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

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

Â to use.

Â In this lesson, we're going to put together

Â the cost equity and the cost of debt.

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

Â the weighted average cost of capital.

Â So if we go back to that very simple balance

Â sheet we did in the first lesson this week,

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

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

Â Well now we've talked about the cost of debt

Â and we've talked about the cost of equity.

Â We said the cost of equity, where we were going

Â to use the capital asset pricing model.

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

Â That gave us the discount rate that we should

Â use depending on the riskiness of an individual stock.

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

Â or, more likely, the ratings adjusted yield

Â to figure out what default and recovery premiums

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

Â Different firms have different kinds of capital structure.

Â Some firms have no debt at all.

Â They're all equity.

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

Â So what their average cost of debt is depends

Â on how much debt and how much equity is financing

Â all the stuff on the left-hand side.

Â And that's ultimately, what we want.

Â What we want is that discount rate to apply

Â to the assets of the firm, the firm overall.

Â So that balance sheet which balances, assets

Â have to equal liabilities plus equity.

Â The balance sheet of risk has to balance, too.

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

Â a weighted average of the debt and the equity

Â to make up the capital structure of the firm.

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

Â or WACC which you can see written under the stuff.

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

Â and R-d, the cost of debt.

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

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

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

Â How much of the firm is equity?

Â That's the weight on equity.

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

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

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

Â How much of the capital structure is debt?

Â Times R-d, my cost of debt.

Â So there's a weighted average here.

Â The weight on the equity, the weight on debt.

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

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

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

Â to reflect the effective cost of debt.

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

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

Â OK.

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

Â The cost of capital to the overall firm reflects

Â that balance between debt and equity.

Â Let's work a simple example together, and I

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

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

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

Â is roughly where their stock price is.

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

Â OK.

Â So 40 billion in equity, 15 billion in debt,

Â that gives us a rough sense of their capital structure.

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

Â and their market beta, that measure of how much

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

Â If I look at some of their published betas

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

Â they all come in around 0.6.

Â So let's call their market beta 0.6.

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

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

Â and the premium 5 1/2%.

Â Let's use those numbers.

Â They're A-rated.

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

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

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

Â when you're cooking.

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

Â we've got all the ingredients that we need.

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

Â What we get, that weighted average cost of capital,

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

Â should Target open new stores?

Â Should they expand into Canada?

Â If they think about weighting those capital expenditures,

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

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

Â as the right discount rate for Target Corporation.

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

Â and work the example together.

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

Â the weighted average cost of capital.

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

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

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

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

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

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

Â How much of the firm is debt.

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

Â plus equity, those two should add to 1.

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

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

Â So this is a big formula.

Â We've got a lot of things to cover.

Â So let's start by writing down our ingredients.

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

Â And then we'll think about cooking.

Â We'll put it all back together and calculate

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

Â We'll do everything sort of step by step.

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

Â Equity value of the firm.

Â Equity value of Target Corporation was around 40 billion.

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

Â So that gives us enough information to calculate our weights.

Â What else are we going to need?

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

Â And that's going to be 2.5%.

Â We're taking that as the ballpark treasury

Â yield on 10-year U.S. treasuries.

Â What else do we need?

Â We're going to need an equity beta.

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

Â that publish betas, or if we calculate one ourselves,

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

Â So about 60% of one serving of the market premium

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

Â And that risk premium, that equity premium,

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

Â We'll use just 5 1/2%.

Â All right, so far, so good.

Â And what else do we need?

Â We said that Target Corporation was a single rated firm

Â and so their debt would trade roughly at a quality

Â spread of about 120 basis points or 1.2%,

Â 1.2% would be 120 basis points spread.

Â OK.

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

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

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

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

Â plus beta times the market premium.

Â Check.

Â D, D, E, 1 minus my tax rate.

Â There's my tax rate.

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

Â Good.

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

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

Â Equity over debt plus equity.

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

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

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

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

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

Â So that's going to be 27.3%.

Â Great, I've got my weights done.

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

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

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

Â premium, or the equity premium.

Â 10:02

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

Â We've got a cost of equity.

Â We've got our weights.

Â We've got a tax rate.

Â And we can put it all together.

Â So let's do that down at the bottom.

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

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

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

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

Â 72.7% times my R-e.

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

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

Â times my cost of debt.

Â My cost of debt is 3.7%.

Â Lots of ingredients.

Â There's my formula.

Â My weighted average cost of capital for Target Corporation

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

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

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

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

Â average investors in the Target Corporation would expect to earn.

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

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

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

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

Â If I bought shares of Target Corporation,

Â I would expect to earn around 5.86%.

Â When I put those two things together reflecting

Â the balance sheet of Target Corporation, I

Â get a weighted average cost of capital of 4.87%.

Â That's the number.

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

Â budgeting tools that we learned in week two.

Â Once I had computed all the free cash flows

Â for target for any new store openings or any geographical expansion

Â that Target had in mind.

Â What discount rate should they use, internally,

Â when they're looking at project feasibility in computing

Â MPV's and IRR's.

Â And paybacks.

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

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

Â we get an answer of 4.87%.

Â That's the discount rate.

Â That's their WACC.

Â