WEBVTT 00:00:00.000 --> 00:00:03.180 So you're tasked with evaluating a massive infrastructure 00:00:03.180 --> 00:00:05.379 project, or maybe you're deciding if a tech startup 00:00:05.379 --> 00:00:08.160 is worth buying, or maybe you're just trying 00:00:08.160 --> 00:00:10.519 to figure out the true efficiency of your own 00:00:10.519 --> 00:00:13.019 personal investments. You always run into this 00:00:13.019 --> 00:00:17.219 great gatekeeper of finance. The impenetrable 00:00:17.219 --> 00:00:19.519 wall of acronyms. Everyone wants to know their 00:00:19.519 --> 00:00:22.160 return, but the language used to calculate it, 00:00:22.179 --> 00:00:24.480 it just feels like a secret code sometimes. It 00:00:24.480 --> 00:00:27.399 absolutely does. And right at the epicenter of, 00:00:27.519 --> 00:00:29.620 I mean, nearly every single capital allocation 00:00:29.620 --> 00:00:32.259 decision in the financial world, from the smallest 00:00:32.259 --> 00:00:34.179 corporate move to the largest private equity 00:00:34.179 --> 00:00:37.789 fund, you'll find one. metric, the internal rate 00:00:37.789 --> 00:00:41.530 of return or IRR. And the thing is, it is simultaneously 00:00:41.530 --> 00:00:45.229 the most indispensable number in finance. And 00:00:45.229 --> 00:00:47.850 you could argue the most dangerous if you misunderstand 00:00:47.850 --> 00:00:50.469 it. And that contrast, right, that tension between 00:00:50.469 --> 00:00:53.429 its power and its flaws, that is the mission 00:00:53.429 --> 00:00:56.310 of this deep dive. We are going to extract the 00:00:56.310 --> 00:00:58.810 essential knowledge you need to be, well, instantly 00:00:58.810 --> 00:01:01.759 fluent in IRR. what it is, the mechanics of how 00:01:01.759 --> 00:01:04.599 it's calculated, why giant corporations will 00:01:04.599 --> 00:01:08.120 literally stake billions on it, and crucially, 00:01:08.219 --> 00:01:10.980 its profound limitations. And our sources for 00:01:10.980 --> 00:01:13.079 this give us a really comprehensive overview. 00:01:13.379 --> 00:01:16.939 They blend the dense mathematical underpinnings 00:01:16.939 --> 00:01:20.400 with real world case studies and even the longstanding 00:01:20.400 --> 00:01:23.459 academic debates about where IRR just falls short. 00:01:23.739 --> 00:01:26.239 So it's the definitive shortcut to understanding 00:01:26.239 --> 00:01:29.159 how finance professionals truly measure capital. 00:01:29.319 --> 00:01:31.579 efficiency. I think so. Okay, so let's unpack 00:01:31.579 --> 00:01:34.560 this core definition. At the highest level, the 00:01:34.560 --> 00:01:36.939 internal rate of return is simply a method, a 00:01:36.939 --> 00:01:39.340 tool, for calculating an investment's expected 00:01:39.340 --> 00:01:42.060 or actual rate of return. Exactly. You might 00:01:42.060 --> 00:01:44.299 hear it called the discounted cash flow rate 00:01:44.299 --> 00:01:48.000 of return, the DCFROR. A bit of a mouthful. Yeah, 00:01:48.000 --> 00:01:50.420 or sometimes just the yield rate. But that word 00:01:50.420 --> 00:01:53.920 internal, it isn't just window dressing. It is 00:01:53.920 --> 00:01:56.299 the critical defining characteristic of the whole 00:01:56.299 --> 00:01:58.879 thing. When we call it internal, we mean the 00:01:58.879 --> 00:02:01.599 calculation is, by its very nature, project specific. 00:02:01.819 --> 00:02:04.799 It's isolated from the wider economy. It deliberately 00:02:04.799 --> 00:02:07.359 abstracts away all those external market factors 00:02:07.359 --> 00:02:10.099 that affect money. So things like general inflation. 00:02:10.580 --> 00:02:13.560 Inflation, the prevailing risk -free rate you 00:02:13.560 --> 00:02:15.759 could get on government bonds, the firm's own 00:02:15.759 --> 00:02:18.599 cost of capital, any specific market volatility, 00:02:18.879 --> 00:02:21.120 all of that is intentionally stripped out. So 00:02:21.120 --> 00:02:23.590 it's a pure measure. Of the project's own profitability, 00:02:23.849 --> 00:02:26.310 then, without any reference to the context it's 00:02:26.310 --> 00:02:28.969 operating in. Precisely. It isolates the rate 00:02:28.969 --> 00:02:31.389 of return generated purely by that project's 00:02:31.389 --> 00:02:34.129 specific sequence of cash inflows and outflows. 00:02:34.349 --> 00:02:36.669 And that isolation is what makes it so useful 00:02:36.669 --> 00:02:39.849 for comparison. Also. Well, you can compare a 00:02:39.849 --> 00:02:42.469 factory in Brazil to a software license deal 00:02:42.469 --> 00:02:44.689 in Germany because the IRR is stripped of all 00:02:44.689 --> 00:02:47.409 that regional economic noise. And because it's 00:02:47.409 --> 00:02:49.469 a calculation that only depends on the project's 00:02:49.469 --> 00:02:51.969 cash flow stream, you can use it both ways, right? 00:02:52.330 --> 00:02:54.349 Looking forward and looking back. That's right. 00:02:54.490 --> 00:02:57.250 We use it ex ante when we're evaluating a proposal. 00:02:57.650 --> 00:03:00.689 We estimate the future cash flows. We calculate 00:03:00.689 --> 00:03:03.250 the resulting IRR. And that helps us decide whether 00:03:03.250 --> 00:03:05.349 to even launch the project. That's its big role 00:03:05.349 --> 00:03:08.090 in capital budgeting. And then years down the 00:03:08.090 --> 00:03:10.419 line, you can apply it ex post. Exactly. You 00:03:10.419 --> 00:03:12.960 take the actual historical cash flows and you 00:03:12.960 --> 00:03:15.500 measure the exact achieved return of that investment. 00:03:15.719 --> 00:03:19.159 It produces a single annualized compounded number 00:03:19.159 --> 00:03:22.000 that's designed to answer one question. What 00:03:22.000 --> 00:03:24.900 annual rate did this venture actually produce 00:03:24.900 --> 00:03:27.699 for the capital we invested? Now that we have 00:03:27.699 --> 00:03:30.180 that intuitive definition, let's dig into the 00:03:30.180 --> 00:03:32.740 technical core. Because I think understanding 00:03:32.740 --> 00:03:35.979 the math behind IRR is probably the only way 00:03:35.979 --> 00:03:38.740 to truly grasp. why it generates some of those 00:03:38.740 --> 00:03:40.240 dangerous pitfalls we're going to cover later. 00:03:40.460 --> 00:03:42.360 Right. And the technical definition connects 00:03:42.360 --> 00:03:45.680 IRR directly to the other giant of finance, net 00:03:45.680 --> 00:03:49.180 present value, or NPV. The IRR of an investment 00:03:49.180 --> 00:03:51.479 is formally defined as the annualized effective 00:03:51.479 --> 00:03:54.360 compounded return rate. Okay. That sets the net 00:03:54.360 --> 00:03:56.879 present value of all cash flows, both the positive 00:03:56.879 --> 00:03:58.599 ones and the negative ones, from that investment 00:03:58.599 --> 00:04:00.800 equal to zero. That sounds dense, but it's the 00:04:00.800 --> 00:04:02.680 pivot point. We're not just looking at total 00:04:02.680 --> 00:04:05.199 cash received versus total cash paid out. We're 00:04:05.199 --> 00:04:07.159 bringing everything back to today. day's dollars. 