CHAPTER 7 6 Bonds and Their Valuation

CHAPTER 7 & 6 Bonds and Their Valuation n n Key features of bonds Bond valuation Measuring yield, yield curve Assessing default risk By Donglin Li 7 -1

What is a bond? n A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond. By Donglin Li 7 -2

Bond markets n n Primarily traded in the over-the-counter (OTC) market with dealers connected electronically. Most bonds are owned by and traded among large financial institutions. Full information on bond trades in the OTC market is not published, but a representative group of bonds is listed and traded on the bond division of the NYSE. Information on small company or municipal issues is difficult to get, treasury securities are an exception. 7 -3 By Donglin Li

Key Features of a Bond n n Par value – face amount of the bond, which is paid at maturity (assume $1, 000). Coupon rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest. Maturity date – years until the bond must be repaid. Current Yield - Annual coupon payments divided by bond price. By Donglin Li 7 -4

WARNING The coupon rate IS NOT the discount rate used in the Present Value calculations. The coupon rate merely tells us what cash flow the bond will produce. Since the coupon rate is listed as a %, this misconception is quite common. By Donglin Li 7 -5

YTM n n Yield to maturity (YTM) - rate of return earned on a bond held until maturity. It is the interest rate (discount rate) for which the present value of the bond’s payments equal the bond price. By Donglin Li 7 -6

Wait a minute, isn’t yield to maturity just the discount rate? n n If the discount rates (interest rates) remain same from year to year, YTM=discount rate (interest rate). Discount rates (interest rates) may be different in different periods. In that case, YTM is some average of the discount rates. By Donglin Li 7 -7

The value of financial assets 0 1 2 r% Value N . . . CF 1 CF 2 By Donglin Li CFN 7 -8

Bond price changes as Rates Change Bond Value = PV of coupons + PV of par= PV annuity + PV of lump sum n As interest rate (discount rate, yields to maturity) increases, the PV’s decrease, so bond prices decrease and vice versa. n By Donglin Li 7 -9

What is the value of a 10 -year, 10% annual coupon bond, if rd = 10%? 0 1 2 r VB = ? n . . . 100 By Donglin Li 100 + 1, 000 7 -10

Using a financial calculator to value a bond n This bond has a $1, 000 lump sum due at t = 10, and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows. (PMT and FV need to have the same sign, PV the opposite sign) OUTPUT 10 10 N INPUTS 100 I/YR PV 1000 PMT FV -1000 By Donglin Li 7 -11

The same company also has 10 -year bonds outstanding with the same risk but a 13% annual coupon rate n This bond has an annual coupon payment of $130. Since the risk is the same the bond has the same yield to maturity as the previous bond (10%). In this case the bond sells at a premium because the coupon rate exceeds the yield to maturity. OUTPUT 10 10 N INPUTS 130 I/YR PV 1000 PMT FV -1184. 34 By Donglin Li 7 -12

The same company also has 10 -year bonds outstanding with the same risk but a 7% annual coupon rate 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%). In this case, the bond sells at a discount because the coupon rate is less than the yield to maturity. OUTPUT 10 10 N INPUTS 70 I/YR PV 1000 PMT FV -815. 66 By Donglin Li 7 -13

Changes in Bond Value over Time n VB What would happen to the value of these three bonds if its required rate of return remained at 10%: 1, 184 13% coupon rate 10% coupon rate. 1, 000 816 7% coupon rate 10 5 By Donglin Li 0 Years to Maturity 7 -14

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. By Donglin Li 7 -15

What is the YTM on a 10 -year, 9% annual coupon, $1, 000 par value bond, selling for $887? n Must find the rd that solves this model. By Donglin Li 7 -16

Using a financial calculator to find YTM n Solving for I/YR, the YTM of this bond is 10. 91%. This bond sells at a discount, because YTM > coupon rate. INPUTS 10 N OUTPUT - 887 I/YR 90 1000 PV PMT FV 10. 91 By Donglin Li 7 -17

