Question

A machine can be purchased for $202,000 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 incomes $18,000 $25,000 $53,000 $58,000 $108,000
Compute the machine’s payback period (ignore taxes).

Answer 1

Answer:

the machine’s payback period is 2 years and 3 months.

Explanation:

First remove the depreciation expense from the net income because this is a non-cash item.

Depreciation Expense (double-declining method) = 2 × SLDP × BVSLDP

SLDP = 100 ÷ Number of useful life

         = 100 ÷ 5

         = 20 %

Year 1

Depreciation Expense = 2 × 20% × $202,000

                                     = $80,800

Year 2

Depreciation Expense = 2 × 20% × ($202,000 - $80,800)

                                     = $48,480

Year 3

Depreciation Expense = 2 × 20% × ($202,000 - $48,480)

                                     = $61,408

Year 4

Depreciation Expense = 2 × 20% × ($202,000 - $61,408)

                                     = $56,237

Year 5

Depreciation Expense = 2 × 20% × ($202,000 - $56,237)

                                     = $58,305

Summary of Cash flows will be :

Year 1 = $18,000 + $80,800 = $98,800

Year 2 = $25,000 + $48,480 = $72,480

Year 3 = $53,000 + $61,408 = $114,408

Year 4 = $58,000 + $56,237 = $114,237

Year 5 = $108,000 + $58,305 = $166,305

Payback period :

$202,000 = Year 1 ($98,800) + Year 2 ($72,480) + $30,720 / $114,408

                 = 2 years and 3 months

Answer 2

Answer:

2.36 years

Explanation:

Payback calculates the amount of time it takes to recover the amount invested in a project from it cumulative cash flows.

To derive cash flows from net income, depreciation expenses should be added to net income.

Depreciation expense using the double declining method = Depreciation factor x cost of the asset

Depreciation factor = 2 x (1/useful life) = 2 / 5 = 0.4

Deprecation expense in year 1 = 0.4 x $202,000 = $80,800

Book value in year 2 = $202,000 - $80,800 = $121,200

Deprecation expense in year 2 = 0.4 x $121,200 = $48,480

Book value in year 3 = $121,200 - $48,480 = $72,720

Deprecation expense in year 3 = 0.4 x $72,720 = $29,088

Book value in year 4 = $72,720 - $29,088 = $43,632

Deprecation expense in year 4 = $43,632 x 0.4 = $17,452.80

Book value in year 5 = $43,632 x 0.4 - $17,452.80 = $26,179.20

Deprecation expense in year 5 = $26,179.20 x 0.4 = $10,471.68

Cash flow in year 1 = $18,000 +  $80,800 = $98,800

Cash flow in year 2 = $25,000 + $48,480 = $73,480

Cash flow in year 3 = $53,000  + $29,088 = $82,088

Cash flow in year 4 = $58,000  + $17,452.80 = $75,452.80

Cash flow in year 5 = $108,000 + $10,471.68 = $118,471.68

Please check the attached image for how the payback period was calculated