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Home > Algebra calculators > Net Present Value (NPV) example
Net Present Value (NPV) example ( Enter your problem )
( Enter your problem )
  1. Example : Single cash flow
  2. Example : Multiple cash flow
1. Example : Single cash flow
(Previous example)

2. Example : Multiple cash flow


1. Calculate Net Present Value for
Initial investment = 50000, Discount rate = 13% and cash flow will be
Year123
Cash Flow130002600023000


Solution:
initial investment = 50000
`i=13%=0.13` per year (Interest rate)

Multiple cash flow NPV
`NPV=sum_{t=0}^(n)(FV_t)/((1+i)^t)`

Method-1:
YearCash FlowPresent value
0`-50000``(-50000)/((1+0.13)^0)=-50000`
1`13000``(13000)/((1+0.13)^1)=11504.42`
2`26000``(26000)/((1+0.13)^2)=20361.81`
3`23000``(23000)/((1+0.13)^3)=15940.15`
`NPV=-2193.61`


Method-2:
YearCash FlowDiscounting FactorPresent value
0`-50000`1`-50000`
1`13000``1/((1+0.13)^1)=0.885``11504.42`
2`26000``1/((1+0.13)^2)=0.7831``20361.81`
3`23000``1/((1+0.13)^3)=0.6931``15940.15`
`NPV=-2193.61`


Since NPV is less than 0, so manager should reject project.
2. Calculate Net Present Value for
Initial investment = 500, Discount rate = 5% and cash flow will be
Year12345
Cash Flow5075100150250


Solution:
initial investment = 500
`i=5%=0.05` per year (Interest rate)

Multiple cash flow NPV
`NPV=sum_{t=0}^(n)(FV_t)/((1+i)^t)`

Method-1:
YearCash FlowPresent value
0`-500``(-500)/((1+0.05)^0)=-500`
1`50``(50)/((1+0.05)^1)=47.62`
2`75``(75)/((1+0.05)^2)=68.03`
3`100``(100)/((1+0.05)^3)=86.38`
4`150``(150)/((1+0.05)^4)=123.41`
5`250``(250)/((1+0.05)^5)=195.88`
`NPV=21.32`


Method-2:
YearCash FlowDiscounting FactorPresent value
0`-500`1`-500`
1`50``1/((1+0.05)^1)=0.9524``47.62`
2`75``1/((1+0.05)^2)=0.907``68.03`
3`100``1/((1+0.05)^3)=0.8638``86.38`
4`150``1/((1+0.05)^4)=0.8227``123.41`
5`250``1/((1+0.05)^5)=0.7835``195.88`
`NPV=21.32`


Since NPV is greater than 0, so manager should accept project.
3. Calculate Net Present Value for
Initial investment = 250000, Discount rate = 10% and cash flow will be
Year12345
Cash Flow100000150000200000250000300000


Solution:
initial investment = 250000
`i=10%=0.1` per year (Interest rate)

Multiple cash flow NPV
`NPV=sum_{t=0}^(n)(FV_t)/((1+i)^t)`

Method-1:
YearCash FlowPresent value
0`-250000``(-250000)/((1+0.1)^0)=-250000`
1`100000``(100000)/((1+0.1)^1)=90909.09`
2`150000``(150000)/((1+0.1)^2)=123966.94`
3`200000``(200000)/((1+0.1)^3)=150262.96`
4`250000``(250000)/((1+0.1)^4)=170753.36`
5`300000``(300000)/((1+0.1)^5)=186276.4`
`NPV=472168.75`


Method-2:
YearCash FlowDiscounting FactorPresent value
0`-250000`1`-250000`
1`100000``1/((1+0.1)^1)=0.9091``90909.09`
2`150000``1/((1+0.1)^2)=0.8264``123966.94`
3`200000``1/((1+0.1)^3)=0.7513``150262.96`
4`250000``1/((1+0.1)^4)=0.683``170753.36`
5`300000``1/((1+0.1)^5)=0.6209``186276.4`
`NPV=472168.75`


Since NPV is greater than 0, so manager should accept project.
4. Calculate Net Present Value for
Initial investment = 95000, Discount rate = 20% and cash flow will be
Year1234
Cash Flow30000470004800032000


Solution:
initial investment = 95000
`i=20%=0.2` per year (Interest rate)

Multiple cash flow NPV
`NPV=sum_{t=0}^(n)(FV_t)/((1+i)^t)`

Method-1:
YearCash FlowPresent value
0`-95000``(-95000)/((1+0.2)^0)=-95000`
1`30000``(30000)/((1+0.2)^1)=25000`
2`47000``(47000)/((1+0.2)^2)=32638.89`
3`48000``(48000)/((1+0.2)^3)=27777.78`
4`32000``(32000)/((1+0.2)^4)=15432.1`
`NPV=5848.77`


Method-2:
YearCash FlowDiscounting FactorPresent value
0`-95000`1`-95000`
1`30000``1/((1+0.2)^1)=0.8333``25000`
2`47000``1/((1+0.2)^2)=0.6944``32638.89`
3`48000``1/((1+0.2)^3)=0.5787``27777.78`
4`32000``1/((1+0.2)^4)=0.4823``15432.1`
`NPV=5848.77`


Since NPV is greater than 0, so manager should accept project.

This material is intended as a summary. Use your textbook for detail explanation.
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1. Example : Single cash flow
(Previous example)


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