The ABC Company has gathered the following information about the cash flows asso
ID: 2772920 • Letter: T
Question
The ABC Company has gathered the following information about the cash flows associated with a capital budgeting opportunity. The Project will cost $10,000,000 to implement, and has a three year estimated economic life.
There is a 50% probability that the economy will be average during the first year of the project, a 30% chance it will be better than average and a 20% chance it will be worse than average. If the economy is average for the first year, there is a 60% chance it will be average in year 2, a 30% chance it will be better than average and a 10% chance it will be below average. If the economy is above average during year I, there is a 50% chance it will be above average during year 2, a 30% chance it will be average and
a 20% chance it will be worse than average. If the economy is below average during the first year, there is a 40% chance it will be below average the second year, a 40% chance it will be average and a 20% chance it will be better than average.
If the economy is average for year 2, there is a 65% chance it will be average in year 3, a 30% chance it will be better than average and a 5% chance it will be below average. If the economy is above average during year 2, there is a 60% chance it will be above average during year 3, a 30% chance it will be average and a 10% chance it will be worse than average. If the economy is below average during the second year, there is a 50% chance it will be below average the second year, a 40% chance it will be average and a 10% chance it will be better than average.
If the economy is average during a year the net cash flow for the year will be $4,000,000. If the economy is better than average during a year the net cash flow for the year will be $5,200,000, and if
the economy during a year is worse than average, the net cash flow for the year will be $3,100,000.
What are the annual net cash flows that should be used to evaluate the opportunity?
What is the internal rate of return for the proposal?
The ABC Company has gathered the following information about the cash flows associated with a capital budgeting opportunity. The Project wilt cost $10,000,000 to implement, and has a three year estimated economic life.
There is a 50% probability that the economy will be average during the first year of the project, a 30% chance it will be better than average and a 20% chance it will be worse than average. If the economy is average for the first year, there is a 60% chance it will be average in year 2, a 30% chance it will be better than average and a 1096 chance it will be below average. If the economy is above average during year I, there is a 50% chance it will be above average during year 2, a 30% chance it will be average and a 20% chance it will be worse than average. If the economy is below average during the first year, there is a 40% chance it will be below average the second year, a 40% chance it will be average and a 20% chance it will be better than average.
If the economy is average for year 2, there is a 65% chance it will be average in year 3, a 30% chance it will be better than average and a 5% chance it will be below average. If the economy is above average during year 2, there is a 60% chance it will be above average during year 3, a 30% chance it will be average and a 10% chance it will be worse than average. If the economy is below average during the second year, there is a 50% chance it will be below average the second year, a 40% chance it will be average and a 10% chance it will be better than average.
If the economy is average during a year the net cash flow for the year will be $4,000,000. If the economy is better than average during a year the net cash flow for the year will be $5,200,000, and if
the economy during a year is worse than average, the net cash flow for the year will be $3,100,000.
What are the annual net cash flows that should be used to evaluate the opportunity?
What is the internal rate of return for the proposal?
Explanation / Answer
Annual Net Cash Flows
Year 1 = 4,180,000
Year 2 = 4,237,000
Year 3 = 4,299,550
IRR of the project is 13%
WORKING
Probabilities Associated with Cash Flows
Three possible cases are
A – Average.500
B – Better than average
C – Worse than average
Year and probabilities
Year 1
Probability
Year 2
Probability
Assoc Prob
Year 3
Probability
Assoc Prob
A
0.50
A
0.60
0.300
A
0.650
0.195
B
0.300
0.090
C
0.050
0.015
B
0.30
0.150
A
0.300
0.045
B
0.600
0.090
C
0.100
0.015
C
0.10
0.050
A
0.400
0.020
B
0.100
0.005
C
0.500
0.025
B
0.30
A
0.30
0.090
A
0.650
0.059
B
0.300
0.027
C
0.050
0.005
B
0.50
0.150
A
0.300
0.045
B
0.600
0.090
C
0.100
0.015
C
0.20
0.060
A
0.400
0.024
B
0.100
0.006
C
0.500
0.030
C
0.20
A
0.40
0.080
A
0.650
0.052
B
0.300
0.024
C
0.050
0.004
B
0.20
0.040
A
0.300
0.012
B
0.600
0.024
C
0.100
0.004
C
0.40
0.080
A
0.400
0.032
B
0.100
0.008
C
0.500
0.040
Associated probability = probability in year 1 * probability in year 2 * probability in year 3 for an event
For example if there is 50% (or 0.5) chance that economy will be average in year 1, then there will be 0.5 * 0.6 = .3 chance that it will be average in year 1 and average in year 2, 0.5 *.3 = 0.15 it will be average in year 1 and above average in year 2 and so on. Similarly for year 3.
