0:00

Okay then, so far we've identified how traditional NPV analysis might

Â lead to incorrect investment decision when it fails to account for the impact of

Â flexibility on the wealth effects of a particular investment proposal.

Â We then spent some time defining and

Â describing three of the most common types of real options found in practice,

Â options to invest or defer, options to expand and options to abandon operations.

Â It seems reasonable now to start thinking about how we might actually attempt to

Â ascribe some value to having the right, but not the obligation, to proceed with

Â a particular course of action in response to changing economic circumstances.

Â So how might we value an option?

Â 0:44

Well, when we're dealing with financial options, that is, options written on

Â financial assets such as shares, we have some fairly decent models in place.

Â Indeed, the Black-Scholes-Merton Option Pricing Model,

Â as detailed in these equations, yielded the Nobel Prize in economics to the two

Â surviving researchers, Robert Merton and Myron Scholes.

Â There are a number of challenges we face in trying to apply these financial option

Â pricing models to settings that involve standalone projects,

Â as is applied by the option to invest, to expand, or to abandon.

Â 1:18

Firstly, the Black-Scholes-Merton Option Pricing Model is a model for

Â the valuation of a European-style option, that is,

Â an option that can only be exercised at expiry.

Â 1:40

Well, that's fine.

Â As a discipline, we've developed a range of what we

Â refer to as numerical techniques, such as binomial lattices,

Â that can help us deal with things like the ability to exercise an option early.

Â 2:08

So where does that leave us?

Â Well, the short story is that it would be really helpful to have an easier way to

Â try to come up with the value implied by a real option, even if the approach itself

Â provides only an approximation of the real option's value.

Â 2:36

Let's demonstrate how decision trees work in practice.

Â We assume that you are trying to decide whether to

Â invest $200,000 up front in a new retail outlet with a life of five years.

Â There's a 50% chance that the outlet will experience high demand in the first year,

Â in which case it would remain high for the remaining four years.

Â Each year, it would generate $150,000 per annum.

Â If demand is low in the first year, then it will remain low for

Â the remaining four years, generating only $50,000 each year.

Â So where is the option?

Â Well, the firm has the ability,

Â at the end of the first year, to expand operations in response to high demand.

Â Doing so will cost the firm $50,000 up front but

Â will increase subsequent annual cash flows to $170,000 per annum.

Â Let's assume a discount rate of 10% per annum, and further assume, for

Â the sake of the example, that all cash flows occur at year end.

Â Let's have a look at that decision tree.

Â So here is the decision tree.

Â The key with decision tree analysis is that before we can assess

Â the decisions that we face soonest, we must first reconcile the decisions that we

Â would make in the future depending upon the circumstances we find ourselves in.

Â 3:58

And then,

Â having made that decision, we can go on to assess whether we should invest at all.

Â So let's do that.

Â Would we spend the $50,000 at the end of the first year to generate

Â an additional $20,000 in net cash flows per annum for the remaining four years?

Â 4:15

The NPV of expanding at the end of the first year, indicated by NPV subscript 1,

Â assuming that demand is high, is $488,877.

Â If we don't expand in the face of high demand at the end of the first year,

Â then we save ourself the $50,000 in expansionary cost.

Â But the flip side is that our revenue stream is $20,000 less for

Â each of the remaining four years.

Â Hence, we know that if demand is high in the first year,

Â then we will choose to expand operations.

Â 4:56

Furthermore, we now know the present value of the expansionary arm

Â of the decision tree is $488,877, but

Â it's important to recognize that this is a valuation in one year's time.

Â Having resolved the most distant decision first,

Â we can now roll back through the decision tree, assessing the next most distant

Â decision, which in this case is the decision about whether we invest at all.

Â So here we are.

Â The wealth associated with investing in this retail outlet is

Â calculated as follows.

Â Firstly, we account for the initial investment of $200,000.

Â Next we consider the low-demand arm of the tree.

Â That's where there's a 50% chance of there being low demand in the first year,

Â in which case low demand will continue.

Â Across each of these five years,

Â we generate net cash flows of only $50,000 per year.

Â So this first expression gives us the present value of that cash flow stream.

Â 5:52

Now switching our attention to the high demand state of the world, where we know

Â we will expand if demand is high enough in the first year, we account firstly for

Â the fact that there's a 50% chance of finding ourselves in that high demand

Â state, which, you will recall, generates $150,000 at the end of the first year,

Â followed, after we expand, by $170,000 in each of the remaining four years.

Â 6:17

Fortunately, we've already calculated the present value of the remaining

Â four payments as $488,877.

Â So working our way through all this now, we end up with

Â an overall NPV of the project of $185,169.

Â Therefore, given the alternative decision,

Â which in this case would be to not invest at all, and therefore,

Â generate an NPV value of 0, our final decision is to invest in the project.

Â 7:32

As you can see, the calculations will be relatively straightforward.

Â And here we go.

Â The net present value of the project without the option to

Â expand is equal to $179,079.

Â We now simply compare this number with the value of

Â the project with the embedded option.

Â And lo and behold, the approximation of the value today of the option to expand

Â operations in the case of high demand in the first year is equal to $6,090.

Â Now why do I keep using the term approximation here?

Â Well, unlike formal option pricing models, which provide very precise values for

Â option, although they're based on a set of sometimes very restrictive assumptions,

Â decision trees are a little bit more haphazard in that they only provide for

Â a set of discrete outcomes.

Â Compare the two figures at the bottom of this slide.

Â The left-hand side figure relates to the changing value of an option

Â as the present value of the cash flows from exercise of the option

Â increase continuously as we move from left to right of the figure.

Â 8:42

If it was not optimal to invest, that is,

Â to exercise the option, in either of those states of the world,

Â the decision tree approach would suggest that the option has zero value.

Â Whereas we know that even where options are deep, deep out of the money,

Â provided there's some remaining term to expiry and

Â some volatility, the option will still have a value.

Â In summary, we've considered in this session together how to

Â use decision trees to evaluate projects that may involve

Â a sequence of decisions that are made over the life of the project.

Â And truth be told, that's one of the real advantages of decision tree analysis.

Â It gets management thinking strategically about

Â optimal decisions to be faced in the future.

Â