So having identified the fact that NPV analysis might lead to incorrect decision making, if it fails to account for the flexibility that management might have in how it conducts its operations. It's now opportune for us to identify the key types of real options that companies come into contact with on a regular basis. So in this session, we're going to discuss the option to invest or to delay investment, which is really just the other side of the same coin. The option to expand operations in response to a positive change in market conditions, and finally, the option to abandon operations as market conditions change adversely and significantly against the firm. So let's begin with the option to invest, or to delay investment. The key feature of this option, is that it's a call option, where the exercise price that you pay when you exercise the option is equal to the up front investment required when you choose to go ahead with the project. The underlying asset that you're purchasing is the equal to the present value of the net cash flows from operating the project. The option premium is the price that you pay for the option and reflects in a project setting, the amount spent so as to build the flexibility in your operations. The volatility of the underlying returns is reflected in the forecast variability of the cash flows promised by the project. And the term to expiry of the option is simply the period of time you have until you no longer have the right to invest in the project. It's when the option disappears. Well, let's have a look at the payoff diagram for this option. So here, the straight red line represents the payoff from the option at expiry, or when the option is exercised. You might recall from our previous discussions of options back in course three of the specialization, that the straight red line represents the intrinsic value of the option. So at expiry of the option, if the present value of the cash flows promised by the project exceed the initial investment outlay required, then the project has a positive NPV and would be entered into. Conversely, at expiry of the option, if the initial investment required were to be greater than the present value of the cash flows promised by the project. Then the project has a negative NPV, and you wouldn't invest in them. The interesting bit comes about when we look at the value of the option to invest, as represented by the curved green line. As you can see, prior to expiry, the value of the option to invest is positive. Even when the present value of the cash flows from commencing operations is less than the investment outlay required. This is because, while the option to invest still has a life, there's a non-zero chance that underlying circumstances might change to make the project positive NPV. Let's demonstrate this with an example. So we return to our pastizzi business. Now you've decided against ever opening the business in your own home. You don't want all that you own smelling of cooked ricotta cheese. The alternative is to open up a dedicated factory. But before you have the right to do so, you will need to have purchased the relevant permits from the local government. Let's say that will cost you £500. You need to pay for these well in advance of the point in time that you might choose to actually open the factory. If you do ultimately choose to go ahead with your factory, then you'll need to pay £40,000 up front. So let's have a look at the payoff diagram for this option. It's an option to invest in the factory, where the exercise price is the investment required which is equal in this case to £40,000. Having the right, but not the obligation to commence factory operations has value, even where the project is not currently wealth producing. But what about the £500 spent on permits? Well, that can be regarded as the price paid to create the option in the first place. Because without those permits, we wouldn't be able to act on our decision to commence operations in the factory. We don't observe the price paid for an option in a payoff diagram, as the payoff diagram reflects the terminal payoff from the option. Instead, we need to look at the profit diagram for the option, and here we have it. This is simply the profit from holding the option, after accounting for the price initially paid for it. You can see that if the option to construct the factory were to remain un-exercised, then we'll be out of pocket to the tune of £500. The horizontal intercept occurs when the present value of the cash flows from operations exceeds the initial investment required by £500. So that point is £40,500. Let's consider another real option. This time, the option to expand operations. So once again, this is an example of a call option. The exercise price in this case is equal to the costs of expanding operations while the underlying asset, which is being purchased by our exercise of the option, is the present value of the incremental cash flows, the extra cash flows, from expanded operations. The option premium, once again, is simply the price paid to establish the option in the first place, while our measure of volatility will reflect our uncertainty about the future incremental cash flows from expanded operations. The term to expiry is the period of time before the right to expand disappears. The payoff diagram for this option looks very similar to that of the option to invest. Here though, the exercise price of the option is the cost of expansion and the asset value is the present value of the incremental cash flows from expanded operations. The point needs to be made once again that the right to expand has value even when the expansion costs currently exceed the present value of