https://file.aiquickdraw.com/mathbot/file/17253991385632ibeyyzd.jpg

To solve the problem in the image, let's break down the process step by step:

### Problem Statement Recap:
- **Project X**:
  - Initial Investment: Rs. 20,000
  - Estimated Life: 6 years
  - Scrap Value: Rs. 1,000

- **Project Y**:
  - Initial Investment: Rs. 30,000
  - Estimated Life: 6 years
  - Scrap Value: Rs. 3,000

### Cash Flows:
- **Project X** Cash Flows (Years 1-6): Rs. 6,000, Rs. 10,000, Rs. 3,000, Rs. 5,000, Rs. 2,000, Rs. 2,000
- **Project Y** Cash Flows (Years 1-6): Rs. 2,000, Rs. 19,000, Rs. 6,000, Rs. 6,000, Rs. 3,000, Rs. 2,000

### Discount Rate:
- **10%**

### Objective:
Calculate the Net Present Value (NPV) for both projects and determine which project should be selected.

### Step-by-Step Calculation:
1. **Compute the Present Value (PV) of cash flows for each year** using the formula:
   \[
   \text{PV} = \frac{\text{Cash Flow}}{(1 + r)^t}
   \]
   where \( r \) is the discount rate (10%), and \( t \) is the year.

2. **Sum the PVs** for each project.

3. **Subtract the initial investment** from the sum of PVs to get the NPV.

### Detailed Calculation:
Let's calculate the NPVs for both projects.

#### Project X:
- Initial Investment: Rs. 20,000
- Cash Flows for Years 1-6: Rs. 6,000, Rs. 10,000, Rs. 3,000, Rs. 5,000, Rs. 2,000, Rs. 2,000

#### Project Y:
- Initial Investment: Rs. 30,000
- Cash Flows for Years 1-6: Rs. 2,000, Rs. 19,000, Rs. 6,000, Rs. 6,000, Rs. 3,000, Rs. 2,000

Let me perform these calculations.### NPV Calculation Results:
- **NPV of Project X**: Rs. 2,323.28
- **NPV of Project Y**: Rs. 811.76

### Conclusion:
Since the NPV of Project X is higher than that of Project Y, **Project X should be selected**.

Would you like any further details or explanations? Here are some related questions you might find interesting:

1. How does changing the discount rate affect the NPV of these projects?
2. What are some limitations of using NPV as a decision-making tool?
3. How would the inclusion of taxes impact the NPV calculations?
4. What if the cash flows were different every year? How would that change the analysis?
5. How does the time value of money concept influence the NPV?

**Tip:** Always consider the sensitivity of your NPV analysis to changes in discount rates and cash flow estimates, as these can significantly alter project rankings.

From the following information, calculate the net present value of the two projects and suggest which of the projects should be accepted assuming a discount rate of 10%. Initial investment, estimated life, scrap value, and cash flows before depreciation are given for Project X and Project Y.

Learn how to calculate the Net Present Value (NPV) for two investment projects, Project X and Project Y, with a discount rate of 10%. The analysis includes cash flow projections, present value calculations, and a decision on which project to accept based on the 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