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Valuation and Characteristics of Bonds

Valuation and Characteristics of Bonds. Characteristics of Bonds Valuation Bond Valuation Bond Quotes Duration. $32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000. 0 6m 1 2 … 28.

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Valuation and Characteristics of Bonds

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  1. Valuation and Characteristics of Bonds • Characteristics of Bonds • Valuation • Bond Valuation • Bond Quotes • Duration

  2. $32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000 0 6m 1 2 … 28 Characteristics of BondsBonds pay fixed coupon (interest) payments at fixed intervals (usually every 6 months) and pay the par value at maturity • Par value = $1000 • Coupon = 6.5% of par value per year = $65 per year ($32.50 every 6 months) • Maturity = 28 years (matures in 2029) • Issued by AT&T

  3. Types of Bonds • Debentures – unsecured bonds • Subordinated debentures – unsecured “junior” debt • Mortgage bonds – secured bonds • Zeros – bonds that pay only par value at maturity; no coupons • Junk bonds – speculative or below-investment grade bonds; rated BB and below. High-yield bonds

  4. Types of Bonds (Continued) • Eurobonds – bonds denominated in one currency and sold in another country. (Borrowing overseas) • example – suppose Disney decides to sell $1,000 bonds in France. These are U.S. $ denominated bonds trading in a foreign country. Why do this? • If borrowing rates are lower in France • To avoid SEC regulations

  5. Bond Indenture • The bond contract between the firm and the trustee representing the bondholders • Lists all of the bond’s features: coupon, par value, maturity, etc • Lists restrictive provisions which are designed to protect bondholders • Describes repayment provisions

  6. Value • Book Value: value of an asset as shown on a firm’s balance sheet; historical cost • Liquidation value: amount that could be received if an asset were sold individually • Market value: observed value of an asset in the marketplace; determined by supply and demand • Intrinsic value: economic or fair value of an asset; the present value of the asset’s expected future cash flows

  7. Security Valuation • In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return • Can the intrinsic value of an asset differ from its market value? • Ct = cash flow to be received at time t • k = the investor’s required rate of return • V = the intrinsic value of the asset

  8. Bond Valuation • Discount the bond’s cash flows at the investor’s required rate of return • the coupon payment stream (an annuity) • the par value payment (a single sum)

  9. Bond Example • Suppose our firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12% (required return), so we decide to offer a 12% coupon interest rate • What would be a fair price for these bonds? • Note: If the coupon rate = required return, the bond will sell for par value

  10. Bond Example (Continued)

  11. Bond Example (Continued) • Suppose interest rates fall immediately after we issue the bonds. The required return on bonds of similar risk drops to 10% • What would be a fair price for these bonds? • Note: If the coupon rate > required return, the bond will sell for a premium

  12. Bond Example (Continued) • Suppose interest rates rise immediately after we issue the bonds. The required return on bonds of similar risk rises to 14% • What would be a fair price for these bonds? • Note: If the coupon rate < required return, the bond will sell for a discount

  13. Bond Example (Continued) • For the last bond example assume that the interest paid semi-annually • What would be a fair price for these bonds?

  14. Bond Example (Continued)

  15. Yield-To-Maturity • The expected rate of return on a bond • The rate of return investors earn on a bond if they hold it to maturity • Suppose we paid $898.90 for a $1,000 par 10% coupon bond with 8 years to maturity and semi-annual coupon payments • What is our yield-to-maturity?

  16. Zero Bond Example • Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity • What is your yield-to-maturity?

  17. The Financial Pages: Corporate Bonds Cur Net Yld Vol Close Chg Polaroid 11 1/2Mat. 19.3 395 59 3/4 ... • What is the yield-to-maturity?

  18. The Financial Pages: Corporate Bonds Cur Net Yld Vol Close Chg HewlPkd Mat. ... 20 51 1/2 +1 • What is the yield-to-maturity?

  19. Bond Markets • Primarily over-the-counter transactions with dealers connected electronically • Extremely large number of bond issues, but generally low daily volume in single issues • Makes getting up-to-date prices difficult, particularly on small company or municipal issues • Treasury securities are an exception • Bond yield information is available online. One good site is Bonds Online • http://www.bondsonline.com/ • Follow the “bond search,” “search/quote center,” “corporate/agency bonds,” and “composite bond yields” links • Observe the yields for various bond types, and the shape of the yield curve.

  20. Corporate Bond Price Reporting • Coupon rate: 8.375% • Coupon payment per year = $83.75 = 0.08375 X 1,000 • Bond matures on July 15, 2033 • Trading volume = $763,528,000 (Face value of bonds traded) • Quoted price: 100.641% of face value, so if face value is 1,000, the price is $1,006.41. • Bond prices are quoted as a percent of par, just as the coupon is quoted as a percent of par. • The bond’s yield (8.316%) is 362 basis points (3.62%) above the comparable maturity Treasury bond yield (30-year Treasury bond yield). • 100 basis points = 1% • Current yield = 8.322% • Computed as annual coupon divided by current price ($83.75 / $1,006.41 = 8.32%)

  21. Corporate Bond Price Reporting – Continued • How can we determine the yield on GM bond? • To do that we use another TI BA II PLUS worksheet – BOND • Date entry: mm.ddyy • 2ND BOND • 2ND CLR WORK • 01.1305 ENTER (Settlement date.) • 8.375 ENTER (Annual coupon interest rate in percent form.) • 07.1533 ENTER (Maturity date.) • 100 ENTER (Face value entered as 100. If the bond has a call price it can be set to that.) • ACT (“ACT” is actual day count. Can be changed to “360” by using 2ND SET) • 2/Y (Coupon payment per year. Can be changed to “1/Y” by using 2ND SET) • Since we are computing yield (YLD) • 100.641 ENTER (Non-negative price of the bond as a % of face value.) • CPT (Go back to “YLD” to compute.) • AI (“AI” is Accrued Interest as dollar amount per face value amount.) • DUR (“DUR” is Duration of the bond – average time it takes to recover the market price.)

