Math Problem Statement

A firm whose cost of capital is 10% is considering two projects (A & B) with an investment of ₹2,00,000 in each. The cash inflows over 5 years are provided for both projects. The task is to compute the Net Present Value (NPV) at 10% and the Internal Rate of Return (IRR) for both projects. Additionally, compute the NPV for Project A at 20% and for Project B at 10% and 15%.

Solution

The case study presents a problem where a firm is evaluating two investment projects (A and B) with the following data provided:

  • Cost of capital (Discount Rate): 10%
  • Investment in both Projects A & B: ₹2,00,000

Cash inflows for each project:

YearProject A (₹)Project B (₹)
140,00090,000
260,00080,000
380,00060,000
41,00,00020,000
51,20,00016,000

The tasks are:

  1. Compute the Net Present Value (NPV) at 10%.
  2. Compute the Internal Rate of Return (IRR) for the two projects.
  3. Additionally, compute the NPV for Project A with a discount rate of 20% and Project B with 10% and 15%.

Let's start by calculating the NPV and IRR for Project A and B at a 10% discount rate.

I will first compute the NPV for each project. Let me proceed.The Net Present Values (NPV) of the projects at a 10% discount rate are:

  • NPV for Project A: ₹88,867.50
  • NPV for Project B: ₹16,607.78

Next, I will compute the Internal Rate of Return (IRR) for both projects, which is the discount rate at which the NPV becomes zero. I'll proceed with these calculations now.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the process of manually calculating the Internal Rate of Return (IRR) and provide more detailed explanations on how to do it.

Would you like to proceed with a manual method or explore other questions related to the analysis?

Here are some additional questions to consider:

  1. How is NPV different from IRR in evaluating projects?
  2. What is the significance of using different discount rates for NPV?
  3. What would be the outcome if the cash inflows were spread differently?
  4. Can the IRR for a project be negative? What would that indicate?
  5. How would the NPV change if the cost of capital were higher than 10%?

Tip: IRR is the discount rate that makes the NPV of a project zero. You can solve it iteratively or use financial calculators/spreadsheets for faster calculations.

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Math Problem Analysis

Mathematical Concepts

Net Present Value (NPV)
Internal Rate of Return (IRR)
Discount Rate
Cash Flows

Formulas

NPV = Σ [Cash flow / (1 + r)^t] - Initial Investment
IRR is the discount rate where NPV = 0

Theorems

Time Value of Money

Suitable Grade Level

Undergraduate/Graduate