# NPV and IRR for mutually exclusive projects

NPV and IRR lead to the same decision for independent projects, not necessarily for mutually exclusive projects. I am not able to understand why. Consider this example: Case 1: a)Projects A and B are independent. b) A’s NPV and IRR are \$10000 and 10%. c) B’s NPV and IRR are \$8000 and 12%. Company will accept both A and B if it has resources, else it will accept only A because of higher NPV. Case 2: Projects A and B are mutually exclusive with the same data as above. Now company will accept A because of higher NPV. Can somebody please guide, what difference did it make from independent to mutually exclusive?

If the firm has \$18,000+ to invest in independent projects then both will be chosen as long as (1) NPV > 0 and (2) IRR > cost of capital. In the other case, when there are mutually exclusive projects the firm can only pick ONE of the choices. In this case (and the rule of thumb) the firm will choose project A because it increases shareholder value the most.

Independent = Company has enough money to finance both projects. Mutually exclusive = Company can only finance 1 project. When dealing with mutually exclusive projects, pursue the project with the higher NPV. NOT the higher IRR. NPV is a better indicator for maximizing shareholder wealth.

When the company has to CHOOSE between projects based on the amount of resources it has available – always use the NPV Rule. Project A has better NPV, lower IRR. Project B has lower NPV, better IRR. When constraints are unlimited (in terms of resources) because both projects have a positive NPV – they add to the company’s bottom line. So both projects may be executed. When constraints are limited (mutually exclusive) – if you went by the NPV rule - you would select A, but with the IRR rule - you would select B. NPV rule is the better one because 1. NPV is adding more to the company’s bottom line. (edit project changed to company) 2. IRR means “internally” you need to be reinvesting everything at that rate, and having a higher IRR does not translate directly to be able to reinvest everything at the IRR rate. You can possibly only reinvest at the company’s cost of funds or cost of capital. CP

Thanks all for the thoughtful answers. So the keyword is “choose”. When projects are mutually exclusive, company has to choose a project, hence NPV overrides IRR.

The NPV of a project depends on the interest rate used to calculate present values. Suppose you have two possible projects: Project CF_0 CF_1 CF_2 CF_3 CF_4 CF_5 CF_6 A -400 100 100 100 100 100 100 B -400 72 85 100 110 120 130 Then Rate NPV_A NPV_B 6% 92 96 8% 62 63 10% 36 34 12% 11 7 That is, NPV_B is greater than NPV_A when the discount rate is below 8.75% (see the bottom of the post) and vice versa. If we look at the IRR of each project, we find IRR_A = 12.98% IRR_B = 12.56% If both projects can be undertaken, then both the IRR and the NPV rule can be interchangeably used to determine whether a specific project should be undertaken. If both projects are mutually exclusive, then the IRR rule favors A over B but the NPV rule favors B when the discount rate is below 8.75 and A otherwise. Hence both rules may yield conflicting answers for mutually exclusive projects. The rate at which NPV_A = NPV_B is the IRR of A minus B: Project CF_0 CF_1 CF_2 CF_3 CF_4 CF_5 CF_6 A-B 0 28 15 0 -10 -20 -30 IRR(A-B) = 8.75%

I have a question on this subject, I’d like to ask it here if you don’t mind. A common example I see used for illustrating NPV and IRR conflict for mutually exclusive projects is as follows: Project A: -200, 50, 50, 50, 50, 50, 50 NPV@5%: 53.78 IRR: 12.98% Project B: -200, 0, 0, 0, 0, 0, 350 NPV@5%: 61.18 IRR: 9.78% Under the above scenario, the rule is to accept Project B and reject Project A if they are mutually exclusive (higher NPV despite the lower IRR - if I did not make a mistake in the calculations). However, those examples assume the same discount rate. But wouldn’t project B carry a higher maturity/default premium? Are we accepting that two mutually exclusive projects will use the same discount rate as an example, or am I misunderstanding discount rates? Thanks.