(12 of 17) Ch.14 - Calculate WACC: example - YouTube

The question is, what is the firm's weighted average cost of capital.

And let's see what we are given about the firm.

This firm finances its operations by issuing equity and debt.

So right away you see that there is no preferred stock in the picture, just common stock or

equity and debt.

And then we are given two columns.

In the first column we have equity information.

In the second column we have debt information.

Let's see what we know about equity.

The firm has 50 million shares, $80 per share.

Beta equals 1.15.

Market risk premium equals 9%.

Risk free rate equals 5%.

Debt information.

One billion dollars in outstanding debt.

In parentheses I explained that this is nothing but the total face value of all bonds.

Then we know current quote equals 110.

Coupon rate equals 9%.

Semi-annual coupons.

Fifteen years to maturity.

And we are also given the tax rate for this firm in the amount of 40%.

OK.

Let's calculate this firm's weighted average cost of capital.

This is the WACC formula, the weighted average cost of capital formula.

On the right I have like a small image of the previous slide with all the information

that's given so we can kind of look things up.

Right away you can cross out the part of the back formula related to preferred stock because

we don't have any preferred stock.

Let's start by calculating RE and RD.

RE, cost of equity.

Remember from way back when in this chapter, one of the very early slides, we looked at

two approaches, two different formulas, and you use the right one based on what you're

given.

Two different formulas how the cost of equity can be calculated.

Because we are given the beta, the market risk premium, and the risk-free rate, we can

use the CAPAM approach, the capital asset price and model approach, which says to calculate

the cost of equity we take the risk-free rate.

We add the product of the beta and the difference between the expected return on the market

portfolio and the risk-free rate.

So, let's plug in the numbers.

The risk-free rate is 5%.

I put 0.05 in decimals plus the beta of the stock is 1.15 so I add 1.15 multiplied by,

and then I just put one number, 0.09, which is the market risk premium of 9%.

And the reason I'm not subtracting the risk-free rate like the CAPAM formula says is because

the market risk premium is already the difference between the expected return on the market

portfolio and the risk-free rate.

So, 9% that's given to us is the entire term in the parentheses.

It's not just E or M. It's E or M minus RF.

OK.

So, the calculations give us 0.1535 which is 15.35%.

So, 15.35% is what it costs the firm every year to give back to stockholders for the

money that they provided for the firm.

So out of the money that they provided to the firm for its businesses, 15.35% of that

needs to go back from the firm every single year.

That's the annual cost of equity.

Then pre-tax cost of debt.

Let's do this part of the back formula.

RD, that's pre-tax cost of debt.

It's the same thing as computing IY in the bond problem.

OK.

So, to compute IY we need N, the number of coupons; PMT, the coupon amount itself; FV

which is the face value on the bond; and PV, the bond price.

What is N?

Let's see what we are given.

Fifteen years to maturity.

Semi-annual coupons which means two per year.

Over 15 years there will be a total of 30 which is 15 times two.

Next, PMT -- that's the coupon.

Because of these semi-annual coupons, we need to find the semi-annual coupon amount.

Per year, it's coupon rate times 1,000.

The coupon rate is 9%, given.

When multiplied by 1,000 it gives $90.

Then we divide it by two which gives $45 for half a year.

FV, the future value or the face value, is always $1,000 even when it's not given.

Just assume it's always $1,000.

So, I put that.

Notice that I'm using both PMT and FV with a positive sign which means that the present

value must be with a negative sign.

So, what is the present value on each bond?

What is the price for each bond?

Let's see.

What else do we know about the firm's debt?

One billion dollars in outstanding debt, which is the same thing as the total face value.

Current quote equals 110.

That's all we have left to figure out the bond price.

Current quote means 110% of the face value.

So, what's 110% of $1,000?

That's $1,100.

So, I guess a good way to remember the trick to go from current quote which is how bond

prices are sort of quoted in the financial world -- how to go from the quote to the price,

you just add one question.

So, 110, if you add one more zero it becomes 1,100.

That's the price for each bond.

And I use a negative sign for it, otherwise the bond calculations will give me an error.

Compute IY.

The answer will be 3.927.

Because it's for half a year I will need to multiply that by two to get the annual cost

of debt or pre-tax cost of debt, 7.854%.

Let's review the bond calculations in the financial calculator.

Let me bring it up.

Let me first clear everything from my earlier calculations.

OK.

So, I have N which is 30.

So, I press 30N.

Then my coupon payment every half a year is $45.

I put 45PMT.

The face value is always $1,000.

So, I press 1,000 and I save it as FV.

And then the bond price is $1,100.

I put 1,100.

Oops.

Yeah.

1,100.

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

And then I save it by pressing the PV button.

Compute IY. 3.93% every half a year.

Actually, if I increase the decimal places I would have gotten a more accurate number,

3.927 when rounded to three decimal places.

And then you multiply that number by two to get 7.854%.

Next, let's focus on the weights, the weight of equity and the weight of debt.

We know that the market value of equity is equal to the number of shares times today's

price per share.

So, you take 50 million and multiply by $80 per share which gives $4 billion.

Market value of debt.

You'd want to do the same thing -- number of bonds times the price per bond.

What is the number of bonds?

If the total face value is one billion and the face value of one bond is 1,000, then

there must be one million bonds.

And the price for each from our last slide was $1,100.

So, you could multiply one million bonds by $1,100 per bond.

Or you could do it a little bit differently.

You could use the quote again.

So again, the current quote means percentage of the face value.

So, 110% of the face value is the market value.

And we can do, apply the quote to the entire book value, the entire one billion dollars.

So, one billion dollars multiplied by 110%, quote, gives $1.1 billion.

That's the market value of debt.

The sum of the market values gives the market value of the firm.

Four billion plus 1.1 billion equals 5.1 billion.

Then we can calculate the weights.

The market value -- sorry.

The weight of equity is four billion divided by 5.1 billion which gives 0.7843 or 78.43%.

The weight of debt is 1.1 billion divided by the same total, 5.1 billion, which gives

0.2157 in decimals or 21.57%.

So, these are our two weights that will then be used in the weighted average cost of capital

formula.

Of course, the weight of debt could be calculated slightly differently because there are only

two things in the firm's capital structure and we already know the weight of the first,

78.43%, the weight of equity.

We can just subtract the weight of equity from a total of 100%.

Or in decimals -- one minus 0.7843 which gives 0.2157, the weight of debt, in decimals.

OK.

So, we have just calculated all the components of the back formula that needed calculation.

The weighted average cost of capital now equals the weight of equity, 0.7843, multiplied by

the cost of equity, 0.1525, plus the weight of debt, 0.2157, multiplied by the pre-tax

cost of debt, 0.07854, times in the parentheses one minus the corporate income tax rate, one

minus 0.40, which is given.

This gives us 0.1306 or 13.06% which means overall considering all the different sources

of money for the firm, it costs our firm 13.06% per year to use the money that was provided

by the investors into the firm who bought the firm's common stocks and bonds.

Let's take one more step, one step further kind of beyond what this problem asked us

to calculate.

What we can now say is that if this firm is considering a new investment project it should

accept the project only if it expects to earn no less than a 13.06% return.

Otherwise, the project will not be profitable enough and the firm won't have enough money

to compensate its investors.