[MUSIC] This is a solution to assignment 3. It starts with a question about the relationship between NPV and stock price, which is a fundamental concept in finance. The reason why NPV and stock prices are equivalent, it really is because they are mathematically equivalent. It's the same formula. To compute an NPV, you discount the incremental cash flows through a project. Whereas to compute a stock price you discount cash flows to the company. So if markets are efficient, then both calculations should be equivalent. The stock price recognizes all the future cash flow to the company, so the market should also recognize the incremental cash flows to a project and adjust the stock price exactly to the amount of the NPV of the project. So, NPV and stock prices are equivalent because of that. If the markets are not efficient, then of course the stock price may not reflect the NPV. Because the stock price may be reflecting other things other than future cash flows, and then since the NPV always requires you to discount future incremental cash flows then NPV and stock prices are going to be different. So, that's why efficient markets are important. Question 2, is just to remind you that the only thing that we are sure with NPV is shareholder value maximization. NPV does not ensure that we're going to eliminate conflicts with society. That's a simple point, but it's worth emphasizing. For example, a cheap technology may maximize NPV because its of lower costs, but it might be bad for the environment at the same time. Or we can think of situations where a company that wants to be socially responsible, may need to pass on positive NPV projects, because they are bad for society. Because they hurt stakeholders, and for other consequences. So, NPV does not assure that companies are doing the best for society because of this potential conflict. Question 3 is a little bit of a trick question, but is important for you to know. So, the situation when the discount rate if lower than the growth rate. The growth rate is 7%, the discount rate is 5, and if you just apply the growing perpetuity formula, it seems that the NPV is negative, which makes no sense. If the asset has a very high growth rate, this would be a great asset. The answer, in fact is that the asset has an infinite value. If you're mathematically inclined you probably know that, but the intuitive way to think about it is that if the cash flow is growing at a faster rate than the discount rate, then every year the discounted cash flow for that year is getting bigger and bigger. It's not converging to a small number. And what this is going to do is that, if you sum all future cash flows, the answer is gonna blow up. It's going to become infinite. The bottom line is that we know infinite does not exist in the real world. Nothing has an infinite value. So, if you do find an infinite value in a present value calculation, it means you've done something wrong. You have to go back and rethink your estimates. Maybe you overestimated growth rates, maybe you underestimated discount rates. Question 4 is to remind you of the important relationship between the rate of return, the IRR and the discount rate. So, the idea that NPV equal 0 is equivalent to having a rate of return greater than the discount rate. If the IRR is bigger than the discount rate, then the NPV is positive. However, remember that the IRR should not be computed if you see a negative cashflow following a positive one. Those are the cases when you can have multiple IRRs, and it might get you in trouble if you try to compute the IRR in those cases. So if you see that, just use NPV. And also be careful when you're using IRR to compute two different investments. As we discussed in the lecture notes, if the investments are of a different magnitude, then the IRR may give you the wrong comparison. As long as you remember these conditions, you should be able to apply this important idea which is the equivalence between the IRR rule and the NPV rule. Question 5 is an application of the notion of incremental cash flows. The problem that really asks you to think about what incremental cash flows are. What's this notion of incremental cash flow? It's a project where a company is thinking about starting to sell a new wallet. And as usual, there is an initial outlay, and the company has estimated wallet cash flows as 450,000 a year. The question is are these the right cash flows? You might know already, obviously not. There lights coming up. So, those are not the right cash flows, there's something else missing. What is missing is that, we haven't fully conceded a notion of incremental cash flows. Remember that the notion of incremental cash flows is this important notion of New- Old. In order to figure out the right cash flow, the right NPV for the project, we have to take in to account all consequences of taking a new project. In this particular exercise is talking about erosion, which is a very common consequence of starting a new project in a company. If a company starts a related project, or if you improve an existing project, you're creating new cash flows. But you're also reducing sales of existing products. In this case, we assume that the sales are going to decease cash flow by 200. However, we are not done because we also have to think about competitors. Competitors are also trying to think about cool new products, so they might decide to produce a wallet. A similar wallet, and which might erode sales anyway. And to really think about this problem, we have to be very careful, and really model this notion of New minus Old. So, that's what I have for you here. Let's really go line by line and think about what changes if you go from no wallet to the wallet project. So of course, the wallet cash flows alone are 450, and you erode, if you sell wallets, you're gonna erode 200. If you don't start the wallet, you're own erosion is 0. However, there is this additional line here, which is that, if you don't start the wallet, your expectation is that your competitors are going to start the wallet anyway. The erosion is not as big as if it was your own wallet. So, it's 100, it's not 200. But it's significant. You have to take that into account. Competitors are going to erode your cash