WEBVTT 00:00:00.000 --> 00:00:02.660 Welcome back to the Deep Dive. Our mission today 00:00:02.660 --> 00:00:05.480 is to really equip you with the knowledge that 00:00:05.480 --> 00:00:07.700 lets you cut through some pretty complex financial 00:00:07.700 --> 00:00:09.919 reports. Right, and understand how wealth is 00:00:09.919 --> 00:00:13.560 actually created. Or destroyed over time. We're 00:00:13.560 --> 00:00:16.379 diving deep into, I think, the foundation of 00:00:16.379 --> 00:00:19.739 all economic and corporate decision making. The 00:00:19.739 --> 00:00:22.760 net present value. Or NVV. NPV. You might also 00:00:22.760 --> 00:00:26.300 hear it called net present worth or NPW. But 00:00:26.300 --> 00:00:28.789 it's all the same idea. It really is. I sometimes 00:00:28.789 --> 00:00:33.350 think of NPV as the financial physicist's approach 00:00:33.350 --> 00:00:35.770 to valuation. It's this universally accepted 00:00:35.770 --> 00:00:38.509 method for measuring the true value of... Any 00:00:38.509 --> 00:00:40.789 asset. Anything that generates cash over time. 00:00:41.009 --> 00:00:43.210 Exactly. Any investment, any capital project. 00:00:43.310 --> 00:00:45.409 It doesn't matter if you're a massive corporation 00:00:45.409 --> 00:00:48.109 looking at a multibillion dollar project or, 00:00:48.130 --> 00:00:50.310 you know, just an individual weighing a new mortgage 00:00:50.310 --> 00:00:53.649 product. NPV is the tool that standardizes that 00:00:53.649 --> 00:00:56.289 comparison. It puts dollars from different times 00:00:56.289 --> 00:00:58.049 on a level playing field. And the whole reason 00:00:58.049 --> 00:01:00.009 we even need this calculation, why we can't just, 00:01:00.070 --> 00:01:02.750 you know, add up the dollars, is this core principle 00:01:02.750 --> 00:01:05.250 of the time value of money. That concept sounds 00:01:05.250 --> 00:01:08.780 simple, but it is. I mean, it's the bedrock of 00:01:08.780 --> 00:01:10.459 everything we're going to talk about today. It 00:01:10.459 --> 00:01:13.280 absolutely is the core philosophy. The time value 00:01:13.280 --> 00:01:16.620 of money, it just states unequivocally that a 00:01:16.620 --> 00:01:19.739 cash flow you get today is inherently more valuable 00:01:19.739 --> 00:01:22.239 than the exact same cash flow you might get in 00:01:22.239 --> 00:01:24.939 the future. And the reason is opportunity. Just 00:01:24.939 --> 00:01:27.920 opportunity. That dollar today can be immediately 00:01:27.920 --> 00:01:30.000 invested. You can put it to work. It can start 00:01:30.000 --> 00:01:31.939 earning returns, interest, dividends, whatever. 00:01:32.180 --> 00:01:35.549 A dollar you get tomorrow just... So let's put 00:01:35.549 --> 00:01:37.510 that into a tangible context right away. Yeah. 00:01:37.590 --> 00:01:39.209 Using one of the examples from the material we 00:01:39.209 --> 00:01:41.329 looked at. Okay. Imagine you're presented with 00:01:41.329 --> 00:01:45.530 two options. Option A, I give you 99 cents right 00:01:45.530 --> 00:01:47.349 here, right now. Okay. I have it in my hand. 00:01:47.390 --> 00:01:50.829 Option B, I promise to give you $1, a full dollar, 00:01:50.890 --> 00:01:54.430 exactly one month from now. Hmm. I think most 00:01:54.430 --> 00:01:56.689 people would probably take the 99 cents. The 00:01:56.689 --> 00:01:59.530 difference is just so negligible, you know, for 00:01:59.530 --> 00:02:01.890 such a short period. The return you'd have to 00:02:01.890 --> 00:02:04.590 earn on that 99 cents over 30 days to make it 00:02:04.590 --> 00:02:07.469 equal a dollar is tiny. What if we stretch that 00:02:07.469 --> 00:02:10.009 out? Now that's where it gets interesting. If 00:02:10.009 --> 00:02:13.150 we shift that time frame dramatically, if that 00:02:13.150 --> 00:02:16.669 same $1 is guaranteed to arrive, say, 20 years 00:02:16.669 --> 00:02:19.090 from now. Even if it's 100 % certain. Even if 00:02:19.090 --> 00:02:22.069 it's certain. Its value today is significantly, 00:02:22.490 --> 00:02:25.330 significantly diminished. And that reduction 00:02:25.330 --> 00:02:28.150 in current value, that's the critical element 00:02:28.150 --> 00:02:30.629 here. That's what's quantified by the discount 00:02:30.629 --> 00:02:33.449 rate. The discount rate, yes. Which represents 00:02:33.449 --> 00:02:35.629 the return you could be earning on that money 00:02:35.629 --> 00:02:37.550 somewhere else. So if you look at a series of 00:02:37.550 --> 00:02:41.030 identical payments. maybe $1 ,000 every year 00:02:41.030 --> 00:02:44.590 for 10 years. Okay. That first $1 ,000 payment 00:02:44.590 --> 00:02:46.590 is the most valuable one. And the 10th is the 00:02:46.590 --> 00:02:49.050 least valuable. Exactly. And the whole purpose 00:02:49.050 --> 00:02:52.210 of NPV is to precisely calculate that rate of 00:02:52.210 --> 00:02:55.129 decay and then sum up the results. And that discount 00:02:55.129 --> 00:02:57.750 rate, it reflects your risk, it reflects your 00:02:57.750 --> 00:03:00.650 inflation expectations, and crucially, your opportunity 00:03:00.650 --> 00:03:04.009 cost. It's the hurdle rate that any investment 00:03:04.009 --> 00:03:06.289 has to clear to even be considered worthwhile. 00:03:06.650 --> 00:03:10.159 Okay, so let's unpack this. Our goal is to move 00:03:10.159 --> 00:03:12.800 beyond the theory and really understand the practical 00:03:12.800 --> 00:03:15.840 application. How does this calculation dictate 00:03:15.840 --> 00:03:18.800 whether a huge corporate initiative. Like a new 00:03:18.800 --> 00:03:21.020 factory. Right. Or developing a new energy source 00:03:21.020 --> 00:03:24.800 or launching some massive new product line. How 00:03:24.800 --> 00:03:27.800 does this tell us if it's genuinely creating. 00:03:28.590 --> 00:03:31.689 economic wealth or if it's just, you know, a 00:03:31.689 --> 00:03:34.409 nominal illusion that's disguised by these big 00:03:34.409 --> 00:03:36.669 flashy revenue projections way out in the future. 00:03:36.849 --> 00:03:39.590 Well, to determine the NPV, you really follow 00:03:39.590 --> 00:03:42.530 a three step process. The first step is all about 00:03:42.530 --> 00:03:44.789 mapping out the cash flows over the entire life 00:03:44.789 --> 00:03:46.770 of the investment. The whole life. The whole 00:03:46.770 --> 00:03:48.930 life. You calculate all the costs, which are 00:03:48.930 --> 00:03:50.789 your negative cash flows, your outflows and all 00:03:50.789 --> 00:03:52.530 the benefits, your positive cash flows, your 00:03:52.530 --> 00:03:55.409 inflows for every single period. So if it's a 00:03:55.409 --> 00:03:58.370 15 year project, we need 15 years. worth of estimates. 00:03:58.569 --> 00:04:00.430 And we have to be really clear about when that 00:04:00.430 --> 00:04:02.310 money is actually supposed to move. Exactly. 00:04:02.530 --> 00:04:05.250 Timing is absolutely everything here. Step two 00:04:05.250 --> 00:04:08.590 is it's the core intellectual work. You take 00:04:08.590 --> 00:04:10.590 the future value of each one of those cash flows. 00:04:10.729 --> 00:04:13.629 One by one. One by one. Whether it's a benefit 00:04:13.629 --> 00:04:16.110 you get in year five or maybe a big maintenance 00:04:16.110 --> 00:04:18.810 cost in year nine. And you discount it back to 00:04:18.810 --> 00:04:22.069 what it's worth today, its present value or PV. 00:04:22.699 --> 00:04:24.500 And you do that using that discount rate we just 00:04:24.500 --> 00:04:26.800 talked about. Using that chosen periodic rate 00:04:26.800 --> 00:04:28.839 of return, yes. Okay, so what's the final defining 00:04:28.839 --> 00:04:33.079 step? Step three. The NPV itself is just the 00:04:33.079 --> 00:04:35.300 sum of all those individually discounted future 00:04:35.300 --> 00:04:38.259 cash flows. And that includes the initial investment. 00:04:38.680 --> 00:04:41.339 Ah, right. So you sum up the present values of 00:04:41.339 --> 00:04:43.879 all the good stuff, the benefits, and you subtract 00:04:43.879 --> 00:04:46.120 the sum of the present values of all the bad 00:04:46.120 --> 00:04:48.800 stuff, the costs. And if you do it right, you're 00:04:48.800 --> 00:04:51.689 left with one single number. One number. The 00:04:51.689 --> 00:04:54.290 project's net value stated in today's dollars. 