Find YTM, if the bond price was $1, 134. 20. n Solving for I/YR, the YTM of this bond is 7. 08%. This bond sells at a premium, because YTM < coupon rate (9%). INPUTS 10 N OUTPUT -1134. 2 I/YR 90 1000 PV PMT FV 7. 08 By Donglin Li 7 -18

Bond Prices: Relationship Between Coupon and Yield If YTM = coupon rate, then par value = bond price n If YTM > coupon rate, then par value > bond price n n n Selling at a discount, called a discount bond If YTM < coupon rate, then par value < bond price n Selling at a premium, called a premium bond By Donglin Li 7 -19

Definitions By Donglin Li 7 -20

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% By Donglin Li 7 -21

Calculating capital gains yield YTM = Current yield + Capital gains yield CGY = YTM – CY = 10. 91% - 10. 15% = 0. 76% 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. By Donglin Li 7 -22

What is interest rate (or price, maturity) risk? n Interest rate risk is the concern that rising rd will cause the value of a bond to fall. rd 5% 10% 15% 1 -year $1, 048 1, 000 956 Change + 4. 8% – 4. 4% 10 -year $1, 386 1, 000 749 Change +38. 6% – 25. 1% The 10 -year bond is more sensitive to interest rate changes, and hence has more interest rate risk. 7 -23 By Donglin Li

Interest Rate Risk Change in price due to changes in interest rates n Long-term bonds have more interest risk than short-term bonds. n Also called maturity risk. n By Donglin Li 7 -24

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. 2 N rd / 2 OK cpn / 2 OK N INPUTS I/YR PV PMT FV OUTPUT By Donglin Li 7 -26

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. OUTPUT 20 6. 5 N INPUTS I/YR 50 PV 1000 PMT FV - 834. 72 By Donglin Li 7 -27

Would you prefer to buy a 10 -year, 10% annual coupon bond or a 10 -year, 10% semiannual coupon bond, all else equal? The semiannual bond’s effective rate is: 10. 25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond. By Donglin Li 7 -28

If the proper price for this semiannual bond is $1, 000, what would be the proper price for the annual coupon bond? n The semiannual coupon bond has an effective rate of 10. 25%, and the annual coupon bond should earn the same EAR. At these prices, the annual and semiannual coupon bonds earn the same effective return. OUTPUT 10 10. 25 N INPUTS I/YR 100 PV 1000 PMT FV - 984. 80 By Donglin Li 7 -29

Zero Coupon Bonds (also called zeros. ) n n n Make no periodic interest payments (coupon rate = 0%) The entire yield-to-maturity comes from the difference between the purchase price and the par value Question: is YTM=CGY for zeros? Will never sell for more than par value Treasury Bills is an example of zeroes. By Donglin Li 7 -30

Government Bonds n Treasury Securities n n T-bills – pure discount bonds with original maturity of one year or less T-notes – coupon debt with original maturity between one and ten years T-bonds coupon debt with original maturity greater than ten years Municipal Securities n n n Debt of state and local governments There is default risk. Interest received is tax-exempt at the federal tax level By Donglin Li 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. By Donglin Li 7 -32

So far, we have used one interest rate for all the cash flows of different periods. n n In fact, the discount rate for one period cash flows can be different from the discount rate for cash flows in other periods. Spot interest rate: the actual interest rate between now and a certain future date, as of now. (r 1, r 2, r 3…) By Donglin Li 7 -33

Value the bond (revisit) n n Here r 1, r 2, …, rt are spot rates for period 1, 2, …, t, respectively. The spot rates (r 1, r 2, …, rt ) for cash flows in different periods are given by the yield curve. By Donglin Li 7 -34

Yield curve and the term structure of interest rates n n n Term structure – relationship between interest rates (or yields) and maturities. The yield curve is a graph of the term structure. A Treasury yield curve from November 2005: By Donglin Li 7 -35

