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Portfolio Management

Prepared By:

Noorulhadi QureshiLecturer Govt College of Management Sciences

Peshawar

LECTURE SEVEN

Bond Evaluation

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Bonds

• A bond is a tradable instrument that represents a debt owed to the owner by the issuer. Most commonly, bonds pay interest periodically (usually semiannually) and then return the principal at maturity.

• Most corporate, and some government, bonds are callable. That means that at the company’s option, it may force the bondholders to sell them back to the company. Ordinarily, there are restrictions on the timing of the call and the amount that must be paid.

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• Par or Face Value:

The amount of money hat is paid to the bond holder at maturity. i.e. its generally represent the amount of money borrowed by the bond issuer.

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Bond Return• Bond Return can be calculated and

expressed in different ways. It is necessary to understand the meaning of each of these expressions.

• Coupon rate: It is the nominal rate of interest fixed and printed on the bond certificate. It is calculate on the face value of the bond. For example if the coupon rate on a bond of face value of Rs. 1000 is 12%, Rs. 120 would be payable by the company to the bondholder annually till maturity. And amount Rs. 120 is known coupon payment.

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Current yield Bond may be trader at secondary market

at different price from face value. The current yield relates the annual interest receivable on a bond to its current market price. For example if a bond face value is Rs. 1000 with coupon rate of 12% and current selling for Rs. 800, the current yield would be

100.Po

InldCurrentYie

In= annual interest

Po= Current market price

%15

100800

120

ldCurrentYie

xldCurrentYie

Current yield may be higher than coupon if

bond trader at discount and may be low if

traded at premium

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Spot Interest Rate

Zero Coupon bond is special type of bond which does not pay annual interest. The return on bond is in the form of discount on issue of the bond. Or example , two year bond of face value is Rs. 1000 at discount for Rs. 797.19 with no coupon or with no annual interest. This type of bond is also called pure discount bond or deep discount bond. And it is calculated as

Discounted Price= (Face value)/(1+k)n (1+k)n =(Face value)/ Discounted Price

1Prcsc/ n iceountDiFaceValueK

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Spot Interest Rate (con’t)

Consider a zero coupon bond whose face value is Rs. 1000 and maturity period is 5 year. If the issue rice of the bond is Rs. 519.37, what is spot interest rate.

1Prcsc/ n iceountDiFaceValueK

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137.519/10005

K

K

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Bond

• Maturity date: The maturity date represent on which the bond is mature and repaid to the bond holder:

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Yield to Maturity

• The compounded rate of return an investor expected to receive from bond purchased at the current market price and held to maturity:

n

nYTM

TV

tYTM

CtMP )

)1(

())1(

(

MP is the current market price of the bond

Ct is the cash inflow from the bond throughout the holding period

TV is the terminal cash inflow received at the end of the holding period.

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YTM (con’t)• A bond face value with Rs. 1000 and coupon rate is 15%, market

price is Rs. 900 with five years maturity period,

)( LowerRateHigherRatelatedValueLowerCalcuedValueHighCacult

MPlatedValueHigheCalcuLowerRateYTM

It will be on the basis on trail and error, assuming 20% YTM, the value of if calculated, is 850.49, so the value is less the market value so this rate to be reduced with another assumption i.e 18% rate is inserted in equation, it gives Rs. 906.18 Now to calculate YTM

n

nYTM

TV

tYTM

CtMP )

)1(

())1(

(

22.18

)1820(49.85018.906

90018.90618

YTM

YTM

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YTM(alternative way Approx)

%89.171789.0950

20150

2/)9001000(

5/)9001000(150

2/)(

/)(

orYTM

YTM

YTM

MPMV

nMPMVIYTM

To avoid trail and error which tedious calculation, YTM maturity can be calculated approximately as

I is annual interest=150

MV is maturity value and=1000

MP is market price, and =900

n is holding period to maturity= 5

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Bond Price

• Bond price refers to the Present value of Bond.

tK

CFtPo

)1( tt

k

MVtK

IPo

)1()1(

Po = Present value, It is the annual interest, MV is maturity value, n is the number of year to maturity and k is the appropriate discount rate.

Let a bond face value is Rs. 1000 issued five years ago at coupon rate of 10% the had had a maturity period of 10 years, so five years are more left from today to maturity the current market rate is 14% the present value would be

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Calculating the Value of a Bond• There are two types of cash flows that are provided

by a bond investments:– Periodic interest payments (usually every six months,

but any frequency is possible)– Repayment of the face value (also called the principal

amount, which is usually $1,000) at maturity

• The following timeline illustrates a typical bond’s cash flows:

0 1 2 3 4 5

100 100 100 100 1001,000

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Calculating the Value of a Bond (cont.)• We can use the principle of value additivity to

find the value of this stream of cash flows• Note that the interest payments are an

annuity, and that the face value is a lump sum• Therefore, the value of the bond is simply the

present value of the annuity-type cash flow and the lump sum:

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Bond Terminology• There are several terms with which you must be

familiar to solve bond valuation problems:– Coupon Rate - This is the stated rate of interest on the

bond. It is fixed for the life of the bond. Also, this rate time the face value determines the annual interest payment amount.

– Face Value - This is the principal amount (nominally, the amount that was borrowed). This is the amount that will be repaid at maturity

– Maturity Date - This is the date after which the bond no longer exists. It is also the date on which the loan is repaid and the last interest payment is made.

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Bond Valuation: An Example

• Assume that you are interested in purchasing a bond with 5 years to maturity and a 10% coupon rate. If your required return is 12%, what is the highest price that you would be willing to pay?

0 1 2 3 4 5

100 100 100 100 1001,000

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Some Notes About Bond Valuation

• The value of a bond depends on several factors such as time to maturity, coupon rate, and required return

• We can note several facts about the relationship between bond prices and these variables (ceteris paribus):– Higher required returns lead to lower bond prices, and vice-

versa– Higher coupon rates lead to higher bond prices, and vice

versa– Longer terms to maturity lead to lower bond prices, and

vice-versa

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Bond Risk

1. Default Risk:

Default risk refers to the possibility that a company may fail to pay the interest rate or principal amount on maturity date

2. Interest Rate Risk

Interest rate risk refers to variation of market interest rate or discount rate compare to coupon rate.

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