In this second session together, dealing with the calculation of a firm's WACC, we're going to concentrate upon debt. Specifically, we're going to concentrate our efforts on working out exactly what is needed in terms of kd, the cost of debt capital, as well as D, which is the market value of debt outstanding. But first, which sources of debt from our balance sheet should be included in this calculation? Let's have a quick look at the excerpt from this summary balance sheet for US food company, Kellogg's. Working our way down the liability section, we see that we must definitely include current maturities of long-term debt instruments, as well as any outstanding short-term securities that are payable in the next 12 months. In the non-current liabilities section, we'd also include the outstanding bonds and debentures that we have on issue and that are captured under long-term debt. But what about the other items? Well we don't include accounts payable as a source of financing for the firm. And the reason for this is that the purchase price that we negotiate for the items we have purchased already reflect the credit terms that have been negotiated for the goods provided. We also exclude income taxes that will be payable, because when we undertake standard NPV analysis the cash flows will generally be recorded on a after tax basis anyway. So the last thing we want to do is double count any tax effects by also including them in our estimation of WACC. Similarly, any pension liabilities that have accrued during the period would be excluded from our estimation of WACC, as we would include these pension entitlements as project cash flows as a standard cost of the project. The catch-all categories of other current and non-current liabilities would need to be carefully broken down and assessed to see if there are any other items that might need to feature on our WACC calculation. Okay, so we've identified the sources of debt that would contribute to our estimation of kd and D. Now what? Well, Kellogg's lists many different sources of long-term debt with different maturity dates. The next step is to identify the current market value and yield to maturity of each relevant source of debt capital. The market value of each source of debt is simply the present value of the payments promised by each source of debt. The yield to maturity is simply the discount rate that we would use to arrive at that present value figure. So it's the relevant discount rate to valued debt. Well how do we do this? Well, let's answer that by firstly heading back to some first principles on bond issuance and valuation. A fixed coupon-paying bond is a bond that promises fixed cash flows, or coupons, over it's life, plus the repayment of the face value at maturity. Coupon payments are calculated by simply multiplying a bond's coupon rate by its face value. Then the value of the bond at any time is simply equal to the present value of all of the remaining coupons, or promised cash flows, where the discount rate, as we've said before, is simply the bond's yield to maturity. So let's consider how bonds are issued, and the relationship between coupon rates, yields to maturity, bond prices, and face values. Now to start with, generally speaking, when bonds are first issued, they're issued with a coupon rate set equal to the bond's yield to maturity at the time, such that the issuing company is able to obtain the face value of the bond from the marketed issuance. Over time, though, yields to maturity change. They change because a yield to maturity is simply a discount rate for a debt security, and a discount rate reflects the time value of money. The time value of money has three components, risk, opportunity cost, that is what rate could be earned from other bonds of similar risk, and expected inflation. All of these influences can change over time and hence, yields to maturity also change over time. Now assuming that coupon has just been paid, so there's one full period until the next coupon. The relationship between coupon rates, yields to maturity, present values, or bond prices, and the bond's face value are fairly straightforward. If the coupon rate is lower than the prevailing yield to maturity, then the bond will be valued at a discount to its face value. If the coupon rate is greater than the yield to maturity, then it will be valued at a premium to its face value. And if the coupon rate is equal to the yield term maturity, then you've got it, the bond will be valued at its face value. Let's have a look at an example here. Way back in 2001, Kellogg's issued $1.1 billion of 30 year bonds with a coupon rate, which seems massive at the moment, of 7.45% per annum, payable each half year. So that implies a half yearly coupon of 3.725% per half year. It used the funds to help it acquire its takeover target, Keebler Foods. Now assuming a $1 million face value for each bond, then this implies that upon issue, the bond was promising 60 half yearly payments of $37,250 each. Now at the time of the bond issue, the coupon rate matched exactly the yield to maturity for the bonds, and hence the firm was able to raise $1 million for each bond issued. Now, as an aside, I have here a small note on how to convert an effective half yearly rate into an effective annual rate, just in case you're curious. All right, fast forward