Time Value of Money and Bond Valuation Please respond to the foll.docx

"Time Value of Money and Bond Valuation" Please respond to
the following:
Examine the concept of time value of money in relation to
corporate managers. Propose two (2) methods in which time
value of money can help corporate managers in general.
Examine the pros and cons of a sinking fund from the viewpoint
of both a firm and its bondholders. Determine the fundamental
manner in which this knowledge could be helpful to a financial
manager. Provide a rationale for your response.
FIN 534 Week 3 Part 1: Time Value of Money
Slide 1
Introduction
Welcome to Financial Management. In this lesson we will
discuss the time value of money.
Next slide
Slide 2
Topics
The following topics will be covered in this lesson:
Timelines;
Future values;
Present values;
Finding the interest rate, I;
Finding the number of years, N;
Annuities;
Future value of an ordinary annuity;
Future value of an annuity due;
Present value of ordinary annuities and annuities due;
Finding annuity payments, periods, and interest rates;
Perpetuities;
Uneven, or irregular, cash flows;

Future value of an uneven cash flow stream;
Solving for I with irregular cash flows;
Semiannual and other compounding periods;
Fractional time periods;
Amortized loans; and,
Growing annuities.
Next slide
Slide 3
Timelines
Recall, the primary objective of financial management is to
maximize the value of the firm’s stock.
Moreover, the value of the firm’s stock depends in part on the
timing of the cash flows investors expect to receive from
investing in the firm.
Hence, it is very important that the financial manager have an
understanding of the time value of money and how it impacts
the firm’s stock price.
Time value of money is also referred to as discounted cash
flow, or DCF, analysis.
As we study this concept it is important to remember that there
is no other concept in finance that is more important than time
value of money or DCF.
When we analyze time value of money it is important to draw a
timeline because this helps us visualize what is happening in a
particular problem and helps us solve the problem. Consider the
timeline shown on the slide.
Time zero is today;
Time one is one from today, or the end of period one;

Time two is two time periods from today, or the end of period
two and so on.
Many times the periods are measured in years, but that is not a
requirement.
Time can be measured in semiannual periods, quarters, months,
or days.
Look that time period one.
The tick mark at time one represents the end of period one and
it also represents the beginning of time two since time one has
just passed.
Cash flows are placed directly underneath the tick marks.
Suppose a lump sum or single amount of cash outflow in the
amount of one hundred dollars is invested at time zero.
The five percent is the interest rate for each of the three time
periods.
Look at time period three.
At time three the cash flow is unknown.
Note that in time periods one and two there are no cash flows
and the interest rate is constant for all three time periods.
Next slide
Slide 4
Future Values
A dollar today is worth more than a dollar in the future

primarily because of inflation.
We refer to the value of a dollar today as present value or PV.
If we invest money today at some interest rate we refer to the
value received in the future as the future value or FV.
The process of going from present value to future value is
referred to as compounding.
I is the interest rate the bank pays on the account each year.
INT is the dollar amount of interest earned during the year. We
calculate this amount by multiplying the beginning amount by I.
Therefore, INT equals PV times I.
FV sub N is the future value, or ending amount, in the account
at the end of N years.
PV is the value today but FV sub N is the value N years in the
future after the interest earned is added to the account.
There are four ways we can solve this problem.
First we can use a step by step approach.
This method requires that we calculate the future value for each
year and then sum the results.
The second method we can use is called the formula approach.
The formula approach uses a mathematical equation to solve
time value of money problems.
In general, FV sub N equals PV times one plus I raised to the N
th

power.
Next we can use a financial calculator to solve time valued
money problems.
Financial calculators have five keys corresponding to the five
variables in the time value equations:
Specifically, N is the number of time periods;
I divided by YR is the interest rate per period;
PV is the present value and since we began by making a deposit
this number is an outflow and must have a minus sign in front
of it;
PMT is the payment –this key is used only if there is a series of
equal payments; in our example this value should be entered as
a zero; and
FV is future value which is automatically determined by the
calculator.
The last method we can use to solve a time value of money
problem is an Excel spreadsheet.
To calculate future value we locate the FV function which is
given by FV.
This formula calculates the FV.
We can set up this formula by using either numbers or cell
references from an Excel spreadsheet and the results are the
same.
Using spreadsheets to solve a time value money problems has

two advantages over the other methods.
First, it is easy to verify the inputs.
Second the analysis is more transparent.
Recall when interest is earned on interest earned in prior
periods it is referred to as compound interest.
If instead interest is earned solely on the principal it is referred
to as simple interest.
Mathematically with simple interest is total interest is given by
PV times I times N or principal times interest times the number
of time periods.
Then the future value equals PV plus PV times I times N.
Next slide
Slide 5
Present Values
Present value is the opposite of future value.
To see that this is true consider the following example. Assume
we have money to invest and a broker offers to sell us a bond
that pays one hundred fifteen dollars and seventy-six cents in
three years.
Assume that banks offer a three year certificate of deposit, or
CD, at five percent and if you don’t purchase the bond you’ll
purchase the CD.
The five percent paid on the CD is called the opportunity cost
or the rate of return we would earn on a different investment of
similar risk.