00:04:07.340 --> 00:04:09.800 And then we're finding the one single interest 00:04:09.800 --> 00:04:12.319 rate that makes the whole thing just balance 00:04:12.319 --> 00:04:15.840 out. Absolutely. Think of it this way. IRR is 00:04:15.840 --> 00:04:17.800 the interest rate at which the present value 00:04:17.800 --> 00:04:20.680 of all the future cash flows you receive is exactly 00:04:20.680 --> 00:04:23.600 mathematically equal to the present value of 00:04:23.600 --> 00:04:25.879 all the cash flows you paid out. Which is usually 00:04:25.879 --> 00:04:28.610 that initial investment. Usually. And if those 00:04:28.610 --> 00:04:30.990 two present values perfectly cancel each other 00:04:30.990 --> 00:04:33.930 out, the total net present value is zero. So 00:04:33.930 --> 00:04:35.730 it really acts like a break -even metric. And 00:04:35.730 --> 00:04:38.350 that break -even rate is what links it so closely 00:04:38.350 --> 00:04:42.009 to NPV for any single project. That's a crucial 00:04:42.009 --> 00:04:45.060 insight. The IRR signifies the required rate 00:04:45.060 --> 00:04:47.279 of return that makes the project only marginally 00:04:47.279 --> 00:04:49.819 justified. If your cost of accessing capital 00:04:49.819 --> 00:04:53.019 is exactly equal to the IRR, you break even in 00:04:53.019 --> 00:04:55.560 present value terms. You haven't destroyed any 00:04:55.560 --> 00:04:57.980 value, but you haven't created any extra wealth 00:04:57.980 --> 00:04:59.980 either. And this is where that classic investment 00:04:59.980 --> 00:05:02.360 decision rule comes from, isn't it? It relies 00:05:02.360 --> 00:05:05.519 on comparing the IRR to your minimum acceptable 00:05:05.519 --> 00:05:08.569 rate of return. Your hurdle rate. Exactly. If 00:05:08.569 --> 00:05:11.350 you calculate a positive NPV using your firm's 00:05:11.350 --> 00:05:13.850 cost of capital as the discount rate, it means 00:05:13.850 --> 00:05:15.949 the project is expected to generate value above 00:05:15.949 --> 00:05:18.250 that hurdle rate. That justifies the investment. 00:05:18.470 --> 00:05:21.350 So if the IRR is higher than the hurdle rate, 00:05:21.529 --> 00:05:26.129 then mathematically that the NPV has to be positive. 00:05:26.170 --> 00:05:28.029 The project is adding value. Right. But wait 00:05:28.029 --> 00:05:30.709 a minute. If NPV tells us the actual dollar value 00:05:30.709 --> 00:05:33.319 created. And that's the ultimate goal, right? 00:05:33.579 --> 00:05:35.879 Maximizing shareholder wealth. Why don't we just 00:05:35.879 --> 00:05:39.860 rely on MTV? Why do we even need IRR, this break 00:05:39.860 --> 00:05:41.860 -even rate? That's a great question. It's because 00:05:41.860 --> 00:05:44.600 the IRR inherently accounts for the time preference 00:05:44.600 --> 00:05:47.779 of money in a way that a simple percentage just 00:05:47.779 --> 00:05:50.480 can't. And it allows for a rate -based comparison 00:05:50.480 --> 00:05:53.800 of capital efficiency. Time preference. The idea 00:05:53.800 --> 00:05:55.899 that a dollar today is better than a dollar tomorrow. 00:05:56.019 --> 00:05:58.139 Right. Because money you receive today can be 00:05:58.139 --> 00:06:00.180 invested immediately and start compounding. That's 00:06:00.180 --> 00:06:01.779 why we have to discount future cash flows in 00:06:01.779 --> 00:06:03.620 the first place. So an investment that returns 00:06:03.620 --> 00:06:07.139 money to you quickly is fundamentally more valuable 00:06:07.139 --> 00:06:08.939 than one that holds onto the money until the 00:06:08.939 --> 00:06:11.920 very end, even if the total dollar profit is 00:06:11.920 --> 00:06:14.420 identical. That's right. And the IRR calculation 00:06:14.420 --> 00:06:17.699 quantifies that time value. Let's say Project 00:06:17.699 --> 00:06:21.000 A and Project B both promise a total profit of 00:06:21.000 --> 00:06:25.339 $10 ,000. But Project A delivers $8 ,000 of that 00:06:25.339 --> 00:06:28.139 in year one, while Project B delivers the whole 00:06:28.139 --> 00:06:30.639 $10 ,000 in year 10. Project A is going to have 00:06:30.639 --> 00:06:34.060 a much higher IRR. significantly higher. The 00:06:34.060 --> 00:06:36.279 discount factor that you apply to that money 00:06:36.279 --> 00:06:38.699 in year one is much smaller than the heavy discount 00:06:38.699 --> 00:06:40.879 you have to apply to the money you receive 10 00:06:40.879 --> 00:06:43.160 years from now. It makes the present value of 00:06:43.160 --> 00:06:46.019 that early money much, much greater. It's a bit 00:06:46.019 --> 00:06:48.540 like duration in the bond world. Fixed income 00:06:48.540 --> 00:06:51.699 assets, like bonds. A bond with a high coupon 00:06:51.699 --> 00:06:54.319 rate is paying out cash earlier, so it has a 00:06:54.319 --> 00:06:56.180 shorter duration. That's a good way to think 00:06:56.180 --> 00:06:58.819 about it. Imagine a simple zero coupon bond. 00:06:59.040 --> 00:07:02.060 You buy it for, say, $800 today, and it pays 00:07:02.060 --> 00:07:06.240 you $1 ,000 in five years. Its IRR is fixed based 00:07:06.240 --> 00:07:08.980 on that one single cash flow in the future. Now, 00:07:09.180 --> 00:07:11.620 compare that to a coupon bond. You buy it for 00:07:11.620 --> 00:07:13.519 $1 ,000, and it pays you these little bits of 00:07:13.519 --> 00:07:16.139 interest every six months until it matures. The 00:07:16.139 --> 00:07:19.360 IRR on that coupon bond. is going to be way more 00:07:19.360 --> 00:07:21.300 sensitive to the timing of all those little payments. 00:07:21.500 --> 00:07:24.100 It is. The IRR effectively measures the average 00:07:24.100 --> 00:07:25.980 time it takes for you to recover your invested 00:07:25.980 --> 00:07:29.379 capital, weighted by the yield. The earlier the 00:07:29.379 --> 00:07:31.720 cash flows, the shorter the duration, and generally 00:07:31.720 --> 00:07:34.600 the more effective the rate of return. This time 00:07:34.600 --> 00:07:37.379 sensitivity is really the engine that IRR uses 00:07:37.379 --> 00:07:40.199 to measure capital efficiency. We've established 00:07:40.199 --> 00:07:42.759 the foundation, but where does this actually 00:07:42.759 --> 00:07:45.699 show up on a corporate balance sheet? Let's talk 00:07:45.699 --> 00:07:48.279 about how corporations use this, starting with 00:07:48.279 --> 00:07:51.000 that really crucial distinction between IRR and 00:07:51.000 --> 00:07:53.680 NPV that our source material highlights. This 00:07:53.680 --> 00:07:56.339 is where we have to draw a hard line. As financial 00:07:56.339 --> 00:07:58.519 metrics, they really do serve different masters. 00:07:59.100 --> 00:08:02.000 IRR is fundamentally an indicator of profitability 00:08:02.000 --> 00:08:05.459 or efficiency or yield. It's a rate. It's a percentage. 00:08:05.699 --> 00:08:08.139 Right. It tells management how effectively they 00:08:08.139 --> 00:08:10.600 are deploying capital relative to the size of 00:08:10.600 --> 00:08:13.259 that investment. In contrast, NPV is the measure 00:08:13.259 --> 00:08:15.879 of magnitude. The actual dollar amount of net 00:08:15.879 --> 00:08:18.000 value the project is projected to add to the 00:08:18.000 --> 00:08:20.379 firm's total wealth. And that's the tension. 00:08:20.600 --> 00:08:24.300 A 40 % IRR on a small pilot project might make 00:08:24.300 --> 00:08:26.720 your internal... management team look great but 00:08:26.720 --> 00:08:29.279 it's adding negligible value compared to a 15 00:08:29.279 --> 00:08:32.580 % IRR project that requires a billion dollar 00:08:32.580 --> 00:08:35.379 investment and adds a hundred million in NPV. 00:08:35.519 --> 00:08:38.159 And that tension is what defines corporate capital 00:08:38.159 --> 00:08:42.419 budgeting. So corporations use IRR as this initial 00:08:42.419 --> 00:08:45.440 filter in a process where they're deciding which 00:08:45.440 --> 00:08:48.559 projects to greenlight. The basic rule is If 00:08:48.559 --> 00:08:50.840 project IRR is greater than the cost of capital, 00:08:51.000 --> 00:08:53.919 the project passes the screen. Correct. But how 00:08:53.919 --> 00:08:55.799 do they even figure out that cost of capital? 