Bond Valuation
Economics 71a: Spring 2007
Mayo Chapter 13
Lecture notes 4.4
Goals
Easy valuation
Present values
Yield
Yield to maturity
Difficult issues
Interest rates
Defaults
Call options
Present Values and Bonds
Bond example:
Par = 1000
Coupon = 5% = $50 (per year)
Required return, k = 7%
Maturity = 3 years
Bond Example
Present Value
50 50 1050
PV =
2
1.07 1.07 1.07 3
PV = 947.51
Bond Pricing
Bonds tradeat a given price
May be above or below your valuation
Strategy
Buy if price present value
Yield
Interest/Price
Example
Par = 1000
Coupon = 5%
Current price = 900
Yield = 50/900 = 5.56%
Yield to Maturity
Required return to get get PV = Price
Similar to internal rate of return
Requires computer
Yield to Maturity
50 50 1050
900 =
2
(1 + k) (1 k) (1 k) 3
k = 8.02%
Semiannual Interest
Pays every 6 months
Par = 1000
Coupon = 5%, pays (1/2)50 = 25 every
6 months
Maturity = 3 years
k = 8% (k per 6 months = 4%)
Semi-annual Bond
5
25 1025
PV =
i1
i
(1 + 0.04) (1 0.04) 6
PV = 921.37
Goals
Easy valuation
Present values
Yield
Yield to maturity
Difficult issues
Interest rates
Defaults
Call
Interest Rates
k = RF + RP
RF = risk free rate
RF rises
Bond price falls
RF falls
Bond price rises
Sensitivity to interest changes =
“Duration”
Bond Prices and Duration
Two bonds: 1 and 5 year zero coupon
RP = 0 (government bond)
Interest rate change 3% to 5%
1 year bond
Price = 970.87 -> 952.38
5 year bond
Price = 862.61 -> 783.53
Longer maturity leads to more interest
sensitivity
The Term Structure
Different rates for different horizons
6 month
1 year
2 years
5 years
10 years
30 years
Yield Curve
Interest Rate
Annual %
5%
1 2 5 10 20
Years into future
Time of maturity
The Yield Curve
The yield curve changes over time
See “The living yield curve” website
Inverted yield curves
The yield curve and GDP
Bond Example
Present Value
50 50 1050
P=
2
(1+ k1 ) (1 k 2 ) (1 k 3 ) 3
Defaults
When bond defaults, investors get firm assets
(likely zero)
Probability related to bond rating
Risk premium increases with probability of
default
k = RF + RP
Higher default probability
Higher RP
Lower price
Call Option
Definition
Option that lets firm buy back bond
Get paid par + some percentage
Shuts down bond investment
refinancing
Similar to
Depends on interest movements
Impacts price, but difficult to value
Final Thoughts on Bonds
Stable income streams
Easier to evaluate than stocks
More structure
Fewer hunches
Easier forsophisticated professionals to
have an edge
Stocks are more guesswork