We want to know how much we should pay for the bond today.
To determine this amount we must calculate the present value
which means we are discounting a future sum.
Recall, to find FV we use the formula FV sub N equals PV
times the quantity one plus I raised to the Nth power.
To find the PV we rearrange the formula and find that PV
equals FV sub N divided by the quantity one plus I raised to the
N
th
power.
We know FV sub N equals one hundred fifteen dollars and
seventy-six cents and I equals five percent.
Then PV equals one hundred fifteen dollars and seventy-six
cents divided by one point zero five cubed which equals one
hundred dollars.
This amount is referred to as the fair price of the bond.
If we could purchase the bond for less than one hundred dollars
we should buy the bond instead of the CD.
If we must pay more than one hundred dollars for the bond we
should purchase the CD.
If the price of the bond is exactly one hundred dollars we are in
different between the bond and the CD.
The one hundred dollars is the present value of one hundred
fifteen dollars and seventy-six cents due in three years when the
interest rate is five percent.

It is important to remember that time value of money problems
can be solved using more than one method.
Additionally always keep in mind that the goal of financial
management is to maximize the company’s intrinsic or
fundamental value.
This value is the present value of the firm’s expected future
cash flows.
Next slide
Slide 6
Finding the Interest Rate, I
So far we’ve calculated FV and PV.
But notice that the equation has four variables.
If we know the values of three of the variables we can easily
calculate the fourth.
Note that the variables are PV, FV, I, and N.
Suppose we know the values for TV, FV and N and we want to
find I.
How do we do this?
Now we know PV, FV, N, and must determine I.
To calculate I we solve the following equation: FV equals PV
times the quantity one plus I raised to the Nth power.
We should use either a financial calculator or the RATE
function in Excel to solve the problem since any other method
would prove to be very difficult and very time-consuming.
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Slide 7

Finding the Number of Years, N
Now suppose we have five hundred thousand dollars to invest
when the interest is four point five percent.
We want to calculate how long it will take five hundred
thousand dollars to accumulate to one million dollars.
To determine N we solve the following the equation:
One million dollars equals five hundred thousand dollars times
the quantity one plus zero point zero four five raised to the Nth
power.
We can solve for N by using a financial calculator, the NPER
function in Excel or by working with natural logarithms using
natural logarithms. Regardless of the method used, the result is
the same.
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Slide 8
Annuities
An annuity is a series of equal payments made at fixed
intervals.
If the payments are made at the end of each period the annuity
is called an ordinary annuity or deferred annuity.
If the payments are made at the beginning of each period the
annuity is called an annuity due.
In finance ordinary annuities are more common than annuities
due.
It is important to observe that in the case of an annuity due,
each payment is shifted back one time period.
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Slide 9
Check Your Understanding

Future Value of an Ordinary Annuity
Suppose we have an ordinary annuity where we deposit one
hundred dollars at the end of each year for three years and earn
five percent per year.
We want to calculate the future value of the annuity or FVA sub
N.
To solve for FVA sub N we can use a step by step formula
approach, a financial calculator or the FV function in Excel.
If we use the step by step approach we set up the problem in the
following way:
FVA sub N equals PMT times the quantity one plus I raised to
the N minus one power plus PMT times the quantity one plus I
raise to the N minus two power plus PMT times a quantity one
plus I raised to the N minus three power.
This equation tells us that the first payment earns interest for
two periods, the second for one period, and the third earns no
interest because the payment is made at the end of the annuity’s
life.
It follows that FVA sub N equals one hundred dollars times one
point zero five squared plus one hundred dollars times one point
zero five plus one hundred dollars which equals three hundred
fifteen dollars and twenty-five cents.
In general, the future value of an annuity is given by FVA sub
N equals PMT times the quantity one plus I raised to Nth power
divided by I minus one divided by I.

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Slide 11
Future Value of an Annuity Due
The future value of an annuity due is larger than that of an
ordinary annuity because in the case of an annuity due payments
are made at the beginning of each time period and for this
reason each payment occurs one period earlier and therefore the
payment earns interest for one additional period. These types of
problems are solved by using either a financial calculator where
we set the calculator to begin mode or the FV function in Excel
where we set Type equal to one.
Additionally, FVA sub due equals FVA sub ordinary times the
quantity one plus I.
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Slide 12
Present Value of Ordinary Annuities and Annuities Due
To calculate the present value of an annuity, with PVA sub N
we can use the step by step approach, the formula approach, a
financial calculator, or the spreadsheet method. Let’s look at the
present value of an ordinary annuity.
The PV of an ordinary annuity can be written as PVA sub N
equals PMT times the quantity one divided by I minus I divided
by I times the quantity one plus I raised to the Nth power.
Additionally, we can use a financial calculator or the PV
function in Excel to solve this problem.
If instead we want to calculate PVA sub due we can use the
following formula:
PVA sub due equals PVA sub ordinary times one plus I.

We use this formula because each payment occurs one period
earlier.
Next slide
Slide 13
Finding Annuity Payments, Periods, and Interest Rates
Assume we need ten thousand dollars in five years.
If we earn six percent interest per year on our money.
How much must we deposit to earn this amount?
In other words, we need to calculate PMT.
We know that FV equals ten thousand dollars, PV equals zero,
N equals five and I equals six percent.
We can use either a financial calculator or the PMT function in
Excel to solve this problem.
In the case of an ordinary annuity we would need to deposit
seventeen hundred seventy three dollars and ninety-six cents per
year.
In the case of an annuity due we would need to deposit sixteen
hundred seventy-three dollars and fifty-five cents at the
beginning of each year.
Continuing with our example, assume we need ten thousand
dollars and decide to make end of year deposits but can only
deposit twelve hundred dollars per year.
Assuming we earn six percent per year how long would it take
to accumulate ten thousand dollars?

