Math Problem Statement
Big Steve's, makers of swizzle sticks, is considering the purchase of a new plastic stamping machine. This investment requires an initial outlay of $90,000 and will generate net cash inflows of $20,000 per year for 8 years. If the discount rate is 7 percent, then the project's NPV is $
Solution
The formula to calculate the Net Present Value (NPV) is:
Where:
- = net cash inflow in year
- = discount rate
- = year (from 1 to the duration of the project)
- = initial outlay
Given:
- Initial outlay () = $90,000
- Cash inflows () = $20,000 per year
- Discount rate () = 7% or 0.07
- Duration = 8 years
We can break this into two steps:
- Calculate the present value of each year's cash inflows.
- Subtract the initial outlay from the total present value of the inflows to get the NPV.
I'll calculate this now.The Net Present Value (NPV) of the project is approximately $29,426.
Would you like more details on this calculation or any clarifications?
Here are 5 related questions for further exploration:
- How does the NPV change if the discount rate increases or decreases?
- What is the Internal Rate of Return (IRR) for this project?
- How would an increase in cash inflows affect the NPV?
- What are the risks associated with the discount rate assumption?
- How does NPV compare to other project evaluation methods like Payback Period or IRR?
Tip: A positive NPV suggests that the project is expected to add value to the company, as the inflows exceed the initial investment when considering the time value of money.
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Math Problem Analysis
Mathematical Concepts
Finance
Investment Analysis
Net Present Value (NPV)
Formulas
NPV = Σ (R_t / (1 + r)^t) - C_0
Theorems
Net Present Value (NPV) Calculation
Suitable Grade Level
College-Level Finance
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