00:08:55.879 --> 00:08:57.720 That sounds like a really complex number on its 00:08:57.720 --> 00:09:00.639 own. It is. The minimum acceptable rate of return, 00:09:00.779 --> 00:09:03.299 that hurdle rate, is usually tied directly to 00:09:03.299 --> 00:09:06.059 the weighted average cost of capital, or WACC. 00:09:06.419 --> 00:09:09.120 WACC? Yeah, WACC is the average rate the company 00:09:09.120 --> 00:09:11.620 pays to finance its assets. It considers the 00:09:11.620 --> 00:09:13.779 cost of its debt, so interest payments, and the 00:09:13.779 --> 00:09:15.799 cost of its equity, which is shareholder expectations. 00:09:16.059 --> 00:09:18.480 But that number is often adjusted upward based 00:09:18.480 --> 00:09:20.539 on the specific risk profile of the project. 00:09:20.970 --> 00:09:23.289 So a high -risk R &D project is going to have 00:09:23.289 --> 00:09:27.190 a much higher IRR hurdle than, say, a stable, 00:09:27.309 --> 00:09:29.889 predictable upgrade to existing infrastructure. 00:09:30.070 --> 00:09:32.429 Oh, absolutely. Much higher. So if they're comparing, 00:09:32.549 --> 00:09:34.889 let's say, building a new regional distribution 00:09:34.889 --> 00:09:38.230 center versus buying a fleet of autonomous delivery 00:09:38.230 --> 00:09:41.830 trucks, they calculate the IRR for both and assuming 00:09:41.830 --> 00:09:44.860 they both pass that hurdle rate. Exactly. And 00:09:44.860 --> 00:09:46.799 the project with the higher IRR is generally 00:09:46.799 --> 00:09:49.580 considered superior, provided the company's capital 00:09:49.580 --> 00:09:52.440 budget is limited. And the goal is to maximize 00:09:52.440 --> 00:09:54.759 the rate of return on invested capital. And that's 00:09:54.759 --> 00:09:56.899 a common situation, right? Even for cash rich 00:09:56.899 --> 00:09:59.360 companies. Yeah. Because management and just 00:09:59.360 --> 00:10:01.559 organizational capacity is always finite. They 00:10:01.559 --> 00:10:04.299 can't do everything. That context of limited 00:10:04.299 --> 00:10:05.919 resources, that brings us to one of the most 00:10:05.919 --> 00:10:08.450 important. practical differentiations in these 00:10:08.450 --> 00:10:11.070 large -scale projects. Yeah. Project IRR versus 00:10:11.070 --> 00:10:14.169 equity IRR. This is a massive distinction, especially 00:10:14.169 --> 00:10:17.529 in private infrastructure deals, real estate, 00:10:17.629 --> 00:10:20.230 and leveraged buyouts. The project IRR measures 00:10:20.230 --> 00:10:23.190 the return of the overall asset itself. Unleveraged. 00:10:23.210 --> 00:10:26.549 Yes, it's the unleveraged return. It calculates 00:10:26.549 --> 00:10:29.129 the return assuming the cash flows directly benefit 00:10:29.129 --> 00:10:31.350 the project, regardless of how that project was 00:10:31.350 --> 00:10:34.110 financed. And the equity IRR is the shareholder's 00:10:34.110 --> 00:10:36.720 return. The view from the investor who actually 00:10:36.720 --> 00:10:39.639 put in the equity capital. Precisely. Equity 00:10:39.639 --> 00:10:41.759 IRR considers the returns for the shareholders 00:10:41.759 --> 00:10:44.799 after all the project's debt obligations. The 00:10:44.799 --> 00:10:47.159 interest payments, principal repayments, all 00:10:47.159 --> 00:10:50.779 of that have been serviced. I see. And if a project 00:10:50.779 --> 00:10:53.139 is highly leveraged, meaning it's financed with 00:10:53.139 --> 00:10:55.399 a large amount of relatively cheap debt, that 00:10:55.399 --> 00:10:58.440 leverage can really turbocharge the equity IRR. 00:10:58.600 --> 00:11:01.980 A project IRR of, say, 12 percent could easily 00:11:01.980 --> 00:11:05.220 translate into an equity IRR of 25 or even 30 00:11:05.220 --> 00:11:07.279 percent. And that's why investors often chase 00:11:07.279 --> 00:11:09.840 those highly leveraged deals. It is. And it makes 00:11:09.840 --> 00:11:12.639 that equity IRR figure crucial for reporting 00:11:12.639 --> 00:11:15.240 back to investors, particularly in private funds. 00:11:15.500 --> 00:11:17.940 It's what the limited partners, the actual investors, 00:11:18.039 --> 00:11:20.940 see. reflects the success of the financial structuring 00:11:20.940 --> 00:11:22.879 just as much as the success of the underlying 00:11:22.879 --> 00:11:25.580 asset. So it's absolutely vital to know which 00:11:25.580 --> 00:11:28.740 figure is being quoted. A high project IRR indicates 00:11:28.740 --> 00:11:32.080 a fundamentally sound asset, whereas a high equity 00:11:32.080 --> 00:11:35.320 IRR might just indicate aggressive but successful 00:11:35.320 --> 00:11:38.480 leverage. You have to ask the question. An IRR's 00:11:38.480 --> 00:11:40.919 application broadens far beyond just corporate 00:11:40.919 --> 00:11:44.340 finance. I mean, it is everywhere. Let's look 00:11:44.340 --> 00:11:47.019 at its usage in fixed income. In the fixed income 00:11:47.019 --> 00:11:50.200 world, IRR is formalized into metrics like yield 00:11:50.200 --> 00:11:54.840 to maturity or YTM. The YTM calculation is structurally 00:11:54.840 --> 00:11:57.879 identical to IRR. It's the single discount rate 00:11:57.879 --> 00:12:00.440 that makes the present value of all the bond's 00:12:00.440 --> 00:12:03.000 future cash flows, the coupons and the principal 00:12:03.000 --> 00:12:05.960 repayment equal to the current market price of 00:12:05.960 --> 00:12:08.320 the bond. That's a perfect example of IRR being 00:12:08.320 --> 00:12:10.639 used to solve for the market implied rate rather 00:12:10.639 --> 00:12:13.759 than a prospective project rate. And in the world 00:12:13.759 --> 00:12:15.659 of savings and loans, when banks talk about the 00:12:15.659 --> 00:12:18.059 true cost of borrowing or the true return on 00:12:18.059 --> 00:12:20.220 a deposit account, they often use the effective 00:12:20.220 --> 00:12:22.500 interest rate. And that rate is simply the IRR 00:12:22.500 --> 00:12:24.299 of the cash flow stream you're committing to, 00:12:24.419 --> 00:12:27.100 factoring in how often it compounds. We also 00:12:27.100 --> 00:12:30.159 noted that IRR can apply to liabilities. If you 00:12:30.159 --> 00:12:32.659 structure some complex financing package, the 00:12:32.659 --> 00:12:35.620 IRR of that liability stream is the true cost 00:12:35.620 --> 00:12:38.039 to the company. Yes. And the evaluation rule 00:12:38.039 --> 00:12:41.500 just flips. For an asset, a higher IRR is better 00:12:41.500 --> 00:12:44.240 because you want a higher return. For liability, 00:12:44.639 --> 00:12:47.559 a lower IRR is vastly preferable. Of course. 00:12:47.740 --> 00:12:51.419 A complex loan with an IRR of 7 % is economically 00:12:51.419 --> 00:12:55.019 superior to one with an IRR of 9 % because that 00:12:55.019 --> 00:12:57.899 9 % rate means the compounded cost of that liability 00:12:57.899 --> 00:13:00.720 is much, much higher over time. This cost evaluation 00:13:00.720 --> 00:13:03.620 also plays a key role in a corporation's capital 00:13:03.620 --> 00:13:06.059 management strategy, particularly when it comes 00:13:06.059 --> 00:13:08.320 to stock buybacks. Share buybacks are, at the 00:13:08.320 --> 00:13:10.659 end of the day, an allocation of capital. When 00:13:10.659 --> 00:13:13.000 a corporation uses its cash to repurchase, its 00:13:13.000 --> 00:13:15.460 own shares, it's essentially investing in itself. 