In this case it is not advisable to use the step by step approach
since it would require a trial and error procedure to determine N
or I for that matter.
Hence, we should use either a financial calculator or the NPER
function in Excel.
It turns out that N equals six point nine six years.
If instead we make deposits at the beginning of each time period
and equals six point six three years.
Now assume we save twelve hundred dollars annually but need
ten thousand dollars in five years.
We need to calculate the rate of return we have to earn in order
to achieve our goal.
In this case we should use either a financial calculator or the
RATE function in Excel.
It turns out we would have to earn twenty-five point seventy-
eight percent on our deposits to accumulate ten thousand dollars
by the end of five years!
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Slide 14
Perpetuities
A perpetuity is a bond that promises to pay interest forever.
Sometimes perpetuities are called consols.
To find the PV of a perpetuity we use the following formula: PV
for a perpetuity equals PMT divided by I.

Assume a consol or perpetuity pays twenty-five dollars per year
and the going interest rate is two point five percent.
In this case the original value or present value of the consol is
given by twenty-five dollars divided by zero point zero two five
which equals one thousand dollars.
What happens to the original value of the console if the interest
rate increases to five point two percent?
Now the PV of the perpetuity equals twenty-five dollars divided
by zero point zero five two which equals four hundred eighty
dollars and seventy-seven cents.
If instead, the interest rate drops to two percent the present
value of the consol is twenty-five dollars divided by zero point
zero two which equals one thousand two hundred fifty dollars.
These examples illustrate a very important point about the
relationship between bonds and interest rates.
Specifically there is an inverse relationship between the price of
outstanding bonds and interest rates.
Hence if interest rates rise, the price of outstanding bonds
decline and if interest rates decline the price of outstanding
bonds increases.
This rule holds true for both consols and bonds with finite
maturities.
Next slide
Slide 15
Uneven, or Irregular, Cash Flows

Recall the definition of an annuity requires that the payments
are identical over a given number periods.
Many times financial decisions involve uneven or irregular cash
flows.
When we work with uneven or irregular cash flows we label
them CF sub t where t denotes the period in which the cash flow
occurs.
There are two types of uneven cash flows that are important in
finance.
The first is one in which the cash flows stream is composed of a
series of annuity payments plus a lump sum paid in year N.
A bond is an example of this type of uneven cash flow. The
second is one in which all the cash flows are uneven.
Stocks and capital investments are examples of this type of
uneven cash flow.
To solve problems in which we have an annuity payment plus a
lump sum we use the following formula:
PV equals summation t equal one to T CF sub T divided by the
quantity one plus I raised to the t
th
power.
Solving problem like these is a two-step process. First we
calculate the present value of the annuity. Then, we calculate
the present value of the final payment. Last we add these
numbers together to find a present value of the income stream.

To calculate these values we can use a financial calculator or
the PV function in Excel.
In cases where the cash flows are all uneven, we can use a step
by step approach, a financial calculator, or the NPV function in
Excel.
If we use a financial calculator we must remember that the cash
flows must be entered into the cash flow register in order to
solve the problem.
Next slide
Slide 16
Future Value of an Uneven Cash Flow Stream
Now let’s look at how to calculate the future value of stream of
uneven cash flows. Sometimes this value is referred to as the
terminal or horizon value.
We calculate it by compounding each payment to the end of the
term and then adding them together.
The mathematical equation we use to calculate the future value
has the form FV equals summation from t equals zero to N CF
sub t times the quantity one plus I raised to the N minus t
power.
Alternatively, we can use a financial calculator or Excel.
If we use Excel, calculating the FV is a two-step process.
First we use the NPV function to calculate NPV.
Second, we use the FV function to compound the NPV to obtain
the future value.

Next slide
Slide 17
Solving for I with Irregular Cash Flows
Now let’s look at how to determine I if we know the values of
the other inputs.
If we have an annuity plus a lump sum it’s easy to determine I.
However it is considerably more difficult to determine I if we
have irregular or uneven cash flows.
When all cash flows are irregular or uneven we use a financial
calculator the internal rate of return, or IRR function in Excel to
solve this problem.
Using a financial calculator requires that we enter the cash
flows into the cash flow register and press the IRR key to obtain
the value for I. This is also called the rate of return on the
investment.
Additionally it is important to remember that the initial
investment at t equals zero must be entered as a negative
number since it is a cash outflow.
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Slide 18
Semiannual and Other Compounding Periods
Up to this point we assumed that interest has compounded
annually.
This is referred to as annual compounding.
Assume we deposit one hundred thousand dollars into a bank
account.
The interest paid on the deposit is six percent but it is paid

every six months.
This is referred to as semiannual compounding.
If we leave the funds in the account how much will we have at
the end of year one?
Since the bank pays six percent interest we receive sixty dollars
at the end of one year.
We receive thirty dollars at the end of six months and another
thirty dollars at the end of the year.
With semiannual compounding we earn interest on the first
thirty dollars during the second six month period.
For this reason, the total amount of interest earned is more than
sixty dollars.
Interest can also be paid quarterly, monthly, weekly or daily.
It is very important to understand nonannual compounding
because many financial instruments pay or charge interest on a
nonannual basis.
If interest is not compounded on an annual basis we must deal
with four types of interest rates, namely, nominal annual rates, I
sub NOM, annual percentage rates, APR, periodic rates, I sub
per, and effective annual rates, EAR or EFF percent.
The nominal or quoted rate, I sub NOM is the rate quoted by
bankers, brokers, and other financial institutions.
Additionally, when the nominal rate is quoted it must include
the number of confounding periods per year.

The nominal rate is never shown on a timeline, nor is it entered
into a financial calculator unless compounding occurs only once
per year.
The periodic rate, I sub PER is the rate charged by a lender or
paid by a borrower each period.
We calculate the periodic rate using the formula I sub PER
equals I sub NOM divided by M where I sub NOM is the
nominal annual rate and M is the number of compounding
periods per year.
Hence, a six percent nominal rate with semiannual payments
yields a periodic rate of I sub PER equals zero point zero six
divided by two which equals zero point zero three. The periodic
rate is the rate shown on timelines and used in calculations.
The effective annual rate EAR or EFF percent is the annual rate
that yields the same result as compounding at the periodic rate
for M times per year.
This rate is determined using the following equation: EAR
equals EFF percent equals the quantity one plus I sub NOM
divided by M raised to the M power minus one where I sub
NOM divided by M is the periodic rate and M is the number of
periods per year.
The EFF percent is used to compare the effect of costs on loans
or rates of return on investments when the payment periods are
different.
They’re rarely used in calculations.
Next slide

Fractional Time Periods
So far we’ve assumed that payments occur either at the
beginning or at the end of the time periods but not within the
time periods.
Solving these types of problems is three-step process.
First, we calculate the periodic rate which yields the interest
rate paid per day.
Second, we calculate the number of days the money will be
invested.
Last, we calculate the final value.
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Slide 20
Amortized Loans
A very important application of compound interest is in the case
of installment loans which are paid overtime.
These loans are repaid in equal amounts on a monthly quarterly
or annual basis and are referred to as amortized loans.
Problems like these require that we determine PMT and we
solve them by using either a financial calculator or the PMT
function in Excel.
Each payment is broken into two parts, that part which is
interest and the second part which is a repayment of principal.
This breakdown is typically shown in an amortization schedule.
Next slide
Slide 21

Growing Annuities
A growing annuity is a series of payments that grows a constant
rate.
One example of a growing annuity is a situation, in which an
individual wants to determine the maximum constant real or
inflation-adjusted withdrawals he or she can make over a given
number of years.
There are two ways in which to solve this problem.
First we can set up a spreadsheet in Excel’s Goal Seek function
which is found under the What If tab in the program.
Second, we can use a financial calculator.
If we use a financial calculator we must first calculate the
expected real rate of interest. Using the real rate of interest we
can solve an annuity due problem.
There’s a third method which we could use to solve this
problem however it is very complicated and time consuming to
use.
The preferred method is either Excel or a financial calculator.
Suppose instead we want to accumulate a certain sum over
given time period.
We plan to make a deposit at time zero and then made nine
more payments at the beginning of each of the next nine years.
If we know the interest rate earned on the deposit and the
expected inflation rate, we can calculate the real rate of interest
and the amount of the initial deposit.

In this case it is easier to use a financial calculator to solve the
problem.
The key is to remember that all variables must be expressed in
real not nominal terms.
Next slide
Slide 22
Check Your Understanding
Slide 23
Summary
We have now reached the end of this lesson. Let’s review what
we’ve covered.
First, we identified that the time value of money is an extremely
important concept in the field of financed. This principle was
demonstrated in the concept of timelines.
Next, we continued with time value of money through an
discussion on future values. Because of inflation, a dollar today
is worth more than a dollar in the future. This lead to presenting
four methods we can use to solve time value of money
problems.
Then, we defined present value as the opposite of future value.
To demonstrate we determined the possible amount on a bon by
calculating the present value and allowing for discounting the
future sum. This followed with identifying the interest rate and
number of years and how they affect the future value of money.
Also, we defined an annuity as a series of equal payments made
at fixed intervals. If the payments are made at the end of each
period the annuity is called an ordinary annuity or deferred

annuity.
Next, we discussed the future value and present value of
ordinary and an annuity due. As an example, the future value of
an annuity due is larger than that of an ordinary annuity because
in the case of an annuity due payments are made at the
beginning of each time period and for this reason each payments
occurs one period earlier and therefore the payment earns
interest for one additional period.
Then, we defined perpetuities as a bond that promises to pay
interest forever. At times, perpetuities are called consols. We
examined some examples that illustrate a very important point
about the relationship between bonds and interest rates.
Also, we covered uneven or irregular cash flows. Many times
financial decisions involve uneven or irregular cash flows.
Solving problems related to cash flows we utilize several
possible formulas. This included calculations for future value
and solving for I with irregular cash flows.
Next, we learned about semiannual and other compounding
periods. This followed with solving problems in fractional time
periods.
Finally, we discussed amortized loans and growing annuities.
Amortized loans are a very important application of compound
interest is in the case of installment loans which are paid
overtime. These loans are repaid in equal amounts on a monthly
quarterly or annual basis. Growing annuities are a series of
payments that grows a constant rate. Excel provides a Goal Seek
function as way to work through problems related to growing
annuities.
This concludes this lesson.

FIN 534 Week 3 Part 2: Bonds, Bond Valuation, and Interest
Rates
Slide 1
Introduction
Welcome to Financial Management. In this lesson we will
discuss the bonds, bond valuation, and interest rates.
Next slide
Slide 2
Topics
The following topics will be covered in this lesson:
Who issues bonds;
Key characteristics of bonds;
Bond valuation;
Changes in bond values over time;
Bonds with semiannual coupons;
Bond yields;
The pre-tax cost of debt: determinants of market interest rates;
The real risk-free rate of interest;
The inflation premium;
The nominal, or quoted, risk-free rate of interest;
The default risk premium;
The liquidity premium;
The maturity risk premium;
The term structure of interest rates;
Financing with junk bonds; and
Bankruptcy and reorganization
Next slide
Slide 3
Who issues bonds
By definition a bond is a long-term contract in which a
borrower makes payments of interest and principal on specific

dates to bondholders.
In general, there are four types of bonds.
Treasury bonds or government bonds are issued by the U.S.
government and they have almost no default risk.
Bonds are also issued by Federal agencies like Fannie Mae and
Freddie Mac.
Federal agencies and government sponsored entities, or GSE,
like the Tennessee Valley authority and the small business
administration issue bonds and their debt is referred to as GSE
debt. Federal agency debt and GSE debt are not backed by the
full faith and credit of the U. S. government.
Corporations issue corporate bonds which are unlike Treasury
bonds because they are exposed to default risk which is
sometimes refer to as credit risk.
If the issuing company were to have financial problems they
may not be able to pay the interest and principal on the bonds.
Depending upon the issuing company’s characteristics and
terms of the specific bond, different corporates bonds have
different levels of default risk.
Municipal bonds or munis are issued by state and local
governments.
While munis are subject to default risk, they have an advantage
over corporate bonds because the interest earned on municipal
bonds is exempt from Federal taxation and from state taxes if
the bondholder is a resident of the issuing state.
Foreign bonds are issued by foreign governments and foreign

corporations.
These types of bonds are subject to default risk if the bond is
denominated in a currency other than that of the investor’s
home currency.
Next slide
Slide 4
Key characteristics of bonds
All bonds have several key characteristics.
A bond’s par value is the face value of the bond which is
usually one thousand dollars.
Bonds issued by a company usually require the company to pay
a fixed number of dollars of interest usually every six months.
This is called the coupon payment and when divided by the par
value yields a coupon interest rate.
Sometimes a bond coupon rate varies over time.
When this happens the bonds are referred to as floating-rate
bonds.
In the case of a floating rate bond the coupon rate is set for
about a six month.
Subsequently, the coupon rate is adjusted every six months
based upon some market rate which could be the U.S. Treasury
bond rate, the London Interbank Offered Rate or another rate.
Bonds that don’t pay a coupon are called zero coupon bonds.
They are issued at a substantial discount from par value and
offer the investor capital appreciation.

Usually zero coupon bonds are issued in the form of Treasury
bonds.
Any bond originally offered at a price substantially below its
par value is referred to as an original issue discount or OID
bond.
Payment-in-kind bonds or PIK bonds don’t pay cash coupons.
Instead their coupons consist of additional bonds or a
percentage of an additional bond.
Typically, PIK bonds are issued by companies with cash flow
problems and for this reason PIK bonds are usually risky
investments.
If a bond includes a step-up provision it means that if a firm’s
bond rating is downgraded, the firm must increase the bond’s
coupon rate. From the company’s viewpoint this can be
dangerous because the downgrade means that the firm is having
difficulty servicing its debt.
The maturity date of the bond is the specific date on which the
par value must be paid.
Many times, especially in the case of corporate bonds, there is a
call provision attached to the bond issue.
This gives the company the right to pay the bondholders an
amount greater than the par value if the bonds are called.
The additional amount paid to the bondholders is called a call
premium.
If the bonds are not callable for five to ten years this is referred

to as a deferred call and the bonds are said to have call
protection.
Sometimes companies issue bonds during periods of high
interest rates.
When this happens there is usually a call provision attached to
the bond issue.
Should interest rates drop, the firm can sell a new issue at a
lower yield and use the proceeds to retire the high rate issue and
therefore reduce its interest expense.
This is referred to as a refunding process.
Bonds are subject to event risk.
Event risk occurs when something happens to change the firm’s
credit risk which lowers the firm’s bond rating and the value of
its outstanding bonds.
Therefore, firms perceived by investors to be subject to event
risk must pay very high interest rates to their bondholders.
To reduce the interest rate, the firm can include a covenant,
called a super poison put, which allows bondholders to turn in
their bonds to the company at par in the event of a takeover,
merger or major recapitalization.
Sometimes a bond issue will include a make-whole call
provision.
This allows a company to call the bond issue but the company
must pay a call price that equals the market value of a similar
noncallable bond.

A make-whole call provision gives the company an easy method
with which to repurchase bonds as part of a financial
restructuring.
When a bond issue includes a sinking fund it enables the orderly
retirement of the bond issue.
The firm can administer the sinking fund in one of two ways.
The firm can call in for redemption at par value a percentage of
the bond issue each year or the firm can purchase the required
number of bonds in the open market.
The firm will choose the least cost method to administer the
sinking fund.
Unlike a refunding call, a sinking fund does not require a call
provision.
Convertible bondholders have the option to convert their bond
holdings into a fixed number of shares of common stock.
Convertibles typically have a lower coupon rate than
comparable nonconvertible bonds because convertible bonds
give the investor the chance to share in the upside if a company
does well.
Warrants give the holder the option to purchase stock at a fixed
price.
Therefore, if the stock price increases the holder gains.
Like convertible bonds, warrants are issued with lower coupon
rates.

