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.