00:13:15.799 --> 00:13:18.320 It reduces the share count, potentially boosts 00:13:18.320 --> 00:13:20.580 earnings per share, but they have to evaluate 00:13:20.580 --> 00:13:23.980 this project using IRR. So they're asking, does 00:13:23.980 --> 00:13:26.480 repurchasing our shares deliver a higher IRR 00:13:26.480 --> 00:13:29.139 than building that new factory or acquiring a 00:13:29.139 --> 00:13:32.769 smaller competitor? Precisely. If the IRR of 00:13:32.769 --> 00:13:35.490 returning capital to shareholders through a buyback, 00:13:35.710 --> 00:13:38.029 and that's calculated based on the cash spent 00:13:38.029 --> 00:13:40.230 and the expected appreciation of the stock price, 00:13:40.409 --> 00:13:43.190 is higher than the IRR of their other available 00:13:43.190 --> 00:13:46.090 investment candidates, the buyback proceeds. 00:13:46.590 --> 00:13:48.629 It's a constant internal competition for the 00:13:48.629 --> 00:13:51.169 company's limited financial resources. And IRR 00:13:51.169 --> 00:13:53.950 is the scorecard they use to compare these fundamentally 00:13:53.950 --> 00:13:56.450 different types of opportunities. And then there's 00:13:56.450 --> 00:13:59.529 a segment where IRR holds this almost sacred... 00:13:59.529 --> 00:14:02.750 status private equity though as we're going to 00:14:02.750 --> 00:14:05.639 see that status is increasingly fraught with 00:14:05.639 --> 00:14:08.919 issues. Private equity funds rely on IRR to measure 00:14:08.919 --> 00:14:10.940 the general partner's success. That's the fund 00:14:10.940 --> 00:14:14.220 manager. For the limited partners, the LPs, the 00:14:14.220 --> 00:14:17.000 IRR calculation is how they gauge the manager's 00:14:17.000 --> 00:14:19.700 ability to efficiently deploy capital, control 00:14:19.700 --> 00:14:22.279 the timing of cash flows, and generate a superior 00:14:22.279 --> 00:14:24.340 rate of return on the capital they committed. 00:14:24.559 --> 00:14:26.799 The timing is key there. The timing of investments 00:14:26.799 --> 00:14:29.200 and distributions, the J -curve effect, makes 00:14:29.200 --> 00:14:31.460 IRR particularly sensitive in that environment. 00:14:33.840 --> 00:14:36.299 math behind IRR is what gives it both its power 00:14:36.299 --> 00:14:38.460 and its complexity. Let's try to make that accessible. 00:14:38.940 --> 00:14:41.779 At the heart of it, it's a quest for that single 00:14:41.779 --> 00:14:44.440 discount rate, we'll call it two, which makes 00:14:44.440 --> 00:14:47.139 the net present value exactly zero. Correct. 00:14:47.379 --> 00:14:50.659 We're trying to solve a specialized algebraic 00:14:50.659 --> 00:14:54.159 equation. The formula for NPV requires summing 00:14:54.159 --> 00:14:56.399 up all the cash flows, let's call them six nulls, 00:14:56.399 --> 00:14:58.659 and discounting each one by one plus two dollars 00:14:58.659 --> 00:15:00.879 raised to the power of the period at none dollars. 00:15:01.000 --> 00:15:03.840 And that entire sum has to equal zero. That initial 00:15:03.840 --> 00:15:06.320 investment, two dollars, is usually your big 00:15:06.320 --> 00:15:08.600 negative number sitting right at time zero. Right. 00:15:08.700 --> 00:15:10.820 And the presence of that discount factor, that 00:15:10.820 --> 00:15:13.200 one dollar plus our day, where two dollars is 00:15:13.200 --> 00:15:14.759 the unknown rate we're trying to find, and then 00:15:14.759 --> 00:15:18.399 goes up to five, ten. maybe 20 years, that creates 00:15:18.399 --> 00:15:20.740 the mathematical challenge. When then gets large, 00:15:20.879 --> 00:15:23.419 this equation becomes a complex rational polynomial 00:15:23.419 --> 00:15:26.240 equation. And what does rational polynomial mean 00:15:26.240 --> 00:15:28.720 in practical terms for an analyst? It means you 00:15:28.720 --> 00:15:30.639 can't just use algebra to rearrange the equation 00:15:30.639 --> 00:15:32.440 and isolate per dollars. It's not that simple. 00:15:32.559 --> 00:15:34.460 If none dollars is greater than four, there is 00:15:34.460 --> 00:15:36.899 generally no closed form analytical solution. 00:15:37.259 --> 00:15:39.820 So you can't solve it directly in a few clean 00:15:39.820 --> 00:15:43.480 steps. No. This is why analysts don't use calculators. 00:15:43.480 --> 00:15:45.720 They use computers and iterative algorithms. 00:15:45.919 --> 00:15:48.139 You need a computer to basically start guessing 00:15:48.139 --> 00:15:51.240 and then refining that guess. Exactly. Tools 00:15:51.240 --> 00:15:53.399 like Microsoft Excel or, you know, specialized 00:15:53.399 --> 00:15:56.100 financial modeling software, they use built -in 00:15:56.100 --> 00:16:00.480 functions like IRR or XIRR. And these employ 00:16:00.480 --> 00:16:03.440 sophisticated methods to iteratively home in 00:16:03.440 --> 00:16:05.820 on the exact rate that balances the equation. 00:16:06.120 --> 00:16:08.139 Let's make this tangible with that specific cash 00:16:08.139 --> 00:16:09.899 flow sequence from our sources. It's a nice, 00:16:09.960 --> 00:16:12.720 clean example. Just over three years. Okay. Let's 00:16:12.720 --> 00:16:14.980 imagine this venture. At year zero, the initial 00:16:14.980 --> 00:16:18.320 outflow, CC dollars dollars, is negative $123 00:16:18.320 --> 00:16:21.649 ,400. That's our investment. Right. Then we have 00:16:21.649 --> 00:16:24.509 positive inflows over the next three years, $36 00:16:24.509 --> 00:16:30.129 ,200 in year one, $54 ,800 in year two, and $48 00:16:30.129 --> 00:16:33.429 ,100 in year three. Now, if you just add up the 00:16:33.429 --> 00:16:35.629 inflows and subtract the outflow, you get a total 00:16:35.629 --> 00:16:39.429 profit of $15 ,700. But that tells us nothing 00:16:39.429 --> 00:16:41.950 about the efficiency or the compounded rate of 00:16:41.950 --> 00:16:44.309 return. We need to find tour dollars, so let's 00:16:44.309 --> 00:16:46.970 just guess that's 1%. We plug it in. We discount 00:16:46.970 --> 00:16:49.450 those three cash flows at 10 % and we find that 00:16:49.450 --> 00:16:53.929 their present value sums to about $116 ,920. 00:16:54.289 --> 00:16:56.610 Which is less than our initial investment of 00:16:56.610 --> 00:17:01.110 $123 ,400. So our MPV is negative. Our guess 00:17:01.110 --> 00:17:04.569 was too high. Way too high. So we need to try 00:17:04.569 --> 00:17:07.450 a lower rate to increase the present value of 00:17:07.450 --> 00:17:09.769 those future dollars. Okay, iterate down. We 00:17:09.769 --> 00:17:12.769 iterate down. If we try 4%, the present value 00:17:12.769 --> 00:17:16.410 of the inflows is 125 ,500, which is now too 00:17:16.410 --> 00:17:20.109 high. That gives us a positive NPV. So by running 00:17:20.109 --> 00:17:22.569 the algorithm between 4 % and 10%, the computer 00:17:22.569 --> 00:17:25.190 finds the precise balance point. And the answer 00:17:25.190 --> 00:17:29.430 is? The internal rate of return is 5 .96%. At 00:17:29.430 --> 00:17:31.390 that specific rate, the present value of the 00:17:31.390 --> 00:17:36.670 inflows equals $123 ,400, and the NPV is zero. 00:17:36.849 --> 00:17:39.150 This necessity for iterative calculation brings 00:17:39.150 --> 00:17:41.750 us to the actual methods used. You mentioned 00:17:41.750 --> 00:17:44.049 the second method earlier. Why is that often 00:17:44.049 --> 00:17:45.869 preferred for solving these types of equations? 00:17:46.269 --> 00:17:48.650 Well, the second method is highly efficient for 00:17:48.650 --> 00:17:50.750 these kinds of functions. It uses successive 00:17:50.750 --> 00:17:53.589 approximations. It takes two initial guesses, 00:17:53.829 --> 00:17:56.950 calculates the NPVs for both, and then it draws 00:17:56.950 --> 00:17:58.690 a straight line, a second line between those 00:17:58.690 --> 00:18:01.369 two points. It then predicts where that line 00:18:01.369 --> 00:18:04.589 would cross the zero NPV axis to provide a third, 00:18:04.710 --> 00:18:07.609 much better guess. It just repeats this process 00:18:07.609 --> 00:18:10.930 very, very quickly until the solution converges 00:18:10.930 --> 00:18:13.640 to the accuracy you need. That iterative process 00:18:13.640 --> 00:18:16.980 is why it's so powerful, but also why that one 00:18:16.980 --> 00:18:20.759 unique case, a single initial outflow followed 00:18:20.759 --> 00:18:24.039 by all inflows is so clean mathematically. Right. 