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Valuing Bonds (Chapter 5)

Valuing Bonds (Chapter 5). Bond Characteristics Bond Prices and Yields Bond prices and interest rates YTM vs. current yield Rate of Return. Bonds Intro. Bond: Security that obligates the issuer to make specified payments to the bondholder. Issuance

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Valuing Bonds (Chapter 5)

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  1. Valuing Bonds(Chapter 5) • Bond Characteristics • Bond Prices and Yields • Bond prices and interest rates • YTM vs. current yield • Rate of Return

  2. Bonds Intro Bond: Security that obligates the issuer to make specified payments to the bondholder. • Issuance • Bond issuers (corporation or government) receive money by selling claims of future payment. • A bond contract specifies the payments to bondholder but not the amount of money received by the bond issuer. • E.g. GM will receive $800 now if it sells one bond to an investor, which obligates it to pay $1000 back after 10 years and $80 every year for ten years. • Maturity (date) • A specified date in future when bond issuing companies need to pay back the money borrowed (face value). • Term to maturity: Time left till maturity.

  3. Bonds Intro (cont.) • Face Value(Par Value or principle) • It is the payment from the bond issuer to bond holder at maturity of the bond. • More often than not, it does not equal to the money received by the bond issuing companies when bonds are issued. • Usually, face value of a corporate bond is $1000. • Bond Price • At issuance, this is the money that bond issuing companies receive when bonds are issued; it is the money investors pay when buying a bond from the issuing companies. • Bond can be issued at a price above, below or at face value (premium bond, discount bond and par bond). • After issuance, there are prices for bonds in secondary market. • More often than not, the price of a bond changes over time from issuance to maturity.

  4. Bonds Intro (cont.) • Coupon - The “interest” payments made to the bondholder. • Coupons are paid by bond issuing companies to bondholders. • Coupons are paid regularly, usually annually or semi-annually, till time of maturity (i.e. the first coupon payment is made 6 months or one year from issuance, while the last is made at maturity) • Coupons are equal payments, specified by coupon rate. • Coupons are not necessarily fair interests for bondholder or the issuing companies. • Coupons can be zero. • Coupon Rate - Annual rate, expressed as a percentage of face value. • Coupon rate are decided by issuing companies according to their preference. • “8% annual coupon” means 8% of $1000 will, i.e. $80, will be paid to bondholders every year till maturity. • “10% semi-annual coupon” means total of 10% of $1000, i.e. $100, will be paid every year, but with two semi-annual payments, $50 each.

  5. Reading Bond Quotes • Bond issuer • Coupon Rate • Percentage of • Maturity Date • Bond Price • a bond with a bid of 94 is trading at 94% of its par value, i.e. the bond of Air Canada is priced at $940 assuming $1000 par value • Yield to Maturity • Annual rate of return if bond are held till maturity

  6. Bond Pricing The fair price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at a reasonable interest rate.

  7. Bond Pricing • The coupon payments create an annuity • PMT=Coupon • The face value is a single future cash flow • Bond price formula can be re-written as:

  8. Bond Pricing Example What is the price of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume interest rate of 3.9%. What is the price of the bond if the interest rate is 6.5 %? And 15 %?

  9. Bond Pricing Example What is the price of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume interest rate of 3.9%. What is the price of the bond if the interest rate is 6.5 %? And 15 %?

  10. Bond Pricing Example What is the price of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume interest rate of 3.9%. What is the price of the bond if the interest rate is 6.5 %? And 15 %? Higher interest rates result in lower bond prices. Why?

  11. Interest Rate and Bond Price • When the interest rate involved exceeds the coupon rate, bonds sell for less than face value; vice versa. • Coupon payment is less than fair interests due every period. • When the interest rate involved is below the coupon rate, bonds sell for more than face value; vice versa. • Coupon payment is more than fair interests due every period. • When the interest rate involved equals the coupon rate, bonds sell at face value, vice versa. • Coupon payment is the same as fair interests due every period. The above rules apply throughout a bond’s life except when at maturity.

  12. Semi-annual Payments Example (continued) What is the price of the bond if the interest rate is 3.9% AND the coupons are paid semi-annually? • The coupon rate is still 6.5%, so $65 will be the total annual amount of the two semi-annual coupons; $65 / 2=$32.5 • Total number of coupon payments is now 2*3=6; • Since coupons are paid semi-annually, we should use semi-annual interest rate Assume that 3.9% is APR, then semi-annual rate is: 3.9% / 2=1.95%

  13. Semi-annual Payments Example (continued) What is the price of the bond if the interest rate is 3.9% AND the coupons are paid semi-annually?

  14. Current Yield • Current Yield - Annual coupon payments divided by bond price. • Current yield measures gains relative to the costs of buying the bond right now. • Current yield is calculated as an annual rate. Note: For semi-annual coupon bonds, current yield are calculated as (semi-annual coupon *2)/Current Bond Price • Current yield only considers coupon payment gain while ignores the possible gain/loss caused by fluctuation of future bond prices.

  15. Current Yield If a bond with face value of $1,000 and a coupon rate of 8% is selling at a price of $970, what is the current yield?

  16. Rate of Return Rate of Return: Earnings per period per dollar invested. (We usually calculate annual rates.) • Rate of return for bonds: • Rate of return considers both coupon gains and capital gains (losses) caused by bond price fluctuations.

  17. Rate of Return The required rate of return for a 10 year bond with 8% annual coupon is 10% right now. Answer following questions: • What is the bond price now? • After one year, if the required rate of return decreases to 9%, what is the rate of return for selling the bond at that time? • If instead, the required rate of return remains 10%, what is the rate of return for selling the bond at that time? • After one year, if the required rate of return decreases to 12%, what is the rate of return for selling the bond at that time?

  18. Yield To Maturity • Yield To Maturity (YTM) - Interest rate for which the present value of the bond’s payments equal the price. • Given bond price, YTM can be obtained by solving the Bond PV formula for interest rate • YTM is the annual rate of return if bond are held till maturity. • Required/expected rate of return implied by the bond price.

  19. Bond Yields Example What is the YTM of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,072.29.

  20. Bond Value Assume that interest rate remains constant • At issuance • Discount bond: If r > coupon rate, bond price is lower than $1000.. • Premium bond: If r < coupon rate, bond price is higher than $1000. • Par bond: If kd = coupon rate, bond price equals $1000. • At maturity The value of any bond must equal its par value. • From issuance till maturity • The value of a premium bond would decrease to $1,000. • The value of a discount bond would increase to $1,000. • A par bond stays at $1,000 if kd remains constant.

  21. Bond Value ($) kd = 7%. kd = 10%. M 1,000 kd = 13%. 30 25 20 15 10 5 0 Years remaining to Maturity

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