CHAPTER 7 Bonds and Their Valuation n n

CHAPTER 7 Bonds and Their Valuation n n Key features of bonds Bond valuation Measuring yield Assessing risk Suggested problems on pages 224 -226: 7 -1 through 7 -10 (all 10 problems) 7 -1

What is a bond? n n n A debt security that will last at least one year from when it is issued n Examples: Treasury bonds, Treasury notes, corporate bonds, municipal bonds (Orange County “muni” bonds) The “issuer” issues the bonds to borrow $ n The issuer agrees to make payments of principal and interest, on specific dates, to the holders (i. e. , investors) of the bond. n Examples: The U. S. Treasury is the “issuer” of T-bonds. Once issued by the borrower, most bonds are invested in, owned, and traded among large financial institutions. n Exceptions: The U. S. Treasury makes it easy for us to invest in Tnotes and T-bonds at www. Treasury. Direct. gov 7 -2

Key Features of a Bond n n Par value (“Principal”) is the amount borrowed by the issuer and is paid back at maturity. Sometimes people call this the “face value”. Coupon interest rate is stated interest rate paid by the issuer. Multiply by par value to get dollar payment of interest. Usually this is a fixed rate that doesn’t change. Exception: Treasury Inflation-Protected bonds. n Issue date is the date when the bond was issued. n Maturity date is the date when the par value (“Principal”) of the bond must be repaid. n “Maturity” is a term sometimes used to describe the amount of time between now and the maturity date n Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”, “opportunity cost” and “discount rate”) 7 -3

Key Features of a Bond n Par value (“Principal”) is the amount borrowed by the issuer and is paid back at maturity. Sometimes people call this the “face value”. n n Coupon interest rate is stated interest rate paid by the issuer. Multiply by par value to get dollar payment of interest. Usually this is a fixed rate that doesn’t change. Exception: Treasury Inflation-Protected bonds. n n Example: Oct 23, 2011 “Maturity” is a term sometimes used to describe the amount of time between now and the maturity date n n Example: Oct 23, 2008 Maturity date is the date when the par value (“Principal”) of the bond must be repaid. n n Example: 10%. Dollar payment = 10% x $1, 000 = $100. Issue date is the date when the bond was issued. n n Example: $1, 000 Example: 3 years Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”, “opportunity cost” and “discount rate”) 7 -4

This is REALLY IMPORTANT: How do we calc. the value of financial assets? How much is thing worth? ? How much should we pay? It should be worth the PV of its cash flows! 0 1 2 r% Value N . . . CF 1 CF 2 CFN 7 -5

Also REALLY IMPORTANT: for bonds, “r” in denominator is not the “coupon rate”. Use the “coupon rate” to calculate the annual cash flows. These are in the numerator. What is “r” in the denominator? ? 0 1 2 r% Value N . . . CF 1 CF 2 CFN 7 -6

The “r” in the denominator goes by many names: yield, opportunity cost, discount rate n The “r” in the denominator equals the rate that could be earned on alternative investments of equal risk. n n This is return people expect to earn if they lend money that has the same risk that the bond has. This return has to compensate the investor for the risk-free rate, inflation, maturity risk, default risk, and the liquidity premium: r = r* + IP + MRP + DRP + LP n The “r” in the denominator is also called the “yield to maturity” or sometimes we just say “yield”. 7 -7

What is the value of a 3 -year, 10% annual coupon bond, if rd = 10%? Assume a par value (“face”) = $1, 000. Annual payment = $100 = 10% annual coupon * $1, 000 face value. Note: $100 is in the numerator; rd = 10% is in the denominator. 0 1 2 r VB = ? 3 . . . 100 100 + 1, 000 7 -8

What is the value of a 10 -year, 10% annual coupon bond, if rd = 10%? Assume a par value (“face”) = $1, 000. Annual payment = $100 = 10% annual coupon * $1, 000 face value. 0 Note: $100 is in the numerator; rd = 10% is in the denominator. 1 2 r VB = ? 10 . . . 100 100 + 1, 000 7 -9

