You have been asked to determine whether the following project is to be taken by
ID: 2760973 • Letter: Y
Question
You have been asked to determine whether the following project is to be taken by your company. The cost of the project is to be incurred over two years. The cash outflow in year 0 will be $160,000 and in year two $190,000. The first positive cash flow will be in years 3 and will be $80,000 after that the cash flows will be $120,000 in year 4; 200,000 in year 5; $300,000 in year 6;and $50,000 in year 7. Calculate the NPV, IRR, Payback period, MIRR, and the Profitability Index of the project. Determine if the project should be taken if the required rate of return is 12.00% and the cutoff payback period is 2.5 years?
Explanation / Answer
Net Present Value
1.12
Year
CashFlow
PV Factor@ 12%
PV
0
(160,000)
1
(160,000.00)
1
-
0.8929
-
2
(190,000)
0.7972
(151,466.84)
3
80,000
0.7118
56,942.42
4
120,000
0.6355
76,262.17
5
200,000
0.5674
113,485.37
6
300,000
0.5066
151,989.34
7
50,000
0.4523
22,617.46
NPV
109,829.92
IRR
Year
Cash Flow
0
(160,000)
1
-
2
(190,000)
3
80,000
4
120,000
5
200,000
6
300,000
7
50,000
IRR
20.71%
Payback Period
Year
CashFlow
Cum Payback Period
0
(160,000)
(160,000)
1
-
(160,000)
2
(190,000)
(350,000)
3
80,000
(270,000)
4
120,000
(150,000)
5
200,000
50,000
6
300,000
350,000
7
50,000
400,000
Payback Period= 4+ 150,000/200,000
=4+ 0.75 =4.75 years
After second investment it is 2.5 years
Discounted Payaback Period
Year
CashFlow
PV Factor@ 12%
PV Cash Flow
Cum PV CashFlow
0
(160,000)
1
(160,000.00)
(160,000.00)
1
-
0.8929
-
(160,000.00)
2
(190,000)
0.7972
(151,466.84)
(311,466.84)
3
80,000
0.7118
56,942.42
(254,524.42)
4
120,000
0.6355
76,262.17
(178,262.25)
5
200,000
0.5674
113,485.37
(64,776.88)
6
300,000
0.5066
151,989.34
87,212.46
7
50,000
0.4523
22,617.46
109,829.92
Payback Period= 5+ 64,776.88/300,000
=4+ 0.21=4.21 years
After second investment it is 2.21 years
MIRR:(7421,296.76/311,466.84) -1
=7 1.352621556-1
= 1.1630225951/7-1
= 1.021809029-1
= 0.021809029 or 2.18%
Profitability index = NPV+ Initial Investment/ Initial Investment
=$109,829.92+ 360,000/360,000=
=$469,829.92/300,000=1.57
if the cutoff payback is 2.5 then project should not be taken
Net Present Value
1.12
Year
CashFlow
PV Factor@ 12%
PV
0
(160,000)
1
(160,000.00)
1
-
0.8929
-
2
(190,000)
0.7972
(151,466.84)
3
80,000
0.7118
56,942.42
4
120,000
0.6355
76,262.17
5
200,000
0.5674
113,485.37
6
300,000
0.5066
151,989.34
7
50,000
0.4523
22,617.46
NPV
109,829.92
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