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JAMES P. WESTON: Hi, welcome back to Finance for Non-finance Professionals.

This week we're talking about the cost of capital and what discount rate

to use.

In this lesson, we're going to put together

the cost equity and the cost of debt.

We're going to put it all together in what we call

the weighted average cost of capital.

So if we go back to that very simple balance

sheet we did in the first lesson this week,

we said there is stuff over on the left-hand side of the balance sheet

and debt and equity over on the right-hand side of the balance sheet.

Well now we've talked about the cost of debt

and we've talked about the cost of equity.

We said the cost of equity, where we were going

to use the capital asset pricing model.

That was risk-free rate plus beta times the market premium.

That gave us the discount rate that we should

use depending on the riskiness of an individual stock.

The debt, we were going to use other historical, or yield-to-maturity

or, more likely, the ratings adjusted yield

to figure out what default and recovery premiums

we should put on debt, risk-free rate plus the risk premium.

Different firms have different kinds of capital structure.

Some firms have no debt at all.

They're all equity.

Other kinds of firms, like maybe an airline company, have lots of debt.

So what their average cost of debt is depends

on how much debt and how much equity is financing

all the stuff on the left-hand side.

And that's ultimately, what we want.

What we want is that discount rate to apply

to the assets of the firm, the firm overall.

So that balance sheet which balances, assets

have to equal liabilities plus equity.

The balance sheet of risk has to balance, too.

And the way that's going to happen is to take

a weighted average of the debt and the equity

to make up the capital structure of the firm.

We're going to call that discount rate the weighted average cost of capital

or WACC which you can see written under the stuff.

And that's going to be the weighted average of R-e, the cost of equity,

and R-d, the cost of debt.

We can think about that, it's kind of a long formula,

but it's relatively simple based on what we've talked about.

What we've got is the proportion of the firm that's over equity plus debt.

How much of the firm is equity?

That's the weight on equity.

And I'm going to use that weight on the cost of equity.

Now, if part of that firm is equity, the other part must be debt.

How much of the firm is debt relative to equity plus debt?

How much of the capital structure is debt?

Times R-d, my cost of debt.

So there's a weighted average here.

The weight on the equity, the weight on debt.

And I'm going to use those to weight R-e and R-d.

Of course, also here we remember that debt is after tax.

So I've got that one minus t in there to adjust the cost of debt

to reflect the effective cost of debt.

When I put those things together and take a weighted average of R-e and R-d,

those weights come together to form the weighted average cost of capital.

OK.

The easiest way to see this is to work through a real example.

The cost of capital to the overall firm reflects

that balance between debt and equity.

Let's work a simple example together, and I

think it'll be a lot more easy to see once we sort of do it in practice.

So let's take the Target Corporation, large department store.

They've got an equity value, let's say of around $40 which

is roughly where their stock price is.

And they've got about 15 billion in outstanding debt at the end of 2015.

OK.

So 40 billion in equity, 15 billion in debt,

that gives us a rough sense of their capital structure.

Let's say they pay about 35% corporate tax rate, which they do,

and their market beta, that measure of how much

they co-mingle, they co-vary with the market.

If I look at some of their published betas

from Bloomberg or Yahoo or Reuters or if I calculate one myself,

they all come in around 0.6.

So let's call their market beta 0.6.

Let's also assume that treasury rates are around 2 1/2%,

was about the yield on a 10-year treasury right now,

and the premium 5 1/2%.

Let's use those numbers.

They're A-rated.

They've got a credit rating of around A, and that's going to give us a quality

spread of around 120 basis points over the treasury rate 2 1/2%.

Using all that information, it's like a list of ingredients

when you're cooking.

And now we're going to take that list of ingredients,

we've got all the ingredients that we need.

And we're going to cook a weighted average cost of capital for Target.

What we get, that weighted average cost of capital,

that's the discount rate that we would use for evaluating things like,

should Target open new stores?

Should they expand into Canada?

If they think about weighting those capital expenditures,

like in the lessons that we did in weeks two and three,

we can use now a discount rate, their WACC, weighted average cost of capital,

as the right discount rate for Target Corporation.

So let's go to the light board with those set of ingredients,

and work the example together.

All right, let's bring it all together, our analysis,

the weighted average cost of capital.

Is do a practical example of calculating the black for the Target Corporation

so let's start writing down our formula for weighted average cost of capital.

The WACC is equal to equity value of the firm over debt plus equity.

So the total of the firm, the proportion of the firm that's equity.

