CF 11-6A – WACC – Corporate Finance

Let's take a look at problem 1168, weighted average cost of capital. This might be my favorite question of the chapter. If I were a professor of your class and I were giving an exam, I would likely give a question that looks like this. Why? Because it requires us to calculate the cost of debt, calculate the cost of common equity, calculate the cost of preferred equity, and once we have those costs, figure out their relative proportions, their relative weights, and take a weighted average. So it's a multi-step problem. It'll take us 10, 15 minutes to get through, but it's a good one. I bet you most intro finance classes have problems like this. Let's go. The following information is known about the company's balance sheet. It gives us info about liabilities, common shares, preferred shares, and some tax rate info, risk-free rate, market risk premium. It says compute the weighted average cost of capital. We're going to compute the cost of debt. As we've gone over, what we're looking for here is always rates. We're looking for the required rate of return for an investor is the same as the cost for the company. When we're calculating rates for a bond, unfortunately, it's just too awkward to do by hand. You have to do a lot of trial and error. So I'll lean on the financial calculator here. You could also use present value tables here, but I think primarily you'll either be given it or given ways to calculate it easily, or you'll have to use a financial calculator. So let's use our financial calculator. I've got the inputs sort of to match my BA 2 plus financial calculator. Let's figure out what our inputs are in this question. So liabilities, we have 1,505% bonds outstanding quoted at $96.5,000 par value. So this is 96.5% of $1,000. So the price today is $965, and in fact, that's the PUV. $1,000 par value means in however many years, we got to pay back 1,000, and they're 5% bonds. So $1,000 times 5% is $50 in interest per year, but they make semiannual payments over the next 10 years. So semiannual means half that in interest, right? That's $50 per year. It would be $25 per six month period. And the number of periods, well, it's 10 years, which is 20 semiannual periods. So we've got all the pieces we're solving for IY. That's our missing number. Let's get it. And this is the required rate of return or the cost of equity for a six month period, because we're doing everything based on six month period. So let's get it. 20 goes in as N. We don't know our IY. 965 goes in as PV. 25 negative goes in as PMT. 1,000 negative goes in as FV. And the reason I put the PMT and FV in as negatives is because we're the borrower. So we're making these payments. We're also paying back the $1,000 at the end. So that's why those go in as negatives. And I compute the IY and I get 2.73%, but that's for six months. So let's multiply by two to get an annualized rate here. And I get 5.46%, 5.46%. Now remember how debt works. A beautiful feature of debt, something that makes debt attractive to companies is interest is tax deductible. So this cost of debt reduces their tax bill. And so we always, when we're coming up with our weighted average cost of capital, do the after tax cost of debt. So we're going to take 25% out of this. So our cost of debt is not 5.46%. It's 5.46% times one minus the tax rate. It's 5.46% times 75%, right? One minus 25% is 75%. So 5.46% times 75% is 4.09%. So our after tax cost of debt is 4.09%. That's the number we're going to use in our calculations. I'll just write it up there. Cost of equity, it's going to depend on the information given to you in the question. If you're given information about dividends and a dividend growth rate, you're going to use the dividend discount model. And this is how it would look. But we aren't. Let's read what we're given. We're given other information. It says common shares, 10,000 common shares outstanding. The market price is $50 per share. The beta is 1.05. Whenever you're given the beta, that's a sure sign they want you to use the CAPM model, the security market line model to solve this thing. So we're given a beta. So the CAPM, here's the CAPM formula. The beta is 1.05. It says the risk-free rate is 3. So 3 plus 1.05 times RM minus RF. That is the market risk premium. And we're given the premium of 9%. So RM minus RF is the market risk premium. So I don't need to say 9 minus 3. That's probably the only tricky part of this one. You have to know the risk-free rate, 3%. If it said the expected return in