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8/9/2019 Bond Valuation & Analysis
1/31
Bond Valuation & Analysis
Concept of Bond
Types of Bonds
The Yield Curve
The Theories of Term Structure
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What is a bond?
A bond is a tradable instrument that represents adebt owed to the owner by the issuer. Mostcommonly, bonds pay interest periodically (usuallysemiannually) and then return the principal at
maturity. The par value is the value stated on the face of the
bond and is the amount issuer promises to pay tothe holder at the time of maturity.
The coupon rate is the interest rate payable to the
bond holder. The maturity date is the date when the principal
amount is payable to the bond holder.
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Reasons for issuing Bonds
Bonds, while a more conservativeinvestment than stocks, can offer certaininvestors some very attractive features:
Safety and reliable income To reduce the cost of capital
To gain the benefit of leverage
To effect tax saving To widen the sources of fundsDiversification
To preserve control
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Types of Bonds
Straight Bonds Convertible and Non Convertible Bonds Zero Coupon Bonds Callable & Puttable Bonds Floating Rate Bond Sinking Fund Bonds Serial Bonds Mortgage or secured Bonds Open end, Close end and limited open
end Collateral Trust Bonds Income Bonds Adjustment Bonds Assumed Bonds Joint Bonds Guaranteed Bonds Redeemable or Irredeemable Bonds Participating Bonds
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Bond Valuation
The intrinsic value of a bond, like stocks, isthe present value of its future cash flows.
B
onds, however, have much morepredictable cash flows and a finite life.
The cash flows promised by a bond are:
A series of (usually) constant interest payments
The return of the face value of the bond atmaturity
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Basic Bond Valuation (cont.)
The value of a bond is determined by four variables: The Coupon Rate This is the promised annual rate of
interest. It is normally fixed at issuance for the life of the bond.To determine the annual interest payment, multiply the couponrate by the face value of the bond. Interest is normally paidsemiannually or annually.
The Face Value This is nominally the amount of the loan tothe issuer. It is to be paid back at maturity.
Term to Maturity This is the remaining life of the bond, andis determined by todays date and the maturity date. Do notconfuse this with the original maturity which was the life of thebond at issuance.
Yield to Maturity This is the rate of return that will be earnedon the bond if it is purchased at the current market price, heldto maturity, and if all of the remaining coupons are reinvestedat this same rate. This is the IRR of the bond.
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Basic Bond Valuation Example
Suppose that you are interested inpurchasing a 3year bond with a 10% semi annual coupon rate and a face value ofRs.1,000. If your required return is 7%, whatis the intrinsic value of this bond?
Here is a timeline showing the cash flows:
0 1 2 3 4 5 6
50 50 50 50 50 501000
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Basic Bond Valuation Example (cont.)
Note that the cash flows of the bond consist of:
An annuity, the interest payments, paid annually. Thisis calculated as:
A lump sum which is the return of the face value of thebond at the end of its life. This payment is made atthe same time as the last interest payment.
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Basic Bond Valuation Example (cont.)
We can find the intrinsic value of these cash flows by findingthe present value of the interest payments and then adding thepresent value of the face value:
Note that the first term is the present value of an annuity, and
the second is the present value of a lump sum Do the math, and youll find that the bond is worth
Rs.1,079.93. Note that this value must decline until it reachesRs.1,000 at maturity.
207.011000
207.0
2
07.01
11
501
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6

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Valuing Bonds Between Coupon Dates
The bond valuation formula just presentedhas one major flaw: It only works on acoupon date.
Since coupon dates (interest payment dates)usually only occur twice per year, chances
are (~ 99.45%) youll buy (or sell) a bondbetween coupon dates.
In this case, we must deal with accruedinterest, and the increase in the bond valuesince the last coupon date.
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Bond Return Measures
There are three ways in which theexpected return of the bond is reported:
Current Yield (CY)
Yield to Maturity (YTM)
Yield to Call (YTC)
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The Current Yield
The current yield on a bond is simply the annualinterest payment divided by its current price.
For our example bond, the current yield is:
Note that the current yield is ignoring the capital lossthat you will suffer over the remaining life of thebond (it must sell for Rs.1,000 at maturity), so itoverstates the expected return for bonds selling at apremium. For discount bonds, the expected returnis understated.
0P
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0926.093.1079
100!!CY
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The Yield to Maturity
The yield to maturity gives the exact returnthat you will actually earn under thefollowing conditions:
You purchase the bond at todays price
You hold the bond to maturity
You reinvest all interest payments at thesame YTM
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The Yield to Maturity (cont.)
Suppose that we didnt know that our requiredreturn was 7% per year, but we did know thatthe current bond price was Rs.1079.93.
We could solve for the yield implied by thatprice (i.e., the YTM).
Unfortunately, there is no closedform solution
to the bond valuation equation, so we need touse a trial and error algorithm to find the yield.
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The Yield to Maturity (cont.)
Here is the bond valuation equation, slightly restatedto make the point:
Note that I have replaced the bonds intrinsic value(VB) with its price (PB), and its required return (kd)with its yield (YTM).
Our problem now is to solve for that YTM given theprice.
NN
B
YTM
FV
YTM
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11
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The Yield to Maturity (cont.)
To find the YTM, we first make a guess at the yield. Say that we choose10%. That gives us a price of Rs.1,000 which is lower than the actualprice. To get the price to go up, we must lower our estimated yield.
Suppose we now try 5%. The price now is $1,137.70 which is too high.We need to try a higher estimated yield.
Now, we know that the YTM must be between 5% and 10%, so lets
split the difference and try 7.5%. We get Rs.1,066.06. Close, but notclose enough. We now know the YTM is between 5% and 7.5%, so choose 5.75%. We
get Rs.1,115.59. We now know the answer is between 5.75% and7.5%.
Next, try 6.625%. We get Rs.1,090.48.
And so on. Keep splitting the difference until you arrive at the correctprice. The yield that achieves this is the YTM. This is the type of process that your calculator goes through when
solving for the YTM (the i key). Eventually, you will find that the actualyield is 7%.
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The Yield to Call
The yield to call (YTC) is exactly the same asthe YTM, except that it assumes that the bondwill be called at the next call date.
The only differences from calculating the YTMare:
We need to change the number of periodsuntil maturity to the number of periods until it
can be called. If a call premium is to be received, we must
add that premium to the face value of thebond.
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Risks of Bonds
Bonds are generally less risky than stocks, but they do sufferfrom several types of risk:
Credit risk Risk of default.
Price risk Risk of unexpected changes in rates, causing acapital loss.
Reinvestment risk Risk that rates will fall and you will reinvestat a lower rate.
Purchasing power risk Risk that inflation will be higher thanexpected.
Call risk Risk that the bond will be called because of lowerrates.
Liquidity risk The risk that you will not be able to sell the bondat a price near its full value.
Foreign exchange risk Risk that a foreign currency will declinein value, causing a decline in the value of your interest paymentsand principal.
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TheTerm Structure of Interest Rates/
Yie
ld Curve
The "term structure" of interest rates
refers to the relationship between bonds