(8 of 17) Ch.14 – Cost of debt: explanation & example


And now let's look at the other source of capital for a firm which is selling corporate bonds to borrow money from investors. So again, the money that goes back from the firm to the bond buyers is what we call cost of debt or cost of raising debt. From the investors' perspective, it's their return that they get every year when they pay money to buy the bonds. So that technically includes corporate bonds and also long-term loans but we will only be talking about corporate bonds on the next couple of slides. So, cost of debt -- the notation is capital R subscript capital D, RD -- is actually nothing but the discount rate that we use in bond problems. The term we were using in chapter seven in which we were covering bonds is yield to maturity, abbreviated as YTM.


So, yield to maturity is basically the discount rate for bonds or the cost of debt, one and the same thing. And just to remind you about bond calculations, there are two percentages that are given in bond problems. One is the discount rate or the yield to maturity or the cost of debt. And the other percentage that's usually given is the coupon rate. The coupon rate is not cost of debt. What's cost of debt is the discount rate or the yield to maturity. OK. Again, this is just a review of what we did when we talked about bonds in chapter seven.


So, let's do, you know, a refresher problem. Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9% and coupons are paid semi-annually. By the way, this is a key word you should always check for before you start solving a bond problem -- are coupons annual or semi-annual? The bond is currently selling for $908.72 per $1,000 bond. What is the cost of debt? Solving for the cost of debt is the same thing as computing IY, the discount rate for the bond, for which we need to know four things: N which is how many coupon payments there will be between now and maturity; PMT which is the coupon payment itself; FV which is the future value but it's also the face value which is typically $1,000 on a bond; and PV, the bond present value which is also nothing but the price per bond today. So, N, how many coupons? Because there are 25 years left to maturity and there are semi-annual payments, two per year, we have a total of 25 times two equals 50 coupons between now and the maturity of these bonds.


PMT, the coupon amount itself -- we always calculate the coupon amount the same way. We take the coupon rate -- that's 9% in our problem -- and multiply by $1,000. That will be the coupon amount per year. However, again, we need to adjust this number for the frequency of the coupons. Because they are paid semi-annually, every half a year, the coupon amount is half of the annual coupon amount.


So, coupon rate times $1,000 and then we need to divide it by two. Plugging in the numbers -- 0.09, coupon rate, times 1,000 divided by two gives 45. So, $45 every half a year -- that's the coupon payment. FV -- that's the face value on the bond paid at maturity at the very end in the future. That's always $1,000. PV -- that's the bond present value or price that's given, 908.72. Notice how I put the signs. This is something I was also emphasizing in chapter seven when we were covering bonds. Everything that's today is one sign. Everything that's in the future is with the opposite sign. So, I used a negative sign for today's price on the bond which means I need to use a positive sign for both the face value and the payment amount, the coupons.


Or I could switch the signs. So, I could also instead use minus 45 for the coupon amount or PMT and minus 1,000 for the face value of the bond or FV. In that case, I would need to keep the bond price, which is PV, in the calculator as positive 908.72. OK. So, let's bring up the financial calculator. Turn it on. N is 15 so I put 15N. Then I put the payment amount which is 45. Forty-five, PMT. And with the same positive sign, I am entering the face value of $1,000 as my FV, future value. One thousand, FV. PV is negative 908.72. So, 908.72. Then I'm changing it to negative -- plus/minus key. And then I save it as PV. And I'm computing IY so I press compute and then IY. Five. 5%. However, as the slide then shows, this is not what we call cost of debt because what all these terms that we are learning in this chapter -- cost of common stock, cost of preferred stock, and cost of debt -- they all are per year.


Is 5% the discount rate per year? No. It's for half a year and that's because of this semi-annual frequency of the coupons for this bond. And so, what we need to do to get the annual discount rate or the cost of debt, we need to then multiply 5% by two to give us ten. So, 10% per year is the cost of debt in this problem. And now, interpretation. It cost the firm 10% per year to use money raised from bond issues. So, if a firm sells a hundred thousand million dollars’ worth of new bonds, then it will cost the firm 10% of that per year.


So, 10% of a hundred million dollars is ten million dollars. So, it will be paying ten million dollars to the investors every single year for the money that the investors have provided..

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