4.2 Decision Tree Approach

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From the course by Yonsei University

Applying Investment Decision Rules for Startups

14 ratings

Yonsei University

Applying Investment Decision Rules for Startups

14 ratings

Course 4 of 5 in the Specialization Valuation and Financial Analysis For Startups

In the previous course, you learned financial statement analysis and how to make estimate of future financial status. In this course, you are going to learn capital budgeting. That is, how to make an investment decision. You would like to select the best project among various projects you can take. Then, you need to know the criteria. In this course, you are going to learn investment decision criteria such as NPV and IRR, which are most popular decision rules. Using financial analysis and discounted cash flow method, you can make pro forma financial statement and estimate project cash flows. Then, you apply investment criteria to determine whether to invest or not. After learning how to apply NPV and IRR method to investment decision, you are going to learn how to evaluate NPV estimate and scenario, what-if analyses and break-even analysis. In addition to NPV and IRR, you are going to learn Payback period method and Profitability method to determine whether to invest or not when there is a political risk or capital rationing.

From the lesson

Real Options in Business Projects

We continue to study analyzing business projects, but the difference in this module is that now we consider the value of "real options" embedded in the project. You will learn how to estimate the project's value by using the decision tree approach or the Black-Scholes option pricing model.

4.1 Options Basics7:00

4.2 Decision Tree Approach7:51

4.3 Black-Scholes Option Pricing Model10:18

4.4 Evaluating Projects Using B-S Model7:15

Meet the Instructors

Saeyeul Park
Assistant Professor
School of Business

Hi, we learned that the traditional NPV analysis has a problem,

because it ignores the adjustment that a firm

can make after a project is accepted which we recall the real options.

We also know that the traditional NPV analysis will underestimate the true

value of the project, because it misses the value of the real options.

In this module, we'll attempt to identify three major types of real options in

business projects and see that the true value of a project

is actually greater than what the NPV on the list suggests.

The first type of real option is the option to expand.

And next, we'll study the option to abandon.

Finally, we'll examine the option to delay.

In examining real options in business projects,

we'll follow the decision tree approach in this module.

Using a decision tree,

we can graphically show the alternatives available to us in each time period.

In the decision tree approach, the modified NPV which is adjusted for

the value of real options is the weighted average of all possible NPVs

in different scenarios where probabilities of different states are used as weights.

The value of real options arises, because we can learn by observing what happens

in the next time period and adapting our behavior based on our observation.

To understand the option to expand, let's consider the following project.

This project requires the initial investment of $10 million today and

expected cash flow from year one to year six are $2 million per year.

The discount rate is given at 20%.

Let's first calculate the NPV of this project without

considering the real option of the project.

Calculating NPV in excel is not something new to us at all.

We've been there done that.

Just remember that the initial cash flow in year zero should not be included in

the NPV function.

This project has a negative NPV and

the traditional NPV analysis will reject this project,

but what if there was some uncertainty about future

annual cash flows from year one to year six?

What if there is actually 50% chance that annual cash

flow will be $5 million per year and

another 50% chance that the annual cash flow will be negative $1 million?

Perhaps the original annual cash flow estimate of 2 million

was just reflecting the expectation regarding the uncertainty and

it's the average of 5 and negative 1 is 2.

We can also assume that we can observe the outcome in year 1 by checking

whether the cash flow in year one is 5 million or negative 1 million.

And more importantly, if scenario one turns out to be correct,

we'd like to exercise the option to expand embedded in this project and

it is expected that we could double the annual cash flows starting from year two.

We'll recalculate the NPV of this project in Excel

now by considering the option to expand.

Now, we have to consider the two different scenarios case one and

case two both of which have the probability of 50% or 0.5.

If we consider the option to expand that we can exercise in year 1,

we would need to rewrite cash flows in case one in row 11.

To calculate NPV, we first consider the initial investment of 10

million in C10 which doesn't change.

But as we know that case one and

two have probabilities of 50% of occurring, we need to use the weighted

average of future cash flows by using the probabilities as weights.

As a result of considerations of options expand in a good state,

we now got a positive NPV for

this project which will change our capital budgeting decision.

So, what is the value of the option to expand in this project?

The value of the real option would be the difference between NPV with

consideration of the option and NPV without consideration of the option.

So for this project,

the value of option to expand seems to be huge which is about $6 million.

Next, let's study the option to abandon.

Managers not only have option to expand, but

also options to abandon the existing projects.

We'll use the same project, but

now assume that the company does not have the option to expand in a good state.

Instead, it could benefit from the option to abandon if the death state occurs.

The assumptions are the same.

We could observe the outcome in year one.

Now if scenario two turns out to be correct,

we'd like to abandon this project.

If we know that annual cash flows will be negative in remaining years,

there's no reason for us to continue operation of this project,

then case two has just a single negative cash flow in year one and

no more cash flows in remaining years.

In Excel, future cash flows of case number 2 should be rewritten as in row 13.

NPV is calculated using the same way.

We can expect that the NPV should be greater than the one we have above,

because we've quit early by exercising the option to abandon if the bad state occurs.

Well, the option to abandon in this example did not make the NPV positive,

but at least made it less negative.

The option to abandon had the value of $1.25 million,

which is the difference between two NPVs shown on the screen.

The option to delay also gives the business project additional value.

Sometimes, you'll find that having a negative NPV today

does not necessarily mean that the project is a bad one.

We can exercise the option to delay and

just wait until the project becomes profitable.

Perhaps oil and mining industry provides the best examples of the option to delay.

Even if you own a gold mine, mining gold could be a negative

NPV project today if the gold price is too low.

However, that does not mean that your gold mine is worthless.

Your gold mine has the option to delay,

which will make you wait until producing gold becomes profitable again.

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