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5.6. Decision trees and the option identification

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Principles of Corporate Finance – A Tale of Value

Institut de physique et de technologie de Moscou

5 (6 notes) | 1.3K étudiants inscrits

Cours 2 de 5 dans Understanding Modern Finance Spécialisation

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The study of Corporate Finance seems to be a very generic part of business education. Still, it either falls in the trap of intimidating formulas or is superficially journalistic. Both extremes preclude the understanding of the core finance ideas, concepts, and models. This Course is an attempt to avoid the above extremes. We discuss the core basis and mechanisms of modern corporate finance in a learner-friendly way. We will analyze the market’s most fundamental problems, realize the intrinsic interests and preferences of investors, reveal the true meaning of specific financial terms, and uncover important issues that are so often ignored in choosing and valuing investment projects. The learners will gain insight into the essence of corporate finance. They will be able to use the obtained knowledge and skills to successfully advance in their career at a financial institution, as well as in the area of financial management at non-financial businesses.

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5 (6 notes)

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Options – Idea, Role, and Valuation

Week 5 of the Course is devoted to options – one of the most interesting and advanced areas in finance. We start with definition, charts, payoffs – the basics of options. Then we move on to option valuation. We discuss replication and risk-neutral approaches and show on clear examples how they allow finding the option’s value under simplifying assumptions. We go further and discuss the generalizations of the simple approaches that lead to the Black–Scholes and binomial option valuation methods. Then we discuss the application of the option theory to valuing real investment projects that contain some options – the timing of investment, the abandonment, the follow up options. We show how decision trees and the option identification contribute to the better choice of investment projects. Finally, we briefly describe one of the most advanced topics in finance – the valuation of fixed-income instruments with embedded options and fixed-income derivatives including mortgage-backed securities and CMO’s.

5.1. The opportunity to change decisions7:28

5.2. Options – definition, charts, payoffs16:34

5.3. Option valuation (1) – ideas and approaches11:08

5.4. Option valuation (2) – Black–Scholes, binomial17:11

5.5. Option application (1) – real investment projects4:40

5.6. Decision trees and the option identification11:03

5.7. Options on future investments9:09

5.8. Option application (2) – valuing risky debt18:56

5.9. Valuing bond options – an overview14:06

Enseigné par

Konstantin Kontor
Director and Professor of Finance and Strategy

Well, in this episode we will analyze the following case, or micro-case if you will.

This can be found in many textbooks, this very case or

the analogous cases, but the idea is as follows.

Let's say that we are planning to build a plant to produce some product and

then sell it.

And one clear option is to just provide some business plan and

then to analyze that and make a decision to start building this plant right now.

However, in this case we have a nice opportunity to avoid

investing all the money right now.

Instead, we can engage in a test phase so

we can make a much smaller investment in a small scale manufacturing process.

And let's say in the year, we will have produced and

we will have sold some of these products that you're planning to manufacture.

And then, we'll see whether it's a good or bad demand,

and what future perspectives are realistic for this project.

And then we'll be able to decide at this point one whether to proceed

to a full pledge plan, or to say well,

it's not going to be that much profitable and put a stop sign.

So we are talking about the abandonment option in this case and

let's put some numbers that will be easier for us to analyze.

So this is the point of receipt right now and we have the ability to, so

this is point zero and this is the timeline.

So we can invest $250,000 at this point,

and then in a year we expect to have one of the two outcomes,

in the good successful outcome that derives the probability one-half.

We see that this is a good product and then we make

a decision here to invest the full $2 million.

All numbers are in thousands here, and that will bring us

starting from year two, $500,000 in perpetuity.

Well, we can arrive at the lower option that also arrives at probability one-half.

But here, we have a nice option to say well, we put a stop sign here.

And do nothing.

Let's see what the NPV of the project would be if

we did not have this abandonment option.

Well, clearly when we sit here, this stage is very risky.

And let's say that for this stage we have the rate of discounting that stays at 25%.

