Math Problem Statement

A firm whose cost of capital is 10% is considering two projects A & B. The investment for each project is ₹2,00,000. The cash inflows for Project A over 5 years are ₹40,000, ₹60,000, ₹80,000, ₹1,00,000, and ₹1,20,000. The cash inflows for Project B are ₹90,000, ₹80,000, ₹60,000, ₹20,000, and ₹16,000. Compute the Net Present Value at 10% and Internal Rate of Return for both projects, and compute the NPV for Project A at 20% and Project B at 10% and 15%.

Solution

The image you uploaded presents data for two projects, A and B, along with the cash flows for each year. The firm has a cost of capital of 10%, and you are asked to calculate:

  1. Net Present Value (NPV) at 10% for both projects.
  2. Internal Rate of Return (IRR) for both projects.
  3. NPV for Project A at 20%.
  4. NPV for Project B at 10% and 15%.

Extracted Data:

  • Investment for both projects: ₹2,00,000.
  • Cash inflows:
    • Project A:
      • Year 1: ₹40,000
      • Year 2: ₹60,000
      • Year 3: ₹80,000
      • Year 4: ₹1,00,000
      • Year 5: ₹1,20,000
    • Project B:
      • Year 1: ₹90,000
      • Year 2: ₹80,000
      • Year 3: ₹60,000
      • Year 4: ₹20,000
      • Year 5: ₹16,000

Let's first compute the Net Present Value (NPV) for both projects at 10% discount rate.

NPV Formula:

NPV=Cash inflowt(1+r)tInitial Investment\text{NPV} = \sum \frac{\text{Cash inflow}_t}{(1 + r)^t} - \text{Initial Investment} Where:

  • rr = Discount rate (10% or 0.10 for the first calculation).
  • tt = Year (1 to 5).

I'll calculate the NPVs now.The Net Present Value (NPV) at a 10% discount rate for both projects is as follows:

  • 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, and the NPVs at different rates for Project A (20%) and Project B (10% and 15%).

Let's start with calculating the IRRs for both projects.It seems like I can’t do more advanced data analysis right now. Please try again later. However, the NPVs at 10% have already been calculated.

Would you like to explore the IRR manually or perform other calculations? Let me know if you have any questions!

Here are some relative questions to expand your understanding:

  1. What is the significance of NPV in capital budgeting decisions?
  2. How does the IRR compare to NPV in determining project viability?
  3. Why is the discount rate crucial for NPV calculation?
  4. What are other methods used to evaluate projects besides NPV and IRR?
  5. How do higher discount rates impact long-term projects?

Tip: NPV and IRR often yield different recommendations; it's wise to consider both when making investment decisions.

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Math Problem Analysis

Mathematical Concepts

Net Present Value (NPV)
Internal Rate of Return (IRR)
Discounting
Capital Budgeting

Formulas

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

Theorems

Time Value of Money

Suitable Grade Level

University Level - Finance