Math Problem Statement
ig Steve's, makers of swizzle sticks, is considering the purchase of a new plastic stamping machine. This investment requires an initial outlay of
$110,000
and will generate net cash inflows of
$17,000
per year for
9
years.
a. What is the project's NPV using a discount rate of
9
percent?
Should the project be accepted? Why or why not?
Solution
To calculate the project's Net Present Value (NPV), we use the following formula:
Where:
- is the initial investment (outlay).
- is the annual cash inflow.
- is the discount rate.
- is the year.
- The summation runs for the number of years over which the cash inflows are received.
Given:
- Initial investment () = $110,000
- Annual cash inflow () = $17,000
- Number of years () = 9
- Discount rate () = 9% or 0.09
Let's calculate the NPV.
I'll compute the NPV now.The Net Present Value (NPV) of the project is approximately -$8,080.80.
Should the project be accepted?
No, the project should not be accepted because the NPV is negative. A negative NPV indicates that the project's cash inflows, discounted at the given rate, are not enough to cover the initial investment, leading to a net loss in present value terms.
Would you like more details or have any questions?
Here are some related questions to consider:
- What is the Internal Rate of Return (IRR) for this project?
- How would the NPV change if the discount rate were 7%?
- What is the Payback Period for this investment?
- How does NPV compare to other methods like IRR or Payback Period?
- Can NPV be positive if cash inflows increase by 10% annually?
Tip: A project is generally considered acceptable if the NPV is positive because it means the project is expected to generate more value than its cost in today's terms.
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Math Problem Analysis
Mathematical Concepts
Net Present Value (NPV)
Discount Rate
Cash Flows
Present Value
Formulas
NPV = Σ (C_t / (1 + r)^t) - C_0
C_0 = Initial Investment
C_t = Annual Cash Inflow
r = Discount Rate
Theorems
Time Value of Money
Suitable Grade Level
Undergraduate Finance/Business
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