Bond Pricing 1 Dr. Craig Ruff Department of Finance J. Mack Robinson College of Business Georgia State University © 2014 Craig Ruff

Jonas and the Howell Industries Bond 2

Howell Industries: Bond A Bond A: Face Value = $1000 Coupon Rate = 8% Maturity = 25 years Semi-Annual coupon payments Howell Industries has decided to build a new factory. To raise the money to build the new factory, Howell Industries decides to issue a bond, called Bond A. Based on consultations with its investment bankers about which maturity, etc. will sell best in the market, Howell industries establishes the following terms for the bond: Key Point: Howell Industries, as the issuer, establishes the features of the bond. As a general rule, companies issuing bonds typically try to set the coupon rate such that the bond will be issued as close to par as possible. These features typically don’t change over the life of the bond. 3

Bond A: Face Value = $1000 Coupon Rate = 8% Maturity = 25 years Semi-Annual Coupon Payments While it is Howell Industries that determines the bond’s features, it is the market that determines the yield it wants to earn on the bond. Key Point: Through the forces of supply and demand, the market determines the ‘yield’ it wants to earn on this bond. The market yield has a variety of names, including: yield-to-maturity, YTM, market rate. Or, we could say the bond is ‘yielding’ 6%, etc. The market yield will constantly change over the life of the bond as economic and company-specific factors change. Market Yield: Based on the credit quality of the issuer, rates on comparable bonds, etc., the market determines that it wants to earn an compound return of 6%, compounded semi-annually. 4 Howell Industries: Bond A

Bond A: Face Value = $1000 Coupon Rate = 8% Maturity = 25 years Semi-Annual Coupon Payments While it is Howell Industries that determines the bond’s features, it is the market that determines the yield it wants to earn on the bond. Key Point: Through the forces of supply and demand, the market determines the ‘yield’ it wants to earn on this bond. The market yield has a variety of names, including: yield-to-maturity, YTM, market rate. Or, we could say the bond is ‘yielding’ 6%, etc. The market yield will constantly change over the life of the bond as economic and company-specific factors change. Market Yield: Based on the credit quality of the issuer, rates on comparable bonds, etc., the market determines that it wants to earn an compound return of 6%, compounded semi-annually. 5 Howell Industries: Bond A

Given that investors want to earn a return of 6%, compounded semi-annually, on Bond A being issued by Howell Industries, how much should they pay today for this bond? As before, the answer is that they will pay the present value of the future expected cash flows, discounted at 6%, compounded semi-annually. On the calculator: FV = 1000 i/y = 3 N = 50 PMT = 40 PV = ? = -$1, Howell Industries: Bond A

Bond A: Face Value = $1000 Coupon Rate = 8% Maturity = 25 years Semi-Annual Coupon Payments In essence, the bond’s features (or, terms) layout the future expected cash flows from the bond. These features will also include promises by the company about collateral backing up the bond, minimal acceptable values for various company financial ratios, whether or not the bond is subordinate to other company debt, etc. Based on a variety of macro and micro factors, the market determines the rate it wants to earn on the bond. These two pieces – cash flows and yield- come together to determine the bond’s price. Yield Determined by Market Market Yield (YTM): 6% Cash Flows Determined By Issuer Present Value Calculation Bond’s Market Price 7 Howell Industries: Bond A

Yield-to-Maturity (YTM) In terms of calculating a bond’s YTM, one would start with the bond’s market price and… Again, there are several terms that we use more-or-less as synonyms…the bond’s yield is 6%, the market rate on the bond is 6%, the bond is yielding 6%, the market wants 6%. Properly speaking, these are all a reference to the bond’s yield-to-maturity (YTM); it is the standard descriptor for a bond’s return. Technical Definition: The YTM is the rate that makes the present value of the cash flows equal to the market price of the bond. (Like the internal rate of return for a bond). That is, you want to solve for the rate that makes the present value of all of the cash flows equal the market price of the bond. On your calculator, you would enter N, PMT, FV, -PV and solve for i/y (don’t forget to double the i/y if the bond pays semi-annual coupon payments). … back-out the bond’s YTM 8

On the calculator: FV = 1000 i/y = ? = 3  unhalf it = 6% N = 50 PMT = 40 PV = ? = -$1, Yield-to-Maturity (YTM)

Jonas Jonas decides to invest in a Bond A being issued by Howell Industries. Thus, he pays $1, to acquire the rights to the future cash flows from the bond. We can say that he has bought the bond. Or, we can say that he has invested in the bond. Or, we can say that he has lent money to Howell Industries so that they can build the new factory. In exchange, Howell Industries has promised to pay him back his money plus interest. This is a primary market transaction. JonasHowell Industries $$$ Bond A 10

