Payback Machine X Cumulative cash flow Machine Y Cumulative cash flow Investment 1,000,000 1,000,000 (1,000,000) (1,000,000) Year 1 $500,000 (500,000) $200,000 (800,000) Year 2 $500,000 0 $300,000 (500,000) Year 3 $300,000 $500,000 0 Year 4 $100,000 $500,000 Payback 2 years 3 years ARR Machine X ARR = Average Profit Average investment Therefore: Depreciation (1000, 000-200,000) /4 = 200000 = 200,000X 4 = 800,000 Profits before depreciation 1400,000 Less depreciation (800,000) Accounting Profit 600,000 Average profits 600,000/4yrs =150,000 Average investment = (initial investment + residual value)/2 = (1,000,000 + 200,000)/2 = 600,000 (Average profit/ average investment) X 100 = (150,000/600,000) X 100 = 25% Machine Y Depreciation (1000, 000-200,000) /4 = 200000 = 200,000X 4 = 800,000 Profits before depreciation 1500,000 Less depreciation (800,000) Accounting Profit 700,000 Average profits 700,000/4yrs =750,000 Average investment = (initial investment + residual value)/2 = (1,000,000 + 200,000)/2 = 600,000 (Average profit/ average investment) X 100 = (750,000/600,000) X 100 = 29% Therefore ARR for X = 25% Y = 29% NPV Net Present Value Machine X Yrs Cash flow Discount factor (7%) Workings Present value DF 19% PV 0 (1000,000) 1 (1000,000 x1) (1000,000) 1 (1,000,000) 1 $500,000 0.9346 500000 x .9346 = 467300 0.8403 420150 2 $500,000 0.8734 500,000 x .8734 = 436700 0.7062 353100 3 $300,000 0.8163 300,000 x .8163 = 244,890 0.5934 178020 4 $100,000 0.7629 100,000 x .7629 76290 0.4987 49870 5 255180 (1140) Machine Y Yrs Cash flow Discount factor (7%) Workings Present value DF 16% PV 0 (1000,000) 1 (1000,000 x1) (1000,000) 1 (1,000,000) 1 $200,000 0.9346 200,000 x .9346 = 186920 .8621 172420 2 $300,000 0.8734 300,000 x .8734 = 262020 .7432 222960 3 $500,000 0.8163 500,000 x .8163 = 408150 .6407 320350 4 $500,000 0.7629 500,000 x .7629 381450 .5523 276150 5 238,540 (8120) IRR Machine X IRR = 7% + (7% X255,180) (255,180 + 1140) IRR = 7% + (7% X 255,180) 256,320 IRR = 7% + (7% X 0.996) IRR = 7% + 7% = 14% Machine Y IRR = 7% + (7% X238,540) (238,540 + 8120) IRR = 7% + (7% X238,540) 246,660 IRR = 7% + (7% X 0.967) IRR = 7% + 10% = 17% Explain which is the most appropriate method to use for selecting the preferred machine for the project.

Payback Machine X Cumulative cash flow Machine Y Cumulative cash flow Investment 1,000,000 1,000,000 (1,000,000) (1,000,000) Year 1 $500,000 (500,000) $200,000 (800,000) Year 2 $500,000 0 $300,000 (500,000) Year 3 $300,000 $500,000 0 Year 4 $100,000 $500,000 Payback 2 years 3 years ARR Machine X ARR = Average Profit Average investment Therefore: Depreciation (1000, 000-200,000) /4 = 200000 = 200,000X 4 = 800,000 Profits before depreciation 1400,000 Less depreciation (800,000) Accounting Profit 600,000 Average profits 600,000/4yrs =150,000 Average investment = (initial investment + residual value)/2 = (1,000,000 + 200,000)/2 = 600,000 (Average profit/ average investment) X 100 = (150,000/600,000) X 100 = 25% Machine Y Depreciation (1000, 000-200,000) /4 = 200000 = 200,000X 4 = 800,000 Profits before depreciation 1500,000 Less depreciation (800,000) Accounting Profit 700,000 Average profits 700,000/4yrs =750,000 Average investment = (initial investment + residual value)/2 = (1,000,000 + 200,000)/2 = 600,000 (Average profit/ average investment) X 100 = (750,000/600,000) X 100 = 29% Therefore ARR for X = 25% Y = 29% NPV Net Present Value Machine X Yrs Cash flow Discount factor (7%) Workings Present value DF 19% PV 0 (1000,000) 1 (1000,000 x1) (1000,000) 1 (1,000,000) 1 $500,000 0.9346 500000 x .9346 = 467300 0.8403 420150 2 $500,000 0.8734 500,000 x .8734 = 436700 0.7062 353100 3 $300,000 0.8163 300,000 x .8163 = 244,890 0.5934 178020 4 $100,000 0.7629 100,000 x .7629 76290 0.4987 49870 5 255180 (1140) Machine Y Yrs Cash flow Discount factor (7%) Workings Present value DF 16% PV 0 (1000,000) 1 (1000,000 x1) (1000,000) 1 (1,000,000) 1 $200,000 0.9346 200,000 x .9346 = 186920 .8621 172420 2 $300,000 0.8734 300,000 x .8734 = 262020 .7432 222960 3 $500,000 0.8163 500,000 x .8163 = 408150 .6407 320350 4 $500,000 0.7629 500,000 x .7629 381450 .5523 276150 5 238,540 (8120) IRR Machine X IRR = 7% + (7% X255,180) (255,180 + 1140) IRR = 7% + (7% X 255,180) 256,320 IRR = 7% + (7% X 0.996) IRR = 7% + 7% = 14% Machine Y IRR = 7% + (7% X238,540) (238,540 + 8120) IRR = 7% + (7% X238,540) 246,660 IRR = 7% + (7% X 0.967) IRR = 7% + 10% = 17% Explain which is the most appropriate method to use for selecting the preferred machine for the project.