flows anyway. If you do take the wallet, what is happening is that the erosion is going down. The erosion of existing cash flows from competitors is going down from 100 to 50. The assumption here is that competitors might also, they might decide to start a wallet anyway. Even if you start your own project, the competitors may also decide to come into the market, so the erosion from the competitors doesn't go to 0. But it is going down. So, your wallet project is also reducing erosion from competitors. This is a third consequence of the project that we have take into account. So, new cash flow from your wallet, your own erosion, and erosion from competitors. After you do all that, you will quickly see that the incremental cash flow is 300. So you erode 200, but you reduce erosion from the competitors by 50. So the bottom line is that the total incremental cash flow for the wallet project is 300, so those are the cash flow that you would discount. This question doesn't ask you to compute NPV because the idea was to allow you to spend the time thinking about how to build the cash flow. So, that's the right answer right there. Question 6 is about opportunity costs. This is what you should have figured out here. The net present value of a full time MBA is going to depend heavily on your opportunity cost. In the case of the MBA, of course, the opportunity cost is going to come from the need that if you're gonna take a full time MBA, you gonna have to quit your job. The total cost of the project is 400, and you're gonna increase your lifetime earnings by 700. But the NPV is not 300. The NPV would be 300 minus whatever you expect to be the reduction in your current earnings. So if you're gonna have to quit your job and you make $100,000 a year, after taxes, then you're gonna have to deduct 200 from the NPV. If you make more money then, of course the NPV is gonna become lower. So that's why it's important when you think about, doing a full time MBA or any type of education, you have to think about what sort of other opportunities I'm missing. If your working that's most people who take a full time MBA are currently working. Then you have to think about what you're missing in terms of your current salary. That's a very good illustration of this notion of opportunity costs. Then you had the question about R&D. In question 7, the R&D that you had to model is slightly different from what we considered in class. Which is the R&D to gather more information about an existing drug that is already viable. In the lecture notes, we considered an R&D to create a viable drug. Now, you have a viable drug, but you have the opportunity to do additional research to try to increase the NPV of the drug. Of course, doing the R&D is going to require you to wait as well. On top of spending more cash you're gonna have to wait a year, so this is a combination of R&D evaluation and the option to wait. So the trade-off in this case, is that waiting is going to cost you 10 million. And it's going to reduce the NPV, if the research is not successful. Notice that, while the NPV is still 200, 200 million next year is worth less than 200 million today. Why? Because the company is foregoing the drug cash flow by 1 year. I mean foregoing the drug cash flow in the current year by waiting. So that's a very, again it's a notion of opportunity cost. So, if you launch today using the problem's numbers, you get an NPV of 200. If you launch tomorrow. If the research is success, well the NPV goes up to 250. If you fail, it's kind of the same drug, you gonna go back to the NPV of 200. So, you can use the formula that we used in class to compute the NPV, 30% times 250. 7% times 200. This counted back to times 0. You get an NPV of 185.45. So, since the NPV of R&D + launch is lower, then the NPV of launching today, the right decision would be to launch today and not do additional R&D. Question 8 is a question about the option to abandon a project. So, it's a conceptual question to make sure that you understand this notion of, what does it mean, what's the benefit to being able to abandon a project? One thing is that, if the cost of abandoning a project is zero, then you would never wait. Why? Let's think about it now. The benefit of course, of waiting as we discussed in the lecture notes, is that you can avoid the loss. So, if the project becomes unprofitable, in our case, the gold price goes down, then opening the mine is going to create a loss. If you wait until next year then you can avoid that loss. The benefit of waiting is that, the cost of waiting is that, if you wait, of course, you're foregoing the current profit. So, by opening now, you get the current profit, if you wait, you're gonna get zero today. So, what happens? If the cost of closing the mine is zero, then what you can easily figure out is that, you can eliminate the loss. If you open now and close tomorrow, you can eliminate the loss. So, instead of a loss here you get a zero. And you also get the current profit. And in addition, in the good state of the world when the gold price goes up, the profit is the same as in the case of waiting. So, now you have a situation where really you can get the best of both worlds. You can get the current profit and you can get zero tomorrow, if the gold price goes down. So what this means is that, if it was cost less to open and start an abandon projects, then companies would never wait. This is the solution in worlds. The idea is that, if the cost of closing the mine is zero, then you can also achieve this payoff of zero by closing tomorrow. So, that's why I called it this is the best of both worlds. Finally, question 9 was about this notion of irreversible investments. So, and this is related to what we just discussed. An irreversible investment is the opposite of a zero cost of abandon. Is an investment that once you start it, it's very hard to go back. So just using our current discussion, it's obvious that it is for these types of investments that your option to wait is going to have a high value. If it's very difficult for a company to go back and abandon a project, then it maybe, it pays off more to made to wait until to make sure that you have all relevant information before you commit cash to this investment.
