(13 of 17) Ch.14 - Calculate WACC & then NPV: example - YouTube

Let's look at the following example.

A company wants to invest $300,000 into a new factory in Texas.

The factory is expected to generate profits equal to $150,000 per year for three years.

What do we know about the company?

It issues debt and equity in equal proportions.

The beta of its equity equals 1.2.

The yield to maturity on its bonds is 10%.

Its corporate income tax rate is 34%.

We also know that the risk-free rate in the economy is 3% and the expected return on the

market portfolio is 20%.

The question in this problem is should the company make the investment?

Let's see how we should approach this problem.

To answer the big question, should the company make the investment, essentially, we would

need to calculate the project's net present value.

So, we need to discount the future cashflows estimated for this project in order to calculate

the project's net present value.

The project's cashflows are given.

We need to invest 300,000 and this three-year project will generate $150,000 per year.

So, the cashflows are not a problem but what we need for the net present value, apart from

the cashflows is the discount rate, project's discount rate.

For that, we can use the weighted average cost of capital.

So, our very first step will be calculating the cost of equity, the cost of debt, and

their weights in order to find the weighted average cost of capital which will then be

used as the discount rate to find the project's net present value.

So, this is our plan.

Let's start with the weighted average cost of capital formula.

Once again, we only have two parts in it rather than three

because we don't have any preferred stock, just debt and equity.

So, we have the equity component in the WACC formula and the debt component in the WACC

formula.

Let's start with the cost of equity, RE.

What are we given about the common stock shares?

The beta, the risk-free rate, and the expected return on the market.

These three are part of the capital asset price and model formula which is the approach

we can use to find the cost of equity.

So, from the CAPAM approach we have the risk-free rate, 3% or 0.03 in decimals, plus the beta

of the stock, 1.2, multiplied by the expected return on the market which is 20% or 0.2 minus

the risk-free rate, 0.03.

This gives us 0.234 or 23.4%.

So, on the money provided by investors who buy the firm's common stock shares, it will

have to pay back every year 23.4% of that money.

That's for the common stock part.

Now what about the bonds?

So, let's calculate the cost of debt which is denoted by RD which is also the same thing

as the pre-tax cost of debt.

The yield to maturity is 10%.

It's already given so there is nothing we really need to calculate.

We don't need to solve any bond problem for IY.

We already know the pre-tax cost of debt.

OK.

Then the tax rate, the corporate income tax rate, TC.

That's also given, 34% or 0.34 in decimals.

Then what you're left in the WACC formula is the capital structure weights.

The weight of equity -- you divide it by V. And the weight of debt -- D divided by V.

Let's see what we are given.

The company issues debt and equity in equal proportions which means both weights are 50%

each or 0.5 in decimals.

OK?

Let's put all the numbers together.

The weighted average cost of capital in this problem equals 0.5, the weight of equity,

multiplied by 0.234, the cost of equity, plus the weight of debt, 0.5, times the pre-tax

cost of debt, 0.10, times one minus the corporate income tax rate, 0.34.

This gives us 0.15 in decimals or 15%.

Fifteen percent is how much it costs the firm every year on the money that stock and bond

buyers provided to the firm.

And so, this is the minimum the firm should want to earn on any new investment project.

So, we are now using 15% as the discount rate for the project in our problem.

The net present value equals minus the initial investment minus $300,000 plus the first year's

cashflow, 150,000, discounted back by one year, so divided by one plus 0.15 -- the WACC.

Then we add the discounted second year's estimated cashflow -- $150,000 divided by squared sum

of one and 0.15.

And then similarly we add the last discounted cashflow.

The third year's $150,000 cashflow divided by cubed one plus 0.15.

This gives us the net present value of $42,484.

Of course, this whole thing, the net present value step, could be calculated in one step

in the financial calculator using the cashflow keys.

Let's review that.

OK.

Let's clear everything.

I am pressing second plus/minus enter.

I press the cashflow button.

For year zero we have the initial investment of $300,000.

So, I press that, 300,000.

I change the sign to negative by pressing the plus/minus key on the bottom.

And then I save it by pressing enter.

Then I press the down arrow key.

It takes me to cashflow number one in the future which is the first year's estimated

cashflow, $150,000 -- 150,000.

I save it by pressing enter.

I press the down arrow key.

The calculator is asking me about the frequency of the cashflow I have just entered.

And this is where we can speed things up a little and change the frequency to three because

we have $150,000 repeating consecutively three times.

I press three, enter, down arrow key.

Cashflow number two -- after my first cashflows have been saved.

There is no cashflow number two.

That's it.

We are done.

Now I press NPV.

The display asks me about the I which is the interest rate or the discount rate.

That's 15% weighted average cost of capital.

I press 15, enter, down arrow key, and the last thing I press is the compute button,

CPT. 42,483.77 or approximately $42,484 like I calculated on the slide earlier.

And now let's interpret this result.

Because the net present value is above zero dollars, the project is worth it.