Well, if we do not have this option,

then we can say what if we apply this rate all the way through?

Let's see what the NPV would be.

Then the NPV is minus 250, which happens now.

And then we have the probability, this doesn't exist.

We say, plus probability one-half of the upper path.

And here, what do we have?

We have an investment of here minus 2 million.

Then we have 500 in perpetuity that we have to divide by 0.25.

This is the rate that we'll use all the way through.

This is the present value of perpetuity at 0.1.

All that should be discounted at 1.25 because that occurs at 0.1.

But you don't have to, because you can see that 501

over 0.25 that's exactly 2,000, so

all this is 0 and we end up with NPV of minus 250.

So what is our decision?

Well, this is a negative NPV project,

we don't have to take it.

However, let's say that we arrived at point one and

we have the option to stop here.

And at this point, we no longer have this dichotomy.

We are not playing further with these probabilities.

So if we sit at point one, then the future of

this project is much less uncertain.

And again, this is only for the sake of simplicity.

Let's say that if we sit here, then the right rate is r cap, which is 10%.

Well, the rate of the first period stays at 25, because this risk and

this uncertainty stays.

However, further on, whether it's the upper path or the lower path,

there's clearly the NPV of 0 here, we can use this rate.

Now, let's recalculate this NPV, I will use the blue.

We have the same minus 250, but we also have the same one half,

because we have to arrive at this point.

We have to discount that by 125, one way, but

here we have minus 2,000 plus 500 divided by 0.1.

And this is 5,000, this is 3,000 and

then if you put everything together you have plus 950.

Well that's a huge difference.

Well, you can say, no wonder, because we used much lower rate here.

And therefore the contribution of $500,000 in perpetuity is much more valuable.

But like I said before, if we do not have this ability to

stop here then we cannot use a different rate at this point in time.

So that is sort of, in a very grossly simplified way,

the idea of this abandonment option.

Now, let me proceed with some more fine tuned idea here,

because strictly speaking, even if I stay at point

zero I do not have to engage in this test project.

So we are producing on this list,

the simplified decision tree.

And we start at point zero here, in which we can go down there and do nothing.

So we can stop right away.

Or we can go ahead and go here, and this is the test.

And here we invest minus 250, exactly as we did before.

And from here, we can go up here, which is a success.

That of course, the probability one-half.

And then if this is a success at this point,

we, the upper, upper path is that we invest here,

2 million and then we get this 500 in perpetuity.

So this is only one path.

But we, here can have a stop.

Let's say indeed this is a good project but for

some reason we decide not to invest this 2 million.

And on the other hand if here this is a failure case.

That also occurs a probability one half.

We may put a stop sign here.

But we also can say, well we still proceed and invest this 2 million,

And let's say here we get just 115 perpetuity.

And that will be at negative NPV situation.

So you can see that here on this upper path,

you will have the NPV of 5 million,

this is at r at 10%, as we know.

Here, we have some other NPVs that you can easily calculate, but

that doesn't really matter.

What I'm saying though, is that now we can see some analogy and

we can say basically that we observe a call option with the price of 250.

This is an option here to make an investment.

So, k is 2 million.

The length for this option is one year.

And then the other thing that we have to know,

so this is some kind of volatility here.

So basically, I just showed that this decision making threes,

they are kind of important in seeing why the ability

to put these red stop signs is so valuable.

Well, it is valuable just because if we, for example,

here, if we could not stop and in case you fail it,

we will be pushed to proceed or arrive at the negative NPV project.

Like I said before in the previous episode,

the key story is the ability to number one, identify the option,

and number two to find proper proxies for option valued drivers.

So in what follows in the next episode we analyze special

keys that is going to be kind of funny also widely discuss.

The idea is that we have the ability to invest in the negative NPV project,

with the future ability to invest in another larger scale,

also negative NPV project.

But this very opportunity is valuable enough to bring us back in the black.

So in the next episode we'll proceed with this discussion.

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