Question

A machine can be purchased for $226,000 and used for five years, yielding the following net incomes. In projecting net incomes, double-declining depreciation is applied using a five-year life and a zero salvage value.

	Year 1				Year 2				Year 3				Year 4				Year 5
Net income		$	22,500			$	44,000			$	77,000			$	46,000			$	108,000

Compute the machine’s payback period (ignore taxes). (Round payback period answer to 3 decimal places.)

	Computation of Annual Depreciation Expense Year Beginning Book Value Annual Depr. (40% of Book Value) Accumulated Depreciation at Year-End Ending Book Value 1 2 3 4 5 Annual Cash Flows Year Net income Depreciation Net Cash Flow Cumulative Cash Flow 0 $(226,000) $(226,000) 1 22,500 2 44,000 3 77,000 77,000 77,000 4 46,000 46,000 123,000 5 108,000 108,000 231,000 Payback period = years

Answer 1

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Introduction i) Double declining depreciation is a method of depreciation in which asset is depreciated at a higher amount in the initial years and lower amount in the later years. This is achieved by a combination of two things:- 1. Doubling the rate of depreciation as applied in the normal Straight Line Method of Depreciation. 2. Using the rate of depreciation arrived in 1. as a rate for the Written Down / Diminishing balance method of Depreciation and adjusting any difference in last year to bring the asset to its Salvage Value ii) Net Cash Flows are arrived at by adding depreciation to the Net Income because Depreciation is a Non-Cash Expense. iii) Payback period is the time period in which the Total Cost of Asset can be recouped from the Net Cash Flows. Where the annual Net Cash Flows are not equal, the Payback period can be computed by looking at the Cumulative Net Cashflows. This method uses a basic assumption that the rate of accruing of Net cashflows is uniform within the year. The Lower Year and Higher Year can be found by looking at Cumulative Cash Flows and ascertaining where does the Total Cost of Asset lies. Hence, the Lower Year and the Difference in Total Cost and Cumulative Cash FlowS(CCF) in Lower Year) divided by (the Difference in CCFs of Higher and Lower Year) Steps:- Step 1 Calculate the normal Rate of Depreciation which would have been used in the Straight Line Method of Depreciation. Note:- Normal Annual Rate of Depreciation = (Total Cost of Asset - Salvage Value) * 100 Life of Asset (in Years) x Total Cost of Asset In given case: - Total Cost of Asset = 226000 Salvage Value = 0 Life of Asset = 5 Years Therefore, Normal Annual Rate of Depreciation = 100 = 20% (226000-0) * 100 5x 226000 Step 2 Double the rate obtained in Step 1. Required Rate of Depreciation in Double Declining depreciation method = 2 x 20% 40%

Step 3 Asset Amortization Chart Using the Rate obtained in Step 2 and using it as a rate for Reducing Balance Method of Depreciation. Year Ending Book Value Beginning Book Value. (2) Table 1 Annual Depr. (40% of Book Value) (3) = 40 % of (2) Accumulated Depreciation at Year-End (4) = Total Cost (ie 226000) - (5) (1) (5) = (2) - (3) or 226000 - (4) 1351 226000 135600 81360 48816 29289.6 90400 54240 32544 19526.4 29289.6 90400 144640 177184 196710.4 226000 81360 48816 29289.6 5 O Note:- In last year (Year 5) a special adjustment is made to bring the asset to its salvage value at the end of useful life which in the given case is 0. Assumptions: - The above Chart has been made on Net Block basis, the same can also be made on Gross Block basis. Step 4 Calculate the Net Cash flows using the Depreciation as calculated in Step 3 Table 2 Depreciation Year Net Income Net Cash Flows Cummulative Net Cash Flows (5) = Sum of (4) (2) (3) = (3) of Table 1 (4) = (2) + (3) 22500 44000 77000 46000 108000 90400 54240 32544 19526.4 29289.6 112900 98240 109544 65526.4 137289.6 112900 211140 320684 386210.4 523500 5

Step 5 Calculate Payback period in Years Total Cost of Asset = 226000 As we can observe from Cummulative Net Cash Flows column of Table 2 , Total Cost of Asset (i.e. 22600) lies Between Year 2 and Year 3 i.e. Between 211140 and 320684 Payback Period = 2 + (Total Cost of Asset - Cumulative Net Cash Flows until Year 2) (Cumulative Net Cash Flows until Year 3- Cumulative Net Cash Flows until Year 2) = 2 + (226000 - 211140) (320684 - 211140) = 2 + 14860 109544 = 2 + 0.135653 = 2.136 Hence, the required payback period for the machine costing 226000 is 2.136 Years.