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?