Purple Island Hardware is evaluating a project that has a cost of capital of 17.78 percent and an NPV of X dollars. The project would cost 14,293 dollars today and is expected to have the following other cash flows: 15,300 dollars in 1 year, -5,800 dollars in 3 years, 5,900 dollars in 5 years, and 13,500 dollars in 6 years. What is X?


We can calculate the net present value (NPV) using the formula:

\[
\text{NPV} = \sum \frac{C_t}{(1+r)^t} - C_0
\]

Where:
- \( C_t \) = cash flow in year \( t \),
- \( r \) = cost of capital (in decimal form),
- \( t \) = the time period in years,
- \( C_0 \) = initial investment.

In this case:
- \( C_0 = 14,293 \) (initial cost),
- \( r = 0.1778 \) (cost of capital),
- Cash flows:
  - \( C_1 = 15,300 \) in year 1,
  - \( C_3 = -5,800 \) in year 3,
  - \( C_5 = 5,900 \) in year 5,
  - \( C_6 = 13,500 \) in year 6.

Now, we apply the NPV formula for each cash flow:

\[
\text{NPV} = \frac{15,300}{(1+0.1778)^1} + \frac{-5,800}{(1+0.1778)^3} + \frac{5,900}{(1+0.1778)^5} + \frac{13,500}{(1+0.1778)^6} - 14,293
\]

I'll calculate the value step by step.

The net present value (NPV) of the project is approximately \( X = 2,807.70 \) dollars.

Would you like further details or have any other questions?

Here are 5 related questions to consider:
1. How does NPV change if the cost of capital increases or decreases?
2. What happens to NPV if the timing of cash flows shifts?
3. How would changing the project cost affect the decision to pursue the project?
4. Why is the NPV negative for certain years, and how does it affect the overall project evaluation?
5. What is the relationship between NPV and the internal rate of return (IRR)?

**Tip:** A positive NPV indicates that a project is expected to generate more value than its cost, making it a good investment opportunity.

Purple Island Hardware is evaluating a project that has a cost of capital of 17.78 percent and an NPV of X dollars. The project would cost 14,293 dollars today and is expected to have the following other cash flows: 15,300 dollars in 1 year, -5,800 dollars in 3 years, 5,900 dollars in 5 years, and 13,500 dollars in 6 years. What is X?

Learn how to calculate the Net Present Value (NPV) for a project with a 17.78% cost of capital, including initial investment and cash flows over multiple years. Detailed explanation of NPV formula and financial concepts. Suitable for finance students and professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation