So in this video, I'm going to discuss something very profound, which is the Net Present Value rule, The NPV rule. It says, accept projects if NPV is greater than 0. Reject projects if NPV is less than 0. And here's the big result, The NPV rule maximizes the value of the corporation. Something so simple, and yet so profound. Why is this? We're going to do a very simple example that consists of a corporation that's just one person. This person we're going to call Suzy. And Suzy has access to a bank account with which she can use to transfer consumption between now and old age. And she also has some access to opportunities. So let's just say Suzy, she has 1 million. She has access to a bank account, With r=20%. Now this 20% may seem crazy high. But the point is that 20% is how she's going to transfer money between now and her old age. So right away, without any investment opportunities, she has a choice. She can consume, 1 million now, or 1.2 million in old age. Or something now, and something in old age. So we can show Suzy's possibilities on a graph. This is dollars today. This is dollars in old age. So for every dollar that Suzy doesn't spend now, she gets that dollar times 1+r in old age. So the slope, =1+r, or 1.2. So let's say she's considering opening a restaurant. The cost of the restaurant is 0.7. So if she spends 0.7 on the restaurant, she'd have 0.3 to consume now. The payoff on the restaurant is 0.8. Should she open the restaurant? Well, we don't have to think too hard to say that the answer is no. Because she could also decide to consume 0.3 now and save the 0.7 in the bank. In which case, it becomes 0.84, if deposited in the bank. So on this graph, the restaurant is here, not a wise investment. Let's think about another example. Okay, Suppose she sees a vineyard. That's going to also cost 0.7. However, the payoff in her old age is going to be 0.91. Well 0.91, that's greater than 0.84. The vineyard is somewhere over here. So question is, should she invest in this vineyard? Seems like a good idea. She could get more money that way. But let's think for a second, is it so obvious? After all, what if this Suzy really likes to spend money now? Maybe she has a good reason for wanting to spend the money now. Maybe she wants to spend more than 0.3, for example. Maybe then she shouldn't do the vineyard. Maybe she should spend the money instead. For instance, maybe she wants to get an MBA, who knows? Maybe she wants to help out a relative who doesn't have any money. There might be very good reasons to spend this money now, and not on the vineyard. Well, so what the NPV rule says is that no matter what her preferences are for consumption now versus consumption the future, in this case, she should go for the vineyard, and she should not go for the restaurant. Why is that? Well, if she wants to spend more, she could borrow the money for the vineyard. Let's see this on the graph. This is dollars now. This is dollars in old age. This is my bank account. And this is the new opportunity set with the vineyard. Why, well first of all, we could always be here, And consume 0.3 now and spend 0.7 in the vineyard. Which will give us, as we talked about, 0.91. But in fact, with the help of the bank, we can be anywhere on this new line. Which, by the way, still has the same slope of 1+r. How does that work? Well, let's take, as an example, this extreme point, right here at the bottom. Suzy wants to consume everything today. So if she wants to consume everything today, What is this point? Well, remember, she has 0.3, That you didn't have to spend on the vineyard. Then she takes the 0.7 and invested in the vineyard, that becomes 0.91 in the future. Now she knows she's going to get 0.91 in the future, and for the sake of the example, the bank knows it, too. So she can borrow against that 0.91 and consume the present value of that 0.91 today. So whereas this point here is 1 million with the vineyard, Keep in mind r here is 20%. With the vineyard, she has the opportunity to consume more, 1.06 million. This point here is 1.06. So regardless of Suzy's preferences for present versus future consumption, she should always choose the project with that as NPV positive. So where does NPV come into all of this? Because I haven't said anything about NPV. Remember, NPV rule says, Accept if the NPV is greater than 0. What's my NPV? NPV is C0+C1 over 1+r. So what I want to know is, is this thing greater than 0? That's the same as asking is C1 bigger than -C0 times 1+r? So let's think about the restaurant. So the restaurant gave us 0.8. So the question is, is this bigger than 0.7? 0.7 is the negative of the cost, times 1+r. Well, 0.7 times 1.2 is 0.84. So no, the restaurant had NPV less than 0, so we should reject it. But the vineyard, In that case, 0.91 was bigger than 0.7 times 1+r. NPV was bigger than 0, so we should accept it. And remember, the fact that we should accept this, it doesn't matter if Suzy wanted to consume the money now versus later, because she could always use the bank. So this brings us to a very important consequence of the NPV rule, something called the Separation Theorem.
