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Last time, we started discussing the different decision tools that managers may

use to decide which projects to accept and which ones to reject.

We looked at what NPV is, how to calculate it, and

how to use it to decide whether to accept or reject a project.

This time we will look at a second decision tool,

namely the internal rate of return, IRR in short.

We will look at how to calculate it and

how to use its value to determine whether to accept or reject a project.

We will also define the third investment decision tool, the payback period.

We will see how to calculate it and

how to use it to decide whether to accept or reject a project.

The internal rate of return tells us what annualized percentage rate of return

a project generates on the initial investment made at time 0.

It is calculated as the discount rate that makes the NPV of a project equal to zero.

Let's revisit our project from last time.

The project required an initial investment of $1 million at time 0,

which resulted in annual end-of-year cash flows of $200,000 for the next nine years.

At a discount rate of 15%, we calculated its NPV to be a negative $45,683.22.

Now we want to find its IRR, which is the discount rate that makes NPV 0.

So we have to solve the following equation.

Minus a million + 200,000 / (1 + IRR) raised to the power of

1 + 200,000 / (1 + IRR) raised to the power of 2 + so on,

until 200,000 / (1 + IRR) raised to the power of 9 equals 0.

However, solving this with a calculator will be difficult as it is a non-linear

equation in IRR that cannot be simply rearranged and solved for IRR.

Luckily for

us, Excel has an inbuilt IRR function that precisely solves this equation.

Input the cash flows in chronological order starting with the initial cash flow

of negative $1 million at time 0.

And then nine annual cash flows of $200,000 each.

This should be spread across ten cells on the Excel spreadsheet, as you can see.

In an empty cell, you may type =IRR, open parenthesis, and

then select all the ten numbers that you just entered into the Excel spreadsheet.

Finally, close parentheses and hit Return.

You should see the IRR value to be 14% in this set.

You can increase the number of decimal places to two and

you will see the IRR is 13.70%.

The annualized rate of return from this project is 13.70%.

But how do we decide if this is return is acceptable or not?

Earlier in the course,

we talked about the discount rate being the cost of raising capital for a company.

It is how much return investors expect as compensation for

holding the risk of the company or project.

We also refer to the discount rate as the hurdle rate.

The hurdle rate is the minimum return investors should expect

to earn from investing in a project or company.

Any return greater than the hurdle rate tells us that the project or

company earns more than what investors want as compensation for risk.

A decision rule for IRR is if the IRR is greater than the hurdle or

discount rate, we should accept the project.

Otherwise we should reject the project.

In most cases, both NPV and IRR will give us the same decision.

If IRR is greater than the hurdle rate, then NPV will be positive.

While if IRR is less than the hurdle ,then NPV will be negative.

We will look at some exceptions to this rule later in the course when we talk

about the drawbacks of these method.

Going back to our example, the project's IRR is 13.7%.

When we calculated its NPV last time we used the discount rate of 15%,

which is its hurdle rate.

Given the risk of the project, investors expect a return of at least 15%.

However, the project returns only 13.7%, and hence we reject the project.

This is the same decision we arrived at using NPV last time.

This is consistent with what I said earlier about IRR and

NPV giving you the same decision in most cases.

Moving on, let's look at the payback period.

This is the third common investment decision tool managers use.

It tells us how soon we recover the initial investments we make in a project.

Let's revisit our example.

The project required an initial investment of $1 million at time 0,

which resulted in annual end of year cash flows of $200,000 for the next nine years.

How soon do we recover the initial investment of $1 million.

We recover $200,000 by the end of the first year.

That means we still have to recover $800,000.

Once we recover $200,000 in the second year, we still have to recover $600,000.

This accumulation of cash flows continues until we recover all $1 million.

By the end of the fourth year, we have recovered $800,000, and have yet

to recover $200,000.

We recover exactly that amount at the end of the fifth year.

It takes five full years to recover the entire initial investment of $1 million,

which means that the project's payback period is five years.

What is the decision here though?

Should we accept or reject the project?

That depends on whether we think five years is an acceptable time to recover our

initial investment of $1 million.

Unlike NPV and IRR, there is no economic rationale for

deciding whether a given payback period is acceptable or not.

We may have a general rule that says that any project with a payback period of three

years or less is acceptable.

In that case this project should be rejected as it takes

longer than three years to recover the initial investment of a $1million.

This is one of the drawbacks of using payback period as an investment decision

tool, but we will discuss this and other drawbacks of these methods later.

Next time, we will look at an example on how to use these decision tools when

comparing two projects.

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