You are considering the following two mutually exclusive projects. The required
ID: 2777068 • Letter: Y
Question
You are considering the following two mutually exclusive projects. The required return on each project is 12 percent. Which project should you accept and what is the best reason for that decision?
Project A Project B
Year 0 -$15,000 -$15,000
Year 1 9,000 3,000
Year 2 8,000 5,000
Year 3 5,000 9,000
Year 4 6,000 11,000
a. Project A; because it pays back faster
b. Project A; because it pays back slower
c. Project B; because it has the higher profitability index
d. Project A; because it has the higher net present value
e. Project B; because it has the higher net present value
Explanation / Answer
Calculation of Payback Period:
Project A
Project B
Cash Flows (CF)
Cummulative CF
Cash Flows (CF)
Cummulative CF
Year 0
$ (15,000)
$ (15,000)
$ (15,000)
$ (15,000)
Year 1
$ 9,000
$ (6,000)
$ 3,000
$ (12,000)
Year 2
$ 8,000
$ 2,000
$ 5,000
$ (7,000)
Year 3
$ 5,000
$ 7,000
$ 9,000
$ 2,000
Year 4
$ 6,000
$ 13,000
$ 11,000
$ 13,000
Payback Period
= 1 + 6000 / 8000
1.75 Years
= 2 + 7000 / 9000
2.77 years
Hence the payback period of Project A is earlier.
Calculation of Profitability Index:
Project A
Project B
Cash Flows (CF)
PVF(12%)
PV = CF *PVF
Cash Flows (CF)
PVF(12%)
PV = CF *PVF
Year 0
$ 15,000
$ 1
$ 15,000.00
$ 15,000
$ 1
$ 15,000.00
PVCO
$ 15,000.00
$ 15,000.00
Year 1
$ 9,000
0.89286
$ 8,035.71
$ 3,000
0.89286
$ 2,678.57
Year 2
$ 8,000
0.79719
$ 6,377.55
$ 5,000
0.79719
$ 3,985.97
Year 3
$ 5,000
0.71178
$ 3,558.90
$ 9,000
0.71178
$ 6,406.02
Year 4
$ 6,000
0.63552
$ 3,813.11
$ 11,000
0.63552
$ 6,990.70
PVCI
$ 21,785.28
$ 20,061.26
Profitability index
= PVCI/PVCO
1.45
Year 2
1.34
Profitability index of Project A is Higher.
Calculation of Net present value:
Project A
Project B
Net present value
= PVCI-PVCO
$ 6,785.28
$ 5,061.26
Hence Net Present value of Project A is higher.
So we should Accept project A , and the best reason is :
d. Project A; because it has the higher net present value
Calculation of Payback Period:
Project A
Project B
Cash Flows (CF)
Cummulative CF
Cash Flows (CF)
Cummulative CF
Year 0
$ (15,000)
$ (15,000)
$ (15,000)
$ (15,000)
Year 1
$ 9,000
$ (6,000)
$ 3,000
$ (12,000)
Year 2
$ 8,000
$ 2,000
$ 5,000
$ (7,000)
Year 3
$ 5,000
$ 7,000
$ 9,000
$ 2,000
Year 4
$ 6,000
$ 13,000
$ 11,000
$ 13,000
Payback Period
= 1 + 6000 / 8000
1.75 Years
= 2 + 7000 / 9000
2.77 years
Hence the payback period of Project A is earlier.
Calculation of Profitability Index:
Project A
Project B
Cash Flows (CF)
PVF(12%)
PV = CF *PVF
Cash Flows (CF)
PVF(12%)
PV = CF *PVF
Year 0
$ 15,000
$ 1
$ 15,000.00
$ 15,000
$ 1
$ 15,000.00
PVCO
$ 15,000.00
$ 15,000.00
Year 1
$ 9,000
0.89286
$ 8,035.71
$ 3,000
0.89286
$ 2,678.57
Year 2
$ 8,000
0.79719
$ 6,377.55
$ 5,000
0.79719
$ 3,985.97
Year 3
$ 5,000
0.71178
$ 3,558.90
$ 9,000
0.71178
$ 6,406.02
Year 4
$ 6,000
0.63552
$ 3,813.11
$ 11,000
0.63552
$ 6,990.70
PVCI
$ 21,785.28
$ 20,061.26
Profitability index
= PVCI/PVCO
1.45
Year 2
1.34
Profitability index of Project A is Higher.
Calculation of Net present value:
Project A
Project B
Net present value
= PVCI-PVCO
$ 6,785.28
$ 5,061.26
Hence Net Present value of Project A is higher.
So we should Accept project A , and the best reason is :
d. Project A; because it has the higher net present value
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