Is it reasonable to use a 12 percent cost of capital for each project even thoug
ID: 2740811 • Letter: I
Question
Is it reasonable to use a 12 percent cost of capital for each project even though their costs and return probability distributions differ? What methods for dealing with risk are available to Mr. Rose?
Townes Computing Corporation
Project A
Project B
Project C
Probability
Cash Inflows
Product
Sq. Deviation
Probability
Cash Inflows
Product
Sq.Deviation
Probability
Cash Inflows
Product
Sq. Deviation
0.01
50,000
500
156,250,000.00
0.05
50,000
2,500
781,250,000.00
0.05
-2,750,000
-137,500
4,500,000
0.05
100,000
5,000
281,250,000.00
0.1
100,000
10,000
562,500,000.00
0.1
0
0
6,250,000,000.00
0.44
150,000
66,000
275,000,000.00
0.35
150,000
52,500
218,750,000.00
0.35
250,000
87,500
0
0.44
200,000
88,000
275,000,000.00
0.35
200,000
70,000
218,750,000.00
0.35
500,000
175,000
21,875,000,000.00
0.05
250,000
12,500
281,250,000.00
0.1
250,000
25,000
562,500,000.00
0.1
750,000
75,000
25,000,000,000.00
0.01
300,000
3,000
156,250,000.00
0.05
300,000
15,000
781,250,000.00
0.05
1,000,000
50,000
28,125,000,000.00
Total
1,050,000
1,050,000
-250,000
Expected Return
175,000.00
175,000
250,000
Expected Variance
1,425,000,000.00
3,125,000,000.00
81,254,500,000
Std Deviation
37,749
55,901
285,051
Probability
Cash Outflows
Probability
Cash Outflows
Product
Probability
Cash Outflows
Product
1
1,250,000
0.05
900,000
45,000
0.05
500,000
25,000
0.15
950,000
142,500
0.15
800,000
120,000
0.6
1,000,000
600,000
0.6
1,000,000
600,000
0.15
1,050,000
157,500
0.15
1,200,000
180,000
0.05
1,100,000
55,000
0.05
1,500,000
75,000
Total
1,250,000
5,000,000
1,000,000
5,000,000
1,000,000
Avg.
NPV of Project A
NPV
IRR
NPV of Project B
IRR
NPV of Project C
IRR
Cash Outflow
(1,250,000)
(1,250,000)
Cash Outflow
(1,000,000)
-1,000,000
Cash Outflow
-1,000,000
-1,000,000
Cash Inflow
175,000
175,000
Cash Inflow
175,000
175,000
Cash Inflow
250,000
250,000
Cost of Capital
12%
14.00%
Cost of Capital
12%
17.50%
Cost of Capital
12%
25.00%
PV of Cash Inflows
1,458,333
1,250,000
PV of Cash Inflows
1,458,333
1,000,000
PV of Cash Inflows
2,083,333
1,000,000
NPV of Project
208,333
-
NPV of Project
458,333
NPV of Project
1,083,333
IRR
14.00%
IRR
17.50%
IRR
25.00%
Is it reasonable to use a 12 percent cost of capital for each project even though their costs and return probability distributions differ? What methods for dealing with risk are available to Mr. Rose?
Townes Computing Corporation
Project A
Project B
Project C
Probability
Cash Inflows
Product
Sq. Deviation
Probability
Cash Inflows
Product
Sq.Deviation
Probability
Cash Inflows
Product
Sq. Deviation
0.01
50,000
500
156,250,000.00
0.05
50,000
2,500
781,250,000.00
0.05
-2,750,000
-137,500
4,500,000
0.05
100,000
5,000
281,250,000.00
0.1
100,000
10,000
562,500,000.00
0.1
0
0
6,250,000,000.00
0.44
150,000
66,000
275,000,000.00
0.35
150,000
52,500
218,750,000.00
0.35
250,000
87,500
0
0.44
200,000
88,000
275,000,000.00
0.35
200,000
70,000
218,750,000.00
0.35
500,000
175,000
21,875,000,000.00
0.05
250,000
12,500
281,250,000.00
0.1
250,000
25,000
562,500,000.00
0.1
750,000
75,000
25,000,000,000.00
0.01
300,000
3,000
156,250,000.00
0.05
300,000
15,000
781,250,000.00
0.05
1,000,000
50,000
28,125,000,000.00
Total
1,050,000
1,050,000
-250,000
Expected Return
175,000.00
175,000
250,000
Expected Variance
1,425,000,000.00
3,125,000,000.00
81,254,500,000
Std Deviation
37,749
55,901
285,051
Probability
Cash Outflows
Probability
Cash Outflows
Product
Probability
Cash Outflows
Product
1
1,250,000
0.05
900,000
45,000
0.05
500,000
25,000
0.15
950,000
142,500
0.15
800,000
120,000
0.6
1,000,000
600,000
0.6
1,000,000
600,000
0.15
1,050,000
157,500
0.15
1,200,000
180,000
0.05
1,100,000
55,000
0.05
1,500,000
75,000
Total
1,250,000
5,000,000
1,000,000
5,000,000
1,000,000
Avg.
NPV of Project A
NPV
IRR
NPV of Project B
IRR
NPV of Project C
IRR
Cash Outflow
(1,250,000)
(1,250,000)
Cash Outflow
(1,000,000)
-1,000,000
Cash Outflow
-1,000,000
-1,000,000
Cash Inflow
175,000
175,000
Cash Inflow
175,000
175,000
Cash Inflow
250,000
250,000
Cost of Capital
12%
14.00%
Cost of Capital
12%
17.50%
Cost of Capital
12%
25.00%
PV of Cash Inflows
1,458,333
1,250,000
PV of Cash Inflows
1,458,333
1,000,000
PV of Cash Inflows
2,083,333
1,000,000
NPV of Project
208,333
-
NPV of Project
458,333
NPV of Project
1,083,333
IRR
14.00%
IRR
17.50%
IRR
25.00%
Explanation / Answer
Since the probability distribution (Risk) for each project is different, it is not reasonable to use the same (12%) cost of capital. The discount rate must reflect the risk of the project. Tools such as co-efficient of variance, sensitivity analysis or scenario analysis can be used.
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