00:18:24.400 --> 00:18:27.039 When you have that very common profile $6 is 00:18:27.039 --> 00:18:29.339 negative and then all the other dollars are positive, 00:18:29.619 --> 00:18:32.220 the NPV function is mathematically well -behaved. 00:18:32.240 --> 00:18:34.299 It's convex and strictly decreasing as the interest 00:18:34.299 --> 00:18:36.660 rate increases. And this beautiful mathematical 00:18:36.660 --> 00:18:39.660 property guarantees that there is always one 00:18:39.660 --> 00:18:43.119 and only one unique real solution for the IRR. 00:18:43.220 --> 00:18:45.480 This is the ideal scenario. But the real world, 00:18:45.539 --> 00:18:47.759 as you noted, rarely involves cash flows happening 00:18:47.759 --> 00:18:50.319 on these neat, tidy annual dates. And that's 00:18:50.319 --> 00:18:52.839 where the XIRR concept or the extended internal 00:18:52.839 --> 00:18:55.940 rate of return comes in. XIRR is the necessary 00:18:55.940 --> 00:18:58.740 adjustment for real -world finance. When cash 00:18:58.740 --> 00:19:01.660 flows occur on irregular dates, say a deposit 00:19:01.660 --> 00:19:06.319 in March 2024, another in October 2025, a withdrawal 00:19:06.319 --> 00:19:09.920 in January 2026, the period dollars in our formula 00:19:09.920 --> 00:19:12.619 has to be replaced by 20. What's a dollar? Two 00:19:12.619 --> 00:19:15.099 to dollars is the exact time difference in years 00:19:15.099 --> 00:19:17.140 between the starting date and the date of that 00:19:17.140 --> 00:19:19.519 specific cash flow. So two dollars isn't a simple 00:19:19.519 --> 00:19:22.049 integer anymore. It's a fractional number. And 00:19:22.049 --> 00:19:24.089 the exponent of $2 is now a decimal. Correct. 00:19:24.269 --> 00:19:27.130 The formula adjusts to reflect that. And because 00:19:27.130 --> 00:19:29.210 the exponent is fractional, the equation becomes 00:19:29.210 --> 00:19:31.609 significantly more complex to solve numerically. 00:19:31.789 --> 00:19:34.210 You often need more robust methods like Newton's 00:19:34.210 --> 00:19:36.490 method. The point is, finding this seemingly 00:19:36.490 --> 00:19:38.930 simple rate requires a lot of computational power 00:19:38.930 --> 00:19:41.720 to manage the time waiting accurately. This complexity 00:19:41.720 --> 00:19:43.720 means that when the math gets even slightly messy, 00:19:43.900 --> 00:19:46.339 the IRR can quickly break down or give you really 00:19:46.339 --> 00:19:48.819 misleading answers. We need to spend significant 00:19:48.819 --> 00:19:51.000 time on the limitations because this is where 00:19:51.000 --> 00:19:52.900 the difference between a great financier and 00:19:52.900 --> 00:19:55.839 a mediocre one really lies. Let's start with 00:19:55.839 --> 00:19:59.339 the central conflict, IRR versus NPV in decision 00:19:59.339 --> 00:20:02.539 making. This is the eternal dilemma in capital 00:20:02.539 --> 00:20:05.140 budgeting. For one standalone project, they're 00:20:05.140 --> 00:20:08.240 equivalent. An IRR above the cost of capital 00:20:08.240 --> 00:20:11.579 means a positive NPV. Simple. But when you're 00:20:11.579 --> 00:20:13.460 choosing between mutually exclusive projects, 00:20:13.819 --> 00:20:16.519 you can build factory A or factory B, but not 00:20:16.519 --> 00:20:19.299 both, they often give conflicting advice. Because 00:20:19.299 --> 00:20:22.140 one maximizes the rate and the other maximizes 00:20:22.140 --> 00:20:24.900 the total value. Exactly. We know that maximizing 00:20:24.900 --> 00:20:28.079 total net dollar value, the NPV, is the theoretical 00:20:28.079 --> 00:20:31.140 goal of the firm. It maximizes shareholder wealth. 00:20:31.720 --> 00:20:34.500 So why does management still so often favor the 00:20:34.500 --> 00:20:37.380 IRR, the rate? It comes down to performance measurement 00:20:37.380 --> 00:20:39.779 and organizational behavior. Sometimes it's called 00:20:39.779 --> 00:20:42.279 the agency problem. Managers often have their 00:20:42.279 --> 00:20:44.539 bonuses or performance reviews tied to achieving 00:20:44.539 --> 00:20:46.380 certain rates of return on invested capital. 00:20:46.759 --> 00:20:49.599 IRR is a measure of capital efficiency and scale 00:20:49.599 --> 00:20:51.720 independent profitability. So it's easier to 00:20:51.720 --> 00:20:53.759 communicate. It's easier for a manager to defend 00:20:53.759 --> 00:20:56.859 a 35 % IRR on a small project than to defend 00:20:56.859 --> 00:21:00.660 a 12 % IRR on a huge complex project, even if 00:21:00.660 --> 00:21:04.059 the latter generates far more overall NPV. IRR 00:21:04.059 --> 00:21:06.299 provides a clean comparative percentage that's 00:21:06.299 --> 00:21:08.240 easily communicated and celebrated internally. 00:21:08.619 --> 00:21:10.900 So we have this conflict driven by the objective. 00:21:11.259 --> 00:21:13.759 Let's dive back into that detailed max value 00:21:13.759 --> 00:21:16.859 versus max return scenario. This really highlights 00:21:16.859 --> 00:21:20.019 the economic chaos that can result from prioritizing 00:21:20.019 --> 00:21:22.259 the rate over the dollar value. Okay, so the 00:21:22.259 --> 00:21:26.779 setup is clear. A $100 ,000 budget limit And 00:21:26.779 --> 00:21:29.660 a 10 % cost of capital. Max value wants the largest 00:21:29.660 --> 00:21:32.140 net worth increase. Max return wants the highest 00:21:32.140 --> 00:21:34.940 rate achieved on any capital deployed. And we 00:21:34.940 --> 00:21:37.940 have project one, big is best. You invest the 00:21:37.940 --> 00:21:41.920 full $100 ,000, you get $132 ,000 back in one 00:21:41.920 --> 00:21:46.279 year. That's a 32 % IRR. And crucially, the MPV. 00:21:46.759 --> 00:21:50.740 discounted at 10%, is a massive $20 ,000. Then 00:21:50.740 --> 00:21:53.420 we have Project 2, Small is Beautiful. You invest 00:21:53.420 --> 00:21:56.980 just $10 ,000, you get $13 ,750 back in one year. 00:21:57.259 --> 00:22:01.299 Its IRR is a whopping 37 .5%. Right. But its 00:22:01.299 --> 00:22:05.440 NPV is only $2 ,500. So Max Value chooses Big 00:22:05.440 --> 00:22:08.339 is Best immediately. She captures $20 ,000 of 00:22:08.339 --> 00:22:11.400 NPV, she exhausts her budget, and she maximizes 00:22:11.400 --> 00:22:13.559 her wealth increase. It's a simple decision for 00:22:13.559 --> 00:22:16.299 her. But Max Return? He chooses small is beautiful, 00:22:16.500 --> 00:22:20.980 locking in that glorious 37 .5 % rate. But now 00:22:20.980 --> 00:22:23.779 he has $90 ,000 of idle cash remaining, which 00:22:23.779 --> 00:22:25.900 he has to hold or invest somewhere else. And 00:22:25.900 --> 00:22:28.059 this is where the whole debate lives. Max Returns' 00:22:28.059 --> 00:22:30.160 decision is only rational if he is absolutely 00:22:30.160 --> 00:22:32.859 certain he can find other high -rate projects, 00:22:32.920 --> 00:22:37.200 say a 40 % IRR project, for that remaining $90 00:22:37.200 --> 00:22:40.240 ,000 before Max Value can reinvest her profit. 