the market, they would have to say 12%. And then you'd calculate the market risk premium. But here, no, no, no. They gave us the market risk premium of 9. So 3 plus 1.05 times 9, 1.05 times 9, 9.45 plus 3, 12.45%. So our cost of equity, 12.45%. Last, we're doing preferred equity. Let's read the thing. It's just up here. The company has 2,000 preferred shares outstanding. The annual dividend is $12 per share. And the per share and share sell for 110 per share. Okay, so remember, preferred equity is a perpetuity. The math around preferred equity tends to be the easiest because it's just like a recurring cash flow is all we're counting on. That typically guaranteed dividend should be very consistent. And so present value of perpetuity is the amount of that recurring payment divided by the required rate of return if you're an investor. Well, now we're the company, we want to sort of rearrange the formula. And for us, it's not a required rate of return. It's a cost of equity. So our cost of equity equals the dividend amount divided by the price today. So the dividend amount is $12. The price today is 110. 12 divided by 110 is 10.9%. Okay, so we have our costs. Our cost of equity, 12.45%. Our cost of preferred equity, our cost of common equity, 12.45%. Their cost of preferred equity, 10.9%. We're good to go. So the next step in calculating the weighted average cost of capital is to calculate the relative weights in our portfolio, or not our portfolio, but in our debt and equity portion of our balance sheet. So let's figure out the size of that portion of our balance sheet. How many dollars do I have in bonds? How many dollars in common shares? And how many dollars in preferred equity? So I have 1,500 bonds. They're quoted at 96.5. So I have 1,500 bonds. That's value today is $965 each. I have 1,447,500 in bonds. I have 50,000 shares. The value of the shares is $50. I have 2.5 million in shares. And in preferred shares, 2,000 preferred shares at $110 per share, $220,000 of preferred shares. Okay, so the total there, the total value of my, on the balance sheet of my common shares, preferred shares and debt, 1,447,500 is 4.1 million, 4,167,500. I need relative weight. So I just divide each number by 4.1 million and I'll get the relative weight. So 1,447,500 divided by 4,167,500, 34.7%. So the weight is 34.7%. Let's do the next one. 2.5 million divided by 4,167,500, 59.98%. I'm going to call that 60. 60% it's going to round up to. And 220 divided by, oops, slippy mouse here. 220 divided by 4,167,500 is 0.0527, 5.3%. And good news. I can just see it in my eyes here. This adds up to a hundred percent, which it must. That's the idea of these weights. So now I just apply the weights to the cost. So I just go, okay, 34.7% of my portfolio costs 4.09%. 60% of my portfolio costs 12.45% and 5% of my portfolio costs 10.9%. Multiply those through, add them up, and that's how you get the weighted average cost of capital. So we've got the cost of capital for each individual item. Now we just want to know the average, but we can't take a simple average because 60% of our portfolio, 60% of our balance sheet essentially is made up of common shares. So that gets more weight in the weighted average cost of capital. So this average is going to be closer to 12% than it will be to 4%. A simple average between the 12 and four would say eight. That's going to be higher than eight. I promise you that it'll be nine or 10 or something like that. Maybe nine and a half. We'll see. Let's crunch the numbers. 34.7% times 4.09, 0.347 times 4.09. I get 1.42. Now this number does not mean anything to me. 60%, 0.6 times 12.45, 7.47. And last 5.3 or 0.053 times 10.9, 0.58, 0.58. And we would expect that to be small because the weight is so small. So we're expecting a small number there. If you end up with a big number, like a number that's larger than any other two, you should just go, oh, I got decimals in the wrong spot. I screwed up. That is by far the most common screw up is people just put the decimal in the wrong spot. 1.42 plus 7.47 plus 0.58. We ended up at 9.47%. That's our weighted average cost of capital. That's the answer to the question. That's what this company, uh, when they're sort of calculating their required rate of return on future projects or purchases or investments, they should use 9.47% as their discount rate. We've done it. We've solved 11.6a. As always, I work hard on these videos. I do them to help you and I hope they help. And if they help you, I hope you'll help me. Have a great day. Bye.