Bond Valuation Chapter 7

What is a bond? 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.

Key Features of a Bond Par value – face amount of the bond, which is paid at maturity (assume $1,000). Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest. Maturity date – years until the bond must be repaid. Issue date – when the bond was issued. Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”).

Determining the Price of a Bond The Bond Valuation Formula The price of a bond is the present value of a stream of interest payments plus the present value of the principal payment. P B = PV(Interest Payments) + PV(Principal Payment)

Bond Prices Bond ABond BBond C Maturity10 Years Coupon Rate13%10%7% Face Value$1000 What is the current price of each bond if the interest rate is 10% ? What is the current price of each bond if the interest rate is 7% ?

Bond Price Characteristics Relationship #1: The value (price) of a bond is inversely related to changes in interest rates (and ytm). Rates  … Price  Rates  … Price 

Bond Price Characteristics Relationship #2: Price (P b ) will be M if c >ytm.  A bond where P b > M is a premium bond.  A bond where P b < M is a discount bond.  A bond where P b = M is a par bond

Bond Price Characteristics Relationship #3: As the maturity date approaches, P b converges to M.  P b increases with maturity if c < ytm.  P b decreases with maturity if c > ytm.

Bond Price Characteristics Example: Assume that the interest rate is 8%. Calculate the price of the following two bonds assuming 20 years to maturity and 1 year to maturity. Bond A Bond B Par Value (M)$1,000 $1,000 Coupon Rate (c)3% 10%

Bond Price Characteristics

Relationship #4:  Long term bond prices are more sensitive to changes in interest rates than are short term bond prices.

Semi-Annual Bonds Multiply years by 2 Divide interest rate by 2 Divide annual coupon by 2 Example: What is the value of a 10-year, 10% semiannual coupon bond, if the interest rate is 13%?

Computing Yield to Maturity Yield to Maturity (YTM) is the rate implied by the current bond price Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)

YTM with Annual Coupons Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. The current price is $ Will the yield be more or less than 10%?

YTM with Semiannual Coupons Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1, Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there? What is the YTM?

Current Yield vs. Yield to Maturity Current Yield = annual coupon / price Yield to maturity = current yield + capital gains yield Example: 10% coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $1, price What is the Current yield? What is the YTM? What is the price of the bond in one year, assuming no change in YTM? What is the Capital gains yield?

The Bond Indenture Contract between the company and the bondholders that includes The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions Call provisions Details of protective covenants

Types of Corporate bonds Mortgage bonds Debentures Subordinated debentures Investment-grade bonds Junk bonds

Government Bonds Treasury Securities Federal government debt 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 Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level

Zero Coupon Bonds 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 Cannot sell for more than par value Treasury Bills and principal-only Treasury strips are good examples of zeroes