 # NPV and IRR

Can anyone please explain why it is that a project with a High NPV will have a lower IRR compared to a project with a Lower NPV but a higher IRR? Project A’s NPV = -1,000 + 750/1.101 + 350/1.102 + 150/1.103 + 50/1.104 = -1,000 + 682 + 289 + 113 + 34 = \$118 Project B’s NPV = -1,000 + 100/1.101 + 250/1.102 + 450/1.103 + 750/1.104 = -1,000 + 91 + 207 + 338 + 512 = \$148 The IRR for Project A is 18.32% and for Project B is 15.03%. Thanks

The two projects have different patterns of cash flows. Project A’s payoffs are decreasing with time while Project B’s payoffs are increasing with time. Project A realises its cashflows earlier, hence the less NPV.

NPV uses marginal cost of capital (usually WACC) to discount cash flows whereas IRR is the rate that discounts CF to equal inflows with outflows. Now see that project A has higher CF in the earlier years therefore you need to use higher rate to discount all CF to 0 than in case of B project. On the other hand if you sum up all cash flows without discounting them you see that project B has +550 and A only 300. Using 10% for NPV calculation discounts B’s cash flows less than A’s and therefore produces higher NPV. Is it clear?

Right, it’s just clicked. : ) Higher earlier cash flows ultimately leads to higher IRR’s… TVM. PS… and assuning the cash flow is reinvested at the IR. Thanks Joe, Tgrycner.

The pattern shown is typical, and likely to show up on an exam. To see what’s going on, create a graph with NPV on the y-axis and the discount rate on the X (this is called an NPV profile). First determine the NPV at a zero discount rate – merely add up the cash flows of the project. This gives you the NPV at a zero rate, and is the point where the NPV profile crosses the Y axis (\$300 for A and \$550 for B). Next, determine the point where the NPV equals zero. By definition, this is the IRR (18.32% for A and 15.03% for B). If you connect the Zero-npv and IRR points for each project, you’ll see that project B starts out with a higher NPV (more total cash flows), but that its NPV falls more rapidly. That’s because B’s cash flows are more heavily weighted into the future than are Project A’s (A’s are more "front-loaded). So, changes in discount rates affect B’s CFs more because of compounding (BTW - this is similar to the concept of “duration” that you’ll see in the Fixed Income material). So, at low discount rates, the “higher total cash flows” of B dominates, giving it a higher NPV. But as the discount rate increases, its NPV falls faster than A’s because of the “back-loaded” nature of its cash flows. At some point, the NPVs cross and its NPV is lower than A’s. To find the point where the NPVs cross (this was asked for asked in another question), use the concept that the IRR is the rate where the NPV=0. So, first create a project C where the cash flows are the difference between A and B (in this case, B-A, but it works with A-B just as well) YEAR CF 0 0 1 -650 2 -100 3 300 4 700 Then, calculate the IRR of project C (the “difference” project). The IRR of this project will be the rate that makes “the NPV of the difference” equal to zero. This is also the rate that makes “the difference in the NPVs” equal to zero. In other words, at this rate, the projects have identical NPVs. Since the NPV of B falls or rises faster than NPV of A, at discount rates lower than this rate, NPV(B) > NPV(A), and at higher rates NPV(B)< NPV(A). The crossover rate, BTW is 11.89%. At that rate, they both have NPVs of about \$88.85.