Bond Valuation 1

8/6/2019 Bond Valuation 1

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Fixed Income Securities:

Types, Valuation & AssociatedRisks1


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What is Debt?

y Means a borrowing, hence to be repaid by:

Periodic Interest payments

Principal Repayment

Brief look at classification of debt according tomaturity:

Less than 1 yr- Money Market instruments

More than 1 yr- Govt. securities, bonds, debenturesetc.

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Types Of Money Market Instruments

y Treasury Bills- They represent short termobligations of GOI. Do not carry an explicit interestrate, as they are issued at a discount and redeemedat par value.

y Certificate of Deposits As the name suggests, it is acertificate of deposit, i.e. negotiable receipt of fundsdeposited in a bank for fixed period, sold at discountand redeemed at par.

y Commercial Papers These are short termunsecured promissory notes issued by firms, whichare considered financially strong.

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Debt instruments more than 1 year old

y Govt. issued securities These are medium to longterm bonds issued by RBI on behalf of the GOI(central & State govt.).

y Corporate Debt These are bonds issued frequentlyby public sector cos, financial institutions, privatecos. Etc.

y Hence Bonds- Financial Contracts between the

issuer and the holder

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Types of Bonds

y Straight Vanilla Bonds

y Zero Coupon or Deep Discount bonds

y Floating rate bonds

y Bonds with embedded options- Convertibles,Warrants

y Callable Bonds

y

Puttable bonds

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Bonds : Formal Definition & Terminologies used

y Bonds are negotiable promissory notes that can beused by individuals, business firms, govt. or govt.agencies

y Some bond related terms:Face Value / Par Value

Coupon Rate

Maturity

Redemption Value

Market Value (Price)

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Basic Bond Valuation Model

y With the above background, it is quite clear that theholder of a bond receives a fixed annual interestpayment for a certain number of years and a fixed

principal repayment( equal to par value) at the timeof maturity. Therefore, the intrinsic value (or thepresent value) of a bond can now be written as:

Value(price of bond) = I/(1+kd)^t +F/(1+kd)^n,

(where t varies from 1 to n)Or

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Basic Bond Valuation Model contd.

y Value = I(PVIFA kd, n) + F(PVIF kd ,n )

Where,

I = annual interest payable on bond

F= Principal amount(Par Value) repayable at thematurity time.

N= maturity period of the bond

Kd = cost of capital( the prevailing interest factor)

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Brain Gym

Q1) A bond whose par value is Rs.1,000 bears acoupon rate of 12% and has maturity period of 3

years. The required rate of return on the bond is

10%. What is the value of the bond?

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Solution to brain Gym

Value = Rs. 120(PVIFA 10%,3yrs.) + Rs. 1000 (PVIF10%, 3 yrs)

= Rs.120 *(2.487) + 1,000(0.751)

= Rs. 298.44 + Rs. 751

= Rs.1,049.44

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Bond Values with Semi annual Interest

y Some of the bonds carry interest payment semi annually. As half- yearly interest amounts can bereinvested the value of such bonds would be more

than the bonds with annual interest payments.Hence our bond valuation model gets modified as:

Value = (I/2)/(1+kd/2)^t + F/(1+kd/2)^2n,

(where t varies from 1 to 2n)

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Brain Gym

Q2) A bond of Rs. 1,000 value carries a coupon rate of10% and a maturity period of 6 years. Interest ispayable semi annually. If the required rate of

return is 12%, calculate the value of the bond.

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Solution to Brain Gym

Value = Rs. 50(PVIFA 6%, 12 yrs) + 1,000(PVIF6%,12 yrs)

=Rs. 50(8.384) + 1,000 (0.497)

= Rs. 419.2 + Rs. 497

= Rs. 916.20

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Bond Yield Measures

y One Period Rate of Return

Eg: X purchased Rs. 1,000 par value bond for Rs.900.The coupon payment on his bond is Rs.80 i.e, 8%.

One yr later he sells the bond for Rs. 800. The rate ofreturn of Mr. X for this one year period is:

= [(800-900) +80]/900

=[-100+80]/900

= - 2.22%

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Bond Yield Measures contd.

y Current Yield It measures the rate of return earnedon a bond if it is purchased at its current marketprice and if the coupon interest is received.

Current yield = Coupon Interest/ Current MarketP

riceIn the previous example, if the current market price ofthe bond is also Rs. 800, then the current yield = 80/ 800

= 10%

Coupon rate and current yield are two differentmeasures. Coupon rate and current yield will beequal if the bonds market price equals its face value.

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Bond Yield Measure: Yield to Maturity(YTM)

Q) How are two bonds compared?

1)On the basis of prices?

or

2) On the basis of yield?

Q) What is yield?

Q) Is yield same as coupon?