the cash flows from expanded operations. Now let's consider an example, once again, in the competitive world of pastizzi manufacturing. You have a choice of two factories, the first, let's call it factory A, has all the space you forecasted you would ever need to meet projected demand. The second factory, factory B, is a larger factory, that could mean increased production but would cost you an additional £1,000 up front. If you ever wanted to actually re-engineer the larger space to boost production, then you'd have to pay an additional £60,000 at that point in time. So what does the payoff structure look like for this option? Well, here we go. Once again, obviously a call option. An exercise price of £60,000 reflected in the additional investment required to boost production. The asset being purchased represents the present value of the additional or incremental net cash flows, from the expanded operations. The option to expand operations has value even where it would not be optimal to exercise such an option at the moment. What about the £1,000 extra we had to pay up front for the larger premises? Well, that's simply the premium paid for the option. So, here's the next question. Are real options ever put options? That is, do they ever represent the right to sell an asset rather than buy an asset? The answer is a most definitive yes. The option to abandon operations is a common example of the real put option. The exercise price of the option to abandon operations is simply the salvage value of the assets that can be disposed of when we decide to wind up operations. The underlining asset is the present value of the cash flows from continuing operations, and the option premium is simply what we paid up front to establish the flexibility to abandon operations down the track. Volatility simply reflects the variability in the forecast cash flows from continuing operations, and the term to expiry is the remaining life of the option to abandon operations. The payoff diagram for this put option looks markedly different of course to the payoff diagrams for the other options we dealt with, which were call options. So what we have here is a situation where if we choose to abandon operations, we give up the present value of the remaining cash flows. And in return, we receive the salvage value of the assets employed in the business. Obviously, it would make no sense to do so if the present value of the cash flows from continuing operations exceeded the salvage value of the assets employed. Well, let's consider an example of an abandonment option, once more related to our fledgling pastizzi business. The local government that we're dealing with to establish operations in the area is very keen to promote small business and to ensure that such businesses are committed for the long term. Therefore, they require new businesses to sign a binding contract that will be guaranteed personally by the company's directors, guaranteeing that they'll remain operating in the area for five years irrespective of market conditions. Alternatively, the business can pay £20,000 up front, which would give the business the right to cease operations at any time and sell off the equipment. The salvage value of our assets in this case, we assume to be £120,000. Let's have a look at the payoff diagram for this option to abandon. So it's a put option as we expect, with an exercise price of £120,000. Well let's say the peas fall right out of the pastizzi market. And the present value of the remaining cash flows from continuing operations immediately falls to £10,000. If you were to exercise your right to abandon operations, then you'd be giving up £10,000 in value from future operations but gaining £120,000 immediately through the asset sale. So your net payoff would be £110,000 immediately. What happens when we account for the price paid to establish the option in the first place? Well, simple. As with the other options, we see a simple downward shift in the diagram, in this case, to the tune of £20,000. There is a final point that we should consider relating to the early exercise of American style real options. Once again, you might recall from our earlier sessions on options in course three of the specialization, that it makes no sense to exercise an American style call option early, unless the underlying asset were about to pay a dividend. Or if we're talking about a put option, unless that option was very, very deep in the money. So what about real options? Does the same logic continue to hold? Well the answer is yes, absolutely. Take for example the option to invest. It might make sense to exercise the option to invest early so as to avoid missing out on the promised cash flows from the project. Perhaps because of the entry of a competitor in the market. These cash flows can be regarded as analogous to the dividends on a share that may prompt the early exercise of an American style call option written on a share. So what about puts? Well, once again, it might be optimal to exercise a deep in the money put option, to abandon operations before expiry, so that we can immediately receive the salvage value of the assets employed, and redeploy those funds in a more profitable, positive NPV activity. In summary, we've considered three common types of real options. The option to invest or delay investment. The option to expand operations, and the option to abandon operations. In addition to highlighting the key characteristics and payoff structures of each of the three types of options, we also considered the circumstances where it might be optimal to exercise these options early. Now the next question we're going to consider is, how can we value real options in practice?