In2012,Goldfieldsembarkedonaproject.Theprojectwillreceiveannualinflowsof GHC30000fromthe3rdyearthroughto10thyearand35000fromthe12thyearthrough totheendoftheprojectslifespanin30yearstime.Inyearstwoandthreehowever, theyarerequiredtoinvest10000ghceachintotheproject.Findthenetpresentvalue oftheproject.
Question
In2012,Goldfieldsembarkedonaproject.Theprojectwillreceiveannualinflowsof GHC30000fromthe3rdyearthroughto10thyearand35000fromthe12thyearthrough totheendoftheprojectslifespanin30yearstime.Inyearstwoandthreehowever, theyarerequiredtoinvest10000ghceachintotheproject.Findthenetpresentvalue oftheproject.
Solution
To calculate the Net Present Value (NPV) of the project, we need to know the discount rate. However, since it's not provided, I'll explain the steps assuming we have a discount rate. Let's call it 'r'.
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Identify the cash flows:
- Years 1-2: -10,000 GHC each (investment into the project)
- Years 3-10: +30,000 GHC each (annual inflows)
- Years 11: 0 GHC (no inflow or outflow)
- Years 12-30: +35,000 GHC each (annual inflows)
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Calculate the present value (PV) of each cash flow. The formula for PV is:
PV = FV / (1 + r)^n
where:
- FV is the future value of the cash flow
- r is the discount rate
- n is the year
You need to do this for each year and sum them all up.
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The NPV of the project is the sum of the present values of all cash flows.
Remember, if the NPV is positive, the project is considered profitable. If it's negative, the project is expected to result in a net loss.
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