Bond Valuation & Analysis

8/9/2019 Bond Valuation & Analysis

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Bond Valuation & Analysis

Concept of Bond

Types of Bonds

The Yield Curve

The Theories of Term Structure



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.



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 funds-Diversification

To preserve control



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



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



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 today¶s date and the maturity date. Do notconfuse this with the ³original´ 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.



Basic Bond Valuation Example

Suppose that you are interested inpurchasing a 3-year bond with a 10% semi -annual coupon rate and a face value of Rs.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



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 you¶ll find that the bond is worth

Rs.1,079.93. Note that this value must decline until it reachesRs.1,000 at maturity.

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Valuing Bonds Betw een 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%) you¶ll 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.



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)



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.

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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 today¶s price

You hold the bond to maturity

You reinvest all interest payments at thesame YTM



The Yield to Maturity (cont.)

Suppose that we didn¶t 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 closed-form solution

to the bond valuation equation, so we need touse a trial and error algorithm to find the yield.




Here is the bond valuation equation, slightly restatedto make the point:

Note that I have replaced the bond¶s 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.

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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 let¶s

³split 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 ³i´ key). Eventually, you will find that the actualyield is 7%.



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 ³call premium´ is to be received, we must

add that premium to the face value of thebond.



R isks of Bonds

Bonds are generally less risky than stocks, but they do suffer from 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 lower rates.

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.



The Term Structure of Interest R ates/

Yie

ld Curv e

The "term structure" of interest rates

refers to the relationship between bonds

of different terms. When interest rates of

bonds are plotted against their terms, thisis called the "yield curve". Economists

and investors believe that the shape of

the yield curve reflects the market's futureexpectation for interest rates and the

conditions for monetary policy.



The Term Structure of Interest R ates/

Yie

ld Curv e

There are three main patterns created by the term structure of interest rates.

1) Normal Yield Curve: As its name indicates, this is the yieldcurve shape that forms during normal market conditions, wherein

investors generally believe that there will be no significantchanges in the economy, such as in inflation rates, and that theeconomy will continue to grow at a normal rate. During suchconditions, the market expects long-term fixed income securitiesto offer higher yields than short-term fixed income securities. Thisis a normal expectation of the market because short-terminstruments generally hold less risk than long-term instruments;the farther into the future the bond's maturity, the more time and,therefore, uncertainty the bondholder faces before being paidback the principal. To invest in one instrument for a longer periodof time, an investor needs to be compensated for undertaking theadditional risk.



Normal Yield Curv e : upward sloping

yields rise w/ maturity (common)

maturity

yield



Flat Yield Curv e

Flat Yield Curve: When a small or negligibledifference between short and long terminterest rates occurs due to higher inflation

expectations and tighter monetary policy thenthe yield curve is known as a "shallow" or "flat" yield curve. The higher short term rates

reflect less available money, as monetarypolicy is tightened, and higher inflation later inthe economic cycle.



Flat Yield Curv e

yields similar for all maturities

maturity

yield



Inv erted Yield Curv e: Downward Slope

Inverted Yield Curve: These yield curves are rare, and they formduring extraordinary market conditions wherein the expectations of investors are completely the inverse of those demonstrated by thenormal yield curve. In such abnormal market environments, bonds withmaturity dates further into the future are expected to offer lower yieldsthan bonds with shorter maturities. The inverted yield curve indicatesthat the market currently expects interest rates to decline as timemoves farther into the future, which in turn means the market expectsyields of long-term bonds to decline. Remember, also, that as interestrates decrease, bond prices increase and yields decline.You may be wondering why investors would choose to purchase long-term fixed-income investments when there is an inverted yield curve,which indicates that investors expect to receive less compensation for taking on more risk. Some investors, however, interpret an inverted

curve as an indication that the economy will soon experience aslowdown, which causes future interest rates to give even lower yields.Before a slowdown, it is better to lock money into long-terminvestments at present prevailing yields, because future yields will beeven lower.



downward sloping (inv erted)

yield falls w/ maturity (rare)

maturity

yield



Term Structure of Interest R ates: Theories

Expectations Theory: In this theory we assume: bond buyers do nothave any preference about maturity i.e. bonds of different maturitiesare perfect substitutes then investors care only about expectedreturn i.e. if they expect better return from ST bonds, only hold STbonds and if expect better return from LT bonds, only hold LTbonds. But investors hold both ST and LT bonds so, must EXPECTsimilar return:

LT yields =average of the expected ST yields

Thus the expectation hypothesis explains the shape of the curve as

Yield Curve Explanation

AscendingS

hort term rates are expected to rise in futureDescending Short term rates are expected to fall in future

Humped Short term rates are expected to rise for a while & then fall.

Flat Short term rates are expected to remain unchanged in future.




Liquidity Preference Theory: In this theory we assumebonds of different maturities are imperfect substitutes,and investors PREFER ST bonds. So if true, investorshold ST bonds UNLESS LT bonds offer higher yield asincentive

higher yield = liquidity premium

IF LT bond yields have a liquidity premium, then usuallyLT yields > ST yields or yield curve slopes up.



Problem

How do we interpret yield curve?

slope due to 2 things:

(1) exp. about futureS

T rates(2) size of liquidity premium

do not know size of liq. prem.



if liquidity premium is small, then ST rates are expected to rise

maturity

yield

yield curve

small liquidity premium



if liquidity premium is larger,

then ST rates are expected to stay the same

maturity

yield

yield curve

large liquidity premium




Preferred Habitat Theory: explains the shape of theyield curve by investors' term preferences. Someinvestors need to deploy their funds for specificperiods of time, hence a preference for long or short

term bonds which is reflected in the shape of theyield curve. An inverted curve can then be seen toreflect a definite investor preference for longer termbonds. Thus this theory assumes bonds of different

maturities are imperfect substitutes, and investor preference for ST bonds OR LT bonds is notconstant. Liquidity premium could be positive or negative and yield curve very difficult to interpret

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Bond Valuation & Analysis