,680
11	2,062,680	123,761	156,491	2,342,932
12	2,342,932	140,576	156,491	2,639,999