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 |
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
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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