Cash Flows Associated with event
Average Year PA– 4,000,000
Better than Average PB – 5,200,000
Worse than Average PC – 3,100,000
Net Cash Flows in Year 1
Net Cash Flow = Cash flow for average * probability + cash flow for better than average * probability + cash flow for below average *probability
Net Cash Flow = 4,000,000 * 0.50 + 5,200,000*0.30 +3,100,000*0.20
= 2,000,000 +1,560,000+620,000 = 4,180,000
Calculation of cash flows for year 2
(portion pertaining to year 2 of above table)
Year 2
Probability
Assoc Prob
cash flow
Net flow
A
0.60
0.300
4000000
1200000
B
0.30
0.150
5200000
780000
C
0.10
0.050
3100000
155000
A
0.30
0.090
4000000
360000
B
0.50
0.150
5200000
780000
C
0.20
0.060
3100000
186000
A
0.40
0.080
4000000
320000
B
0.20
0.040
5200000
208000
C
0.40
0.080
3100000
248000
Net Cash Flow
4237000
Calculation of Cash flows for year 3 ( portion of table pertaining to year 3)
Year 3
Probability
Assoc Prob
cash flow
net flows
A
0.65
0.195
4000000
780000
B
0.3
0.09
5200000
468000
C
0.05
0.015
3100000
46500
A
0.3
0.045
4000000
180000
B
0.6
0.09
5200000
468000
C
0.1
0.015
3100000
46500
A
0.4
0.02
4000000
80000
B
0.1
0.005
5200000
26000
C
0.5
0.025
3100000
77500
A
0.65
0.0585
4000000
234000
B
0.3
0.027
5200000
140400
C
0.05
0.0045
3100000
13950
A
0.3
0.045
4000000
180000
B
0.6
0.09
5200000
468000
C
0.1
0.015
3100000
46500
A
0.4
0.024
4000000
96000
B
0.1
0.006
5200000
31200
C
0.5
0.03
3100000
93000
A
0.65
0.052
4000000
208000
B
0.3
0.024
5200000
124800
C
0.05
0.004
3100000
12400
A
0.3
0.012
4000000
48000
B
0.6
0.024
5200000
124800
C
0.1
0.004
3100000
12400
A
0.4
0.032
4000000
128000
B
0.1
0.008
5200000
41600
C
0.5
0.04
3100000
124000
Total cash flows
4299550
IRR of the project can be calculated using the formula of NPV where NPV is equal to zero
NPV = - 10,000,000 + 4,180,000/1+r + 4,237,000/(1+r)^2 + 4,299,550/(1+r)3
r will be IRR when NPV = 0 that is
- 10,000,000 + 4,180,000/1+r + 4,237,000/(1+r)^2 + 4,299,550/(1+r)3 = 0
Using IRR function in excel IRR can be found to be 13%
Year 1
Probability
Year 2
Probability
Assoc Prob
Year 3
Probability
Assoc Prob
A
0.50
A
0.60
0.300
A
0.650
0.195
B
0.300
0.090
C
0.050
0.015
B
0.30
0.150
A
0.300
0.045
B
0.600
0.090
C
0.100
0.015
C
0.10
0.050
A
0.400
0.020
B
0.100
0.005
C
0.500
0.025
B
0.30
A
0.30
0.090
A
0.650
0.059
B
0.300
0.027
C
0.050
0.005
B
0.50
0.150
A
0.300
0.045
B
0.600
0.090
C
0.100
0.015
C
0.20
0.060
A
0.400
0.024
B
0.100
0.006
C
0.500
0.030
C
0.20
A
0.40
0.080
A
0.650
0.052
B
0.300
0.024
C
0.050
0.004
B
0.20
0.040
A
0.300
0.012
B
0.600
0.024
C
0.100
0.004
C
0.40
0.080
A
0.400
0.032
B
0.100
0.008
C
0.500
0.040
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