Question

Refer totheinformation in Exercise 24-3 and assume instead that double-declining depreciation is applied. Compute the machine’s payback period (ignore taxes). (Round the payback period to three decimals.)

Short answer

The payback period is 2.26 years.

Step-by-step solution

Step-by-Step SolutionStep 1 Computation of depreciation

Year	Beginning book value	Annual dep (1/5)*200% = 40%	Accumulated depreciation	Ending book value
1	$150,000	$60,000	$60,000	$90,000
2	90,000	36,000	96,000	54,000
3	54,000	21,600	117,600	32,400
4	32,400	12,960	130,560	19,440
5	$19,440	$7,776	$138,336	$11,664

Computation of payback period.

Year	Net Income	Depreciation	Net cash flow	Cumulative cash flow
0			-$150,000	-$150,000
1	$10,000	$60,000	70,000	-80,000
2	25,000	36,000	61,000	-19,000
3	50,000	21,600	71,600	52,600
4	37,500	12,960	50,460	103,060
5	$100,000	$7,776	$107,776	$210,836

The payback period is between 2 and 3

$$\begin{gathered} \mathbf{Remaining}\mathbf{}\mathbf{period}\mathbf{=}\frac{\mathrm{Numerator}\mathrm{for}\mathrm{partial}\mathrm{year}}{\mathrm{Denominator}\mathrm{for}\mathrm{partial}\mathrm{year}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$19,000}{\$71,600} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{26}\mathbf{years} \end{gathered}$$

The payback period will be 2.26 years.