00:04:54.910 --> 00:04:57.769 That distinction, benefits versus costs, I find 00:04:57.769 --> 00:05:01.350 that really helpful. So essentially, NTV is like 00:05:01.350 --> 00:05:03.550 the financial residue. That's a great way to 00:05:03.550 --> 00:05:05.589 put it. It's the leftover amount, the difference 00:05:05.589 --> 00:05:07.589 between the total present value of the cash coming 00:05:07.589 --> 00:05:10.009 in and the total present value of the cash going 00:05:10.009 --> 00:05:12.509 out. So it's comparing the money you get versus 00:05:12.509 --> 00:05:14.870 the money you spend, but it's adjusted for those 00:05:14.870 --> 00:05:18.079 three critical factors. inflation, the riskiness 00:05:18.079 --> 00:05:20.000 of it all, and the opportunity you're giving 00:05:20.000 --> 00:05:22.019 up to make returns somewhere else. And because 00:05:22.019 --> 00:05:24.240 of that clarity and because it can handle these 00:05:24.240 --> 00:05:26.759 really complex long -term streams of income, 00:05:27.139 --> 00:05:29.899 NPV is the central component of what we call 00:05:29.899 --> 00:05:33.379 discounted cash flow analysis. DCF. DCF, which 00:05:33.379 --> 00:05:35.920 is the gold standard for valuing businesses, 00:05:36.160 --> 00:05:39.180 assets, you name it. It's used across finance, 00:05:39.240 --> 00:05:41.120 economics, and corporate accounting. I mean, 00:05:41.139 --> 00:05:44.430 globally. So once we have that number, That final 00:05:44.430 --> 00:05:48.009 calculated NTV, how do we actually use it to 00:05:48.009 --> 00:05:50.129 make a decision? That brings us to what's called 00:05:50.129 --> 00:05:52.910 the net present value rule. It's remarkably elegant 00:05:52.910 --> 00:05:55.629 in its simplicity. If the NPV is greater than 00:05:55.629 --> 00:05:59.110 zero. A positive number. A positive number. The 00:05:59.110 --> 00:06:01.550 project is projected to add value to the firm. 00:06:01.689 --> 00:06:03.889 It means the present value of all the benefits 00:06:03.889 --> 00:06:06.550 exceeds the present value of all the costs. So 00:06:06.550 --> 00:06:08.750 you should do it. You should pursue it. Assuming, 00:06:08.750 --> 00:06:10.750 of course, you have the capital to fund it in 00:06:10.750 --> 00:06:13.569 the first place. So it represents genuine net 00:06:13.569 --> 00:06:16.290 wealth creation above and beyond what it costs 00:06:16.290 --> 00:06:19.160 you to just finance the project. Precisely. Now, 00:06:19.220 --> 00:06:21.920 conversely, if the NPV is less than zero, so 00:06:21.920 --> 00:06:24.579 a negative number. That's bad. That's bad. The 00:06:24.579 --> 00:06:26.839 investment is expected to subtract value from 00:06:26.839 --> 00:06:29.420 the firm. The projected earnings, once you adjust 00:06:29.420 --> 00:06:31.920 them for time and risk, they just don't cover 00:06:31.920 --> 00:06:34.459 the present value of the costs. So that project 00:06:34.459 --> 00:06:37.279 is financially on sound. You reject it. Generally, 00:06:37.399 --> 00:06:40.040 yes. You reject it. OK, but what about that tricky 00:06:40.040 --> 00:06:42.680 middle ground? What if the NPV lands exactly 00:06:42.680 --> 00:06:46.129 on zero? That indicates a state of, well, financial 00:06:46.129 --> 00:06:48.910 indifference. At an NPV of zero, the project 00:06:48.910 --> 00:06:51.310 is projected to neither gain nor lose monetary 00:06:51.310 --> 00:06:54.170 value. It basically means the investment's own 00:06:54.170 --> 00:06:57.050 internal rate of return exactly matches your 00:06:57.050 --> 00:06:59.389 required discount rate. It's a wash. It's a wash 00:06:59.389 --> 00:07:02.170 financially. So in that scenario, the decision 00:07:02.170 --> 00:07:04.970 to go ahead or not has to rely completely on 00:07:04.970 --> 00:07:08.300 non -monetary criteria. Like what? Oh, maybe 00:07:08.300 --> 00:07:11.279 regulatory compliance or strategic positioning, 00:07:11.459 --> 00:07:13.819 you know, blocking a competitor. Or maybe it 00:07:13.819 --> 00:07:16.160 supports another part of your business. But financially, 00:07:16.339 --> 00:07:19.199 it's neutral. Okay, that really sets the stage 00:07:19.199 --> 00:07:21.680 for how to interpret the result. But to truly 00:07:21.680 --> 00:07:24.259 understand why some projects fail this test, 00:07:24.399 --> 00:07:27.920 we have to look under the hood. Let's get into 00:07:27.920 --> 00:07:29.879 the mathematical components. I think we have 00:07:29.879 --> 00:07:32.019 to. Let's break down the variables in that formula. 00:07:32.430 --> 00:07:33.850 Understanding the formula, it really connects 00:07:33.850 --> 00:07:36.709 all the concepts we've discussed. The correlationship 00:07:36.709 --> 00:07:39.810 starts with calculating the present value, the 00:07:39.810 --> 00:07:42.850 PV, of just a single future cash flow. Okay. 00:07:42.930 --> 00:07:46.730 That formula is... PV equals the cash flow at 00:07:46.730 --> 00:07:50.350 time T, which we call R sub T, divided by the 00:07:50.350 --> 00:07:53.490 quantity 1 plus I, all raised to the power of 00:07:53.490 --> 00:07:56.569 T. Right. And the generalized NPV is just summing 00:07:56.569 --> 00:07:59.370 all of those individual present values up from 00:07:59.370 --> 00:08:01.550 time zero all the way to the final period, which 00:08:01.550 --> 00:08:03.810 we call N. Right. The summation. So let's define 00:08:03.810 --> 00:08:05.930 those variables again, just to be crystal clear, 00:08:05.990 --> 00:08:08.990 starting with T. So T is simply the time period 00:08:08.990 --> 00:08:11.209 when the cash flow happens. It starts at T equals 00:08:11.209 --> 00:08:13.269 zero for your initial investment. The day you 00:08:13.269 --> 00:08:15.189 write the check. The day you write the check. 00:08:15.389 --> 00:08:17.589 And the convention here, which is really important 00:08:17.589 --> 00:08:20.649 for mathematical rigor, is that we assume future 00:08:20.649 --> 00:08:23.550 flows happen at the end of each period. The end 00:08:23.550 --> 00:08:25.350 of the year or the end of the quarter. Exactly. 00:08:25.629 --> 00:08:27.370 And that's the standard because it's the most 00:08:27.370 --> 00:08:30.129 conservative approach. And I, this is the rate 00:08:30.129 --> 00:08:32.549 we've been really emphasizing. I is the discount 00:08:32.549 --> 00:08:35.840 rate. You should think of it as the minimum hurdle 00:08:35.840 --> 00:08:38.860 the project has to clear just to earn its spot 00:08:38.860 --> 00:08:41.240 at the investment table. Right. It's the required 00:08:41.240 --> 00:08:44.139 return on an investment with similar risk. And 00:08:44.139 --> 00:08:46.600 it incorporates that opportunity cost of capital, 00:08:46.759 --> 00:08:49.100 what the firm is giving up, by putting its money 00:08:49.100 --> 00:08:52.440 here instead of the next best alternative. And 00:08:52.440 --> 00:08:55.440 R sub T is just the money itself moving in or 00:08:55.440 --> 00:08:58.870 out. R sub T is the net cash flow. So inflow 00:08:58.870 --> 00:09:02.110 minus outflow at that specific time T. And we 00:09:02.110 --> 00:09:04.470 have to remember, it can be positive, you know, 00:09:04.470 --> 00:09:07.450 revenue or benefits, or it can be negative, like 00:09:07.450 --> 00:09:10.889 costs and expenses. And at time zero, T equals 00:09:10.889 --> 00:09:14.230 zero, that R sub zero is usually a big negative 00:09:14.230 --> 00:09:16.649 number. It's usually your big initial cash outlet, 00:09:16.769 --> 00:09:18.769 yes. The denominator, that's the key to that 00:09:18.769 --> 00:09:21.220 financial erosion we talked about. It's the engine 00:09:21.220 --> 00:09:24.299 of discounting. That one, divided by 1 plus i 00:09:24.299 --> 00:09:26.379 to the t part, is called the discount factor, 00:09:26.679 --> 00:09:29.080 or sometimes the present value factor. And if 00:09:29.080 --> 00:09:31.100 you think about it... The higher the rate I, 00:09:31.240 --> 00:09:34.000 or the longer the time T, the smaller that factor 00:09:34.000 --> 00:09:36.879 becomes. It shrinks exponentially. If T's is 00:09:36.879 --> 00:09:41.580 20 years and I is 10%, that factor is tiny. It 00:09:41.580 --> 00:09:44.279 makes that future dollar worth very, very little 00:09:44.279 --> 00:09:46.440 today. And this is the part I find really fascinating, 00:09:46.580 --> 00:09:49.159 connecting this sort of technical formula to 00:09:49.159 --> 00:09:52.830 a much clearer concept. We defined... the generalized 00:09:52.830 --> 00:09:55.929 formula as this single sum. But the sources point 00:09:55.929 --> 00:09:58.090 out that it's often cleaner for decision makers 00:09:58.090 --> 00:10:00.470 to express it as a difference. Right. The difference 00:10:00.470 --> 00:10:03.210 between discounted benefits and costs, that's 00:10:03.210 --> 00:10:06.049 the conceptual heart of it. NPV equals the present 00:10:06.049 --> 00:10:08.490 value of the benefits minus the present value 00:10:08.490 --> 00:10:11.309 of the costs. So you do two separate calculations. 00:10:11.610 --> 00:10:13.830 Two separate summations. You calculate the PV 00:10:13.830 --> 00:10:16.009 of all your future benefits, B, and then you 00:10:16.009 --> 00:10:18.289 calculate the PV of all your future costs, C. 00:10:18.409 --> 00:10:20.389 The difference between those two totals, once 00:10:20.389 --> 00:10:22.620 they're both in today's dollars, is your net 00:10:22.620 --> 00:10:26.100 present value. That framework really helps managers 00:10:26.100 --> 00:10:28.639 visualize the trade -off, doesn't it? It clearly 00:10:28.639 --> 00:10:31.259 separates the money coming in from the money 00:10:31.259 --> 00:10:34.399 going out, all standardized to the present. I 00:10:34.399 --> 00:10:36.220 always picture the CEO standing there with the 00:10:36.220 --> 00:10:39.240 checkbook open at T equals zero. That initial 00:10:39.240 --> 00:10:42.720 cash goes out immediately. No discounting needed. 00:10:43.039 --> 00:10:45.240 And that visualization relates directly back 00:10:45.240 --> 00:10:48.279 to that initial investment, R sub zero. The general 00:10:48.279 --> 00:10:50.220 convention is that your initial investments, 00:10:50.340 --> 00:10:53.000 your cash outlays, they're summed up as a negative 00:10:53.000 --> 00:10:55.960 cash flow, but they're not mathematically discounted. 00:10:55.960 --> 00:10:58.759 Why not? Because they happen immediately at time 00:10:58.759 --> 00:11:01.500 T equals zero. They are already at their present 00:11:01.500 --> 00:11:04.580 value. Okay. To really drive home the power of 00:11:04.580 --> 00:11:06.700 this discounting process, I think we have to 00:11:06.700 --> 00:11:09.759 move away from the algebra and get into a detailed 00:11:09.759 --> 00:11:12.330 corporate scenario. I agree. This is the moment 00:11:12.330 --> 00:11:14.409 where those nominal future dollars just sort 00:11:14.409 --> 00:11:16.549 of collapse under the weight of time. Let's use 00:11:16.549 --> 00:11:18.450 the specific project decision that was outlined 00:11:18.450 --> 00:11:20.929 in the material. A corporation is evaluating 00:11:20.929 --> 00:11:23.129 whether to launch a new product line. And it 00:11:23.129 --> 00:11:25.830 requires a significant capital investment right 00:11:25.830 --> 00:11:28.549 up front. Okay, so the initial capital expenditure 00:11:28.549 --> 00:11:32.110 at time t equals zero is a negative cash flow 00:11:32.110 --> 00:11:35.730 of negative $100 ,000. $100 ,000 out the door 00:11:35.730 --> 00:11:39.230 today. Then the product is expected to generate 00:11:39.230 --> 00:11:42.289 these really reliable, consistent benefits cash 00:11:42.289 --> 00:11:47.090 inflows of $10 ,000 a year for 12 years. And 00:11:47.090 --> 00:11:50.029 that starts at year one. Starting at T equals 00:11:50.029 --> 00:11:52.230 one. And we'll assume those are net figures. 00:11:52.289 --> 00:11:54.250 So operating costs are already taken out. OK, 00:11:54.350 --> 00:11:56.590 let's stop right there. If we were, you know, 00:11:56.590 --> 00:11:58.669 amateur analysts, we would just add up the nominal 00:11:58.669 --> 00:12:03.970 values. $100 ,000 investment yields $120 ,000 00:12:03.970 --> 00:12:07.100 in total returns. Right. 12 years times 10 ,000. 00:12:07.159 --> 00:12:10.039 That's a $20 ,000 profit. Seems like an obvious 00:12:10.039 --> 00:12:12.720 yes. It seems obviously profitable if you ignore 00:12:12.720 --> 00:12:15.659 the time value of money. But we have to apply 00:12:15.659 --> 00:12:18.179 the firm's effective annual discount rate. And 00:12:18.179 --> 00:12:21.340 in this case, it's 10%. 10%. This represents 00:12:21.340 --> 00:12:23.500 what they could reliably earn somewhere else 00:12:23.500 --> 00:12:26.220 on a project with similar risk. Now we have to 00:12:26.220 --> 00:12:28.220 walk through the calculation and watch that profit 00:12:28.220 --> 00:12:33.159 just vanish. Okay, so the $100 ,000 cost at T 00:12:33.159 --> 00:12:36.570 equals zero. That stays $100 ,000. That's our 00:12:36.570 --> 00:12:38.309 benchmark. That's the benchmark. Now for the 00:12:38.309 --> 00:12:41.389 inflows. That first $10 ,000, the one you receive 00:12:41.389 --> 00:12:44.330 in year one, is discounted once. Okay. So its 00:12:44.330 --> 00:12:48.009 present value is just over $9 ,090. We've already 00:12:48.009 --> 00:12:50.990 lost almost $1 ,000 in present value in just 00:12:50.990 --> 00:12:54.190 12 months. And by year two, that $10 ,000 is 00:12:54.190 --> 00:12:57.250 only worth about $8 ,200. The compounding effect 00:12:57.250 --> 00:13:00.629 is now fully in play. And the decay just accelerates. 00:13:00.669 --> 00:13:02.669 By the time we look at the cash flow arriving 00:13:02.669 --> 00:13:05.899 five years from now, That same $10 ,000 is only 00:13:05.899 --> 00:13:09.879 worth $6 ,209 today. Wow. The firm is waiting 00:13:09.879 --> 00:13:12.879 five years to get that money. During that time, 00:13:12.899 --> 00:13:15.000 it could have been generating a 10 % compounded 00:13:15.000 --> 00:13:18.059 return if it had it sooner. This compounding 00:13:18.059 --> 00:13:20.779 effect is staggering. If we jump all the way 00:13:20.779 --> 00:13:24.019 to the end, to T equals 12. The final payment. 00:13:24.259 --> 00:13:27.320 That final $10 ,000 payment is worth a mere $3 00:13:27.320 --> 00:13:31.059 ,186 in present -day money. Less than a third 00:13:31.059 --> 00:13:33.620 of its face value. It is the ultimate illustration 00:13:33.620 --> 00:13:36.580 of why distance and time is the enemy of value. 00:13:36.980 --> 00:13:40.340 So when we do the full summation, the total present 00:13:40.340 --> 00:13:43.539 value of all 12 of those $10 ,000 cash flows 00:13:43.539 --> 00:13:49.580 comes to only $68 ,136 .91. So what does this 00:13:49.580 --> 00:13:51.919 all mean for the decision maker? Well, the present 00:13:51.919 --> 00:13:55.019 value of all the benefits is $68 ,000. The present 00:13:55.019 --> 00:13:58.220 value of the cost is $100 ,000. So the NPV is 00:13:58.220 --> 00:14:03.820 negative $31 ,863. A huge loss. The project should 00:14:03.820 --> 00:14:06.399 be shelved immediately. While it looks like it 00:14:06.399 --> 00:14:08.860 makes a nominal profit of $20 ,000, the calculation 00:14:08.860 --> 00:14:11.460 reveals that by tying up that $100 ,000 for 12 00:14:11.460 --> 00:14:14.340 years, the company is actually destroying value. 00:14:14.700 --> 00:14:17.379 It's equivalent to just losing almost $32 ,000 00:14:17.379 --> 00:14:20.700 today. Exactly. That is a stunning real world 00:14:20.700 --> 00:14:24.279 application. It really proves why NPV is so essential. 00:14:24.460 --> 00:14:27.259 Yeah. But this analysis, as rigorous as it is, 00:14:27.379 --> 00:14:30.080 it rests on some key... implicit assumptions 00:14:30.080 --> 00:14:33.139 that we have to make explicit. Yes, every model 00:14:33.139 --> 00:14:35.799 has them. So what are the constraints that are 00:14:35.799 --> 00:14:38.440 baked into this simple 12 -year example? Well, 00:14:38.500 --> 00:14:40.779 the first assumption is about the project lifecycle. 00:14:41.320 --> 00:14:43.960 We're assuming that the investment horizon of 00:14:43.960 --> 00:14:46.820 this project, 12 years, is equally acceptable 00:14:46.820 --> 00:14:49.500 when you compare it to any other competing project. 00:14:49.820 --> 00:14:53.039 We're treating a 12 -year commitment as neither 00:14:53.039 --> 00:14:55.720 good nor bad compared to a five -year one. Which 00:14:55.720 --> 00:14:58.080 might not be true. It often requires further 00:14:58.080 --> 00:15:00.820 analysis to justify. Okay, what's the second 00:15:00.820 --> 00:15:04.360 assumption? It involves the rate itself. We assumed 00:15:04.360 --> 00:15:07.299 a 10 % discount rate. We have to assume that 00:15:07.299 --> 00:15:09.980 this rate is appropriate, that it's stable, and 00:15:09.980 --> 00:15:12.539 that it accurately reflects the risk level of 00:15:12.539 --> 00:15:15.240 this specific practice for the entire 12 years. 00:15:15.419 --> 00:15:17.259 A lot of assumptions there. A lot of assumptions. 00:15:17.539 --> 00:15:19.980 And the third one brings it back to corporate 00:15:19.980 --> 00:15:22.919 governance. We are assuming that the firm's owners, 00:15:23.059 --> 00:15:25.980 the shareholders, can't achieve a better return, 00:15:26.120 --> 00:15:29.500 a return above that 10 % somewhere else at a 00:15:29.500 --> 00:15:31.460 similar risk level. Ah, right. If they could 00:15:31.460 --> 00:15:33.990 get 12 % on their own. If external investors 00:15:33.990 --> 00:15:37.649 could reliably earn 12 percent on a similar risk 00:15:37.649 --> 00:15:40.190 investment, the firm should just liquidate the 00:15:40.190 --> 00:15:42.610 project, return the capital and let the shareholders 00:15:42.610 --> 00:15:45.370 invest it themselves. That would maximize their 00:15:45.370 --> 00:15:47.529 collective wealth. That brings it right back 00:15:47.529 --> 00:15:50.190 to opportunity cost, which is just the relentless 00:15:50.190 --> 00:15:53.809 driver behind all sound financial theory. The 00:15:53.809 --> 00:15:55.750 capital has to be employed in its most efficient 00:15:55.750 --> 00:15:58.789 use. Always. And to make that opportunity cost 00:15:58.789 --> 00:16:02.460 even more. visceral, let's revisit that simple 00:16:02.460 --> 00:16:05.980 lottery analogy. Imagine you win a $500 million 00:16:05.980 --> 00:16:09.100 lottery, but it's paid out in equal installments 00:16:09.100 --> 00:16:11.440 over 20 years. That's the nominal value, $500 00:16:11.440 --> 00:16:13.639 million. But when you choose the cash option, 00:16:13.879 --> 00:16:17.059 you get a single immediate lump sum. And that 00:16:17.059 --> 00:16:19.519 lump sum, which is the MPV of that future stream 00:16:19.519 --> 00:16:22.879 of payments, is usually about $285 million. Right. 00:16:22.940 --> 00:16:25.539 So where did the other $215 million go? It's 00:16:25.539 --> 00:16:27.919 not a scam or a deduction. Not at all. It is 00:16:27.919 --> 00:16:30.620 the financial value of the time difference. It's 00:16:30.620 --> 00:16:32.620 the amount that the lottery commission expects 00:16:32.620 --> 00:16:35.620 to earn by investing that cash stream over 20 00:16:35.620 --> 00:16:37.500 years before they have to pay it all out to you. 00:16:37.620 --> 00:16:40.559 So that value belongs to whoever holds the capital. 00:16:40.679 --> 00:16:42.940 Exactly. And if you take the lump sum, you get 00:16:42.940 --> 00:16:44.820 the opportunity to earn that return yourself. 00:16:45.179 --> 00:16:48.299 That example really shows that everything hinges 00:16:48.299 --> 00:16:50.820 on that discount rate, the 10 % or whatever rate 00:16:50.820 --> 00:16:53.379 we choose. But what happens if we get that critical 00:16:53.379 --> 00:16:57.139 variable either wrong? How do sophisticated firms 00:16:57.139 --> 00:17:00.450 decide which rate to use? The selection of the 00:17:00.450 --> 00:17:03.029 discount rate is probably the single most important 00:17:03.029 --> 00:17:05.369 and frankly the most frequently debated step 00:17:05.369 --> 00:17:07.910 in the entire NPV process. I can imagine. The 00:17:07.910 --> 00:17:10.309 most common choice, sort of the starting point, 00:17:10.509 --> 00:17:12.869 is the firm's weighted average cost of capital. 00:17:13.089 --> 00:17:16.549 The WACC. The WECC. This represents the blended 00:17:16.549 --> 00:17:18.650 average rate the company pays to finance its 00:17:18.650 --> 00:17:21.130 assets, considering both its debt and its equity, 00:17:21.250 --> 00:17:23.730 and it's usually calculated after tax. So why 00:17:23.730 --> 00:17:27.529 is WACC the default baseline? Because the WACC 00:17:27.529 --> 00:17:30.140 represents the minimum return the firm has to 00:17:30.140 --> 00:17:33.240 earn on its existing asset base just to satisfy 00:17:33.240 --> 00:17:36.339 its creditors and its shareholders. So if a new 00:17:36.339 --> 00:17:39.680 project can't even earn the WACC, it's mathematically 00:17:39.680 --> 00:17:42.920 diluting shareholder value. Assuming the new 00:17:42.920 --> 00:17:44.660 project has the same risk as the rest of the 00:17:44.660 --> 00:17:47.180 company. That's the key assumption, yes. But 00:17:47.180 --> 00:17:49.700 it's just a baseline, and many experts argue 00:17:49.700 --> 00:17:53.019 for adjustments. They do. In practice, WACC gets 00:17:53.019 --> 00:17:56.140 adjusted in two main ways. First, professionals 00:17:56.140 --> 00:17:59.180 will often argue for a higher discount rate to 00:17:59.180 --> 00:18:01.759 adjust for higher perceived risk in a specific 00:18:01.759 --> 00:18:05.119 project. Or to better reflect the true opportunity 00:18:05.119 --> 00:18:08.059 cost of that capital. Right. And second? Second, 00:18:08.160 --> 00:18:10.500 they might use a variable discount rate, so you'd 00:18:10.500 --> 00:18:12.380 apply higher rates to cash flows that happen 00:18:12.380 --> 00:18:15.019 much, much further in the future. This reflects 00:18:15.019 --> 00:18:17.539 what's called the yield curve premium, where 00:18:17.539 --> 00:18:20.019 long -term debt often requires higher yields 00:18:20.019 --> 00:18:22.240 than short -term debt just because there's more 00:18:22.240 --> 00:18:24.839 uncertainty over longer horizons. Tell us more 00:18:24.839 --> 00:18:27.259 about the opportunity cost method. It seems a 00:18:27.259 --> 00:18:29.099 bit more sophisticated than just using a blended 00:18:29.099 --> 00:18:32.819 corporate average like WACC. It is. The opportunity 00:18:32.819 --> 00:18:35.279 cost approach dictates that the discount rate 00:18:35.279 --> 00:18:37.900 you use for a specific project should be the 00:18:37.900 --> 00:18:40.299 rate of return that the capital for that project 00:18:40.299 --> 00:18:43.299 could return if you invested it in the best available 00:18:43.299 --> 00:18:46.440 alternative. So an example. Let's say Project 00:18:46.440 --> 00:18:49.680 A requires $100 million in capital, and the firm 00:18:49.680 --> 00:18:52.119 knows that same $100 million could reliably earn 00:18:52.119 --> 00:18:55.240 8 % in Project B. Then you have to use 8 % for 00:18:55.240 --> 00:18:58.000 Project A. You should use 8 % as the discount 00:18:58.000 --> 00:19:00.640 rate for Project A. That ensures that Project 00:19:00.640 --> 00:19:03.420 A is only accepted if it actually outperforms 00:19:03.420 --> 00:19:06.099 the next best option you have. Which makes perfect 00:19:06.099 --> 00:19:08.319 sense. And this leads directly to the concept 00:19:08.319 --> 00:19:11.099 of the firm's internal reinvestment rate. The 00:19:11.099 --> 00:19:13.220 reinvestment rate is the average rate of return 00:19:13.220 --> 00:19:15.980 the firm achieves on its general pool of internal 00:19:15.980 --> 00:19:18.940 investments. So why would a firm choose to use 00:19:18.940 --> 00:19:22.799 the reinvestment rate instead of WACC? I mean, 00:19:22.819 --> 00:19:25.539 isn't WACC usually close enough? That's a good 00:19:25.539 --> 00:19:28.900 challenge. WACC is easy to calculate. It's legally 00:19:28.900 --> 00:19:31.140 defensible, however, in a capital -constrained 00:19:31.140 --> 00:19:33.380 environment. Meaning you have more good ideas 00:19:33.380 --> 00:19:36.500 than you have cash? Exactly. You have more positive 00:19:36.500 --> 00:19:40.200 NPV projects than available cash. In that world, 00:19:40.440 --> 00:19:43.279 the true opportunity cost is often much higher 00:19:43.279 --> 00:19:47.200 than the WACC. Imagine a firm with high internal 00:19:47.200 --> 00:19:50.079 demand for capital. Every dollar you commit to 00:19:50.079 --> 00:19:52.619 a new factory means a dollar that you can't use 00:19:52.619 --> 00:19:54.819 to upgrade software that's currently yielding 00:19:54.819 --> 00:19:57.660 a 20 % return. So in that scenario? In that scenario, 00:19:57.839 --> 00:20:00.339 using the firm's average reinvestment rate, which 00:20:00.339 --> 00:20:02.539 captures the high return of those internal projects, 00:20:02.759 --> 00:20:05.579 gives you a much better benchmark for maximizing 00:20:05.579 --> 00:20:09.440 value than the potentially lower blended WACC 00:20:09.440 --> 00:20:13.000 would. So the goal dictates the rate. If you 00:20:13.000 --> 00:20:15.099 just want to know if a project clears the basic 00:20:15.099 --> 00:20:18.519 hurdle of funding, WACC is fine. It works. But 00:20:18.519 --> 00:20:20.640 if you're trying to maximize value and prioritize 00:20:20.640 --> 00:20:23.119 between competing mutually exclusive projects, 00:20:23.359 --> 00:20:25.819 the corporate reinvestment rate might be superior 00:20:25.819 --> 00:20:28.619 because it's benchmarking against the best internal 00:20:28.619 --> 00:20:31.059 use of that limited cash. That is the critical 00:20:31.059 --> 00:20:33.220 distinction. And speaking of sophisticated adjustments, 00:20:33.619 --> 00:20:35.539 the sources introduce a superior methodology 00:20:35.539 --> 00:20:38.059 for handling risk, though it does require a bit 00:20:38.059 --> 00:20:40.680 more analytical work. And that is the risk adjusted 00:20:40.680 --> 00:20:44.440 net present value or RMPV. I understand that 00:20:44.440 --> 00:20:46.819 just adding a premium to the discount rate for 00:20:46.819 --> 00:20:49.980 risk is a bit imprecise because of that compounding 00:20:49.980 --> 00:20:53.119 effect. So how does RMPV solve that? Well, RNPV 00:20:53.119 --> 00:20:55.579 separates the risk quantification from the time 00:20:55.579 --> 00:20:58.259 value calculation. So instead of just bumping 00:20:58.259 --> 00:21:00.660 up the discount rate I, the RNPV methodology 00:21:00.660 --> 00:21:03.240 suggests explicitly correcting the cash flows 00:21:03.240 --> 00:21:05.480 themselves for risk first. How do you do that? 00:21:05.599 --> 00:21:07.900 You use a probability factor, let's call it P, 00:21:08.099 --> 00:21:11.259 to reduce the expected cash flow, R sub T, reflecting 00:21:11.259 --> 00:21:13.920 the probability of success or failure. So if 00:21:13.920 --> 00:21:17.440 a drug trial in year three has only a 60 % chance 00:21:17.440 --> 00:21:20.839 of success, we only value 60 % of that potential 00:21:20.839 --> 00:21:23.619 cash flow. Exactly. The formula essentially becomes 00:21:23.619 --> 00:21:26.099 you discount the quantity of P times R sub T, 00:21:26.240 --> 00:21:28.079 you correct the cash flow for the probability 00:21:28.079 --> 00:21:30.480 of ever receiving it, and then you discount that 00:21:30.480 --> 00:21:32.960 adjusted cash flow using the firm's normal standard 00:21:32.960 --> 00:21:36.160 WACC or risk -free rate. So you separate the 00:21:36.160 --> 00:21:38.519 two problems, valuing the risk and then valuing 00:21:38.519 --> 00:21:41.220 the time. Much cleaner. Much cleaner, much less 00:21:41.220 --> 00:21:43.519 subjective, and it gives you a much more robust 00:21:43.519 --> 00:21:46.740 framework for risk management. This is particularly 00:21:46.740 --> 00:21:49.619 crucial for, say, international projects or R 00:21:49.619 --> 00:21:52.500 &D, where success rates are highly variable. 00:21:52.779 --> 00:21:55.599 The last application in this section, it deals 00:21:55.599 --> 00:21:57.480 with a really common challenge for managers. 00:21:58.500 --> 00:22:01.480 How do you compare projects of wildly different 00:22:01.480 --> 00:22:04.500 scales, especially when capital is limited? The 00:22:04.500 --> 00:22:06.680 bang for your buck problem. This is the concept 00:22:06.680 --> 00:22:09.230 of capital efficiency. measured by the net present 00:22:09.230 --> 00:22:13.210 value per dollar invested, or NPVI. This metric 00:22:13.210 --> 00:22:15.950 answers that exact question. Which project yields 00:22:15.950 --> 00:22:18.650 the biggest bang for my buck? It adjusts the 00:22:18.650 --> 00:22:21.849 raw NPV result to show the project's contribution 00:22:21.849 --> 00:22:24.910 per dollar of initial investment. It's a prioritization 00:22:24.910 --> 00:22:27.130 tool. How do we calculate it? The standard calculation 00:22:27.130 --> 00:22:29.769 is your discounted benefits minus your discounted 00:22:29.769 --> 00:22:32.450 costs, all divided by the discounted costs. But 00:22:32.450 --> 00:22:34.309 it's often mathematically equivalent to just 00:22:34.309 --> 00:22:37.130 taking the raw NPV and dividing it by the initial 00:22:37.130 --> 00:22:39.390 investment cost. Okay, let's use the sources 00:22:39.390 --> 00:22:41.990 example to make that ratio concrete. So suppose 00:22:41.990 --> 00:22:45.029 we have Project A. The discounted benefits over 00:22:45.029 --> 00:22:48.309 its life are $100 million. The discounted costs 00:22:48.309 --> 00:22:51.799 are $60 million. So the NPV is $40 million. The 00:22:51.799 --> 00:22:55.799 NTV is 40 million. The NPV is that 40 million 00:22:55.799 --> 00:22:58.859 divided by the 60 million in costs, which comes 00:22:58.859 --> 00:23:02.539 out to about 0 .6667. Okay, what does that number 00:23:02.539 --> 00:23:05.259 mean? It means for every single dollar the firm 00:23:05.259 --> 00:23:08.720 commits to Project A, it generates about 67 cents 00:23:08.720 --> 00:23:12.190 of net present value wealth. Okay. Now, what 00:23:12.190 --> 00:23:15.069 about Project B? Now, imagine Project B has a 00:23:15.069 --> 00:23:19.089 lower NPV, say $30 million, but it only requires 00:23:19.089 --> 00:23:22.869 a $20 million initial investment. Its NPVI is 00:23:22.869 --> 00:23:25.369 $30 million divided by $20 million. Which is 00:23:25.369 --> 00:23:29.309 1 .5. 1 .5. Wait, so Project A has a higher absolute 00:23:29.309 --> 00:23:32.130 NPV, the $40 million, but Project B has a far 00:23:32.130 --> 00:23:34.950 higher NPVI. Exactly. And if the FERP is capital 00:23:34.950 --> 00:23:37.230 constrained and can only afford one or the other, 00:23:37.349 --> 00:23:39.069 or if they need to stretch their limited budget, 00:23:39.490 --> 00:23:42.029 Project B, despite its lower... absolute NPV 00:23:42.029 --> 00:23:44.470 is the superior investment. Because it's more 00:23:44.470 --> 00:23:47.869 efficient. It yields $1 .50 of value for every 00:23:47.869 --> 00:23:50.910 dollar you invest, compared to Project A's 67 00:23:50.910 --> 00:23:54.890 cents. NPVI maximizes the efficient deployment 00:23:54.890 --> 00:23:57.990 of scarce capital. That's powerful. It moves 00:23:57.990 --> 00:24:00.430 us away from just ranking by the raw dollar amount 00:24:00.430 --> 00:24:03.200 to ranking by... Capital productivity. Yeah. 00:24:03.380 --> 00:24:05.740 OK, let's shift gears into some of the theoretical 00:24:05.740 --> 00:24:08.019 nuances and assumptions that are buried in these 00:24:08.019 --> 00:24:10.359 mechanics, especially around time. Right. We 00:24:10.359 --> 00:24:12.339 talked about T, the timing of the cash flows 00:24:12.339 --> 00:24:14.299 and how that assumption matters. And it matters 00:24:14.299 --> 00:24:17.960 significantly. As we noted, the standard NTV 00:24:17.960 --> 00:24:20.900 formula, it assumes all your benefits and costs 00:24:20.900 --> 00:24:23.559 occur precisely at the end of each period. Which 00:24:23.559 --> 00:24:26.160 is simple, but not very realistic. Not always. 00:24:26.990 --> 00:24:29.069 And it's considered the most conservative approach. 00:24:29.369 --> 00:24:31.750 Why conservative? Because by pushing the income 00:24:31.750 --> 00:24:33.849 to the latest possible date, the end of the year, 00:24:33.990 --> 00:24:36.450 you maximize the duration of time over which 00:24:36.450 --> 00:24:39.130 it has to be discounted. This gives you the lowest 00:24:39.130 --> 00:24:43.170 possible or most conservative NPV result. And 00:24:43.170 --> 00:24:45.569 in finance, conservatism is generally preferred. 00:24:46.130 --> 00:24:48.390 But if cash flows are really spread out through 00:24:48.390 --> 00:24:50.410 the year, we might be misrepresenting the true 00:24:50.410 --> 00:24:53.250 value of the project. And that's where mid -period 00:24:53.250 --> 00:24:56.519 discounting comes in. In many projects, you know, 00:24:56.539 --> 00:24:59.420 like retail sales or utility billing, cash flows 00:24:59.420 --> 00:25:02.039 arrive more or less continuously throughout the 00:25:02.039 --> 00:25:04.420 year. Right. So if we assume the cash flow is 00:25:04.420 --> 00:25:07.359 distributed evenly, the average time the money 00:25:07.359 --> 00:25:10.279 is received is the middle of the period. So we 00:25:10.279 --> 00:25:14.000 discount from T minus 0 .5. And what's the impact 00:25:14.000 --> 00:25:17.519 on the final number? It results in a higher NPV 00:25:17.519 --> 00:25:19.519 than the standard method because you're discounting 00:25:19.519 --> 00:25:22.380 the benefits for half a period less time. So 00:25:22.380 --> 00:25:24.420 it gives you a more accurate representation if 00:25:24.420 --> 00:25:26.900 the cash flows are genuinely continuous, but 00:25:26.900 --> 00:25:29.220 it's inherently less conservative. And then there's 00:25:29.220 --> 00:25:31.440 the least conservative method of all. Which is 00:25:31.440 --> 00:25:34.519 beginning of period discounting. This assumes 00:25:34.519 --> 00:25:36.960 all cash flows arrive immediately at the start 00:25:36.960 --> 00:25:39.420 of the period. This gives you the highest possible 00:25:39.420 --> 00:25:42.650 least conservative NPV. It's not standard for 00:25:42.650 --> 00:25:45.109 external reporting, but understanding these timing 00:25:45.109 --> 00:25:47.670 nuances is really critical for internal managers 00:25:47.670 --> 00:25:50.170 who want their models to closely match the reality 00:25:50.170 --> 00:25:53.069 of their operational cash cycles. Okay, now for 00:25:53.069 --> 00:25:55.829 a brief moment of high -level theory. I think 00:25:55.829 --> 00:25:57.849 it's useful to see that NPV isn't just some accounting 00:25:57.849 --> 00:26:00.829 trick, but it's a profoundly rigorous concept. 00:26:01.150 --> 00:26:04.309 Absolutely. What's fascinating here is that the 00:26:04.309 --> 00:26:08.029 time -discrete NPV summation that we use is functionally 00:26:08.029 --> 00:26:10.710 equivalent to an integral transform of the cash 00:26:10.710 --> 00:26:13.910 flow stream. It's similar to how electrical engineers 00:26:13.910 --> 00:26:16.309 analyze signals. We don't need the calculus here, 00:26:16.390 --> 00:26:18.490 but what's the conceptual link? The conceptual 00:26:18.490 --> 00:26:21.500 takeaway is powerful. The discount rate, it essentially 00:26:21.500 --> 00:26:24.440 represents the damping inherent in the system. 00:26:24.559 --> 00:26:27.400 In system dynamics, the math separates complex 00:26:27.400 --> 00:26:30.960 values into real and imaginary parts. The real 00:26:30.960 --> 00:26:33.500 part relates directly to the effect of compound 00:26:33.500 --> 00:26:36.880 interest, that relentless exponential decay of 00:26:36.880 --> 00:26:39.920 value over time. It shows how a fixed cash flow 00:26:39.920 --> 00:26:42.140 signal is dampened as it moves into the future. 00:26:42.339 --> 00:26:44.420 So the higher the real part, which is like a 00:26:44.420 --> 00:26:47.099 higher discount rate, the faster the signal fades 00:26:47.099 --> 00:26:49.660 and the lower the present value. Precisely. And 00:26:49.660 --> 00:26:52.640 the imaginary parts describe cyclical or oscillating 00:26:52.640 --> 00:26:54.480 behavior. Now, in finance, this doesn't mean 00:26:54.480 --> 00:26:56.700 your cash flows are literally oscillating, but 00:26:56.700 --> 00:27:00.160 it provides a framework to analyze business phenomena 00:27:00.160 --> 00:27:02.799 like cyclical revenues, inventory management 00:27:02.799 --> 00:27:06.240 cycles, or price shifts like the famous pork 00:27:06.240 --> 00:27:08.900 cycle in agriculture. The fact that the financial 00:27:08.900 --> 00:27:11.559 discount rate maps to these dynamic system concepts, 00:27:11.740 --> 00:27:14.619 it just confirms the deep theoretical rigor that's 00:27:14.619 --> 00:27:17.680 underpinning NPV analysis. So we can view a project 00:27:17.680 --> 00:27:20.799 not as a static stream, but as a dynamic system 00:27:20.799 --> 00:27:23.720 responding to time and rates. That's the idea. 00:27:23.900 --> 00:27:27.369 That provides fantastic context. It ensures we 00:27:27.369 --> 00:27:29.650 know this tool is built on solid, fundamental 00:27:29.650 --> 00:27:32.250 mathematics. Let's pivot now to the critical 00:27:32.250 --> 00:27:34.750 analysis, the advantages, the disadvantages, 00:27:35.089 --> 00:27:37.690 and the dangerous pitfalls managers can run into. 00:27:37.910 --> 00:27:40.450 Starting with the advantages, which are why it's 00:27:40.450 --> 00:27:42.910 the standard tool. First and foremost, NPV is 00:27:42.910 --> 00:27:45.009 the only method that rigorously and consistently 00:27:45.009 --> 00:27:47.309 considers the time value of money. Which makes 00:27:47.309 --> 00:27:49.269 it consistent with maximizing shareholder wealth. 00:27:49.710 --> 00:27:51.890 Entirely. It's measuring true economic profit. 00:27:52.269 --> 00:27:54.730 Second, it gives you an unambiguous dollar value. 00:27:54.849 --> 00:27:57.250 There's no confusion. A project with an NPV of 00:27:57.250 --> 00:27:59.450 plus 20 million is just quantitatively better 00:27:59.450 --> 00:28:02.369 than one with an NPV of plus 5 million, assuming 00:28:02.369 --> 00:28:05.640 your inputs were right. And crucially... It accounts 00:28:05.640 --> 00:28:07.880 for differences in cash flow timing and size. 00:28:08.180 --> 00:28:11.019 Because every single cash flow is adjusted individually 00:28:11.019 --> 00:28:13.299 based on how far away it is and how big it is, 00:28:13.380 --> 00:28:16.900 it handles uneven or irregular cash flow patterns 00:28:16.900 --> 00:28:19.819 perfectly. And finally, that additivity property 00:28:19.819 --> 00:28:22.900 is immensely useful for corporate finance. It 00:28:22.900 --> 00:28:25.619 is. The NPVs of separate independent projects 00:28:25.619 --> 00:28:27.859 can just be summed up to calculate the total 00:28:27.859 --> 00:28:30.500 expected change in the firm's wealth. If a firm 00:28:30.500 --> 00:28:33.299 takes on five projects, the sum of their individual 00:28:33.299 --> 00:28:39.599 NPVs is the expected Okay, now for the critical 00:28:39.599 --> 00:28:42.660 disadvantages, because no model is perfect. The 00:28:42.660 --> 00:28:44.940 first problem, which I imagine gives planners 00:28:44.940 --> 00:28:48.000 a lot of anxiety, is the heavy reliance on subjective 00:28:48.000 --> 00:28:50.740 inputs. It's the garbage in, garbage out problem. 00:28:51.000 --> 00:28:53.680 Yeah. NPV's accuracy is hypersensitive to the 00:28:53.680 --> 00:28:55.839 correctness of your inputs. You need to correctly 00:28:55.839 --> 00:28:59.259 predict future cash flow amounts, often 10, 15, 00:28:59.339 --> 00:29:01.079 even 20 years out. Which is basically impossible. 00:29:01.380 --> 00:29:04.250 It's an educated guess at best. You need the 00:29:04.250 --> 00:29:07.009 precise timing of those flows, the project's 00:29:07.009 --> 00:29:10.089 exact lifespan. If the cash flows you predicted 00:29:10.089 --> 00:29:14.130 for year 15 are off by even 15%, your final NPV 00:29:14.130 --> 00:29:16.750 is structurally flawed. And this is why we need 00:29:16.750 --> 00:29:19.329 sensitivity analysis. You have to do it. Any 00:29:19.329 --> 00:29:21.569 responsible financial analyst performs sensitivity 00:29:21.569 --> 00:29:25.190 analysis. They model how the NPV changes if they 00:29:25.190 --> 00:29:27.630 vary the discount rate or the initial cost or 00:29:27.630 --> 00:29:30.230 the future revenue forecasts. This helps you 00:29:30.230 --> 00:29:32.390 identify the key variables that carry the most 00:29:32.390 --> 00:29:35.400 risk and uncertainty. It turns the NPV from a 00:29:35.400 --> 00:29:37.519 single number into a range of possibilities. 00:29:37.960 --> 00:29:40.200 The second major disadvantage is the reliance 00:29:40.200 --> 00:29:42.460 on the discount rates, accuracy and stability. 00:29:42.619 --> 00:29:45.200 Yes. We've emphasized that the discount rate 00:29:45.200 --> 00:29:47.299 is supposed to represent the true risk premium, 00:29:47.500 --> 00:29:49.680 but it's typically assumed to be constant over 00:29:49.680 --> 00:29:51.799 the entire investment life. Which is never true. 00:29:51.940 --> 00:29:53.920 In reality, the cost of capital changes over 00:29:53.920 --> 00:29:56.619 time. If a firm's credit rating improves or if 00:29:56.619 --> 00:29:58.599 market interest rates spike three years into 00:29:58.599 --> 00:30:01.180 a project, the true cost of capital is different 00:30:01.180 --> 00:30:03.900 from that constant. you assumed. The whole result 00:30:03.900 --> 00:30:06.359 is only as accurate as that initial hurdle rate 00:30:06.359 --> 00:30:10.200 choice. Third, N by Z is purely quantitative. 00:30:10.519 --> 00:30:12.579 It's like a financial calculation, which means 00:30:12.579 --> 00:30:15.200 it suffers from a lack of context. It gives you 00:30:15.200 --> 00:30:17.880 a number, but it completely ignores critical 00:30:17.880 --> 00:30:20.839 non -financial metrics. Doesn't factor in employee 00:30:20.839 --> 00:30:23.660 morale, brand reputation, regulatory burden, 00:30:23.839 --> 00:30:26.799 market dominance or the strategic value of blocking 00:30:26.799 --> 00:30:29.180 a competitor. And those qualitative factors might 00:30:29.180 --> 00:30:33.160 easily outweigh a small positive. Easily. but 00:30:33.160 --> 00:30:35.640 the model itself can't capture them. And finally, 00:30:35.720 --> 00:30:37.799 the difficulty of comparing mutually exclusive 00:30:37.799 --> 00:30:40.720 projects with different investment horizons. 00:30:40.880 --> 00:30:42.839 This is a classic problem. If you're comparing 00:30:42.839 --> 00:30:45.579 two machines, machine A lasts three years, machine 00:30:45.579 --> 00:30:48.200 B lasts seven years, and you can only buy one, 00:30:48.400 --> 00:30:51.759 the raw NPV calculation can be misleading. You 00:30:51.759 --> 00:30:53.440 generally have to use more advanced techniques 00:30:53.440 --> 00:30:55.720 to standardize the comparison. Okay, now let's 00:30:55.720 --> 00:30:57.579 talk about the common pitfalls, those hidden 00:30:57.579 --> 00:31:00.160 traps that non -specialists frequently fall into 00:31:00.160 --> 00:31:03.119 when they start using NPV in spreadsheets. The 00:31:03.119 --> 00:31:06.400 first one is entirely counterintuitive. The effect 00:31:06.400 --> 00:31:09.440 of late negative cash flows. This is a critical 00:31:09.440 --> 00:31:12.720 warning. Imagine a mining company or maybe a 00:31:12.720 --> 00:31:15.779 nuclear power plant project. The big positive 00:31:15.779 --> 00:31:19.079 cash flows happen in years 5 through 15. Right. 