Now use the financial calculator: What is the value of a 10 -year, 10% annual coupon bond, if rd = 10%? Assume a par value (“face”) = $1, 000. 1) A bond is just an annuity (pmt = coupon in $) PLUS lump sum at time “n”. 2) Hint: lump sum principal is also called “face value” -- initials “FV”!! For FV, enter the principal only. (Do not add the last payment to it. The annuity accounts for all of the coupon payments. ) 3) Use end mode because 1 st payment at end of 1 st period. 4) Use P/yr = 1. Enter n = 10, FV = 1000, I/yr = 10, PMT = $100. 5) Note: the 10 entered in I/yr is the 10% discount rate, not the coupon rate. 5) Solve for PV. That’s what the bond is worth today to buy or sell. 6) If coupon rate = discount rate, PV = FV! And we say bond is trading “at par”. Although the coupon rate = discount rate in this example, this will not always be the case. INPUTS OUTPUT 10 10 N I/YR PV 1000 PMT FV -1000 7 -10

What if the same company whose bonds we just looked at issues 10 -year bonds with the same risk but a 13% annual coupon rate? Again assume a par value of $1, 000. n n Because the bonds have the “same risk”, investors will expect the same return. In other words, the discount rate (i. e. , yield, opportunity cost) will have to be the same as on the last problem (=10%). This bond has an annual coupon payment of $130 (= 13% x par value). This bond sells for $1, 184, which is more than its par value of $1, 000. We say that it therefore sell at a “premium” (to par). It is worth more than par because the coupon rate exceeds the yield to maturity. INPUTS OUTPUT 10 10 N I/YR PV 130 1000 PMT FV -1184. 34 7 -11

What if the same company whose bonds we just looked at issues 10 -year bonds with the same risk but a 7% annual coupon rate? Again assume a par value of $1, 000. n This bond has an annual coupon payment of $70. Since the risk is the same the bond has the same yield to maturity as the previous bonds (10%). This bond sells at a discount ($815. 66 < $1, 000). It sells for below par because the coupon rate is less than the yield to maturity. INPUTS OUTPUT 10 10 N I/YR PV 70 1000 PMT FV -815. 66 7 -12

Changes in Bond Value over Time What would happen to the value of each of these three bonds as time passes if required rate of return remains at 10%? As time passes, “n” gets smaller. Graph shows how PV changes. V Check for yourself: calculate each of our 3 bonds when maturity = 5. B 1, 184 13% coupon rate 10% coupon rate. 1, 000 816 7% coupon rate 10 5 0 Years to Maturity 7 -13

Bond values over time n n At maturity, the value of any bond must equal its par value. If rd remains constant: n The value of a premium bond would decrease over time, until it reached $1, 000. n The value of a discount bond would increase over time, until it reached $1, 000. n A value of a par bond stays at $1, 000. 7 -14

What is the “yield to maturity” (or “YTM” or “yield” on a 10 -year, 9% annual coupon, $1, 000 par value bond, selling for $887? n n Must find the rd that solves this equation. “INT” stands for the coupon payment (in $). “M” is the par value. This is the same equation as on slide 7 -5, just using different notation. Hint: Use your financial calculator. 7 -15

Find YTM for a bond price that is trading at a price of $887. Par = $1, 000. N =10. Coupon rate = 9%. n n n Solving for I/YR, the YTM of this bond is 10. 91%. We say that this bond sells at a discount (to par). It does so because YTM > coupon rate. Hint: Enter PV as negative, PMT and FV positive. INPUTS 10 N OUTPUT I/YR - 887 90 1000 PV PMT FV 10. 91 7 -16