Yield Curve Last September Date 1 mo 3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr 30 yr 09/01/10 0. 16 0. 13 0. 19 0. 25 0. 50 0. 75 1. 41 2. 02 2. 58 3. 35 3. 65 09/02/10 0. 15 0. 14 0. 18 0. 25 0. 50 0. 76 1. 43 2. 06 2. 63 3. 41 3. 72 09/03/10 0. 15 0. 14 0. 19 0. 25 0. 52 0. 81 1. 49 2. 14 2. 72 3. 49 3. 79 09/07/10 0. 13 0. 14 0. 18 0. 25 0. 49 0. 77 1. 41 2. 04 2. 61 3. 37 3. 67 09/08/10 0. 14 0. 19 0. 24 0. 52 0. 80 1. 46 2. 09 2. 66 3. 42 3. 72 09/09/10 0. 14 0. 19 0. 26 0. 57 0. 87 1. 57 2. 20 2. 77 3. 54 3. 84 09/10/10 0. 14 0. 19 0. 27 0. 58 0. 88 1. 59 2. 24 2. 81 3. 58 3. 88 09/13/10 0. 15 0. 19 0. 26 0. 53 0. 82 1. 51 2. 15 2. 74 3. 52 3. 83 09/14/10 0. 11 0. 15 0. 20 0. 26 0. 50 0. 77 1. 43 2. 09 2. 68 3. 48 3. 79 09/15/10 0. 11 0. 15 0. 20 0. 26 0. 50 0. 77 1. 46 2. 13 2. 74 3. 55 3. 87 09/16/10 0. 12 0. 16 0. 20 0. 25 0. 48 0. 77 1. 48 2. 17 2. 77 3. 61 3. 92 09/17/10 0. 12 0. 16 0. 20 0. 26 0. 48 0. 75 1. 46 2. 14 2. 75 3. 60 3. 90 09/20/10 0. 12 0. 17 0. 20 0. 26 0. 47 0. 73 1. 43 2. 10 2. 72 3. 57 3. 87 By Donglin Li 7 -36

Yield Curve in February Date 02/01/11 1 mo 0. 16 3 mo 0. 15 6 mo 0. 18 1 yr 0. 27 2 yr 0. 61 3 yr 1. 04 5 yr 2. 02 7 yr 2. 79 10 yr 3. 48 20 yr 4. 37 30 yr 4. 62 02/02/11 0. 15 0. 16 0. 18 0. 28 0. 67 1. 12 2. 10 2. 84 3. 52 4. 39 4. 64 02/03/11 0. 14 0. 18 0. 29 0. 71 1. 19 2. 18 2. 92 3. 58 4. 43 4. 67 02/04/11 0. 13 0. 15 0. 18 0. 31 0. 77 1. 25 2. 27 3. 01 3. 68 4. 51 4. 73 02/07/11 0. 13 0. 16 0. 18 0. 31 0. 78 1. 28 2. 29 3. 03 3. 68 4. 50 4. 71 02/08/11 0. 14 0. 15 0. 18 0. 31 0. 86 1. 40 2. 39 3. 12 3. 75 4. 56 4. 76 02/09/11 0. 14 0. 18 0. 30 0. 81 1. 34 2. 33 3. 05 3. 65 4. 49 4. 71 02/10/11 0. 08 0. 12 0. 16 0. 30 0. 85 1. 40 2. 40 3. 10 3. 70 4. 55 4. 75 02/11/11 0. 08 0. 12 0. 16 0. 30 0. 85 1. 40 2. 38 3. 05 3. 64 4. 49 4. 71 02/14/11 0. 09 0. 13 0. 17 0. 30 0. 87 1. 41 2. 37 3. 04 3. 62 4. 46 4. 67 02/15/11 0. 13 0. 17 0. 30 0. 84 1. 39 2. 35 3. 03 3. 61 4. 45 4. 66 02/16/11 0. 10 0. 12 0. 16 0. 29 0. 86 1. 40 2. 37 3. 04 3. 62 4. 46 4. 67 02/17/11 0. 08 0. 09 0. 15 0. 27 0. 80 1. 33 2. 30 2. 99 3. 58 4. 44 4. 66 02/18/11 0. 08 0. 10 0. 15 0. 28 0. 78 1. 32 2. 30 2. 99 3. 59 4. 46 4. 70 By Donglin Li 7 -37