00:31:19.180 --> 00:31:21.900 But there are massive environmental cleanup or 00:31:21.900 --> 00:31:25.079 decommission costs, huge negative cash flows 00:31:25.079 --> 00:31:28.839 way out in year 25. So if the firm uses a very 00:31:28.839 --> 00:31:31.559 high discount rate, say 18 percent. to reflect 00:31:31.559 --> 00:31:33.859 the risk of the industry, that high rate should 00:31:33.859 --> 00:31:36.460 signal caution, right? And that's the trap. A 00:31:36.460 --> 00:31:38.859 high discount rate is actually optimistic when 00:31:38.859 --> 00:31:40.819 it comes to future costs. How can that be? Because 00:31:40.819 --> 00:31:44.400 the discount factor shrinks exponentially. Discounting 00:31:44.400 --> 00:31:46.920 that massive negative cleanup cost in year 25 00:31:46.920 --> 00:31:50.640 by 18 % reduces its present value effect to almost 00:31:50.640 --> 00:31:53.480 nothing. The present value of that enormous future 00:31:53.480 --> 00:31:56.779 liability is artificially minimized. The project 00:31:56.779 --> 00:31:58.900 looks artificially profitable today because the 00:31:58.900 --> 00:32:01.079 future loss is mathematically neutralized by 00:32:01.079 --> 00:32:03.359 the high discount rate. That is a crucial distinction. 00:32:03.960 --> 00:32:07.059 High discount rates minimize future negative 00:32:07.059 --> 00:32:09.619 impacts, which makes them dangerous when liabilities 00:32:09.619 --> 00:32:12.359 are involved. And that connects directly to the 00:32:12.359 --> 00:32:16.109 second pitfall. The error of just adjusting for 00:32:16.109 --> 00:32:18.410 risk by adding a premium to the discount rate. 00:32:18.549 --> 00:32:20.809 It's the most common shortcut and it's often 00:32:20.809 --> 00:32:24.569 the most flawed. If the firm's WACC is 8 % and 00:32:24.569 --> 00:32:27.710 the project is risky, a manager might instinctively 00:32:27.710 --> 00:32:30.609 say, oh, let's just add a 5 % risk premium. Making 00:32:30.609 --> 00:32:33.390 the discount rate 13%. The problem isn't the 00:32:33.390 --> 00:32:35.529 premium itself, but the compounding effect over 00:32:35.529 --> 00:32:38.460 time. Exactly. When you compound that extra 5 00:32:38.460 --> 00:32:41.480 % risk premium over 20 years, the resulting NTV 00:32:41.480 --> 00:32:43.920 is far, far lower than if you had handled the 00:32:43.920 --> 00:32:46.859 risk explicitly using RMPV or scenario analysis. 00:32:47.480 --> 00:32:50.380 It disproportionately penalizes your future cash 00:32:50.380 --> 00:32:52.740 flows for risk. So marginally profitable projects 00:32:52.740 --> 00:32:55.160 get rejected. They get unjustly rejected because 00:32:55.160 --> 00:32:57.960 the compounded discount rate reduces the true 00:32:57.960 --> 00:33:00.740 value of future gains too aggressively, making 00:33:00.740 --> 00:33:03.650 the firm unduly conservative. The third pitfall 00:33:03.650 --> 00:33:06.029 involves what we call double counting the time 00:33:06.029 --> 00:33:08.650 value of money. And this relates directly back 00:33:08.650 --> 00:33:12.670 to how we define that cash flow, R sub T. This 00:33:12.670 --> 00:33:14.789 error happens when financial modeling relies 00:33:14.789 --> 00:33:17.130 on cash flows calculated after you've already 00:33:17.130 --> 00:33:20.210 deducted interest expense. This is a common accounting 00:33:20.210 --> 00:33:23.970 practice, but it's deadly for MTV. Why? Remember, 00:33:24.069 --> 00:33:26.130 the discount rate is supposed to represent the 00:33:26.130 --> 00:33:28.690 firm's cost of capital, which includes the cost 00:33:28.690 --> 00:33:32.559 of debt, which is interest. Ah. So if you calculate 00:33:32.559 --> 00:33:35.200 the cash flow after deducting interest and then 00:33:35.200 --> 00:33:38.200 you discount that cash flow stream using a rate 00:33:38.200 --> 00:33:40.759 that already incorporates the cost of debt. You're 00:33:40.759 --> 00:33:42.319 effectively accounting for the cost of capital 00:33:42.319 --> 00:33:45.240 twice. You should always use free cash flow to 00:33:45.240 --> 00:33:48.220 the firm or FCFF as the basis for NTV calculations. 00:33:48.539 --> 00:33:51.059 That measures the cash generated before any interest 00:33:51.059 --> 00:33:53.799 deductions. Using cash flow after interest gives 00:33:53.799 --> 00:33:56.160 you a systematically miscalculated and usually 00:33:56.160 --> 00:33:59.420 understated NPV. And finally, a very practical 00:33:59.420 --> 00:34:01.480 warning for anyone who might. actually use this 00:34:01.480 --> 00:34:03.859 in a professional environment. The standard spreadsheet 00:34:03.859 --> 00:34:06.730 function error. This is critical for practical 00:34:06.730 --> 00:34:09.489 application. The standard spreadsheet function 00:34:09.489 --> 00:34:13.550 NPV rate value one, value two. It assumes two 00:34:13.550 --> 00:34:16.250 things that are often wrong. First, it assumes 00:34:16.250 --> 00:34:19.050 constant, perfectly equidistant time periods 00:34:19.050 --> 00:34:21.489 between all your cash flows, which is rarely 00:34:21.489 --> 00:34:23.610 true in a real project. And the second error 00:34:23.610 --> 00:34:25.730 is more dangerous. It's about the initial investment. 00:34:25.969 --> 00:34:28.769 It is. The function incorrectly assumes the item 00:34:28.769 --> 00:34:30.769 in the first position of your cash flow array 00:34:30.769 --> 00:34:33.269 is period one, which means it discounts that 00:34:33.269 --> 00:34:35.650 first value by one period. period too many. But 00:34:35.650 --> 00:34:37.809 the initial investment is period zero. It's R 00:34:37.809 --> 00:34:40.710 sub zero, and it should not be discounted. So 00:34:40.710 --> 00:34:43.210 this function reduces the value of your initial 00:34:43.210 --> 00:34:45.889 outlay, giving you an inaccurate NPV right from 00:34:45.889 --> 00:34:48.690 the start. So the essential takeaway, if you 00:34:48.690 --> 00:34:50.650 have cash flows that are irregular in size or 00:34:50.650 --> 00:34:52.789 timing, or if you need to include the initial 00:34:52.789 --> 00:34:55.070 investment, you have to use the XNTV formula. 00:34:55.519 --> 00:34:59.460 XNPV rate values dates. It handles irregular 00:34:59.460 --> 00:35:01.760 time periods and correctly treats the initial 00:35:01.760 --> 00:35:05.159 investment at t equals zero as non -discounted. 00:35:05.179 --> 00:35:08.039 Or if you must use the standard NPV function, 00:35:08.320 --> 00:35:11.320 you have to manually add the initial non -discounted 00:35:11.320 --> 00:35:13.760 investment to the result of the function, which 00:35:13.760 --> 00:35:16.179 starts its discounting at year one. This detailed 00:35:16.179 --> 00:35:18.860 critique really shows us that while MTV is foundational, 00:35:19.360 --> 00:35:22.039 it's not omniscient. It needs to be part of a 00:35:22.039 --> 00:35:24.369 larger toolkit. So let's round out our discussion 00:35:24.369 --> 00:35:26.190 by outlining some of the alternative capital 00:35:26.190 --> 00:35:29.130 budgeting methods, many of which address NPV's 00:35:29.130 --> 00:35:31.789 specific drawbacks. I think we have to. Managers 00:35:31.789 --> 00:35:35.130 rarely rely on just a single metric. These alternative 00:35:35.130 --> 00:35:37.309 methods provide different lenses through which 00:35:37.309 --> 00:35:40.050 to view a project's viability, its risk, and 00:35:40.050 --> 00:35:42.349 its structural fit within the organization. Okay, 00:35:42.389 --> 00:35:43.730 let's start with the most famous counterpart 00:35:43.730 --> 00:35:48.230 to NPV, the internal rate of return. IRR. IRR. 00:35:48.670 --> 00:35:51.469 IRR is the calculated rate of return of a project. 00:35:51.710 --> 00:35:53.750 It's defined as the discount rate at which the 00:35:53.750 --> 00:35:56.769 NPV of the project becomes exactly zero. It's 00:35:56.769 --> 00:35:58.969 immensely popular because managers often prefer 00:35:58.969 --> 00:36:01.050 talking in percentages. This project returns 00:36:01.050 --> 00:36:04.690 15%. Right, rather than, this project adds $20 00:36:04.690 --> 00:36:08.090 million in value. But the drawback is that it 00:36:08.090 --> 00:36:10.650 completely disregards the absolute dollar amount 00:36:10.650 --> 00:36:13.010 you gain. So a tiny project could have a huge 00:36:13.010 --> 00:36:16.760 IRR. Exactly. You could have a tiny $1 ,000 project 00:36:16.760 --> 00:36:20.699 with a 50 % IRR and a massive factory that returns 00:36:20.699 --> 00:36:25.260 a 15 % IRR. The 15 % project adds significantly 00:36:25.260 --> 00:36:28.159 more actual wealth to the firm, despite the lower 00:36:28.159 --> 00:36:31.320 percentage. IRR can lead to poor decisions when 00:36:31.320 --> 00:36:32.960 you're comparing projects of different sizes. 