Another example: Find YTM for the same bond as the last example if the bond price is $1, 134. 20. Par = $1, 000. N =10. Coupon rate = 9%. n n n Solving for I/YR, the YTM of this bond is 7. 08%. We say this bond sells at a premium (to par). This is because YTM < coupon rate. Hint: Enter PV as negative, PMT and FV positive. INPUTS 10 N OUTPUT I/YR -1134. 2 90 1000 PV PMT FV 7. 08 7 -17

What is interest rate (or price) risk? Does a 1 -year or 10 -year bond have more interest rate risk? n § Interest rate risk is the concern that rising rd will cause the value of a bond to fall. rd 1 -year Change 10 -year 5% $1, 048 + 4. 8% $1, 386 +38. 6% 10% 1, 000 15% 956 – 4. 4% – 25. 1% 749 Change The 10 -year bond is more sensitive to interest rate changes, and hence has more interest rate risk. 7 -18

Illustrating Interest Rate Risk 10 -Year Bond 1 -Year Bond 7 -19

What is reinvestment rate risk? n Reinvestment rate risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $500, 000 playing the lottery. You intend to invest the money and live off the interest. 7 -20

Reinvestment rate risk example n n You may invest in either a 10 -year bond or a series of ten 1 -year bonds. Both 10 -year and 1 -year bonds currently yield 10%. If you choose the 1 -year bond strategy: n n After Year 1, you receive $50, 000 in income and have $500, 000 to reinvest. But, if 1 -year rates fall to 3%, your annual income would fall to $15, 000. If you choose the 10 -year bond strategy: n You can lock in a 10% interest rate, and $50, 000 annual income. 7 -21

Conclusions about interest rate and reinvestment rate risk Short-term AND/OR Long-term AND/OR High coupon bonds Low coupon bonds Interest rate risk Low High Reinvestment rate risk High Low n CONCLUSION: Nothing is riskless! 7 -22

YTM can be broken down into 2 components: “current yield” and “capital gains yield” 7 -23

An example: Current and capital gains yield n Find the current yield and the capital gains yield for a 10 -year, 9% annual coupon bond that sells for $887, and has a face value of $1, 000. Current yield = $90 / $887 = 0. 1015 = 10. 15% 7 -24

Calculating capital gains yield YTM = Current yield + Capital gains yield CGY = YTM – CY = 10. 91% - 10. 15% = 0. 76% How did we get the YTM of 10. 91%? Solve for I/yr: N = 10, PV = -887, pmt =$90, FV = 1, 000. 7 -25

Alternative method for Calculating capital gains yield Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer. One year from now N = 9. Calculate PV for N = 9. PV = $893. 78 CGY = ($893. 78 - $887)/$887 = 0. 76% 7 -26

Semiannual bonds 1. 2. 3. Multiply years by 2 : number of periods = 2 N. Divide nominal rate by 2 : periodic rate (I/YR) = rd / 2. Divide annual coupon by 2 : PMT = ann cpn / 2. INPUTS 2 N rd / 2 OK cpn / 2 OK N I/YR PV PMT FV OUTPUT 7 -27

What is the value of a 10 -year, 10% semiannual coupon bond, if rd = 13%? 1. 2. 3. Multiply years by 2 : N = 2 * 10 = 20. Divide nominal rate by 2 : I/YR = 13 / 2 = 6. 5. Divide annual coupon by 2 : PMT = 100 / 2 = 50. INPUTS OUTPUT 20 6. 5 N I/YR PV 50 1000 PMT FV - 834. 72 7 -28

Some bonds are issued with a call provision n n Allows issuer to refund the bond issue. The issuer wants to do this if interest rates in the economy decline (helps the issuer, but hurts the investor). Borrowers are willing to pay a higher yield, and lenders require a higher yield, for callable bonds. Treasury bonds do not have call provisions. Used by some corporations. Most common use is by corporations with poorer credit ratings (higher default risk). Bottom line: all else equal, if bond has call provision, PV is lower and YTM is higher. And we need to calculate the Yield to Call (YTC). 7 -29

