Accounts & Finance

"a) The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of an investment project equal to zero. The NPV of a project is the sum of the present values of all cash flows associated with the project, discounted at the given rate of return.

Let's calculate the IRR and NPV for both projects:

Project A:

Initial Investment (Year 0): -$500

Cash Inflow (Year 1): $650

NPV(A) = Cash Inflow / (1 + Discount Rate)^Year - Initial Investment

NPV(A) = $650 / (1 + 0.10)^1 - $500

NPV(A) = $590.91

Project B:

Initial Investment (Year 0): -$250

Cash Inflow (Year 1): $350

NPV(B) = Cash Inflow / (1 + Discount Rate)^Year - Initial Investment

NPV(B) = $350 / (1 + 0.10)^1 - $250

NPV(B) = $295.45

To calculate IRR, we need to find the discount rate that makes NPV equal to 0 for each project:

For Project A:

NPV(A) = $0 = $650 / (1 + IRR)^1 - $500

Solving for IRR, IRR(A) ≈ 30.18%

For Project B:

NPV(B) = $0 = $350 / (1 + IRR)^1 - $250

Solving for IRR, IRR(B) ≈ 40.00%

So, the IRR for Project A is approximately 30.18%, and for Project B, it's approximately 40.00%.

The NPV of Project A is $590.91 and the NPV of Project B is $295.45."