Net present value vs Internal rate of return

Net present value (NPV) and Internal rate of return (IRR) are used to determine whether to accept a project or not.

Net Present Value (NPV)
Net present value is the difference between the present value of cash inflows and the present value of cash outflows. It is used in capital budgeting to analyze the profitability of an investment or project.

NPV= sum[CF_t/(1+r)^t]-C₀
Where:
CF_t– cash flow in the time t
C₀ – initial investment
r – periodic interest rate

NPV rule:

• Accept all independent projects with NPV greater than 0 as they add value to shareholder. In case of mutually exclusive projects, the project with the highest NPV should be chosen.

Advantages:

• Direct measure of the dollar contribution to the stockholders.
• NPV method is preferable for non-normal cash flows (e.g. negative cash flows)

Disadvantage:

• Does NOT measure the project size.

Internal Rate of Return (IRR)
The discount rate makes the net present value of all cash flows from a project equal to zero. The higher a project's internal rate of return, the more desirable it is to undertake the project. IRR can be used to rank several prospective projects a firm is considering.

NPV= Sum[CF_t/(1+r)^t]–C₀

r = internal rate of return (IRR)

IRR rule:

• Accept all independent projects with IRR greater than cost of capital. In case of mutually exclusive projects, the project with the highest IRR should be chosen.

Advantages:

• Show you the return rate on the original money invested.

Disadvantages:

• Give you conflicting answers when compared to NPV for mutually exclusive projects.
• Multiple IRR for non-normal cash flows (when the project operates at a loss or the company needs to contribute more capital)

Conflicts between NPV and IRR Methods
For an independent project that the decision to invest in a project is independent of any other projects, both the NPV and IRR will always give the same result.

For mutually exclusive projects that the decision must be one project or another, NPV and IRR can lead to a conflicting result due:

• Different timing of cash flows
• Different project sizes.
  
  
  
  If the cost of capital greater than the crossover rate, NPV and IRR provide the same result;
  If the cost of capital smaller than crossover rate, conflict exists and use the NPV decision;
  
  Notes:
• NPV assures reinvestment at cost of capital; IRR assures reinvestment at IRR.