Yield Curve This Month 09/01/11 0. 02 0. 05 0. 10 0. 19 0. 31 0. 90 1. 49 2. 15 3. 10 3. 51 09/02/11 0. 02 0. 05 0. 10 0. 20 0. 33 0. 88 1. 41 2. 02 2. 92 3. 32 09/06/11 0. 02 0. 07 0. 13 0. 21 0. 33 0. 88 1. 40 1. 98 2. 86 3. 26 09/07/11 0. 00 0. 02 0. 06 0. 11 0. 21 0. 34 0. 92 1. 45 2. 05 2. 96 3. 36 09/08/11 0. 02 0. 07 0. 12 0. 19 0. 33 0. 88 1. 41 2. 00 2. 92 3. 32 09/09/11 0. 00 0. 01 0. 05 0. 11 0. 17 0. 31 0. 81 1. 34 1. 93 2. 86 3. 26 09/12/11 0. 01 0. 05 0. 11 0. 21 0. 35 0. 87 1. 38 1. 94 2. 84 3. 24 09/13/11 0. 00 0. 01 0. 05 0. 10 0. 21 0. 35 0. 89 1. 42 2. 00 2. 92 3. 32 By Donglin Li 7 -38

Term Structure of Interest Rates The previous graph is based on treasury securities, so the yields do not reflect the default risk, liquidity effect, etc. n Yield curve: n Normal – upward-sloping, long-term yields are higher than short-term yields n Inverted – downward-sloping, long-term yields are lower than short-term yields n By Donglin Li 7 -39

Upward-Sloping Yield Curve By Donglin Li 7 -40

Downward-Sloping Yield Curve By Donglin Li 7 -41

Example n Please use the following information to value a 10%, four years coupon bond, if the term structure is: Year Spot rate 1 5% 2 5. 4% 3 5. 7% 4 5. 9% By Donglin Li 7 -42

Solution n The interest payment is $100 every year. By Donglin Li 7 -43

What is the opportunity cost of debt capital? n The discount rate (ri ) is the opportunity cost of capital, and is the rate that could be earned on alternative investments of equal risk. ri = r* + IP + MRP + DRP + LP By Donglin Li 7 -44

What else determines interest rates of corporate bonds? ri = r* + IP + MRP +DRP + LP ri = required return on a debt security r* = real risk-free rate of interest IP = inflation premium MRP= maturity risk premium (also called interest rate risk premium) DRP = default risk premium LP = liquidity premium By Donglin Li 7 -45

Premiums added to r* for different types of debt IP S-T Treasury S-T Corporate LP L-T Treasury MRP DRP By Donglin Li 7 -46

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. By Donglin Li 7 -47

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 D n Bond ratings are designed to reflect the probability of a bond issue going into default. By Donglin Li 7 -48

Factors affecting default risk and bond ratings n Financial performance n n n Debt ratio Current ratio Bond contract provisions n n Secured vs. Unsecured debt Senior vs. subordinated debt Guarantee and sinking fund provisions Debt maturity By Donglin Li 7 -49

Bankruptcy n Two main chapters of the Federal Bankruptcy Act: n n n Chapter 11, Reorganization Chapter 7, Liquidation Typically, a company wants Chapter 11, while creditors may prefer Chapter 7. By Donglin Li 7 -50

Priority of claims in liquidation 1. 2. 3. 4. 5. 6. 7. 8. Secured creditors from sales of secured assets. Trustee’s costs Wages, subject to limits Taxes Unfunded pension liabilities Unsecured creditors Preferred stock Common stock By Donglin Li 7 -51