And the proportion of the firm times our E, the cost of equity,

plus D over D plus E, the proportion of the firm that's debt.

How much of the firm is debt.

So these two weights here, equity over debt plus equity and debt over debt

plus equity, those two should add to 1.

Times 1 minus the tax rate, the corporate tax rate.

We remember that the cost of debt is after tax, times R-d, cost of debt.

So this is a big formula.

We've got a lot of things to cover.

So let's start by writing down our ingredients.

Everything that's going to go into this for this example.

And then we'll think about cooking.

We'll put it all back together and calculate

our weights, and our R-e and our R-d.

We'll do everything sort of step by step.

The first thing we'll do is write down our ingredients.

Equity value of the firm.

Equity value of Target Corporation was around 40 billion.

The value of their outstanding long-term debt was around 15 billion.

So that gives us enough information to calculate our weights.

What else are we going to need?

We're going to need a risk-free rate to calculate our R's.

And that's going to be 2.5%.

We're taking that as the ballpark treasury

yield on 10-year U.S. treasuries.

What else do we need?

We're going to need an equity beta.

If we go to Yahoo Finance or Bloomberg terminal or any of the people

that publish betas, or if we calculate one ourselves,

we'll see the Target Corporation's beta is around 0.6.

So about 60% of one serving of the market premium

is what an investor in Target's shares would want to earn.

And that risk premium, that equity premium,

which we talked about in one of our lessons this week.

We'll use just 5 1/2%.

All right, so far, so good.

And what else do we need?

We said that Target Corporation was a single rated firm

and so their debt would trade roughly at a quality

spread of about 120 basis points or 1.2%,

1.2% would be 120 basis points spread.

OK.

That's about everything that we need except for a tax rate.

And our tax rate for Target we'll assume is 35%.

Let's make sure we've got all our ingredients.

I've got an E, I've got a D. I'm going to calculate my R-e as risk-free rate

plus beta times the market premium.

Check.

D, D, E, 1 minus my tax rate.

There's my tax rate.

R-d is going to be risk free plus the quality spread.

Good.

We've got all our ingredients and we're ready to go.

Let's think about calculating the first thing, which is just E over D plus E.

Equity over debt plus equity.

That's going to be 40 over 40 plus 15.

I reversed those, but you can see what's going on,

and that's going to be about, let's see, 72.7%.

If we do the other weight, D over D plus E, that's going to come out to,

well, it's going to be 1 minus 72.7%.

So that's going to be 27.3%.

Great, I've got my weights done.

Now let's calculate the cost of equity, R-e.

We remember from our lesson on beta and the cost of equity,

that the cost of equity is the risk-free rate plus beta times the market

premium, or the equity premium.

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Great, now we've got a cost of debt.

We've got a cost of equity.

We've got our weights.

We've got a tax rate.

And we can put it all together.

So let's do that down at the bottom.

Let's take our WACC formula, and let's put it all in.

I'll start over here so I have enough room.

So our WACC is equal to equity over debt plus equity, 72.7%--

let me put a line under here so we keep straight what we're doing--

72.7% times my R-e.

My R-e was, here it is, 5.85% plus my deadweight.

My deadweight is 27.3% times 1 minus my tax rate, 1 minus 35%

times my cost of debt.

My cost of debt is 3.7%.

Lots of ingredients.

There's my formula.

My weighted average cost of capital for Target Corporation

is going to be 72, 73% equity, plus 27%, roughly debt, after tax.

When I put it all together, what's that going to give me?

That's going to give me a WACC of about 4.87%.

That WACC, right here is, 4.87%, is how much

average investors in the Target Corporation would expect to earn.

It's a balance between the 5.8% the equity investors would expect to earn,

and 3.7% that the debt holders would expect to earn right now.

If I bought A-rated debt for a 10-year maturity in Target Corporation,

I would expect to earn about 3% or 4% on that debt.

If I bought shares of Target Corporation,

I would expect to earn around 5.86%.

When I put those two things together reflecting

the balance sheet of Target Corporation, I

get a weighted average cost of capital of 4.87%.

That's the number.

That's the discount rate that I would use for all the capital

budgeting tools that we learned in week two.

Once I had computed all the free cash flows

for target for any new store openings or any geographical expansion

that Target had in mind.

What discount rate should they use, internally,

when they're looking at project feasibility in computing

MPV's and IRR's.

And paybacks.

What's the discount rate that Target Corporation should be using internally?

Based on our analysis of the weighted average cost of capital,

we get an answer of 4.87%.

That's the discount rate.

That's their WACC.