Development cost	$1,600,000	
Estimated development time	9	months
Pilot testing	$200,000	
Ramp-up cost	$400,000	
Marketing and support cost	$150,000	per year
Sales and production volume	60,000	per year
Unit production cost	$100	
Unit price	$240	
Interest rate	8%	

What are the yearly cash flows and their present value (discounted at 8 percent) of this project? What is the net present value?
Note: Enter your answer in thousands of dollars. Do not round any intermediate calculations. Round your answer to the nearest thousand.

Find NPV


To calculate the Net Present Value (NPV) of the project, we need to follow these steps:

### **Step 1: Determine the cash flows for each year.**

**Initial Investment (Year 0):**
- Development Cost: $1,600,000
- Pilot Testing: $200,000
- Ramp-up Cost: $400,000
- **Total Initial Investment (Year 0):** $1,600,000 + $200,000 + $400,000 = $2,200,000

**Year 1 onwards:**
- Revenue per year = Sales volume × Unit price = 60,000 units × $240 = $14,400,000
- Cost per year (excluding marketing and support) = Sales volume × Unit production cost = 60,000 units × $100 = $6,000,000
- Gross profit per year = Revenue - Cost = $14,400,000 - $6,000,000 = $8,400,000
- Marketing and support cost per year = $150,000
- **Net Cash Flow per year (Years 1 and onwards):** $8,400,000 - $150,000 = $8,250,000

### **Step 2: Discount the cash flows to their present value using the 8% interest rate.**

- The cash flow in Year 0 is simply the initial investment: $-\$2,200,000$.

- For subsequent years (Year 1 onward), we discount the net cash flows at the 8% discount rate using the present value formula:
  \[
  PV = \frac{\text{Cash Flow}}{(1 + r)^t}
  \]
  where $r = 8\% = 0.08$ and $t$ is the year.

### **Step 3: Calculate NPV by summing the present values.**

I'll now compute these values.The Net Present Value (NPV) of the project is **$49,337,000**.

### **Yearly Cash Flows and Present Value:**

1. **Year 0 (Initial Investment):** 
   - Cash Flow: $-\$2,200,000$
   - Present Value: $-\$2,200,000$

2. **Years 1 to 9 (Operating Years):**
   - Cash Flow: \$8,250,000 per year
   - Present Value (Discounted at 8%): Calculated yearly and summed to obtain NPV.

**Net Present Value (NPV):** \$49,337,000

### Questions for Further Exploration:
1. What is the break-even point in terms of years?
2. How would the NPV change if the interest rate were 10%?
3. What would be the impact on NPV if the unit production cost increased by 10%?
4. How does the NPV change if the sales volume decreases by 10%?
5. What is the internal rate of return (IRR) for this project?

### Tip:
When analyzing investment projects, always compare NPV across different scenarios to understand the sensitivity of the project to changes in key assumptions.

Learn how to calculate the Net Present Value (NPV) and yearly cash flows for a project with specific financial data. Understand the importance of discounted cash flow (DCF) analysis and how interest rates affect project valuation. Explore detailed calculations and interpretations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation