LONG-TERM DEBT
A major source of financing for companies is long-term debt. Some of the terminology
associated with debt should be distinguished first.

Indenture – The indenture to a bond issue is the actual contract that delineates the
obligations of the borrow, the rights of the lender, and the actions to be taken in the event of
default. In short, if it is not in the indenture, it does not apply. The indenture will state the
interest that must be paid (and when) as well as the principal payments. Oftentimes, the
indenture will include restrictive, or negative, covenants designed to protect the lenders. For
instance, the firm may be required to maintain a minimum current ratio or quick ratio, set a
maximum for the debt ratio, or restrict dividend payments as long as the specific debt is
outstanding. Violating any of these covenants is a technical default and the debt can
become immediately due and payable upon such default.

Debenture – Most long-term bonds of corporations are debentures which are not secured
by the pledge of any specific asset. Rather, they are secured by the general assets of the
firm.

Subordinated Bonds – A subordinated bond is one that is made secondary to the claims of
some other obligation. For instance, a mortgage bond is one that is secured by the pledge
of specific real property (land and buildings). In the event of bankruptcy, the property
securing the mortgage bond is sold. If the property is sold form more than the amount of
mortgage debt, the extra money goes toward paying off other obligations. If there is
insufficient funds to pay off the mortgage balance, any amount that remains unpaid
becomes a general claim against other assets. Hence, a debenture is subordinated to a
mortgage bond. A debenture can also be subordinated to other debentures and would be
referred to as a junior debenture.

Call Provision – A call provision gives the company the right to recall the bonds (buy them
back) at a stated price, the call price. The call price is composed of par plus a call premium.
If a bond has a call provision, how would you find out about it? Look in the indenture. As an
investor, would you like to see a call provision on a bond? No. If interest rates fall, the
company is likely to recall the bond issue and issue a new bond at the lower rate of interest.
Consequently, the investor who had a good investment (one that paid a higher rate of
interest than the new market rate) loses it and must reinvest the cash at lower interest rates.
Typically, a bond with a call provision will not be callable in the first few years.

Sinking Fund Provision – A sinking fund provision is used to provide for the orderly
retirement of a bond issue. A sinking fund provision will require that regular payments be
made to a trustee. For example, if a firm issued $50 million of 30-year bonds with a sinking
fund provision, it would be typical if no payment were required in the first five years, but then
an annual payment of $2 million would have to be made for the remaining 25 years of the
bond issue’s life so that the $50 million would have accumulated by the time the bonds
matured. The trustee could then invest the money (so that, actually, an amount less than $2
million per year would be needed since interest would be earned), or use the proceeds to
retire outstanding bonds. The bonds could be retired through a lottery process if they were
callable (since each bond has a unique serial number), or the trustee could buy them in the
open market. Buying them in the open market would be advantageous if interest rates had
risen since they could then be bought at a discount to par value (as shown below in the
valuation of bonds). This would also put upward pressure on the bond’s price and perhaps
help keep the firm’s cost of debt slightly lower. Would an investor like to see a sinking fund
provision? Yes, because it provides more assurance that the principal will be repaid by the
company.

Income Bond – An income bond only pays interest if the corporate income exceeds a
certain dollar level. Typically, an income bond is issued during a financial reorganization of
a company near bankruptcy. It will formalize past due obligations without forcing the
company into bankruptcy if income is low (which is likely since it is trying to turn itself around
anyway). Income bonds are generally cumulative (that is, unpaid interest accumulates and
must be paid in the future when the company has sufficient liquidity) and typically are
convertible into common stock.

Ratings Agencies – Many companies pay ratings agencies to rate their outstanding bonds.
The most well-known of the agencies is Moody’s and Standard and Poor’s, although other
agencies exist but tend to specialize in the type of bond that they will rate.
Advantages of Debt to the Bondholder



The risk is reduced – the bondholder receives fixed income and there is a definite maturity
when the principal is to be repaid.
The bondholder has a prior claim to income over stockholders.
The bondholder has a prior claim in the event of liquidation of the firm.
Disadvantages of Debt to the Bondholder


The bondholder has no vote and, hence, no say in how the company is run.
The bondholder does not participate in the growth of the company.
Advantages of Debt to the Company




The cost is limited and known and cheaper than the cost of equity (because it is less risky to
the investor who therefore requires a lower required rate of return).
The interest is tax-deductible, unlike dividend payments, which makes the cost even
cheaper in comparison to equity.
There is no dilution of control when debt is issued.
The debt can be terminated (if a call provision was included).
Disadvantages of Debt to the Company


There is always the possibility of default if income is low. The company must pay interest,
even if it means taking out additional debt to do so.
The cost of equity rises as more debt is used. The higher leverage results in higher risk to
shareholders who will require a higher rate of return.
Bond Valuation
The easiest thing to value (conceptually) is a bond since the promised cash flows are
known with certainty.
Consider a bond that pays a 10% coupon (or stated) rate of interest, has a par (or stated
or face) value of $1,000 and matures in 5 years. Suppose also that the market rate of interest
for such a bond (i.e., your required rate of return, r) is 8%. Thus,
Par = $1,000
Coupon Rate = 10%
Maturity = 5 years
r = 8%
The cash flows that are promised by the company include interest payments of $100 per
year (although most corporate bonds pay interest semi-annually, we will assume annual
payments—we have already seen how to adjust for semi-annual cash flows) for five years and
the payment of the face value (stated, or par, value) of $1,000 at the end of five years.
0
1
2
3
4
100
100
100
100
5
100
1,000
1,100
PVIFA 8%,4 = 3.3121
331.21
PVIF 8%,5 = .6806
748.66
$1,079.87
On your calculator,
PMT = 100
FV = 1,000
N=5
I/Y = 8
PV = ?????? = 1,079.87 (ignoring the negative sign for an investment)
The value of the bond is $1,079.87 which is selling at a premium relative to the par value
of $1,000. (A bond selling at less than par is said to be selling at a discount.)
What does the premium represent? As we saw when we looked at present values, it
represents the present value of the additional interest of $20 per year (because it pays $100 in
interest when we only require $80 for a $1,000 investment ($20 * 3.9927 = $79.85 with two
cents rounding error). Any time the market rate of interest is less than the coupon rate of
interest, the bond will sell at a premium. Similarly, when market rates of interest are greater
than the coupon rate, the bond will sell at a discount. Recall from economics that, when interest
rates go up, bond prices go down, and when interest rates go down, bond prices go up. This is
a consequence of the mathematics of present value calculations.
Suppose we purchase the bond for $1,079.87. After one year, we collect $100 in
interest. The $100 represents a 9.26% return on our investment of $1,079.87, not an 8% rate of
return. What are we ignoring?
The 9.26% is referred to as the current yield (as in accounting, where “current” refers to
within one year). What is being ignored is the fact that we paid a premium for the bond which,
at maturity will be worth only $1,000. Thus, over the five years to maturity, the value of the bond
will decrease. Let’s look at what the bond will be worth one year from now. In one year, there
will only be four years left to maturity:
0
1
2
3
4
100
100
100
100
1,000
PVIFA 8%,4 = 3.3121
331.21
PVIF 8%,4 = .7350
735.00
$1,066.21
On your calculator,
PMT = 100
FV = 1,000
N=4
I/Y = 8
PV = ?????? = $1,066.21
Note that this time, the interest payment in the last year was included as a part of the
present value of an annuity calculation while the par value was discounted as a lump sum of
