https://file.aiquickdraw.com/mathbot/file/1731033160793ccxdhtj9.jpg

The Net Present Value (NPV) is calculated using the formula:

\[
\text{NPV} = \frac{\text{Expected Sale Price}}{(1 + r)^n} - \text{Cost Today}
\]

where:
- $ r $ is the discount rate,
- $ n $ is the number of years (in this case, $ n = 5 $).

For Mountain Ridge:
- **Expected Sale Price** = $18,000,000
- **Cost Today** = $3,000,000
- **Discount Rate (r)** = 15%
- **n** = 5 years

Plugging in these values:

1. Calculate the present value of the expected sale price in Year 5:

\[
\text{Present Value} = \frac{18,000,000}{(1 + 0.15)^5}
\]

2. Then, subtract the initial cost:

\[
\text{NPV} = \frac{18,000,000}{(1.15)^5} - 3,000,000
\]

Calculating each part:

\[
(1.15)^5 = 2.0113571875
\]

\[
\frac{18,000,000}{2.0113571875} = 8,949,181.07
\]

\[
\text{NPV} = 8,949,181.07 - 3,000,000 = 5,949,181.07
\]

This is approximately $5,949,181, matching the answer provided in the table.

Would you like further details or have any questions?

---

Here are some additional questions related to this calculation:

1. How would changing the discount rate affect the NPV?
2. What is the relationship between IRR and NPV?
3. How does the investment horizon (number of years) impact the NPV?
4. What would be the NPV if the cost today increased by 10%?
5. Why is NPV an important measure for investment decisions?

**Tip:** When calculating NPV, ensure that the discount rate and period align (e.g., annual rate with annual periods) to avoid errors.

Learn how to calculate the Net Present Value (NPV) for Mountain Ridge real estate investment with a discount rate of 15% and a 5-year horizon. Detailed step-by-step breakdown of the formula, showing how the expected sale price and initial cost contribute to the NPV calculation. Ideal for finance students or professionals learning about discounted cash flow (DCF) and NPV.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation