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Bond Valuation

Bond Valuation. January 30 th 2007 Erica Berczynski Peter Huang. Question 1. When would you have a premium on a bond? When coupon rate > internal rate of return When interest rate > internal rate of return When the bond matures in > 10 years When the bond’s redemption value > 1,000.

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Bond Valuation

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  1. Bond Valuation January 30th 2007 Erica Berczynski Peter Huang

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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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, 2005. • $961.07 • $964.90 • $1,035.85 • $1,039.85

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

  9. 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, 2005. 8/15/01 2/15/02 8/15/02 2/15/03 8/15/03 2/15/04 8/15/04 2/15/05 8/15/05 $35 $35 $35 $35 $35 $35 $35 $1,035 Price

  10. Simple Bond Problem Equation: Calc Keys: N=8, I/Y=3, PMT=35, FV=1000 8/15/01 2/15/02 8/15/02 2/15/03 8/15/03 2/15/04 8/15/04 2/15/05 8/15/05 $35 $35 $35 $35 $35 $35 $35 $1,035 Price 35 1.03 35 (1.03)2 35 (1.03)3 35 (1.03)4 1,035 (1.03)8 Price = + + + + . . . +

  11. Accrued Interest Bond Problem • The 3rd 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.

  12. Accrued Interest Bond Problem • 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 $973.35 Calculator key: N=6 I/Y=3.5 PMT=30 FV= 1000 CPT PV= 973.35 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: 2nd 9. SDT= 2.2807, CPN=6, RDT= 2.1510, RV=100, 360, 2/y, yld= 7, CPT Price= $973.61, CPT AI= $2.17

  13. 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 P (1+Yld/2)2n Ct (1+Yld/2)n 2n ∑ + i=1

  14. 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.

  15. Any Questions?

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