Which one of the following is correct about NPV and IRR of project (A) and project (B)?

Correct option is A

Net Present Value (NPV):

• NPV measures the present value of cash inflows minus the present value of cash outflows.

• It is an additive measure, meaning that the total NPV of two projects is simply the sum of their individual NPVs.

• Mathematically:

  NPV (A + B) = NPV (A) + NPV (B)

Internal Rate of Return (IRR):

• IRR is the discount rate at which the NPV of a project becomes zero.

• Unlike NPV, IRR is not additive—you cannot sum the IRRs of individual projects to get the IRR of combined projects.

• IRR follows complex nonlinear relationships, making it unreliable for combination calculations.

Information Booster:

• NPV is always additive, meaning that the value of a combined project equals the sum of the NPVs of its individual components.

• NPV is a more reliable decision-making tool than IRR, especially when projects have different durations, cash flow patterns, or discount rates.

• IRR does not follow a simple arithmetic relationship—it is derived from a polynomial equation, making its combination unpredictable.

• If two projects are mutually exclusive, relying on IRR alone can lead to misleading decisions.

Additional Knowledge:

1. Option (2) NPV (A) = NPV (B) ≠ NPV of (A + B) (Incorrect)

   • This statement suggests that NPVs of A and B remain separate and do not combine, which is incorrect.

   • NPV is always additive, so the combined NPV is the sum of individual NPVs.

2. Option (3) IRR (A) + IRR (B) = IRR of (A + B) (Incorrect)

   • IRR is not additive; the IRR of a combined project is not the sum of individual IRRs.

   • This is because IRR is derived from cash flow discounting and follows nonlinear behavior.

3. Option (4) IRR (A) × IRR (B) ≠ IRR (A - B) (Incorrect)

   • There is no direct multiplication or subtraction relationship between IRRs.

   • IRR depends on the timing and magnitude of cash flows, making it impossible to combine mathematically like this.​