00:22:40.480 --> 00:22:42.900 And if he can't. If he can't, and that $90 ,000 00:22:42.900 --> 00:22:45.619 is simply invested at the 10 % cost of capital, 00:22:45.779 --> 00:22:48.960 his total combined NPV will be lower than Max 00:22:48.960 --> 00:22:52.960 Value's $20 ,000. He sacrificed guaranteed total 00:22:52.960 --> 00:22:55.259 wealth today for the hope of higher rates tomorrow. 00:22:55.559 --> 00:22:59.359 That is a profound conceptual point. IRR implicitly 00:22:59.359 --> 00:23:01.319 assumes you have the opportunity to reinvest 00:23:01.319 --> 00:23:03.099 the remaining capital at a sufficiently high 00:23:03.099 --> 00:23:05.700 rate to compensate for foregoing the larger NPV 00:23:05.700 --> 00:23:08.559 project. If your future opportunities are only 00:23:08.559 --> 00:23:10.319 marginally better than your cost of capital, 00:23:10.420 --> 00:23:12.509 you made the wrong decision. And that leads to 00:23:12.509 --> 00:23:14.769 another structural limitation people often overlook. 00:23:15.230 --> 00:23:17.890 IRR really shouldn't be used to compare projects 00:23:17.890 --> 00:23:21.029 of vastly different scales or durations. A low 00:23:21.029 --> 00:23:23.789 IRR long duration project might deliver massive 00:23:23.789 --> 00:23:26.549 NPV simply because the cash flow is run for 40 00:23:26.549 --> 00:23:30.289 years. While a high IRR short duration project 00:23:30.289 --> 00:23:33.509 maximizes the rate but adds very little net dollar 00:23:33.509 --> 00:23:36.630 value to the firm. Exactly. IRR obscures the 00:23:36.630 --> 00:23:39.109 sheer volume of cash involved. The second massive 00:23:39.109 --> 00:23:41.859 mathematical hurdle is the multiple IRR problem, 00:23:42.119 --> 00:23:44.240 which is just a mathematical nightmare caused 00:23:44.240 --> 00:23:47.240 by non -standard cash flows. This happens when 00:23:47.240 --> 00:23:49.480 the cash flow stream changes sign more than once. 00:23:49.599 --> 00:23:52.079 The standard project is negative, your initial 00:23:52.079 --> 00:23:55.059 investment, then positive all the profits. The 00:23:55.059 --> 00:23:56.680 trouble starts when the pattern is negative, 00:23:56.779 --> 00:23:59.279 then positive, then negative again. Can you give 00:23:59.279 --> 00:24:01.799 us a real world scenario for that? Where a project 00:24:01.799 --> 00:24:04.460 starts requiring cash, generates profit, and 00:24:04.460 --> 00:24:07.160 then suddenly requires a huge cash outflow years 00:24:07.160 --> 00:24:10.099 later. Oh, the classic examples are environmental 00:24:10.099 --> 00:24:12.900 liabilities or regulatory requirements. Think 00:24:12.900 --> 00:24:15.299 strip mines, chemical processing plants, nuclear 00:24:15.299 --> 00:24:18.960 power facilities. You invest heavily today. That's 00:24:18.960 --> 00:24:21.160 your first negative. You run the facility for 00:24:21.160 --> 00:24:24.539 decades, generating massive positive cash flow. 00:24:24.759 --> 00:24:27.619 But then 25 years later, you are legally mandated 00:24:27.619 --> 00:24:30.480 to decommission the site, clean up toxic residue. 00:24:30.599 --> 00:24:33.519 or dismantled the reactor, resulting in an enormous 00:24:33.519 --> 00:24:36.359 negative cash flow in the final years. So this 00:24:36.359 --> 00:24:38.220 pattern negative, positive, negative creates 00:24:38.220 --> 00:24:41.039 the mathematical possibility of two or sometimes 00:24:41.039 --> 00:24:44.880 even more real IRRs. Why does that happen? It's 00:24:44.880 --> 00:24:46.700 because the cash flows are being viewed from 00:24:46.700 --> 00:24:48.980 two competing perspectives across the timeline. 00:24:49.660 --> 00:24:52.299 In the initial phase, a high discount rate is 00:24:52.299 --> 00:24:54.599 great because it means your return is high. But 00:24:54.599 --> 00:24:57.579 when you hit that final large negative cash flow, 00:24:58.269 --> 00:25:00.609 the liability, a high discount rate, is suddenly 00:25:00.609 --> 00:25:02.230 terrible because you don't want your cost to 00:25:02.230 --> 00:25:04.630 compound quickly. So a low rate is good for costs. 00:25:04.869 --> 00:25:07.509 A low rate is good for costs. So the equation, 00:25:07.650 --> 00:25:10.049 which is trying to find a single rate that works 00:25:10.049 --> 00:25:12.269 for both the profit phase and the cost phase, 00:25:12.509 --> 00:25:14.829 can find two rates that balance everything out 00:25:14.829 --> 00:25:17.500 to zero. That's incredible. It is. Our source 00:25:17.500 --> 00:25:19.880 gives the example of cash flows of negative 10, 00:25:20.059 --> 00:25:23.359 then positive 21, then negative 11. And for that 00:25:23.359 --> 00:25:26.700 stream, both 0 % and 10 % are mathematically 00:25:26.700 --> 00:25:29.920 correct IRRs. An analyst could choose either 00:25:29.920 --> 00:25:32.500 one to present. So if management prefers high 00:25:32.500 --> 00:25:35.869 rates, they might just choose the 10%. Even if 00:25:35.869 --> 00:25:38.690 zero is also valid. It creates ambiguity, and 00:25:38.690 --> 00:25:41.069 that ambiguity renders the IRR metric essentially 00:25:41.069 --> 00:25:43.490 meaningless for decision -making purposes in 00:25:43.490 --> 00:25:46.329 these complex projects. So the knowledge to extract 00:25:46.329 --> 00:25:48.890 here, based on Descartes' rule of signs, is that 00:25:48.890 --> 00:25:51.490 the number of real IRRs you can potentially find 00:25:51.490 --> 00:25:54.349 is constrained by the number of times the sign 00:25:54.349 --> 00:25:56.349 of the cash flow stream changes. If it changes 00:25:56.349 --> 00:25:58.990 twice, you can have up to two real IRRs. That's 00:25:58.990 --> 00:26:01.690 the danger zone. Absolutely. And this mathematical 00:26:01.690 --> 00:26:04.349 instability is why, for complex projects like 00:26:04.349 --> 00:26:06.930 energy infrastructure or mining, analysts have 00:26:06.930 --> 00:26:09.150 to rely on alternatives like MER, which we'll 00:26:09.150 --> 00:26:11.569 discuss in a bit, to impose economic reality 00:26:11.569 --> 00:26:14.670 back onto the equation. Okay, now let's move 00:26:14.670 --> 00:26:17.690 to the most controversial aspect of IRR, one 00:26:17.690 --> 00:26:19.930 that has been debated in finance textbooks for 00:26:19.930 --> 00:26:24.069 half a century, the reinvestment debate. Does 00:26:24.069 --> 00:26:27.710 IRR assume that interim cash flows are reinvested 00:26:27.710 --> 00:26:30.430 at the IRR itself? This is an incredibly sticky 00:26:30.430 --> 00:26:32.769 point, largely because the language used in textbooks 00:26:32.769 --> 00:26:36.130 is, well, often an oversimplification. There 00:26:36.130 --> 00:26:40.109 are two strong camps. Camp A says, yes, implicitly 00:26:40.109 --> 00:26:42.250 the calculation assumes any intermediate profits 00:26:42.250 --> 00:26:45.049 generated are reinvested at the calculated IRR 00:26:45.049 --> 00:26:47.410 until the end of the project. And Camp B? Camp 00:26:47.410 --> 00:26:50.750 B says, absolutely not. The calculation makes 00:26:50.750 --> 00:26:53.109 no economic assumptions about future reinvestment. 00:26:53.230 --> 00:26:55.470 It merely calculates the rate of the original 00:26:55.470 --> 00:26:58.079 cash flow series. The nuance is subtle. But it's 00:26:58.079 --> 00:27:00.500 crucial. Let's use that three -year bond example 00:27:00.500 --> 00:27:02.380 from the source material to cut through the confusion. 