Income bonds are riskier than regular bonds because they are
required to pay interest only if the firm’s earnings are high
enough to cover the interest expense.
Additionally bondholders do not have the right to force the firm
into bankruptcy if the interest is not paid.
When interest payments and principal payments of bonds
increase with inflation they are referred to as indexed bonds or
purchasing power bonds.
In January nineteen ninety-seven the U.S. Treasury began
issuing indexed bonds called Treasury inflation protected
securities or TIPS.
TIPS can be used to approximate the risk-free rate of interest.
Corporate bonds are typically traded in electronic and or
telephone markets instead of organized exchanges.
The market for them is small because they are owned and traded
by a small number of very large financial institutions and
investors.
Next slide
Slide 5
Bond valuation
The value of a financial asset is the present value of the cash
flows the asset is expected to generate over time.
In the case of a regular bond, the cash flows are composed of
interest payments during the life of the bond and a lump sum
payment at maturity.
To calculate the present value of any bond we can use one of
the following the equation:

V sub B equals INT times the total quantity of one divided by r
sub d minus one divided the quantity of r sub d times the
quantity one plus r sub d plus M divided by the quantity one
plus r sub d raised to the N
th
power
where r sub d is the required rate of return or the market rate of
interest for that type of bond;
N is the number of years before the bond matures;
INT are the dollars of interest paid each year which is equal to
the coupon rate times the par value; and
M is the par value or maturity value of the bond usually one
thousand dollars.
When a bond is first issued the coupon rate is set at the going
rate.
However, after the bond is issued the coupon rate remains fixed
but market interest rates fluctuate.
Hence, when r sub d increases the price of an outstanding bond
falls and when r sub d decreases the price of an outstanding
bond increases. Whenever r sub d increases above the coupon
rate a fixed rate bond’s price falls below which par value and it
is referred as a discounted bond.
If on the other hand, r sub d falls below the coupon rate a fixed
rate bond’s price is above par value and it is referred to as a
premium bond.
Next slide
Slide 6

Changes in bond values over time
The market value of a bond changes over time.
When a bond is first issue, the coupon is usually set at a rate
that causes the market price of the bond too equal to its par
value.
At this time the bond is referred to as a new issue.
A bond is usually classified as an outstanding issue or a
seasoned issue about one month after the first issue.
While a newly issued bond usually sells for close to par, the
prices of seasoned issues vary substantially.
Except for floating-rate bonds, coupon payments are fixed.
Hence, when economic conditions change a ten percent coupon
bond with a one hundred dollars coupon that sold at par when it
was first issued sells for more or less than one thousand dollars
subsequent to the first issue.
There are other yields or returns attached to bond issues.
The first is the
current yield which is defined as the annual coupon rate divided
by the current market price
.
This is also referred to as the rate of return due to the interest
payment.
The second yield is the capital gains yield and is defined as the
profit or loss from the sale of the capital asset for more or less
than its purchase price.

The third yield is a
total yield or bond yield and is determined by adding the current
yield to the capital gains yield.
If interest rates increase, the market value of the bond decreases
below one thousand dollars and therefore the bond sells at a
discount.
There is an important relationship between interest rates and the
market value of bonds:
First, when r sub d equals the coupon rate a fixed rate bond
sells at par;
Second, when interest rates change over time the coupon rate
remains fixed. If r sub d rises above the coupon rate a fixed rate
bond sells at a discount because its price falls below par value;
Third, when r sub d falls below the coupon rate a fixed rate
bonds sells at a premium because its price rises above par value;
Fourth, an increase in interest rates results in the prices of
outstanding bonds falling and a decrease interest rates results in
the prices of outstanding bonds increasing; and
Fifth the market value of a bond always approaches par value as
its maturity date approaches assuming the firm remains solvent.
Next slide
Slide 7
Bonds with semiannual coupons
Most bonds pay interest semiannually.
In order to evaluate bonds with semiannual payments we must

modify our valuation model.
To do this, first divide the annual coupon interest by two.
Doing this expresses the interest payments on a semiannual
basis.
Second multiply the years to maturity, N, by two to express it
on a semiannual basis.
Third divide the nominal interest rate r sub d by two to express
it on a semiannual basis.
Making these changes to the valuation model gives us a
mathematical equation that has the following form:
V sub B equals summation t equals one through two times N
INT divided by two divided by the quantity one plus r sub d
divided by two raised to the t power plus M divided by the
quantity one plus r sub d divided by two raised to the two times
N power
.
Under semiannual compounding the bond’s value is somewhat
higher because interest payments are received sooner.
Next slide
Slide 8
Bond yields
While a bond’s coupon interest rate remains fixed its yield
varies on a daily basis depending on market conditions.
All bonds have three yields attached to them.
The first is the yield to maturity or YTM.

If we hold the bond to maturity what is rate of return on our
investment?
This rate is called the YTM and we calculate the YTM by
solving the following equation for r sub d by using either a
financial calculator or the RATE function in Excel:
Bond price equals summation t equals one through N INT
divided by the quantity one plus YTM raised to the t
th
power plus M divided by the quantity one plus YTM raise to
the Nth power
.
The YTM is the bond’s promised rate of return and is the return
the investor earns provided all promised payments are made.
The YTM is the expected rate of return only if the probability
of the firm’s default to zero and there is no call feature attached
to the bond.
The yield to call or YTC is the rate of interest on a bond if it is
called.
To calculate the YTC we solve the following the equation for r
sub d using either a financial calculator:
Price of a callable bond equals summation t equals one through
N INT divided by the quantity one plus r sub d raised to the t
th
power plus the call price divided by quantity one plus r sub d
raised to the N
th
power;

