Bond Valuation Module

7/29/2019 Bond Valuation Module

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Bond ValuationLearning Module


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Definitions

Par or Face Value - The amount of money that is paid to the bondholders at

maturity. For most bonds this amount is $1,000. It also generally

represents the amount of money borrowed by the bond issuer.

Coupon Rate - The coupon rate, which is generally fixed, determines the

periodic coupon or interest payments. It is expressed as apercentage of the bond's face value. It also represents theinterest cost of the bond to the issuer.


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Definitions

Coupon Payments - The coupon payments represent the periodic interest payments

from the bond issuer to the bondholder. The annual coupon

payment is calculated by multiplying the coupon rate by thebond's face value. Since most bonds pay interest semiannually,generally one half of the annual coupon is paid to thebondholders every six months.

Maturity Date - The maturity date represents the date on which the bond

matures, i.e., the date on which the face value is repaid. Thelast coupon payment is also paid on the maturity date.


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Definitions

Original Maturity - The time from when the bond was issued until its maturity date.

Remaining Maturity - The time currently remaining until the maturity date.

Call Date - For bonds which are callable, i.e., bonds which can be redeemed

by the issuer prior to maturity, the call date represents theearliest date at which the bond can be called.


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Definitions

Call Price - The amount of money the issuer has to pay to call a callable

bond (there is a premium for calling the bond early). When a

bond first becomes callable, i.e., on the call date, the call priceis often set to equal the face value plus one year's interest.

Required Return - The rate of return that investors currently require on a bond.


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Definitions

Yield to Maturity - The rate of return that an investor would earn if he bought the

bond at its current market price and held it until maturity.

Alternatively, it represents the discount rate which equates thediscounted value of a bond's future cash flows to its currentmarket price.

Yield to Call - The rate of return that an investor would earn if he bought a

callable bond at its current market price and held it until thecall date given that the bond was called on the call date.


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Bond Valuation

Bonds are valued using time value of moneyconcepts.

Their coupon, or interest, payments aretreated like an equal cash flow stream(annuity).

Their face value is treated like a lump sum.


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Example Assume Hunter buys a 10-year bond from the KLM

corporation on January 1, 2003. The bond has a facevalue of $1000 and pays an annual 10% coupon. The

current market rate of return is 12%. Calculate the priceof this bond today.

1. Draw a timeline

$100 $100$100

$100$100

$100$100

$100$100$100

$1000

+

?

?


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Example

2. First, find the value of the coupon stream Remember to follow the same approach you use

in time value of money calculations.

You can find the PV of a cash flow stream PV = $100/(1+.12)1 + $100/(1+.12)2 + $100/(1+.12)3

+ $100/(1+.12)4 + $100/(1+.12)5 + $100/(1+.12)6 +$100/(1+.12)7 + $100/(1+.12)8 + $100/(1+.12)9+$100/(1+.12)10

Or, you can find the PV of an annuity PVA = $100 * {[1-(1+.12)-10]/.12}

PV = $565.02


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Realized Return

Sometimes you will be asked to find the realized rateof return for a bond.

This is the return that the investor actually realizedfrom holding a bond.

Using time value of money concepts, you are solvingfor the required rate of return instead of the value ofthe bond.


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Example Doug purchased a bond for $800 5-years ago and he sold

the bond today for $1200. The bond paid an annual 10%coupon. What is his realized rate of return?

n

PV = S [CFt / (1+r)t]t=0

$800 = [$100/(1+r) + $100/(1+r)2 + $100/(1+r)3 +$100/(1+r)4 + $100/(1+r)5] + [$1200/(1+r)5]

To solve, you need use a trail and error approach. Youplug in numbers until you find the rate of return that solvesthe equation.

The realized rate of return on this bond is 19.31%.


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Example

This is much easier to find using a financial calculator:

n = 5PV = -800FV = 1200PMT = 100i = ?, this is the realized rate of return on this bond

Note that if the payments had been semiannual,

n=10, PV=-800, FV=1200, PMT=50, i=?=9.47%. Thus, therealized return would have been 2 * 9.47% = 18.94%.

Bond Valuation Module

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