What is the “yield to call” (or “YTC”) on a 10 -year bond with a 14% annual coupon, $1, 000 par value bond, that can be called in 5 years for a 9% call premium? Assume today the bonds sell for $1, 000. n “INT” stands for the coupon payment (in $). N = number of years to the date when the issuer can call the bond. Call price = par value + 9% of call premium = 1. 09*1, 000 = $1090. n Hint: Use your financial calculator. n n n N = 5, PV = -1, 000, PMT = 14% of 1, 000 = $140, FV = $1090. n Solve for Yield to Call = I/yr = 15. 03%. 7 -30

When is a call more likely to occur? n n In general, if a bond sells at a premium, then (1) coupon > rd, so (2) a call is more likely. So, expect to earn: n n YTC on premium bonds. YTM on par & discount bonds. 7 -31

Other types (features) of bonds n n n Convertible bond – may be exchanged for common stock of the firm, at the holder’s option. Warrant – long-term option to buy a stated number of shares of common stock at a specified price. Putable bond – allows holder to sell the bond back to the company prior to maturity. Income bond – pays interest only when interest is earned by the firm. Indexed bond – interest rate paid is based upon the rate of inflation. 7 -32

What is a sinking fund? n n Provision to pay off a loan over its life rather than all at maturity. Similar to amortization on a term loan. Reduces risk to investor, shortens average maturity. But not good for investors if rates decline after issuance. 7 -33

Default risk n n If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return. Influenced by the issuer’s financial strength and the terms of the bond contract. 7 -34

Evaluating default risk: Bond ratings Investment Grade Junk Bonds Moody’s Aaa Aa A Baa Ba B Caa C S&P AAA AA A BBB BB B CCC C n Bond ratings are designed to reflect the probability of a bond issue going into default. 7 -35

Factors affecting default risk and bond ratings n Financial performance n n Debt ratio TIE ratio Current ratio Bond contract provisions n n Secured vs. Unsecured debt Senior vs. subordinated debt Guarantee and sinking fund provisions Debt maturity 7 -36

Other factors affecting default risk n n n n Earnings stability Regulatory environment Potential antitrust or product liabilities Pension liabilities Potential labor problems Accounting policies THE ECONOMY 7 -37

And speaking of default risk … What’s Bankruptcy? n Two main chapters of the Federal Bankruptcy Act: n n n Chapter 11, Reorganization Chapter 7, Liquidation Typically, a company’s management wants Chapter 11, while creditors may prefer Chapter 7. 7 -38

“Chapter 11” Bankruptcy (aka Reorganization) n If company can’t meet its obligations … n n It files under Chapter 11 to stop creditors from foreclosing, taking assets, and closing the business and it has 120 days to file a reorganization plan. Court appoints a “trustee” to supervise reorganization. Management usually stays in control. Company must demonstrate in its reorganization plan that it is “worth more alive than dead”. n If not, judge will order liquidation under Chapter 7. 7 -39

“Chapter 11” Bankruptcy (aka Reorganization) -- continued n n In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back. Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success. 7 -40

“Chapter 7” Bankruptcy (aka Liquidation) n n In a “liquidation”, the company is deemed to be worth more “dead” than “alive”. If bankruptcy court orders liquidation: n Assets are auctioned off n Cash is then distributed in pecking order of priority of claims as specified in the Chapter 7 Bankruptcy code n People who hold the common stock usually get nothing because the cash usually isn’t enough to cover the debts. 7 -41

You may be surprised to learn: n n Many companies go bankrupt Many of them emerge from bankruptcy reorganizations and thrive n Examples: United Airlines, GM? If you have bonds in the company that goes bankrupt, how much you recover will depend on the terms of your type of bond also how much of a “haircut” was negotiated. Common shareholders, unlike bondholders, usually get nothing! That stock you’re considering that looks like a good gamble at $1/share may go to $0! 7 -42