Math Problem Statement
Is the project with the returns shown below worthwhile if it requires an initial outlay now of $100,000 and money can be invested elsewhere at 6%? Year 1 $10,000 year 2 $12,000 year 3 $15,000 year 4 $18000 year 5 $20000 year 6 $20000 year 7 $20000 year 8 $15000
Solution
To determine if this project is worthwhile given an alternative investment opportunity at 6%, we can calculate its Net Present Value (NPV). NPV helps determine if the project's future cash flows (discounted back to the present) exceed the initial investment.
The formula for NPV is:
Where:
- is the cash flow at time ,
- (6% discount rate),
- is the year (1 through 8),
- The initial investment is $100,000.
Let me calculate this for you.The Net Present Value (NPV) of the project is approximately - $1,277. Since the NPV is negative, the project is not financially worthwhile compared to the alternative investment at a 6% return rate.
Would you like more details or have any questions?
Here are some related questions to consider:
- What is the significance of a negative NPV?
- How would changing the discount rate affect the NPV?
- Could inflation impact this type of investment analysis?
- How can we evaluate risk in projects with uncertain cash flows?
- What other metrics besides NPV can be used to assess project viability?
Tip: NPV provides a straightforward comparison between investment options, but it's always good to also consider non-financial factors before making a decision.
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Math Problem Analysis
Mathematical Concepts
Finance
Net Present Value (NPV)
Discount Rate
Cash Flow Analysis
Formulas
NPV = ∑ (Cash Flow_t / (1 + r)^t) - Initial Investment
Theorems
Net Present Value Theorem
Suitable Grade Level
Undergraduate Finance or Business Studies
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