



A borrowing arrangement where the borrower
issues an IOU to the investor. 







Treasury Bonds and Notes 

Corporate Bonds 

Other Issuers 

State and Local Governments (Munis) 

Government Agencies 




Callable Bonds 

Convertible Bonds 

Puttable Bonds 

Floating Rate Bonds 

Preferred Stock 




Allows the issuer to repurchase the bond at a
specified price (call price) before
the maturity date. 

Frequently, there is a period of call
protection, during which the bonds cannot be called. Such bonds are called deferred callable
bonds. 




Bondholders get the option to exchange each bond
for a specified number of shares of stock for each bond (conversion ratio). 

Example: 

Bond selling at 990; convertible into 40 shares. 

Current share price = $20; value of converted
shares = $800 (conversion value)  conversion suboptimal 

Conversion premium = $990  800 = $190. 




The put bond gives the investor the option to
extend or retire the bond at the call date. 

If the bond’s coupon rate exceeds market yields,
the bondholder will choose to extend 

If the bond’s coupon rate is too low, it will be
optimal to retire the bond and reinvest the proceeds at current yields. 




Interest payments are tied to some measure of
current market rates. E.g., the
rate might be adjusted annually to Prime plus 2%. 

However, payments are not adjusted for changes
in the firm’s financial condition. 

The risk to the firm is that the yield spread is
fixed over the life of the bond. 





Preferred stock is equity, because: 

dividends are paid at the firm’s discretion 

payment priority at liquidation is below all
bonds. 

It resembles debt because: 

Dividend amounts are fixed, and potentially 

adjustable like coupon payments. 





Corporate bonds are subject to potential
default. Therefore, the promised yield is the maximum possible yield to
maturity of the bond, not necessarily the actual yield to maturity. 

To compensate investors for the possibility of
bankruptcy, a corporate bond must offer a default premium, a differential
between the promised yield and the expected yield to maturity. 

The default premium depends on : 

the probability of default 

the likely loss in the event of default. 




Assume 

the probability of default, p, is constant from
year to year, 

the loss on a bond that defaults equals a
proportion l of the bond's market price in the previous year 

y = the promised yieldtomaturity 

y* = the expected yieldtomaturity 

d = y  y* = default premium 




Risky bonds may also have to provide a risk
premium. 

The risk premium is the difference between the
expected yield and the yield on a comparable defaultfree Tbond. 

A risk premium is needed only if the bond risk
is not diversifiable. 




Sinking Funds 

Limitations on Further Debt issuance 

Subordination of Further Debt 

Negative Pledge 

Dividend Restrictions 

Collateral 

Restrictions on Sale and Leaseback 




A Tperiod bond with coupon payments of $C per
period and a face value of F. 







The value of this bond can be computed as the
sum of the present value of the annuity component of the bond plus the
present value of the FV. 




Normally, bonds pay semiannual coupons: 





The bond value is given by: 



where the first component is, once again, the
present value of an annuity, and y is the bond’s yieldtomaturity. 




If F = $100,000; T = 8 years; the coupon rate is
10%, and the bond’s yieldtomaturity is 8.8%, the bond's price is computed
as: 







= $106,789.52 






Consider a 2 year, 10% coupon bond with a $1000
face value. If the bond yield is
8.8%, the price is 50 +
1000/(1.044)^{4} = 1021.58. 

Now suppose the market bond yield drops to
7.8%. The market price is now given
by 50 + 1000/(1.039)^{4}
= 1040.02. 



As the bond yield drops, the bond price rises,
and viceversa. 





Yield to Maturity
A measure of the average rate of return on a bond if held to
maturity. To compute it, we define
the length of a period as 6 months, and then calculate the internal rate of
return per period. Finally, we
double the sixmonthly IRR to get the bond equivalent yield, or yield to
maturity. 

Effective Annual Yield
Take the sixmonthly IRR and annualize it by compounding. 




An 8% coupon, 30year bond is selling at
$1276.76. First solve the following
equation: 





This equation is solved by r = 0.03. 



The yieldtomaturity is given by 2 x 0.03 = 6% 

The effective annual yield is given by (1.03)^{2}
 1 = 6.09% 




A 3 year, 8% coupon, $1000 bond, selling for
$949.22 

Period Cash flow Present Value 

9%
11% 10% 

1
40 $38.28 $37.91 $38.10 

2
40 $36.63 $35.94 $36.28 

3
40 $35.05 $34.06 $34.55 

4
40 $33.54 $32.29 $32.91 

5
40 $32.10 $30.61 $31.34 

6 1040 $798.61 $754.26
$776.06 

Total $974.21 $925.07 $949.24 

The bond is selling at a discount; hence the
yield exceeds the coupon rate. At a
discount rate equal to the coupon rate of 8%, the price would be 1000. Hence try a discount rate of 9%. At 9%, the PV is 974.21, which is too
high. Try a higher discount rate of 11%, with a PV of $925.07, which is too
low. Trying 10%, which is between
9% and 11%, the PV is exactly equal to the price. Hence the bond yield = 10%. 





If a bond is selling at par, yield = coupon
rate. If the bond sells at a
discount, yield > coupon rate.
Hence the following approximation: 






The YieldtoMaturity measure implicitly assumes
that all coupons can be invested at the internal rate of return. 

An alternative expost yield measure can be
computed that takes the actual reinvestment rates. 




The holding period return differs from the
previous two measures in that it is computed for the actual period of time
that the bond is held. 

Example:
If a bond is purchased for $1100, pays a coupon of $120 at the end of the
year, and is then sold for $1210, the holding period return = (120 +
12101100)/1100 = 20.91% 




Bonds, like any other asset, represent an
investment by the bondholder. 

As such, the bondholder expects a certain total
return by way of capital appreciation and coupon yield. 

This implies a particular pattern of bond price
movement over time. 





Coupons are paid semiannually. Hence the bond price would increase at
the required rate of return between coupon dates. 

On the coupon payment date, the bond price would
drop by an amount equal to the coupon payment. 

To prevent changes in the quoted price in the
absence of yield changes, the price quoted excludes the amount of the
accrued coupon. 

Example: An 8% coupon bond quoted at 96 5/32 on
March 31, 1996 would actually require payment of 961.5625 + 0.5(80/2) =
$981.5625 




The price appreciation on original issue
discount (OID) bonds is an implicit interest payment. Hence the IRS calculates a price
appreciation and imputes taxable interest income. Additional gains or losses due to market yield changes are
treated as capital gains. 

Example: An 8% 30 yr. bond issued at 81.071% of
par is sold for 820.95 at the end of the year. If interest income is taxed at 36% and capital gains at 28%,
the tax paid equals 0.36(80 + 811.80  810.71) + 0.28(820.95811.80) =
$31.75.
(YTM at issue = 10%; yearend price using this YTM = 811.80) 