So, Jonas buys the bond with a yield (yield-to-maturity, YTM) of 6%. But will Jonas really earn a compound rate of return of 6%, compounded semi-annually, over the life of his investment in Bond A? It is not likely. To actually earn 6%, compounded semi-annually, as a compound return on his investment, he would have to: 1)Get all the cash flows as promised, and 2)Be able to reinvest the intermediate cash flows at 6%, and 3)Hold the investment to maturity (or, sell the bond into a 6% market). In general, if any of these assumptions are not met, then Jonas will not earn the YTM as a compound rate of return over the life of his investment in the bond. 11 Jonas

So, Jonas buys the bond with a yield (yield-to-maturity, YTM) of 6%. But will Jonas really earn a compound rate of return of 6%, compounded semi- annually, on his investment? It is not likely. To actually earn 6%, compounded semi-annually, as a compound return on his investment, he would have to: 1)Get all the cash flows as promised, and 2)2) Be able to reinvest the intermediate cash flows at 6%, and 3) Hold the investment to maturity (or, sell the bond into a 6% market). In general, if any of these assumptions are not met, then Jonas will not earn the YTM as a compound rate of return over the life of the investment in the bond. Quick Comment: Yield-to-maturity is often called the ‘Promised Yield’ but, as we have noted, it is very unlikely to be the compound rate of return you will actually earn on an investment in a bond (or bond portfolio). 12 Jonas

The point is that there are a set of risks to Jonas not earning a compound return of 6%, compounded semi-annually, on his investment in Bond A. These risks are called: 1) Get all the cash flows as promised… credit risk or default risk (and, if the bond had any embedded options, we would also have option risk) 2) Be able to reinvest the intermediate cash flows at 6%... reinvestment rate risk 3) Hold the investment to maturity (or, sell the bond into a 6% market)… price risk or interest-rate risk 13 Jonas

Before we leave Jonas, let’s establish that if these three conditions hold, that Jonas will indeed earn a compound return of 6%, compounded semi-annually, on his investment in Bond A, issued by Howell Industries. 14 Jonas

First, let’s establish that if these three conditions hold, that Jonas will earn a compound return of 6%, compounded semi-annually, on his investment in Bond A, issued by Howell Industries. To see this we will need to know the balance in his imaginary bank account at the end of the 25 years, making all of the assumptions. We would deposit the $40 every six months in the imaginary bank account at a rate of 6%, compounded semi-annually. Plus, we would get the $1,000 face value at the end. Next, we find the compound return we earned over the 25 year period (you would likely do this on your calculator as the FV of a single sum and solve for the missing i/y). Solving for r (and doubling it), we get 6%, compounded semi-annually. FV???==> PV0 i/y3 N50 PMT40 $4, $1000 = 5, = t=25 imaginary bank balance 15 Jonas

You can also imagine Jonas’s imaginary bank account growing each year by a combination of coupon payments and interest on the previous coupon payments…. Period (t) Addititon or Subtraction to Account Imaginary Account Balance 0.5$40 1 $ $40$ $40$ $40$4, $40$4, $1,040$5, Jonas

Recap: Finding the Bond’s Price versus Yield to Maturity If we discount the bond’s stated cash flows by the bond’s yield-to-maturity (YTM), we get the bond’s price. To get the Bond’s YTM, we simply turn this around. To get the bond’s YTM, we start with the bond’s price and then back out the YTM by finding the compound rate that makes the present value of the bond’s cash flows equal to the bond’s price. 17

Bond’s Cash Flows – timing and amount Market Yield (Yield- to-Maturity, YTM) Present Value Calculation Bond’s Price Finding the bond’s price…. 18 Recap: Finding the Bond’s Price versus Yield to Maturity

Coupon +Face Value MARKETP RICE WHAT COMPOUND RATE MAKES THE PV OF ALL OF THE CASH FLOWS EQUAL TO THE BOND”S PRICE? Finding the bond’s YTM…. 19 Recap: Finding the Bond’s Price versus Yield to Maturity

If Coupon Rate > Market Yield  Market Price > Par Value If par value is $1000, then it will sell for more than $1000. For instance, a 10% coupon bond in an “8% market.” This is a “premium bond” If Coupon Rate < Market Yield  Market Price < Par Value If par value is $1000, then it will sell for less than $1000. For instance, a 6% coupon bond in an “8% market.” This is a “discount bond” If Coupon Rate = Market Yield  Market Price = Par Value This is a “par bond” 20 Premium, Discount and Par Bonds

21 If rates go up  bond prices go down If rates go down  bond prices go up Yields and Prices 1) Memorize this. 2) Remember the basic bond price formula: The yield is in the denominator. If the denominator gets bigger, the whole thing gets smaller and vice versa.

22 If rates go up  bond prices go down If rates go down  bond prices go up Yields and Prices 3) Plus in a simple nond in your calculator. Make something up. FV=1000, PMT= 50, N=20, IY =5. Calculate the PV. Now put in IY=10. See that the PV went down. 4) The bond’s payments are already set. To earn a higher yield, people will have to pay less for the bond. That is, to earn a higher yield, the price will have to go down, and vice versa.