00:36:33.300 --> 00:36:35.260 Following that is the modified internal rate 00:36:35.260 --> 00:36:38.139 of return, MIR. MIR tries to fix the main flaw 00:36:38.139 --> 00:36:42.469 of standard IRR. Traditional IRR implicitly assumes 00:36:42.469 --> 00:36:44.570 that the cash flows generated by the project 00:36:44.570 --> 00:36:47.489 can be reinvested at the project's own high IRR 00:36:47.489 --> 00:36:50.090 rate, which is often unrealistic. So MIR is more 00:36:50.090 --> 00:36:52.610 realistic. It forces the manager to make an explicit, 00:36:52.710 --> 00:36:54.929 specified assumption about the reinvestment rate, 00:36:55.010 --> 00:36:58.230 usually the firm's WACC. This makes MIR a superior 00:36:58.230 --> 00:37:00.070 calculation, though it's still not as robust 00:37:00.070 --> 00:37:03.110 as NPV. Next we have the simplest metric, the 00:37:03.110 --> 00:37:05.710 payback period. The payback period just measures 00:37:05.710 --> 00:37:08.349 the time required for the cash inflows to equal 00:37:08.349 --> 00:37:10.730 the initial outlay, the time it takes you to 00:37:10.730 --> 00:37:13.750 break even. So it's a measure of risk, not return. 00:37:14.230 --> 00:37:17.309 Exactly. A shorter payback period signals a less 00:37:17.309 --> 00:37:19.769 risky project because your capital is exposed 00:37:19.769 --> 00:37:22.889 for a shorter time. But it's fundamentally flawed 00:37:22.889 --> 00:37:25.449 for valuation because it completely ignores any 00:37:25.449 --> 00:37:27.929 cash flows that happen after the break even point. 00:37:28.280 --> 00:37:30.719 So a project could pay back in two years and 00:37:30.719 --> 00:37:33.059 then lose a fortune in year three. And the payback 00:37:33.059 --> 00:37:35.179 period would miss that entirely. Then there's 00:37:35.179 --> 00:37:37.800 the accounting rate of return, ARR. ARR is a 00:37:37.800 --> 00:37:40.059 ratio that accountants often use. It looks at 00:37:40.059 --> 00:37:42.519 the average annual net income generated against 00:37:42.519 --> 00:37:45.300 the initial investment. It's simple, but its 00:37:45.300 --> 00:37:47.460 structural flaw, and why finance departments 00:37:47.460 --> 00:37:50.119 reject it, is that ARR does not account for the 00:37:50.119 --> 00:37:52.500 time value of money. It treats a dollar in year 00:37:52.500 --> 00:37:55.119 one the same as a dollar in year 10. Okay, moving 00:37:55.119 --> 00:37:57.500 to more advanced specialized techniques, we have 00:37:57.500 --> 00:38:01.380 the adjusted present value, APV. APV is specifically 00:38:01.380 --> 00:38:04.059 designed to value projects that involve complex 00:38:04.059 --> 00:38:07.039 or changing capital structures. It separates 00:38:07.039 --> 00:38:09.280 the investment decision from the financing decision. 00:38:09.619 --> 00:38:12.639 How does it do that? First, the analyst values 00:38:12.639 --> 00:38:15.500 the project as if it were financed entirely by 00:38:15.500 --> 00:38:19.010 equity, the unleveraged value. Then separately, 00:38:19.269 --> 00:38:22.030 they calculate and add the present value of all 00:38:22.030 --> 00:38:24.449 the benefits that come from the financing, particularly 00:38:24.449 --> 00:38:26.710 the tax shield you get from using debt. And why 00:38:26.710 --> 00:38:29.110 separate those? Because the value of the project 00:38:29.110 --> 00:38:31.369 itself is independent of how the firm chooses 00:38:31.369 --> 00:38:34.730 to finance it. APV explicitly shows the value 00:38:34.730 --> 00:38:37.630 the firm gets just from the tax benefit of taking 00:38:37.630 --> 00:38:41.150 on debt, which standard NTV calculations often 00:38:41.150 --> 00:38:43.769 just lump into the WACC, making it harder to 00:38:43.769 --> 00:38:46.329 see the individual value components. Next, the 00:38:46.329 --> 00:38:50.389 equivalent annual cost. or EAC. This addresses 00:38:50.389 --> 00:38:52.570 that problem of unequal project lifespans we 00:38:52.570 --> 00:38:54.789 mentioned earlier. EAC is exceptionally useful 00:38:54.789 --> 00:38:57.150 for comparing mutually exclusive assets with 00:38:57.150 --> 00:38:59.789 unequal life cycles, like comparing a three year 00:38:59.789 --> 00:39:01.929 truck replacement plan against a seven year machinery 00:39:01.929 --> 00:39:03.809 lease. So puts them on a level playing field. 00:39:03.949 --> 00:39:06.829 It calculates the cost per year of owning and 00:39:06.829 --> 00:39:10.179 operating an asset over its entire life. It essentially 00:39:10.179 --> 00:39:13.260 transforms the total negative NTV into an equivalent 00:39:13.260 --> 00:39:16.239 annual expense, allowing you to compare the normalized 00:39:16.239 --> 00:39:18.800 annualized cost of the three -year plan directly 00:39:18.800 --> 00:39:21.079 against the seven -year plan. Assuming they have 00:39:21.079 --> 00:39:23.820 equal risk. That is the vital caveat, yes. And 00:39:23.820 --> 00:39:26.380 finally, the broadest framework, cost -benefit 00:39:26.380 --> 00:39:31.139 analysis. CBA. CBA is a systematic approach often 00:39:31.139 --> 00:39:33.260 used in public policy and infrastructure planning 00:39:33.260 --> 00:39:36.360 that goes beyond pure cash flow. It attempts 00:39:36.360 --> 00:39:38.539 to estimate the strengths and weaknesses of alternatives 00:39:38.539 --> 00:39:41.420 by including non -cash societal issues alongside 00:39:41.420 --> 00:39:44.159 the monetary costs and benefits. So when a government 00:39:44.159 --> 00:39:47.300 decides on a new highway, they use CBA to value 00:39:47.300 --> 00:39:49.400 things like reduced travel time or increased 00:39:49.400 --> 00:39:51.800 productivity or maybe reduced pollution? Yes. 00:39:51.800 --> 00:39:54.360 It tries to quantify the value of time savings 00:39:54.360 --> 00:39:56.920 or environmental impact and includes those in 00:39:56.920 --> 00:39:59.219 the discounted cash flow framework. It introduces 00:39:59.219 --> 00:40:01.460 a lot of subjective valuations. How do you accurately 00:40:01.460 --> 00:40:04.920 value reduced travel time? But it offers a necessary 00:40:04.920 --> 00:40:08.059 holistic picture that pure NPV, which is restricted 00:40:08.059 --> 00:40:10.739 to internal cash transactions, just cannot provide. 00:40:11.039 --> 00:40:14.639 This entire deep dive really shows that NPV is 00:40:14.639 --> 00:40:18.019 an elegant and powerful mechanism. It transforms 00:40:18.019 --> 00:40:20.800 this scattered stream of future dollars into 00:40:20.800 --> 00:40:24.699 one single comparable current day value. It really 00:40:24.699 --> 00:40:26.739 is the essential filter for financial decisions 00:40:26.739 --> 00:40:29.840 aimed at maximizing wealth. It is. We've established 00:40:29.840 --> 00:40:32.440 that NPV is the rigorous calculation for what 00:40:32.440 --> 00:40:34.940 should happen in a fixed scenario. The models 00:40:34.940 --> 00:40:37.559 assume you decide today and you follow that plan 00:40:37.559 --> 00:40:40.239 relentlessly for the next 15 years. But we know 00:40:40.239 --> 00:40:42.300 that in the real world, management is dynamic. 00:40:42.320 --> 00:40:44.619 They have flexibility. They might see a market 00:40:44.619 --> 00:40:47.119 opportunity in year five and choose to expand 00:40:47.119 --> 00:40:49.639 the factory. Or see a new competitor and decide 00:40:49.639 --> 00:40:52.239 to abandon the project in year two. Right. And 00:40:52.239 --> 00:40:55.380 precisely, that managerial flexibility, the right 00:40:55.380 --> 00:40:57.739 but not the obligation to change your strategy, 00:40:57.900 --> 00:41:01.019 has a quantifiable value that the static NPV 00:41:01.019 --> 00:41:03.980 calculation completely ignores. And this leads 00:41:03.980 --> 00:41:06.079 to our provocative final thought for you to consider. 00:41:06.219 --> 00:41:08.400 Which is the field of real options. Real options 00:41:08.400 --> 00:41:11.849 attempts to value that optionality. Yes. If NPV 00:41:11.849 --> 00:41:14.409 is the rigorous calculation for what should happen 00:41:14.409 --> 00:41:16.949 under a fixed set of assumptions, how should 00:41:16.949 --> 00:41:19.130 we quantify the intrinsic value of having the 00:41:19.130 --> 00:41:21.690 option to change our minds? If a company can 00:41:21.690 --> 00:41:24.050 pay slightly more today for a facility that allows 00:41:24.050 --> 00:41:26.269 them to double capacity in three years if the 00:41:26.269 --> 00:41:29.090 market improves, that option itself is an asset. 00:41:29.289 --> 00:41:31.269 And that's often the most valuable asset in an 00:41:31.269 --> 00:41:33.889 uncertain business climate. It is. And modern 00:41:33.889 --> 00:41:36.429 financial theory is constantly pushing the boundaries 00:41:36.429 --> 00:41:38.949 of how to integrate that real options valuation 00:41:38.949 --> 00:41:42.079 onto top of the traditional NPV result. Understanding 00:41:42.079 --> 00:41:44.599 what NPV measures and what it deliberately leaves 00:41:44.599 --> 00:41:47.320 out is the key to becoming a truly well -informed, 00:41:47.340 --> 00:41:48.500 modern decision maker.