  22. Clean and Dirty Price of a Bond • How much do you think you will pay for the previous bond per $100 par value? • Price a buyer would pay will include “Accrued Interest” (AI) if a bond is purchased after the last coupon but before the next coupon payment • This is because a seller is entitled to receive some of the next coupon payment based on the fraction of six month period she owned it. • A quotation excluding AI is called “Clean Price” • What you pay for the bond is called “Dirty Price” • Dirty Price = Clean Price + Accrued Interest • Dirty Price = $100.641 + $4.142 = $104.783 • AI is quite close to 8.375 / 2 = 4.1875 since we are short by two days to make it a full six month period (1/13/05 vs. 1/15/05) • 4.1875 × 178/180 = 4.141 • You pay Dirty Price (Clean Price + AI) to the seller and get the next coupon in two days in full

  23. More on Clean and Dirty Price of a Bond • Why do dealers quote clean price then? • Clean prices excludes price drops of bonds due to a coupon payment. • This drop can also be observed for stock when there is a dividend payment. • Clean prices change not because of a coupon payment but rather because of a change in general direction of interest rates or a change in the credit quality of borrower

  24. The Financial Pages: Treasury Bonds Maturity Ask Rate Mo/Yr Bid Asked Chg Yld 9 Nov 18 139:14 139:20 -34 5.46 • What is the yield-to-maturity using ASK price with 35 periods? • PV = (139 + 20/32)% of 1,000 = 1,396.25

  25. Treasury Bond Price Reporting • Coupon rate = 9% • Matures in November 2018 • Bid price (Dealer’s Bid – dealer is willing to pay) is 145 and 25/32 percent of par value. • 145:25 = (145+25/32)% of par value = 145.78125% of par value • If you want to sell $100,000 par value T-bonds, the dealer is willing to pay 1.4578125(100,000) = $145,781.25 • Ask price (Dealer’s Ask – dealer is willing to receive) is 145 and 26/32 percent of par value. • 145:26 = (145+26/32)% of par value = 145.8125% of par value • If you want to buy $100,000 par value T-bonds, the dealer is willing to sell them for 1.458125(100,000) = $145,812.50 • The difference between the bid and ask prices is called the bid-ask spread and it is how the dealer makes money. • Note that Ask Price is higher than Bid Price. Why is that? • The price changed by 22/32 percent or $687.50 for a $100,000 worth of T-bonds (22/32)% of par. • (22/32)% = 0.6875% and 0.6875% X $100,000 = $687.50. • The yield based on the ask price is 4.51%

  26. Treasury Bond Price Reporting – Continued • If the date of quotation is January 14, 2005 and exact maturity date is 11/15/2018 what is the yield based on ask price? • 2ND BOND • 2ND CLR WORK • 01.1405 ENTER (Settlement date.) • 9.000 ENTER (Annual coupon interest rate in percent form.) • 11.1518 ENTER (Maturity date.) • 100 ENTER (Face value entered as 100. If the bond has a call price it can be set to that.) • ACT (“ACT” is actual day count. Can be changed to “360” by using 2ND SET) • 2/Y (Coupon payment per year. Can be changed to “1/Y” by using 2ND SET) • Since we are computing yield (YLD) • 145.8125 ENTER (Non-negative price of the bond as a % of face value.) • CPT (Go back to “YLD” to compute.

  27. Bond Pricing Theorems • The following statements about bond pricing are always true. • Bond prices and market interest rates move in opposite directions • When a bond’s coupon rate is (greater than / equal to / less than) the market’s required return, the bond’s market value will be (greater than / equal to / less than) its par value • Given two bonds identical but for maturity, the price of the longer-term bond will change more than that of the shorter-term bond, for a given change in market interest rates • Given two bonds identical but for coupon, the price of the lower-coupon bond will change more than that of the higher-coupon bond, for a given change in market interest rates • Last two have implications for bond price volatility

  28. Factors Affecting Bond Price Volatility • The longer the maturity, • The lower the coupon rate, • The lower the initial required yield, ===> the larger is the effect of a change in the required yield on the price of a bond.

  29. Bond Price Volatility and Duration • The Duration of a bond is a linear approximation of the percentage change in its price given a 100 basis point (one percent) change in required yield • Measures a bond’s percentage price volatility • For example, a bond with a duration of 7 will gain about 7% in price if required yield falls 1%

  30. Bond Duration

  31. Duration Example • Calculating the duration of a 4-year bond with an 8 percent coupon rate (annual payments). The required return of this bond is 9%, and the maturity value is $1,000

  32. Duration Example (Continued)

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