bond valuation january 30 th 2007 erica berczynski peter huang
TRANSCRIPT
Bond Valuation
January 30th 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, 2005.
a) $961.07b) $964.90c) $1,035.85d) $1,039.85
Bond Valuation Equation
∑ Ct
(1+Yld/2)ni=1
2n
+P
(1+Yld/2)2n
Where:C = coupon paymentYld = annual internal rate of returnn = periodP = 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, 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
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
351.03
35(1.03)2
35(1.03)3
35(1.03)4
1,035(1.03)8
+ . . . ++ + +Price =
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.
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 $973.35Calculator key: N=6 I/Y=3.5 PMT=30 FV= 1000 CPT PV= 973.35With 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
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
∑ Ct
(1+Yld/2)ni=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?