00:27:02.819 --> 00:27:05.200 It supports the argument that the IRR calculation 00:27:05.200 --> 00:27:07.720 is fundamentally neutral to reinvestment. Okay. 00:27:07.819 --> 00:27:10.700 The setup is a $1 ,000 face value, three -year 00:27:10.700 --> 00:27:14.200 bond with a 5 % coupon. The bond's IRR, its yield, 00:27:14.299 --> 00:27:18.059 is exactly 5%. Scenario A. The investor gets 00:27:18.059 --> 00:27:20.579 the $50 coupon payments every year and just spends 00:27:20.579 --> 00:27:23.740 them. Or, you know, put some in a shoebox. Total 00:27:23.740 --> 00:27:27.319 cash received is $150 in coupons plus the $1 00:27:27.319 --> 00:27:29.960 ,000 principle at the end. Right. Scenario B. 00:27:30.039 --> 00:27:32.460 The investor immediately reinvests those $50 00:27:32.460 --> 00:27:35.119 coupons back into the project or a similar 5 00:27:35.119 --> 00:27:39.140 % vehicle. By year three, those compounded coupons 00:27:39.140 --> 00:27:42.759 total $157 and change. The total dollar return 00:27:42.759 --> 00:27:45.869 is higher. But, and this is the key part, when 00:27:45.869 --> 00:27:48.210 you run the IRR calculation on both sets of cash 00:27:48.210 --> 00:27:50.710 flows, the set where coupons were spent and the 00:27:50.710 --> 00:27:52.869 set where the larger final amount was received, 00:27:53.130 --> 00:27:56.329 the calculated IRR remains 5 % in both cases. 00:27:56.529 --> 00:27:59.029 The reason is that IRR is an equilibrium rate. 00:27:59.480 --> 00:28:01.619 In scenario A, you discount the early coupons 00:28:01.619 --> 00:28:04.579 back at 5%. In scenario B, you receive a larger 00:28:04.579 --> 00:28:07.039 lump sum later, but you apply the same heavy 00:28:07.039 --> 00:28:10.140 5 % discount over three years. The present value 00:28:10.140 --> 00:28:13.220 of both streams at 5 % equals the initial $1 00:28:13.220 --> 00:28:16.099 ,000 investment. So the calculation itself doesn't 00:28:16.099 --> 00:28:18.980 require a reinvestment assumption. It just finds 00:28:18.980 --> 00:28:20.940 the rate that makes the present value of the 00:28:20.940 --> 00:28:23.539 stream equal to the outflow, regardless of what 00:28:23.539 --> 00:28:25.099 the investor does with the money in the middle. 00:28:25.180 --> 00:28:27.650 That's the most accurate way to frame it. The 00:28:27.650 --> 00:28:30.750 IRR is a mathematical construct reflecting the 00:28:30.750 --> 00:28:32.890 rate inherent in the timeline of the payments. 00:28:33.130 --> 00:28:36.049 The economic feasibility of replicating that 00:28:36.049 --> 00:28:38.650 rate by reinvesting the interim cash flows is 00:28:38.650 --> 00:28:41.390 a separate real world quarter. And our final 00:28:41.390 --> 00:28:44.710 major limitation focuses on private equity, where 00:28:44.710 --> 00:28:47.069 IRR figures can be highly misleading because 00:28:47.069 --> 00:28:50.529 of strategic timing. The critique by the academic 00:28:50.529 --> 00:28:54.400 Ludovic Falepo is particularly potent here. Falapu 00:28:54.400 --> 00:28:56.740 argues that private equity IRR is inherently 00:28:56.740 --> 00:28:59.799 gameable. Because IRR is so heavily weighted 00:28:59.799 --> 00:29:02.640 toward early cash flows, fund managers, the general 00:29:02.640 --> 00:29:05.440 partners, can significantly inflate the headline 00:29:05.440 --> 00:29:08.859 IRR figure by achieving early successes and ensuring 00:29:08.859 --> 00:29:11.119 a quick distribution of those profits back to 00:29:11.119 --> 00:29:13.599 investors. Right. If a fund has a quick, successful 00:29:13.599 --> 00:29:16.640 exit in year two, that early positive cash flow 00:29:16.640 --> 00:29:19.660 dramatically increases the IRR because it's barely 00:29:19.660 --> 00:29:22.910 discounted at all. Exactly. That early win can 00:29:22.910 --> 00:29:26.170 make the entire fund since inception IRR artificially 00:29:26.170 --> 00:29:29.049 sticky and high, even if the remaining 80 percent 00:29:29.049 --> 00:29:31.109 of the portfolio underperforms over the next 00:29:31.109 --> 00:29:34.529 eight years. Wow. Felicto points out that LPs, 00:29:34.809 --> 00:29:37.250 the investors, often get distracted by these 00:29:37.250 --> 00:29:39.750 inflated IRR figures, which often aren't even 00:29:39.750 --> 00:29:42.390 comparable across funds or to public stock market 00:29:42.390 --> 00:29:45.630 indices. So the recommendation is to focus less 00:29:45.630 --> 00:29:48.710 on the rate, the IRR, and more on the money on 00:29:48.710 --> 00:29:51.140 money multiple, the MOM. which is just how many 00:29:51.140 --> 00:29:52.960 dollars were returned for every dollar invested, 00:29:53.279 --> 00:29:55.539 that seems much harder to manipulate with timing. 00:29:55.740 --> 00:29:57.980 Mom, while it ignores the time value of money, 00:29:58.079 --> 00:30:00.720 it gives you that necessary perspective on magnitude 00:30:00.720 --> 00:30:04.380 and total wealth creation. It forces the LP to 00:30:04.380 --> 00:30:06.319 step back from the game of timing that a high 00:30:06.319 --> 00:30:09.700 IRR encourages. Given these profound flaws, the 00:30:09.700 --> 00:30:12.259 conflict with NPV, the multiple solution problem, 00:30:12.359 --> 00:30:14.539 the potential for gaming, it's no surprise that 00:30:14.539 --> 00:30:16.140 finance professionals developed alternatives 00:30:16.140 --> 00:30:19.039 designed specifically to stabilize the rate calculation. 00:30:19.660 --> 00:30:21.779 And the most well -known fix is the modified 00:30:21.779 --> 00:30:25.339 internal rate of return, or MIR -R. MIR -R was 00:30:25.339 --> 00:30:27.920 created to address the two main conceptual flaws 00:30:27.920 --> 00:30:31.200 of traditional IRR, that mathematical instability 00:30:31.200 --> 00:30:34.059 that creates multiple solutions and the ambiguity 00:30:34.059 --> 00:30:36.700 around the reinvestment rate. And it does this 00:30:36.700 --> 00:30:39.000 by abandoning the internal nature of the metric. 00:30:39.200 --> 00:30:41.819 By abandoning the internal nature, Mirror forces 00:30:41.819 --> 00:30:45.000 the analyst to explicitly state the external 00:30:45.000 --> 00:30:48.000 rates that govern the project. It uses two crucial 00:30:48.000 --> 00:30:50.779 external rates. First, it uses the company's 00:30:50.779 --> 00:30:52.819 cost of capital as the discount rate for all 00:30:52.819 --> 00:30:55.660 the outflows, all the costs. Second, and most 00:30:55.660 --> 00:30:58.140 importantly, it assumes that all positive interim 00:30:58.140 --> 00:31:01.339 cash flows, the benefits, can only be reinvested 00:31:01.339 --> 00:31:03.920 at a realistic external reinvestment rate. Which 00:31:03.920 --> 00:31:05.569 is often the cost of... capital again or some 00:31:05.569 --> 00:31:08.369 predetermined safe rate. Exactly. So MIR essentially 00:31:08.369 --> 00:31:11.269 consolidates all future cash inflows to the project's 00:31:11.269 --> 00:31:13.470 end date, compounding them forward at that external 00:31:13.470 --> 00:31:15.809 reinvestment rate. And then it discounts that 00:31:15.809 --> 00:31:18.490 single terminal value back to the present using 00:31:18.490 --> 00:31:20.910 the cost of capital. That transformation achieves 00:31:20.910 --> 00:31:23.549 three vital things. It anchors the project's 00:31:23.549 --> 00:31:25.470 performance to the real economic conditions of 00:31:25.470 --> 00:31:27.589 the firm's financing. It gives a better idea 00:31:27.589 --> 00:31:29.670 of the return the firm will actually realize. 00:31:29.890 --> 00:31:32.589 And most importantly, because it transforms the 00:31:32.589 --> 00:31:35.150 complicated cash flow stream. into a single initial 00:31:35.150 --> 00:31:38.789 outflow followed by a single final inflow, it 00:31:38.789 --> 00:31:41.769 mathematically guarantees a unique single solution. 