Individual Income Taxes

43rd Edition

ISBN:9780357109731

Author:Hoffman

Publisher:Hoffman

Chapter18: Accounting Periods And Methods

Section: Chapter Questions

Problem 10DQ

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Question

Payback

	Machine X	Cumulative cash flow	Machine Y	Cumulative cash flow
Investment	1,000,000		1,000,000
		(1,000,000)		(1,000,000)
Year 1	$500,000	(500,000)	$200,000	(800,000)
Year 2	$500,000	0	$300,000	(500,000)
Year 3	$300,000		$500,000	0
Year 4	$100,000		$500,000
Payback	2 years		3 years

ARR

Machine X

ARR = Average Profit

Average investment

Therefore: Depreciation (1000, 000-200,000) /4 = 200000

= 200,000X 4 = 800,000

Profits before depreciation 1400,000

Less depreciation (800,000)

Accounting Profit 600,000

Average profits 600,000/4yrs =150,000

Average investment = (initial investment + residual value)/2

= (1,000,000 + 200,000)/2 = 600,000

(Average profit/ average investment) X 100

= (150,000/600,000) X 100 = 25%

Machine Y

Depreciation (1000, 000-200,000) /4 = 200000

= 200,000X 4 = 800,000

Profits before depreciation 1500,000

Less depreciation (800,000)

Accounting Profit 700,000

Average profits 700,000/4yrs =750,000

Average investment = (initial investment + residual value)/2

= (1,000,000 + 200,000)/2 = 600,000

(Average profit/ average investment) X 100

= (750,000/600,000) X 100 = 29%

Therefore ARR for X = 25%

Y = 29%

NPV

Net Present Value Machine X

Yrs	Cash flow	Discount factor (7%)	Workings	Present value	DF 19%	PV
0	(1000,000)	1	(1000,000 x1)	(1000,000)	1	(1,000,000)
1	$500,000	0.9346	500000 x .9346 =	467300	0.8403	420150
2	$500,000	0.8734	500,000 x .8734 =	436700	0.7062	353100
3	$300,000	0.8163	300,000 x .8163 =	244,890	0.5934	178020
4	$100,000	0.7629	100,000 x .7629	76290	0.4987	49870
5				255180		(1140)

Machine Y

Yrs	Cash flow	Discount factor (7%)	Workings	Present value	DF 16%	PV
0	(1000,000)	1	(1000,000 x1)	(1000,000)	1	(1,000,000)
1	$200,000	0.9346	200,000 x .9346 =	186920	.8621	172420
2	$300,000	0.8734	300,000 x .8734 =	262020	.7432	222960
3	$500,000	0.8163	500,000 x .8163 =	408150	.6407	320350
4	$500,000	0.7629	500,000 x .7629	381450	.5523	276150
5				238,540		(8120)

IRR

Machine X

IRR = 7% + (7% X255,180)

(255,180 + 1140)

IRR = 7% + (7% X 255,180)

256,320

IRR = 7% + (7% X 0.996)

IRR = 7% + 7% = 14%

Machine Y

IRR = 7% + (7% X238,540)

(238,540 + 8120)

IRR = 7% + (7% X238,540)

246,660

IRR = 7% + (7% X 0.967)

IRR = 7% + 10% = 17%

Explain which is the most appropriate method to use for selecting the preferred machine for the project.

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