Where N is the number of years until the bond is called, r sub d
is the YTC and the call price is the price the firm must pay to
call the bond.
Usually, the call price is set equal to the par value plus one
year’s interest.
The
current yield of a bond equals the annual interest payment
divided by the bond’s current price
.
If we hold a bond with a ten percent coupon that currently sells
for nine hundred eighty-five dollars the bond’s current yield is
equal to one hundred dollars divided by nine hundred eighty-
five dollars which equals ten point one five percent.
The current yield is not equal to the return investor should
expect on the bond.
Instead, it provides information about the cash income the bond
generates in any given year.
In general, the yield to maturity equals current yield plus
capital gains yield.
Next slide
Slide 9
Check your understanding
Slide 10
The pre-tax cost of debt: determinants of market interest rates
The pretax cost of debt equals either the YTM or the YTC if it
is likely the firm will call the bond.

Additionally, the cost of debt impacts the firm’s weighted
average cost of capital, or WACC the cause from the company’s
perspective the cost of debt is due required return from the
debtholders’ perspective.
Since different debt securities have different market rates, it
follows that the nominal rate of interest on a debt security, r sub
d decomposes into several factors.
The formula for:
R sub d equals r star plus IP plus DRP plus LP plus MRP equals
r sub RF plus DRP plus LP plus MRP
.
Let’s look briefly at each of these variables.
Next slide
Slide 11
The Real Risk-Free Rate of Interest, R*
The risk free rate of interest, r star, equals the interest rate that
exists on a riskless security if no inflation is expected.
We think of r star as the rate on short term U.S. Treasury
securities in an inflation free world.
However, this rate is not static it changes over time with
economic conditions that depend on the rate of return
corporations and other borrowers expect to earn on productive
assets and people’s time preferences for current vs. future
consumption.
Next slide
Slide 12

The Inflation Premium (IP)
Since every investor is aware of the impact inflation has on
interest rates, when they lend money they add an inflation
premium or IP to r star.
The IP is equal to the average expected inflation rate over the
life of the security.
In the case of a short term default free U.S. Treasury bill the
actual interest rate charged:
R sub T-bill, equals the real risk – free rate, r star plus the
inflation premium so that r sub T-bill equals r sub RF which
equals r star plus IP
.
Next slide
Slide 13
The Nominal, or Quoted, Risk-free Rate of Interest
The nominal, or quoted, risk free rate, r sub RF equals the real
risk, free rate plus a premium for expected inflation.
It is important to understand that there is no security that is
truly risk free.
Therefore, we use a proxy for the risk-free rate.
We use the T-bill rate to approximate the short-term risk free
rate.
To approximate the long-term risk-free rate we use the T bond
rate.
Hence, we can express the risk-free rate :
R sub d equals r sub RF plus DRP plus LP plus MRP where r

sub d equals r star plus IP
.
Next slide
Slide 14
The Default Risk Premium (DRP)
The default risk premium, DRP, represents the possibility that
the bond issuer will not pay the interest or principal and in the
stated an amount and at the stated time
.
The greater the perceived risk of default on the part of the firm,
the greater the DRP and the higher the bond’s yield to maturity.
For U.S. Treasuries the DRP is virtually zero. Default risk is
affected both by the financial strength of the issuer and the
terms of the bond contract.
Let’s look at several types of contract provisions.
A bond indenture is a legal document that details the rights of
the bondholders and the issuing corporation. It includes the
provision for a trustee who represents the bondholders and
ensures that the terms of the indenture are satisfied.
An indenture includes restrictive covenants that covers the
conditions under which the issuer may pay off the bonds before
maturity, the levels at which certain ratios must be maintained,
and restrictions against the payment of dividends unless
earnings meet certain specifications.
If a firm issues a mortgage bond it must pledge assets as
security.
A mortgage bond may be a senior or first mortgage or a junior
or second mortgage bond.

If a firm issues a second or junior mortgage, it is paid only after
the first mortgage bondholders are paid.
A debenture is an unsecured bond and hence has no lien against
any specific asset of the firm as collateral for the obligation.
For this reason, debenture holders are referred to as general
creditors and their claims are protected by property not pledged
to other obligations.
If a debenture is a subordinate debenture its claim cannot be
paid until all senior debt has been paid.
Development bonds or pollution control bonds are issued by
state and local governments.
Under certain circumstances, state and local governing agencies
are permitted to sell tax – exempt bonds with the proceeds made
available to firms for specific uses.
The bonds are guaranteed by the firm that uses the funds and
since they are tax-exempt, these types of bonds have a relatively
low interest rate.
Many times municipalities purchase insurance to guarantee
coupon and principal payments of their bonds.
This, in turn, reduces the risk to the investors who are willing to
accept a lower coupon rate because the bond issue is insured.
There are three major bond rating agencies.
These are Moody’s Investors Service, Standard and Poor’s
Corporation, and Fitch ratings.

So long as a bond issue is rated BBB or better it is considered
an investment grade bond but if the bond issue is rated below
BBB it is considered a speculative or junk bond.
Bond ratings are based on quantitative and qualitative factors.
First, financial ratios are important.
Specifically, the return on assets, debt ratio, and the interest
coverage ratio are very important in predicting financial
distress.
Second, the bond contract terms includes information regarding
issues such as whether the bond is secured by specific assets,
whether the bond is considered subordinate debt, and any
sinking fund provisions.
Some of the qualitative factors that should be considered are the
sensitivity of the firm’s earnings to the strength of the
economy, the impact of inflation on the firm, whether the firm
has or may have labor problems, and potential antitrust
problems.
Bond ratings are important for three reasons.
First, most bonds are purchased by large institutional investors
and most are restricted to investment grade securities.
Second, many times bond covenants include a provision that
stipulates the coupon rate must be increased if the bond rating
falls below a certain level.
Last, a bond’s rating is an indicator of default risk which
influences the bond’s yield since lower-rated bonds have higher
yields.

