Why doesn't changing the Discount Rate change IRR?

I have an analysis for a real estate project done and I'm changing the discount rate but IRR is not affected. I don't understand why this is...? It seems that changing the discount rate would change the NPV, changing the point where NPV=0.

• Is this a homework problem in an economics or accounting course or a prep course for a real estate broker license exam? – Dilip Sarwate Jul 1 '13 at 13:44

Because the IRR doesn't depend on discount rate.

Instead, the IRR is a discount rate.

The IRR is the discount rate that makes the NPV=0.

Put another way, the IRR is the discount rate that causes projects to break even.

Raising or lowering the discount rate in a project does not affect the rate that would have caused it to break even.

• Thanks, Paul. I should get it in my mind that NPV calculations and IRR are separate. For some reason I keep mixing them. – Moi Jul 1 '13 at 20:22
• Looks like I spoke too soon. My situation is that I have a degree in real estate finance....from 18 years ago. I'm getting back into real estate and some things are coming back quickly and I have holes in other places. In school we focused on IRR and FMRR. When I have an investor who wants a 12% return on a building purchase I just use DCF at 12% to get the target purchase price. I know that if that's the price it's bought at then NPV = 0 = discount rate. That's the break even point of the investment. (more continued) – Moi Jul 2 '13 at 2:06
• "Raising or lowering the discount rate in a project does not affect the rate that would have caused it to break even." This is probably my hole. In my mind if you are paying 15% interest and you find a new loan at 5% interest then your cost of capital (discount rate) changes and your IRR would change as well. Can you explain more about how the break even point is not affected? – Moi Jul 2 '13 at 2:17
• Moi, suppose there is a real estate project with IRR=6%. The investor finds a loan with rate=3%, therefore he believes the investment will be profitable since NPV(r) should be positive for r below IRR%. However, it turns out the loan was an adjustable loan that changes after 1 month to 7.99%. Now the investor should know that since 7.99% is above IRR=6% the project will have negative NPV and therefore yield a loss. The fact that the loan rate changed does not affect that the IRR was 6% and that with financing at 6%, NPV would be zero (break even). – Paul Jul 2 '13 at 2:40
• There is an analogy with household budget. If Fred needs \$3,500/month salary to break even on his household bills, we mean that at that salary of \$3500/mo he has exactly no money left over. If S is the salary, we could say his disposable income is S-3500. If his salary goes down to \$2000/mo, his disposable income is 2000-3500=-1500 and he still needs \$3500/mo to break even. If his salary goes up to \$4000/mo, his disposable income is now 4000-3500=500 and that is good, he needed \$3500/mo to break even. The break even math is the same. It is only a model, as real people do adjust spending.. – Paul Jul 2 '13 at 2:47

If you have a schedule of discount rates then the IRR you seeking is the interest rate at which net present value of the investment discounted using a schedule of rates is the same as the net present value of investment using a single rate. Think of this a interest rate shocks over the term of the investment and the investor is seeking a single rate that will offer the same return on investment as those offered by the schedule of discount rates.