Bond Valuation January 30 th 2007 Erica Berczynski Peter Huang

Question 1 When would you have a premium on a bond? a) When coupon rate > internal rate of return b) When interest rate > internal rate of return c) When the bond matures in > 10 years d) When the bond’s redemption value > 1,000

Bonds What is a corporate bond? – Fixed-income security that represents the long-term debt of a company – Normally pay semi-annual coupons and have a single maturity date – Government Bonds: debt of the federal government backed by the US Treasury; considered risk-free – Municipal Bonds: debt of state and local government; tax-free at the federal and state level

Corporate Bonds Callable Bonds – a bond in which the issuer reserves the right to pay off the bond early – Can be called after a specified date, usually at a higher redemption value Junk Bonds – a high-yield bond with a low or no rating – Usually have a high default rate

Definitions Coupons  set interest payment a company makes semi-annually to a bondholder Principal  face value of bond; coupons are determined from this value; most commonly paid at maturity date Maturity Date  date at which final principal payment is made

More Definitions Yield  internal rate of return on the bond Par  when a bond sells for its face value Premium  when a bond sells for more than its face value – When coupon rate > internal rate of return Discount  when a bond sells for less than its face value – When coupon rate < internal rate of return

Question 2 What is the price of a bond on August 15, 2001 if there is a 6% internal rate of return and 5% semi-annual coupon payments. The bond matures on August 15, a) $ b) $ c) $1, d) $1,039.85

Bond Valuation Equation ∑ C t (1+Yld/2) n i=1 2n + P (1+Yld/2) 2n Where: C = coupon payment Yld = annual internal rate of return n = period P = principal

Simple Bond Problem What is the price of a bond on August 15, 2001 with 7% semi-annual coupon payments and a 6% internal rate of return. The bond matures on August 15, /15/012/15/028/15/022/15/038/15/032/15/048/15/042/15/058/15/05 $35 $1,035 Price

Simple Bond Problem Equation: Calc Keys: N=8, I/Y=3, PMT=35, FV=1000 8/15/012/15/028/15/022/15/038/15/032/15/048/15/042/15/058/15/05 $35 $1,035 Price (1.03) 2 35 (1.03) 3 35 (1.03) 4 1,035 (1.03) Price =

Accrued Interest Bond Problem The 3 rd row key in your calculator only works if you are trading your bond on a coupon date. If you are buying or selling the bond on a non- coupon date. You need to take in consideration of accrued interest. Note: Corporate bond’s accrued interest is calculated on a 360 days basis.

For example…. A $1,000 face value bond with 6% coupon matures on 2/15/2010. You purchase the bond on 2/28/2007. Assume 7% interest rate. What is the price of the bond? What is the accrued interest? If it were traded on 2/15/2007. The bond would be priced at $ Calculator key: N=6 I/Y=3.5 PMT=30 FV= 1000 CPT PV= With no accrued interest However, the bond is traded on 2/28/2007. To do this, we need to use the bond worksheet. Calculator keys: 2 nd 9. SDT= , CPN=6, RDT= , RV=100, 360, 2/y, yld= 7, CPT Price= $973.61, CPT AI= $2.17 Accrued Interest Bond Problem

Risk Structure of a Bond There are 6 primary attributes that are significant in determining the return or yield of a bond: Term to maturity Coupon Rate Call Provisions Liquidity Risk of Default Tax Status ∑ C t (1+Yld/2) n i=1 2n + P (1+Yld/2) 2n

Risk Structure of a Bond Risk Premium – difference between yield-to-maturity and the expected yield-to-maturity of a risk-free bond Default Premium – difference between yield-to-maturity and the promised yield-to-maturity Promised Yield to maturity: the YTM calculated on the assumption that coupon and principal payments will be paid in full on the dates specified by the bond. Expected Yield to Maturity: The YTM adjusted for the probability that not all coupon and principal payments will be paid in full on the dates specified by the bond.

Any Questions?