Next slide
Slide 15
The liquidity premium (LP)
Recall, a liquid asset is one that can be converted to cash
quickly and at fair market value.
Financial assets are usually more liquid than real assets.
For this reason investors include a liquidity premium or LP
when the market rate of the security is set.
Corporate bonds issued by small firms tended to be less liquid
than those issued by large corporations and therefore have a
higher liquidity premium.
Next slide
Slide 16
The maturity risk premium (MRP)
The maturity risk premium, known as MRP, affects all bonds
including Treasury bonds and is the net effect of interest rate
risk and reinvestment risk.
Interest rate risk arises because bond prices decline when
interest rates increase. The longer the maturity of the bond the
greater the price change in response to a given change in the
interest rate.
The risk of a reduction in income because of a decrease in
interest rates is called reinvestment risk.
How does this happen?
Assume a retiree as a bond portfolio and lives off the income it
produces.
The bonds, on average, have a coupon rate of ten percent and

suppose interest rates dropped from ten percent to five percent.
When short-term bonds mature they must be replaced with
lower yielding bonds.
To the extent that long-term bonds are callable these too must
be replaced with the lower-yielding five percent bonds.
In this way the retiree suffers a reduction in income.
Next slide
Slide 17
The Term Structure of Interest Rates
The relationship between long term and short term rates is
called the term structure of interest rates.
It is important to both corporate treasurers who must decide
whether to borrow by issuing short-term or long-term securities
and investors who must decide whether to invest short-term or
long-term.
We can obtain interest rates for bonds with different maturities
from sources like The Wall Street Journal and Bloomberg.
When we plot a graph with interest rates on the Y-axis and
maturity dates on the X-axis, this set of data for a given date is
called the yield curve for that date.
An example of the yield curve for U.S. Treasury bonds is show
on this slide.
A normal yield curve is upward sloping because historically
longer term rates are usually higher than short term rates
because of the maturity risk premium.
The yield curve for March two thousand nine is an example of a

normal yield curve.
Any other shape for the yield curve is considered abnormal
.
Over time the yield curve can change. An inverted or downward
sloping yield curve existed in March nineteen eighty and was
downward sloping because the IP was larger for short term
bonds than four long term bonds.
In March two thousand nine
the yield curve was humped because medium term rates were
higher than either short term or long term rates.
Next slide
Slide 18
Financing with junk bonds
Junk bonds are rated less then BBB and are considered
noninvestment grade debt.
A bond can become a junk bond in one of two ways.
First, the bond may have been investment grade when it was
first issued but its rating declined because the firm suffered
financial difficulties.
Second, some bonds have junk status when they are issued.
In the nineteen eighties using junk bonds as part of leveraged
buyouts was a popular method of financing the purchase of
companies.
Next slide
Slide 19
Bankruptcy and Reorganization
A firm becomes insolvent when it does not have sufficient cash
to meet its interest and principal payments.

In this case it is necessary to decide whether to dissolve the
company through either liquidation or chapter seven
bankruptcy, or reorganization or chapter eleven bankruptcy.
If the firm is reorganized its debt is usually restructured so that
the firm’s financial charges are reduced to a level that can be
covered by the firm’s cash flow. Liquidation occurs when the
firm’s financial situation is so dire it is better to sell off the
assets.
In this case there is a priority of claims stipulated by the
Bankruptcy Act.
Next slide
Slide 20
Check your understanding
Slide 21
Summary
We have now reached the end of this lesson. Let’s review what
we’ve covered.
First, we learned about bonds, bond valuation, and interest
rates. Bonds are issued by various government entities and
corporations. At any point in time the value of a bond is given
by the present value of the cash flows an asset backing the bond
is expected to generate over time. While most bonds pay a
coupon rate, zero coupon bonds and PIK bonds are exceptions.
Also, we learned that there is an inverse relationship between
the market value of bonds and interest rates. Even though a
bond’s coupon rate is fixed, its yield varies with market
conditions. Bond rating agencies use quantitative and
qualitative factors to assign a rating to a bond issue. The higher

the rating the lower the perceived risk associated with the bond
issue. Because of perceived risk, investors attach premiums to
the rate of return they require.
This concludes this lesson.
REFERENCES PREFERRED
CNN Money. (2013). General format. Retrieved from
http://money.cnn.com/
Criniti, A. (2013).
The necessity of finance
. Philadelphia, PA: Criniti Publishing Company.
Fidelity Investments, Inc. SWOT analysis. (2013).
Fidelity Investments
,
Inc
.
SWOT Analysis
, 1-8.
Hasseltoft, H. (2012).
Stocks, bonds, and long-run consumption risks
.
Journal of Financial & Quantitative Analysis, 47(
2), 309-332. doi: 10.1017/S0022109012000075
Kumar, A. (2009). Who gambles in the stock market?
Journal of Finance
,
64
(4), 1889-1933.
Learn About Finance. (2013). General format. Retrieved from
http://learn-about-finance.com/
Why Learn Finance. (2013). General format. Retrieved from
https://twitter.com/WhyLearnFinance/finance-list

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