## Presentation on theme: "2-1 Copyright © 2006 McGraw Hill Ryerson Limited prepared by: Sujata Madan McGill University Fundamentals of Corporate Finance Third Canadian Edition."— Presentation transcript:

2-2 Copyright © 2006 McGraw Hill Ryerson Limited Chapter 5 Valuing Bonds Bond Characteristics Bond Prices and Yields

2-3 Copyright © 2006 McGraw Hill Ryerson Limited Bond Characteristics Terminology  Governments and corporations borrow money for the long term by issuing securities called bonds.  The interest payment paid to the bondholders is called the coupon.  The payment at the maturity of the bond is called the face value or par value.  The date on which the loan will be paid off is the maturity date.

2-4 Copyright © 2006 McGraw Hill Ryerson Limited Bond Characteristics Coupon Rate vs Discount Rate  The coupon rate is the annual interest payment divided by the face value of the bond.  The interest rate (or discount rate) is the rate at which the cash flows from the bond are discounted to determine its present value. Note: The coupon rate and the discount rate are NOT necessarily the same!

2-5 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Price of a bond  The price of a bond is the present value of all its future cash flows, that is, it is the present value of the coupon payments and the face value of the bond.  Careful…..always discount the cash flows at the appropriate opportunity cost!

2-6 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Example  Calculate the current price of a 6.5 % annual coupon bond, with a \$1,000 face value which matures in 3 years. Assume a required return of 5.1%. 0 1 2 \$65 3 \$1,065

2-7 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Example  Calculate the current price of a 6.5 % annual coupon bond, with a \$1,000 face value which matures in 3 years. Assume a required return of 6.5%. 0 1 2 \$65 3 \$1,065

2-8 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Example  Calculate the current price of a 6.5 % annual coupon bond, with a \$1,000 face value which matures in 3 years. Assume a required return of 15%. 0 1 2 \$65 3 \$1,065

2-9 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields How Bond Prices Vary with Interest Rates Coupon RateInterest RatePrice of Bond 6.5% 5.1%\$1,038.05 6.5% 6.5%\$1,000.00 6.5% 15.0%\$ 805.93 Notice that the price of a bond decreases with increasing interest rate.

2-10 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields How Bond Prices Vary with Interest Rates

2-11 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Semi-annual coupon payments  Calculate the current price of a 6.5 % semi-annual coupon bond, with a \$1,000 face value which matures in 3 years. Assume a required return of 6%.  Semi-annual coupon payments implies that the annual coupon payment is paid in two equal installments, every six months.  Thus, the time line must be in six-month periods.  And, you need to compute the six-month required return.

2-12 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Semi-annual coupon payments  Calculate the current price of a 6.5 % semi-annual coupon bond, with a \$1,000 face value which matures in 3 years. Assume a required return of 6%. 0 2 4 \$32.50 6 1 3 5 \$1,032.50

2-13 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Notice….  When the coupon rate is equal to the required return, the bond sells at face value [at par].  When the coupon rate is higher than the required return, the bond sells above face value [at a premium].  When the coupon rate is lower than the required return, the bond sells below face value [at a discount].

2-14 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields More terminology  Current Yield: Annual coupon payments divided by bond price.  Yield To Maturity: Interest rate for which the present value of the bond’s payments equal the price.  Rate of Return: Earnings per period per dollar invested.

2-15 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Current Yield  Current Yield = Coupon Payments Bond Price  You are buying a bond with:  Coupon Payments = \$100 per year.  Price of \$1,136.16. Current Yield = \$100 = 0.088 = 8.8% \$1,136.16

2-16 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Yield to Maturity  Yield to maturity is defined as the discount rate which makes the PV of the bond’s cash flows equal to its price.

2-17 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Yield to Maturity  A 3-year, 10% annual coupon bond, with a face value of \$1,000 sells for \$1,136.16. Solving for r, we calculate the YTM to be 5%

2-18 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields When Price = \$1,136.16 the discount rate = 5% (ytm is 5%)

2-19 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Rate of Return  You buy a \$1,000 par, 3-year, 10% annual coupon bond for \$1,136.16. One year later, you sell it for \$1,130. Rate of return = coupon income + price change investment = \$100 + (\$1,130 - \$1,136.16) \$1,136.16 = 0.083 = 8.3%

2-20 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Interest Rate Risk  Interest rate risk is the risk in bond prices due to fluctuations in interest rates.  Different bonds are affected differently by interest rate changes.

2-21 Copyright © 2006 McGraw Hill Ryerson Limited Interest Rate Risk 3 yr bond 30 yr bond When the interest rate equals the 6.5% coupon rate, both bonds sell at face value

2-22 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Default Risk  Both corporations and the Government of Canada borrow money by issuing bonds.  Corporate borrowers can run out of cash and default on their borrowings.  The Government of Canada cannot default – it just prints more money to cover its debts.

2-23 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Default Risk  Default risk (or credit risk) is the risk that a bond issuer may default on its bonds.  The default premium or credit spread is the difference between the promised yield on a corporate bond and the yield on a Canada bond with the same coupon and maturity.

2-24 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Default Risk  The safety of a corporate bond can be judged from its bond rating.  Bond ratings are provided by companies such as:  Dominion Bond Rating Service (DBRS).  Moody’s.  Standard and Poor’s.

2-25 Copyright © 2006 McGraw Hill Ryerson Limited Bond Prices and Yields Default Risk  Bonds rated BBB and above are called investment grade bonds.  Bonds rated BB and below are called speculative grade, high yield, or junk bonds.

2-26 Copyright © 2006 McGraw Hill Ryerson Limited Summary of Chapter 5  Cou pon rate is the bond’s coupon divided by its face value.  Current yield is the bond’s coupon divided by its current price.  Yield to maturity measures the average return to an investor who purchases the bond and holds it until maturity.  Bond prices and yield to maturity vary inversely.

2-27 Copyright © 2006 McGraw Hill Ryerson Limited Summary of Chapter 5  Bond prices fluctuate in response to changes in interest rates. This risk of price change is called interest rate risk.  Long term bonds have greater interest rate risk than short term bonds.  Investors use bond ratings to determine the risk of default on a bond.  The additional return that investors demand for bearing credit risk is called the default premium.