We're going to talk about what the weighted average cost of capital is and how you would go about calculating it and then we'll walk through an example. When we think about WACC this weighted average cost of capital really what we've got is we've got the financing of the firm. Let's say we've got a firm here, now this firm is going to be financed from two primary sources:
- Debt
- Equity
What does that mean? Well, the firm can get money from borrowing or people can put up equity maybe shareholders or the owner themselves. So what we're thinking about here is, we're looking at this mix of debt and equity, and then we're going to go ahead and calculate the cost for each one, the cost of equity that's the (Re) and then the cost of debt (Rd) after factoring in the tax considerations. We're basically going to assign a cost to each one but we have to wait because we don't know how much of the mix this debt or the equity is. So the debt for the firm might be just 10% of its financing whereas the equity is the other 90%. We can't just go ahead and say we'll take a 50/50 split.
The Weighted Average Cost of Capital (WACC) Formula
The weighted average cost of capital is equal to we've got the firm's equity, now it depends, if you take finance you'll be using the market value of the firm's equity and if you're taking an accounting course it might just settle for the book value of equity but in any case, we'll just what's called equity here. The firm's equity is divided by the total of the firm's debt and equity. Now when we're talking about debt here what we mean is interest-bearing debt. So we're not just talking about liabilities in general which might include things like unearned revenue, we want to talk about interest-bearing debt bonds that the firm has or something like that. What we're trying to do is calculate that proportion of the firm that is being financed by equity and then we're going to multiply it by the cost of the firm's equity. So the main idea here is that we have to figure out the proportion of the firm that is financed by equity and then multiply that by the cost associated with that equity.
Now we've got all kinds of one big component of the equity side but now we've got the debt side. So debt is part of this financing of the firm and so we'll take a look at the firm's interest-bearing debt and then see what proportion that is of the debt plus equity and then we're going to multiply that by the cost of debt (Rd) this would be like the yield to maturity on the bonds or something like that. The cost of the firm's debt and then we're going to multiply that by (1 - the tax rate). Now, why are we doing that? because we have to remember that we want the after-tax cost of debt as there's a tax shield associated with interest. Well, I have a different article on that but just bear in mind that's why we're multiplying by (1 - the tax rate) due to this tax shield.
Example of The Weighted Average Cost of Capital (WACC)
So basically we've got a big long equation here to calculate WACC but all we're really doing is saying what is the proportion of the firm that is financed by equity and what's the proportion that is financed by debt. Then we're going to take those proportions, those weights, and then we're going to multiply them by the associated cost, the cost of equity, and the cost of debt. Let's work through an example and I think that you'll find it to be a lot easier when we do so. So we've got an example here where you start a firm by borrowing $2,000 from the bank and the bank's going to charge you 6% interest (Rd) and then you put up some of your own money, some equity of $8,000, and then let's just say the cost of equity is 12.5%. The tax rate was 40%.
So the weighted average cost of capital (WACC) we can't just take these costs of equity and cost of debt and add those up and divide them by 2, why can't we do that? Well, because debt is only $2,000 of the financing and equity is $8,000. So the WACC is going to be equal to, let's do the equity side first. We've got $8,000 in equity, to calculate the proportion of equity we say $8,000 over $2,000 of debt plus $8,000 of equity [8000/(2000+8000)]. Why are we doing this? We've got $8,000 in equity up here but we know that the firm's total financing is both of this equity and debt. So to get the proportion we're taking $8,000 and then dividing it by that total. Now we have to multiply this by the cost of equity which is 12.5% which is the same as 0.125. Now we've got the equity component here and now we have to add in the cost of the weighted average cost to debt components.
Now we're going to go and basically do something very similar, just take now the $2,000 debt and put that $2,000 over $2,000 plus $8,000 [2000/(2000+8000)]. Now we're going to multiply that by the cost of debt that's 6%. Now we have to factor in that after-tax cost of debt, so what we're going to have is (1 - the tax rate) which is 1 minus 0.4. So now we've got this big long equation but let me just save your time, if we take this whole equity piece what that comes out to is 1. This other debt piece over here if we calculate that then this piece is 0.0072. So we add these together and it's 0.1072 and that is equivalent to 10.72%.
So the weighted average cost of capital for this firm that we start here is 10.72%. Let's go back to our example for a minute and if you calculate let's add up 6% and 12.5% and we'll divide it by two and get the cost of capital, well what you're doing is now you're just getting the average cost of capital. Because you're just taking two different costs of capital the debt cost and the equity cost and you're just dividing that by two. Here we are taking the average but there are different weights that should be assigned here because 80% of our firm is actually being financed by equity. So more weight is being given to the equity component of our cost of capital and that's why we call it the weighted average cost of capital.
