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.

FINANCIAL ACCOUNTING
10th Edition
ISBN:9781259964947
Author:Libby
Publisher:Libby
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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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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