00:31:41.930 --> 00:31:45.509 It solves the multiple IRR problem. That makes 00:31:45.509 --> 00:31:48.049 MIR a far more robust decision -making tool, 00:31:48.190 --> 00:31:50.549 though the original IRR still seems to reign 00:31:50.549 --> 00:31:53.109 supreme in terms of just popularity and historical 00:31:53.109 --> 00:31:55.970 usage. It does, but academics continue to push 00:31:55.970 --> 00:31:58.740 for improvement. Our sources mention even newer, 00:31:58.819 --> 00:32:00.920 more rigorous approaches designed to solve the 00:32:00.920 --> 00:32:04.500 18 specific flaws noted in traditional IRR, like 00:32:04.500 --> 00:32:06.700 the average internal rate of return or error. 00:32:06.940 --> 00:32:09.740 The IRR approach, introduced by Magni in the 00:32:09.740 --> 00:32:12.819 early 2010s, tries to ground the concept in the 00:32:12.819 --> 00:32:15.559 intuitive notion of the mean, or an average. 00:32:15.819 --> 00:32:18.619 Yes. Instead of relying on that complex discounting 00:32:18.619 --> 00:32:21.319 formula, IRR focuses on calculating a rate that 00:32:21.319 --> 00:32:23.420 represents the time -laden average rate of return 00:32:23.420 --> 00:32:25.920 realized over the investment's life. It makes 00:32:25.920 --> 00:32:27.859 it behave much more like an annualized average 00:32:27.859 --> 00:32:30.160 interest rate. It's highly complex to calculate, 00:32:30.380 --> 00:32:32.440 but its development really shows the continuing 00:32:32.440 --> 00:32:35.220 struggle to create a single, perfect metric for 00:32:35.220 --> 00:32:37.660 capital efficiency. Finally, let's look at how 00:32:37.660 --> 00:32:40.880 IRR translates to your personal finances. This 00:32:40.880 --> 00:32:42.539 is where it becomes a money -weighted performance 00:32:42.539 --> 00:32:44.980 measure for investments, like your brokerage 00:32:44.980 --> 00:32:46.799 account. When you look at your investment performance, 00:32:47.039 --> 00:32:49.500 you typically see two measures. Time -weighted 00:32:49.500 --> 00:32:52.980 return, TWR, and money -weighted return, MWR. 00:32:53.569 --> 00:32:56.009 TWR is what mutual funds and index funds use. 00:32:56.210 --> 00:32:58.650 It removes the effect of your deposits and withdrawals 00:32:58.650 --> 00:33:00.490 to just measure the performance of the manager. 00:33:01.410 --> 00:33:04.529 MWR, which is exactly where IRR is used, measures 00:33:04.529 --> 00:33:07.549 your personal performance. So the IRR of my personal 00:33:07.549 --> 00:33:10.539 portfolio is essentially asking... What annual 00:33:10.539 --> 00:33:14.039 interest rate would an idealized fixed rate savings 00:33:14.039 --> 00:33:16.859 account need to have in order to achieve the 00:33:16.859 --> 00:33:19.579 exact same ending balance, given the exact size 00:33:19.579 --> 00:33:21.880 and timing of all the deposits and withdrawals 00:33:21.880 --> 00:33:23.960 I made? It's highly personalized and extremely 00:33:23.960 --> 00:33:26.380 sensitive to timing. If you're diligent and you 00:33:26.380 --> 00:33:28.559 invest a large sum right before a major market 00:33:28.559 --> 00:33:31.799 rally, your MWR, your IRR, will look spectacular. 00:33:32.119 --> 00:33:34.799 And conversely, if you dump cash into the market 00:33:34.799 --> 00:33:38.579 right before a crash, your MWR will suffer disproportionately. 00:33:39.279 --> 00:33:41.640 even if the underlying asset class eventually 00:33:41.640 --> 00:33:44.519 recovers. It's a measure of investor behavior 00:33:44.519 --> 00:33:46.819 as much as asset return. That's a perfect way 00:33:46.819 --> 00:33:49.680 to put it. But even here, that multiple IRR problem 00:33:49.680 --> 00:33:52.759 can show up if you use the traditional calculation 00:33:52.759 --> 00:33:55.619 on a portfolio that goes negative, say, if you 00:33:55.619 --> 00:33:57.890 borrow on margin. This is a classic dilemma. 00:33:58.569 --> 00:34:00.529 Mathematically, the traditional IRR calculation 00:34:00.529 --> 00:34:03.309 assumes that the interest rate you earn on positive 00:34:03.309 --> 00:34:06.029 balances is identical to the cost of capital 00:34:06.029 --> 00:34:08.610 charged on negative balances, which is, of course, 00:34:08.610 --> 00:34:11.059 not true. Not true at all. In the real world, 00:34:11.099 --> 00:34:13.239 if you borrow on margin, the brokerage charges 00:34:13.239 --> 00:34:15.679 you a much higher external rate for that debt. 00:34:15.900 --> 00:34:18.400 And that economic reality is what necessitated 00:34:18.400 --> 00:34:21.179 the fixed rate equivalent, or FREQ solution. 00:34:21.539 --> 00:34:24.440 FREQ. FREQ is a calculation tailored for personal 00:34:24.440 --> 00:34:27.179 finance that solves that multiple solutions issue. 00:34:27.380 --> 00:34:29.940 It introduces a realistic externally supplied 00:34:29.940 --> 00:34:32.679 cost of borrowing the actual margin rate for 00:34:32.679 --> 00:34:35.199 any negative balances. It brings the theoretical 00:34:35.199 --> 00:34:37.619 return much closer to the economic reality the 00:34:37.619 --> 00:34:39.849 investor is actually facing. What does this all 00:34:39.849 --> 00:34:42.449 mean for you, the listener? The internal rate 00:34:42.449 --> 00:34:45.409 of return is undeniably a foundational concept. 00:34:45.630 --> 00:34:47.869 It's the lingua franca of finance when you're 00:34:47.869 --> 00:34:50.650 discussing efficiency and yield, but it has to 00:34:50.650 --> 00:34:53.099 be viewed as an incomplete picture. That is the 00:34:53.099 --> 00:34:56.539 ultimate synthesis. IRR is a magnificent tool 00:34:56.539 --> 00:34:58.699 for measuring the rate of return inherent in 00:34:58.699 --> 00:35:01.599 a sequence of cash flows, but its internal nature 00:35:01.599 --> 00:35:04.119 is its greatest weakness. You must never rely 00:35:04.119 --> 00:35:06.460 on it in isolation, especially when you are comparing 00:35:06.460 --> 00:35:09.559 two projects of vastly different scale or those 00:35:09.559 --> 00:35:11.760 with non -standard cash flow patterns that might 00:35:11.760 --> 00:35:14.420 risk the mathematical chaos of multiple solutions. 00:35:14.800 --> 00:35:17.519 Because if you rely purely on IRR to rank projects, 00:35:17.840 --> 00:35:20.769 you risk making the max return mistake. You maximize 00:35:20.769 --> 00:35:23.030 your percentage rate return while sacrificing 00:35:23.030 --> 00:35:26.030 millions in total net dollar value created for 00:35:26.030 --> 00:35:28.869 the firm. It's the constant tension between rate 00:35:28.869 --> 00:35:32.329 and scale. Max Return, having chosen the highest 00:35:32.329 --> 00:35:36.849 IRR project for $10 ,000, was left with $90 ,000 00:35:36.849 --> 00:35:39.929 sitting idle. And so here's our final provocative 00:35:39.929 --> 00:35:42.849 thought for you to mull over. If you were max 00:35:42.849 --> 00:35:45.090 return and maximizing your rate was everything, 00:35:45.449 --> 00:35:47.869 how certain, what level of confidence would you 00:35:47.869 --> 00:35:51.570 have to hold that a new, better than 37 .5 % 00:35:51.570 --> 00:35:54.210 IRR project would appear tomorrow before you 00:35:54.210 --> 00:35:57.190 would choose the guaranteed $20 ,000 NPV project 00:35:57.190 --> 00:35:59.190 today? The difficulty of answering that question 00:35:59.190 --> 00:36:02.250 shows why IRR, despite its usefulness, can never 00:36:02.250 --> 00:36:04.869 fully replace the goal of maximizing total value. 00:36:05.230 --> 00:36:07.070 And for those of you eager to see how modern 00:36:07.070 --> 00:36:09.190 financial theory tries to resolve this conundrum, 00:36:09.230 --> 00:36:11.150 exploring the average internal rate of return 00:36:11.150 --> 00:36:13.530 the ARR and its approach to capital efficiency 00:36:13.530 --> 00:36:15.329 is certainly the next logical step.