 # Simple IRR question

Hey guys, i’m a little confused about IRR and was figuring some of the geniuses on here could help me out: 1. The IRR is defined as the “rate of return at which a project’s NPV equals zero”, or in other words, the rate of return at which PV cash inflows equals PV cash outflows. That being said, the text also says the greater the IRR is above the hurdle rate, the greater the NPV and vice versa". Now, definitionally, the IRR is a SINGLE VALUE, the rate at which NPV = 0. So how can the NPV be higher or lower then 0 based on the IRR? 2. I may be wrong here, but as I understand it, you can calculate the IRR by making different cost-of-capital (discount rate) assumptions, and seeing which one brings you closest to the NPV being 0, and the highest IRR will mean the highest NPV for the project. Now again, ignoring my confusion in Question 1, why are we saying that the project with the HIGHEST IRR (or in other words, highest cost of capital assumption) will have the highest NPV. Shouldn’t the lowest IRR have the highest NPV, as cost of capital is less? Also, the text I’m using says you can think of the IRR as both a rate of return, and the cost of capital. How can it be both those things, as an increase in a cost of capital would directly reduce the rate of return? I think I’m missing a piece to complete this puzzle, I appreciate any help! I just started off with my studying, so this is all new to me. Thanks

You kind of answered your own question. The IRR is the point at which NPV equals 0. If this equals the discount rate or cost of capital, any IRR value higher than this would indicate that the PV of cash flows is > than the PV of the initial outlay. Vice versa if the IRR is lower than the discount rate. So when they say you can think of it as the rate of return and the discount rate, they are correct. It’s the discount rate that makes the NPV=0 for that specific project. However this isn’t the actual firm’s discount rate used firmwide when evaluating capital expenditures. Since it’s also the project’s rate of return you compare to the firmwide discount rate and if > you accept the project, if < you reject. The higher it is over the firmwide discount rate, the higher the NPV is for that specific project. You just need to think about it as a discount rate for a specific project vs the discount rate aka cost of capital for the entire firm. You then compare the discount rate for the project to the one for the firm. If greater it will add value, if lower it will subtract value. It tells you that the rate of return for the project is either higher/lower than how much it will cost the firm to fund the project. You then accept/reject accordingly. You can probably use examples from the books to help you understand that have a positive NPV and maybe change one of the cash inflows to make it larger. Then compute the IRR. You’ll notice the higher NPV value you would get a higher IRR as well. The reason is that the discount rate for the project to make the NPV=0 will now have to increase since the cash flow just increased(this should just make sense intuitively). The PV of FCF’s is now larger so you need a higher IRR to make the NPV = 0. Try adding a cash outflow to now lower the PV of FCF’s. You’ll see the IRR decrease accordingly. Hope that helps a little.

brafique Wrote: ------------------------------------------------------- > Hey guys, i’m a little confused about IRR and was > figuring some of the geniuses on here could help > me out: > > 1. The IRR is defined as the “rate of return at > which a project’s NPV equals zero”, or in other > words, the rate of return at which PV cash inflows > equals PV cash outflows. That being said, the text > also says the greater the IRR is above the hurdle > rate, the greater the NPV and vice versa". > > Now, definitionally, the IRR is a SINGLE VALUE, > the rate at which NPV = 0. So how can the NPV be > higher or lower then 0 based on the IRR? > > 2. I may be wrong here, but as I understand it, > you can calculate the IRR by making different > cost-of-capital (discount rate) assumptions, and > seeing which one brings you closest to the NPV > being 0, and the highest IRR will mean the highest > NPV for the project. > > Now again, ignoring my confusion in Question 1, > why are we saying that the project with the > HIGHEST IRR (or in other words, highest cost of > capital assumption) will have the highest NPV. > Shouldn’t the lowest IRR have the highest NPV, as > cost of capital is less? > > Also, the text I’m using says you can think of the > IRR as both a rate of return, and the cost of > capital. How can it be both those things, as an > increase in a cost of capital would directly > reduce the rate of return? > > I think I’m missing a piece to complete this > puzzle, I appreciate any help! I just started off > with my studying, so this is all new to me. > > Thanks > seeing which one brings you closest to the NPV > being 0, and the highest IRR will mean the highest > NPV for the project. Highest IRR doesn’t necessarily mean highest NPV. A \$100 project with \$30 return vs \$1,000,000 project and \$200,000 return will have conflicting values. IRR will pick highest return percentage return (\$30, 30%), but NPV will pick highest Net Present Value, the \$1,000,000 project.

Thanks for the answers guys, especially jlive, I really appreciate that you took the time to write out such a detailed reply! It really helped me out. I had a similar question regarding IRR though, but in regards to YTM calculations with Bond Valuations - of course, YTM and IRR are basically identical concepts. Anyway, my question was this: The book says: Bond selling at Par: Coupon = Current Yield = YTM Given that YTM takes into account capital gain/loss and reinvestment of received cash flows, I can understand how a bond bought at par where n = 1 (one coupon payment, then repayment of principal) will have the Coupon and YTM equal. However, if you purchased a similar bond where n=2 (two coupon payments, then repayment of principal), wouldn’t that reinvestment of the 1st period cash flow as assumed under the YTM push the YTM higher as compared to the Coupon rate or CY? Also, the text says that the Current Yield does not take capital gain/loss into account. However, it also says that CY is greater when the bond is selling at a discount, and smaller when the bond is selling at a premium. The bond selling at a discount or a premium adds a capital gain or loss respectively, so if that causes the CY to increase or decrease respectively, then how can one say that the CY does not consider capital gain or loss at all? I hope my questions are clear, thanks!