1. (Provide Explanation) Project Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Cash
ID: 2761659 • Letter: 1
Question
1. (Provide Explanation)
Project
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Cash Flow
Cash Flow
Cash Flow
Cash Flow
Cash Flow
Cash Flow
A
-14000
6000
6000
6000
6000
6000
B
-15000
7000
7000
7000
7000
7000
C
-18000
12000
2000
2000
2000
2000
The cash flows for three projects are shown above. The cost of capital is 9.5%. If an investor decided to take projects with a payback period of 2 years or less, which of these projects would he take?
A) Investment A
B) Investment B
C) Investment C
D) none of these investments
Project
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Cash Flow
Cash Flow
Cash Flow
Cash Flow
Cash Flow
Cash Flow
A
-14000
6000
6000
6000
6000
6000
B
-15000
7000
7000
7000
7000
7000
C
-18000
12000
2000
2000
2000
2000
Explanation / Answer
Calculation of Payback Period:
Investment A:
Year
Cash Flows (CF)
PVF (9.5%)
PV = CF*PVF
Cumulative PV
Year 0
$ (14,000.00)
1.00000
$ (14,000.00)
$ (14,000.00)
Year 1
$ 6,000.00
0.91324
$ 5,479.45
$ (8,520.55)
Year 2
$ 6,000.00
0.83401
$ 5,004.07
$ (3,516.48)
Year 3
$ 6,000.00
0.76165
$ 4,569.92
$ 1,053.44
Year 4
$ 6,000.00
0.69557
$ 4,173.45
$ 5,226.89
Year 5
$ 6,000.00
0.63523
$ 3,811.37
$ 9,038.25
Cumulative PV becomes Positive in year 3, hence Payback Period shall be =
= 2 Years + 1 Year* 3516.48 / 4569.92
= 2.77 Years
Investment B:
Year
Cash Flows (CF)
PVF (9.5%)
PV = CF*PVF
Cumulative PV
Year 0
$ (15,000.00)
1.00000
$ (15,000.00)
$ (15,000.00)
Year 1
$ 7,000.00
0.91324
$ 6,392.69
$ (8,607.31)
Year 2
$ 7,000.00
0.83401
$ 5,838.08
$ (2,769.23)
Year 3
$ 7,000.00
0.76165
$ 5,331.58
$ 2,562.35
Year 4
$ 7,000.00
0.69557
$ 4,869.02
$ 7,431.37
Year 5
$ 7,000.00
0.63523
$ 4,446.59
$ 11,877.96
Cumulative PV becomes Positive in year 3, hence Payback Period shall be =
= 2 Years + 1 Year* 2769.23 / 5331.58
= 2.52 Years
Investment C:
Year
Cash Flows (CF)
PVF (9.5%)
PV = CF*PVF
Cumulative PV
Year 0
$ (18,000.00)
1.00000
$ (18,000.00)
$ (18,000.00)
Year 1
$ 12,000.00
0.91324
$ 10,958.90
$ (7,041.10)
Year 2
$ 2,000.00
0.83401
$ 1,668.02
$ (5,373.07)
Year 3
$ 2,000.00
0.76165
$ 1,523.31
$ (3,849.77)
Year 4
$ 2,000.00
0.69557
$ 1,391.15
$ (2,458.62)
Year 5
$ 2,000.00
0.63523
$ 1,270.46
$ (1,188.16)
Cumulative PV does not becomes Positive till year 5, hence Payback Period shall be =
= More than 5 years
If an investor decided to take projects with a payback period of 2 years or less, then none of these investments shall be taken, because all investment shall take more than 2 years to payback.
Calculation of Payback Period:
Investment A:
Year
Cash Flows (CF)
PVF (9.5%)
PV = CF*PVF
Cumulative PV
Year 0
$ (14,000.00)
1.00000
$ (14,000.00)
$ (14,000.00)
Year 1
$ 6,000.00
0.91324
$ 5,479.45
$ (8,520.55)
Year 2
$ 6,000.00
0.83401
$ 5,004.07
$ (3,516.48)
Year 3
$ 6,000.00
0.76165
$ 4,569.92
$ 1,053.44
Year 4
$ 6,000.00
0.69557
$ 4,173.45
$ 5,226.89
Year 5
$ 6,000.00
0.63523
$ 3,811.37
$ 9,038.25
Cumulative PV becomes Positive in year 3, hence Payback Period shall be =
= 2 Years + 1 Year* 3516.48 / 4569.92
= 2.77 Years
Investment B:
Year
Cash Flows (CF)
PVF (9.5%)
PV = CF*PVF
Cumulative PV
Year 0
$ (15,000.00)
1.00000
$ (15,000.00)
$ (15,000.00)
Year 1
$ 7,000.00
0.91324
$ 6,392.69
$ (8,607.31)
Year 2
$ 7,000.00
0.83401
$ 5,838.08
$ (2,769.23)
Year 3
$ 7,000.00
0.76165
$ 5,331.58
$ 2,562.35
Year 4
$ 7,000.00
0.69557
$ 4,869.02
$ 7,431.37
Year 5
$ 7,000.00
0.63523
$ 4,446.59
$ 11,877.96
Cumulative PV becomes Positive in year 3, hence Payback Period shall be =
= 2 Years + 1 Year* 2769.23 / 5331.58
= 2.52 Years
Investment C:
Year
Cash Flows (CF)
PVF (9.5%)
PV = CF*PVF
Cumulative PV
Year 0
$ (18,000.00)
1.00000
$ (18,000.00)
$ (18,000.00)
Year 1
$ 12,000.00
0.91324
$ 10,958.90
$ (7,041.10)
Year 2
$ 2,000.00
0.83401
$ 1,668.02
$ (5,373.07)
Year 3
$ 2,000.00
0.76165
$ 1,523.31
$ (3,849.77)
Year 4
$ 2,000.00
0.69557
$ 1,391.15
$ (2,458.62)
Year 5
$ 2,000.00
0.63523
$ 1,270.46
$ (1,188.16)
Cumulative PV does not becomes Positive till year 5, hence Payback Period shall be =
= More than 5 years
If an investor decided to take projects with a payback period of 2 years or less, then none of these investments shall be taken, because all investment shall take more than 2 years to payback.
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