$1,000. As indicated, the value of the bond when only four years to maturity remain is only
$1,066.21. This is a decrease in value of $13.66. When expressed as a percentage of the
original value of $1079.87, this represents a loss of 1.26%. The total return of 8% that we built
into our valuation when the bond had five years left to maturity is comprised of two components:
Total Yield = Current Yield + Capital Gain Yield
Current Yield = One Year’s Interest/Current Price
Total Yield = 9.26% + <1.26%>
= 8.00%
Note that the premium for the four-year bond is smaller than the premium for the fiveyear bond since we are only paying for four years’ worth of additional interest payments.
Bond Maturities & Premiums/Discounts
If a five-year bond sells at a premium of $1,079.87, what do you think the premium for a
ten-year bond will be? (Recall that the premium is the present value of the additional amount of
interest being paid.) A ten-year 10%, $1,000 par value bond should sell at a larger premium
since we are paying for ten years’ worth of an extra $20 per year of interest. For example,
Par = $1,000
Coupon Rate = 10%
Maturity = 10 years
K = 8%
0
1
100
2
3
4
5
6
7
8
9
100
100
100
100
100
100
100
100
PVIFA 8%,10 = 6.7101
10
100
1,000
671.01
PVIF 8%,10 = .4632
$ 463.20
$1,134.21
On your calculator,
PMT = 100
FV = 1,000
N = 10
I/Y = 8
PV = ?????? = $1,134.21
As was expected, the additional five years’ worth of an extra $20 per year in interest
payments results in a larger premium for a ten-year bond relative to a five-year bond.
Sensitivity to Changes in Interest Rates
As we determined previously, as interest rates fall, bond prices rise. Which type of bond
rises more, short-term or long-term bonds? (Hint: Do we really care what interest rates do
today for a bond that matures tomorrow?)
Suppose that interest rates fall from 8% to 6%. Let’s see what happens to the values of
our five-year and ten-year bond prices.
0
1
2
3
4
5
100
100
100
100
100
1,000
PVIFA 6%,5 = 4.2124
421.24
PVIF 6%,5 = .7473
747.30
$1,168.54
On your calculator,
PMT = 100
FV = 1,000
N=5
I/Y = 6
PV = ?????? = $1,168.54
The value of the five-year bond has increased from $1,079.87 to $1,168.54 or $88.67
due to the fall in market rates of interest from 8% to 6%. The $88.67 increase in price
represents an 8.2% appreciation relative to its original value.
The ten-year bond’s increase in price is calculated in the following manner:
0
1
100
2
3
4
5
6
7
8
9
100
100
100
100
100
100
100
100
PVIFA 6%,10 = 7.3601
10
100
1,000
736.01
PVIF 6%,10 = .5584
$ 558.40
$1,294.41
On your calculator,
PMT = 100
FV = 1,000
N = 10
I/Y = 6
PV = ?????? = $1,294.41
The increase in price for the ten year bond amounts to $160.20 or 14.1%. Why do we
calculate the change in price as a percent of its original value?
The reason the change in price is much larger for a long-term bond is due to the fact that
the longer period of time for compounding has a more pronounced effect on the ten-year bond
than it does on a five-year bond since, on average, the five-year bond is generating cash flows
much sooner than the ten-year bond. If long-term bonds are more sensitive to changes in
interest rates than short-term bonds, can you guess whether a high coupon bond or a low
coupon bond is more sensitive to changes in interest rates? (See Handout #2.)
The equation for the value of a bond can be written as follows:
N
Bond Value  
t 1
Interest
Par

t
(1  rd )
(1  rd ) N
 Interest * (PVIFA)  Par * (PVIF)
 Present Value of the Interest Payments  Present Value of the Par
Perpetuities
There is a type of bond that never matures called a perpetuity, or a consol. (The term
“consol” comes from the fact that the first perpetuities were issued by the British government
following the Napoleonic Wars to “consolidate” their war debts.) Canada issued some
perpetuities in the late 1970s. If long-term bonds are more sensitive to changes in interest rates
than short-term bonds, what type of bond is the most sensitive to interest rate changes? (A
consol, of course.)
When N is infinity, the value of a perpetual bond reduces to
Value of a Perpetuity 
Interest
rd
While there are not a lot of perpetuities that trade in the marketplace, there is a financial
security which is, essentially, a perpetuity. Do you know what security pays a constant dollar
amount each year and never matures?