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:

NPV=(Cash Flowt(1+r)t)Initial Investment\text{NPV} = \sum \left( \frac{\text{Cash Flow}_t}{(1 + r)^t} \right) - \text{Initial Investment}

Where:

  • Cash Flowt\text{Cash Flow}_t is the cash flow at time tt,
  • r=0.06r = 0.06 (6% discount rate),
  • tt 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:

  1. What is the significance of a negative NPV?
  2. How would changing the discount rate affect the NPV?
  3. Could inflation impact this type of investment analysis?
  4. How can we evaluate risk in projects with uncertain cash flows?
  5. 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