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Earlier in the course, we talked about the main objective of a manager being

maximizing shareholder wealth.

How does a manager go about achieving this?

This requires a manager to select projects that add to shareholder wealth.

But usually, there are a large number of projects to choose from.

Further, the manager does not have unlimited access to capital.

So, there are constraints on how much capital she has for investments.

During the potentially large number of projects to choose from and

the limited amount of capital available at the manager's disposal,

how does she decide which projects to invest in?

This is the area of capital budgeting.

Starting with this video we will look at a number of decision

tools that managers may use to identify profitable investment opportunities.

The first of which is the net present value NPV in short.

We will see how to calculate the NPV and how to interpret the NPV

which forms the basis for accepting or rejecting a project.

Let's start off by seeing how to calculate the NPV of a project.

As the name suggest, we have to calculate the present value of a series of cash

flows including some negative ones to determine the NPV of a project.

Let's start with a simple example to enlist it how to calculate NPV.

Let's say that a project requires an initial investment of $1 million today.

This investment will in turn generate cash flows of $200,000 a year for

the next nine years, which is the end of the project's useful life.

Assume that the cash flows are realized at the end of each year.

The appropriate discount rate for this project is 15%.

To calculate the NPV of this project we need to discount all cash flows back

to today using the discount rate of 15% and

then add them all up, including today's investment of a million dollars.

The NPV of this project is hence minus a million plus 200,000

divided by 1 + 0.15 raised to the power of 1 plus 200,000

divided by 1 plus 0.15 raised to the power of 2, plus so on.

Until 200,000 divided by 1 plus 0.15 raised to the power of 9.

Ignoring the initial investment of a million dollars,

the annual cash flows of $200,000 from a nine payment ordinary annuity.

We can use the formula we saw earlier to calculate the present value of this

ordinary annuity.

Alternatively we can use the PV function in Excel to calculate

the present value of the ordinary annuity.

The first import is a discount rate which is entered as a decimal number 0.15.

The second input is the number of payments which is nine for this ordinary annuity.

The third input is the amount of each payment which is $200,000.

The final two inputs to the PV formula are not relevant here and so

we can ignore them.

The PV function returns a value of $954, 316.78 cents which

is the present value of annual inflows of $200,000 for the next nine years.

To get the NPV of this project, we need to subtract the initial investment

of $1 million from the present value of 954,316.78.

We do not have to discount the initial investment as it is already measured in

present value.

Subtracting the $1 million from 954,316.78

gives us a NPV of -45,683.22.

So what does this number mean?

Note, we will always denote cash in flows with a positive sign, and

cash outflows with a negative sign.

In this example since the NPV is negative,

it is telling us that the present value of outflows are greater than the present

value of inflows generated from the project.

That is, we do not recover our initial investment of $1 million from the project.

Hence, our decision would be to reject the project.

The NPV specifically tells us how much additional shareholder wealth is created

are destroyed by the project.

Here a negative NPV tells us that if the company were to accept the project,

shareholder wealth would reduce by $45, 683.22.

This is inconsistent with the managers objective of maximizing

shareholder wealth.

And hence the project is rejected.

A general formula for

NPV is the present value of inflows minus the present value of outflows.

Inflows are benefits, outflows are costs.

If the NPV is positive, then benefits are greater than cost, and

we will have a positive NPV.

This means that the projects adds to shareholder wealth, and

hence must be accepted.

On the other hand, having a negative NPV means costs outweigh the benefits, and

the project reduces shareholder wealth.

And hence it must be rejected.

In summary, accept positive NPV projects and reject negative NPV projects.

You are indifferent between accepting and rejecting a project if NPV equals zero,

as it neither increases nor decreases shareholder wealth.

Next time, we will look at the second type of investment decision rule, namely,

the internal rate of return.

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