now to 2015. There are now 32 coupon payments left. The coupon rate remains unchanged at 3.725% per half year, but the market required rate of return has probably changed quite markedly. The rate that we need in this calculation is the rate that Kellogg's would need to promise today in order to issue new bonds at face value with 16 years until maturity. That is, what is the coupon rate that Kellogg's would have to promise today to issue 16 year bonds at face value? Well to answer that you need to understand what drives the relationship between interest rates and the term to maturity of a bond. That relationship is what we call the term structure of interest rates. Now one of the most widely accepted explanations for why short-term rates differ to longer term rates is that longer term rates reflect the market's expectation about future short-term rates. All right, let me explain that. Let's assume that you observe that if you were to invest in a one year bond, you'd be promised 4% per annum. But if you invested in a two year bond with the same underlying risk profile, then you're promised 5% per annum. It seems reasonable to interpret this interest rate differential as simply indicating that the market expects that the one year rate that could be earned beginning in one year's time is higher than the current one year rate of 4%. That is, the market expects interest rates to increase. Well to demonstrate, let’s compare two strategies. Firstly, we can invest for one year at 4% and then in a year's time, re-invest for another year at whatever the prevailing one year rate is. The alternative strategy would be to invest at 5% per annum for two years. Now if both strategies had equal risks, that is equal risk of default, then we could work out what the implied one year rate is for execution one year from now. That's what we call a forward rate. Well as we see, it works out to be a little bit over 6% per annum because of the compounding effect. Let's have a look at how the term structure of interest rates have actually varied through time. Here we have the yield to maturity on a variety of government securities issued in the US in 2001. As you can see, the so-called yield curve, that's the diagrammatic representation of the term structure of interest rates, that yield curve is fairly flat between 4 and 5% for securities issued with only a few months to expiry, as well as those with 30 years until expiry. Fast forward to January, 2015, it's quite a different story. With short-term rates very close to zero, and longer-term rates 250 basis points, that is about 2.5% per annum. There's also a number of other issues we should consider when embarking upon the debt valuation exercise. Some securities, known as zero-coupon securities, might not pay any coupons at all. Well to value these, it's very simple, we simply discount the final face value promised at expiry of the security. In contrast, a coupon-paying bond might pay a coupon that periodically resets according to some benchmark rate. For example, LIBOR plus 100 basis points. Provided the spread promised by such a bond adequately reflects the risk of the bond, the bond's value will periodically reset to its face value, which makes valuation relatively straightforward. Finally, provided that bank overdraft represents a permanent source of debt financing for the firm, it should also be included in your estimation of the cost of debt capital. So how do we actually use these numbers? Well, let's go through an example. Once we value each source of debt and identify its relevant cost today, it's all pretty straightforward. Let's say we have three sources of debt, bonds maturing in 2031, others maturing in 2020, and a series of short-term notes maturing over the next year. The first step is to arrive at a current valuation for each source of debt. Now there's two ways we can do this. We can observe values on the market if these are traded debt securities. Or we can simply value them ourselves by discounting the cash flows promised by each debt issue, and that's what's included in column one. As we see, the total value of debt is $20 billion, which represents capital D in our WACC equation. We work out the proportion of total debt that each source represents, and that's provided in column two. We then identify the current per annum cost of each source of funding. That's included in column three here. And multiplying column two by column three gives us the contribution to the overall cost of debt capital of each individual source of debt. When we add these together, we end up with the weighted average cost of debt capital, which features in our WACC equation as kd. That's pretty simple, huh? So, to summarize. In this session we highlighted the key elements to be included in the estimation of kd and D in the weighted average cost of capital formula, while stressing the need to utilize current market values and current cost of capital. We also touched upon the fundamental principles of bond valuation, differentiating between coupon rates and yields to maturity, as well as between face values and present values, or prices. Finally, we demonstrated how to estimate the weighted average cost of debt, which is a key input into the weighted average cost of capital. In our next session together, we're going to deal with equity as a source of capital.