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Bond Yield Measure: Yield to Maturity(YTM)

y Yield to Maturity It is the rate of return earned by aninvestor who purchases a bond and holds it till maturity.The YTM is the discount rate which equals the present

value of promised cash flows to the current marketprice(purchase price).

y Eg: Consider a Rs. 1,000 par value bond whose currentmarket price is Rs. 850. The bond carries a coupon rateof 8% and has a maturity period of 9 years. What would

be the rate of return that an investor earns ifhepurchases the bond and holds till maturity??

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Solution

y Rs 850 = Rs.80( PVIFA kd%, 9yrs) + Rs. 1000 (PVIFkd%, 9yrs)

Use Interpolation to find the YTM

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Solution , approximate Formulae

y We find that the YTM comes to 10.71%

Approximate Formulae:

YTM [I +(F-P)/n] / [0.4F +0.6P]

Where,

I= annual interest payment

F= par value or redemption value of the bond

P= current market price of the bondN= years to maturity

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Brain Gym

Q3) Zeta Industries Ltd. Bond a par value of Rs. 500 iscurrently traded at Rs. 435. The coupon rate is 12%and it has a maturity period of 7 yrs. What is the

YTM? (use approximate formulae)

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Solution to Brain Gym

y YTM [ 60 + (500 -435)/7]/[(0.4*500)+(0.6*435)]

15%

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Bond Value Theorems

y Relationship between the required rate of return andthe coupon rate.

y Number of the years to maturity

y Yield to maturity

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Relationship between required rate andcoupon rate

y Eg: Consider a bond of Kenstar Intermediaries Ltd.With the following features:

y Par Value : Rs.100

y Coupon Rate: 12%y Years to maturity: 5 years

Find the value of the bond if the required rate of returnis 12%?

- Do a quick calculation using approximate formulae

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y We find that the value of the bond equals Rs.100,hence it can be said that When the required rate ofreturn is equal to the coupon rate, the value of the

bond is equal to its par valuey Now consider the same example if the required rate

of return is 14%. ( Do a quick calculation usingapproximate formulae. Keep the answer as a secret)

y Now consider the same example if the required rateof return is 10%.

y So what do you conclude??????????

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y Hence we see that:

If Kd = Coupon rate, Value of bond= Par value

If Kd> Coupon rate, Value of bond< Par value

If Kd< Coupon rate, Value of bond> Par Value

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Effect of Number of years to maturity onBond Value

y Eg: Consider a bond of Enucon Ltd. with thefollowing features:

y Par Value: Rs.1000

y Coupon rate: 11%y Years to Maturity: 7

If the required rate of return is 13%, then the value ofthe bond is.(Do a quick calculation)

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y We see that the value of the bond is approx = Rs.911.53

y One year from now , when the maturity period will

be 6 years, the value of the bond will be:y Rs. 919.78

y For a required rate of return of 13%, the value of thebond will increase with the passage of time, i.e until

maturity

y Look at the following table:

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Years to Maturity Bond V alue

5 929.87

4 940.14

3 952.71

2 966.48

1 982.35

0 1,000.00

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y Hence what do you conclude????

y For a required rate of return of 13%( which is greaterthan the coupon rate of 11%), the value of the bond

will increase with the passage of time, i.e. until itsmaturity.

y Hence, When the required rate of return (kd) isgreater than the coupon rate, the discount on the

bond declines as the maturity approachesy What would you say if the required rate of return(kd)

is less than the coupon rate???????

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Home exercise

y Prove that if the required rate of return is less thanthe coupon rate, the premium on the bond declinesas maturity approaches

y Use the previous example with the required rate ofreturn 9% in this case.

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Effect of YTM on bond prices

y As the YTM determines a bonds market price andvice-versa, we can say that the bonds price willfluctuate in response to the change in market

interest rates.y Eg: The YTM of a Rs. 1,000 par value bond bearing a

coupon rate of 10% and maturing in 10 years is 12%.Thus, the market value of the bond is Rs.887( as

calculated previously, do a quick calculation). If theYTM increases to 14%, the market value of the bondwill drop to Rs.791.60 9 do a quick calculation)

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Effect of YTM on bond prices

y Hence what do we conclude????

y A bonds price moves inversely proportional to itsYield To Maturity

y The present value principle states that the presentvalue of a cash flow varies in inverse proportion tothe interest rate used as a discount rate. As such ifthe YTM of the bond rises, the bonds market price

drops and if the YTM falls, the bonds market pricerises.

y How would this relation look graphically????

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Risks associated in Debt Investments

y Interest Rate Risk Price Risk and ReinvestmentRisk

y Inflation Risk/ Purchasing Power Risk

y Default / Credit Risky Call Risk

y Liquidity Risk

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Yield Curve

Yield Curve shows the relation between YTM (in %)and the term to Maturity ( in yrs). It plots theinterest rate, at a set point of time of bonds having

equal credit quality, but different maturity dates.

The shape of the yield curve is closely scrutinized,because it helps to give an idea of future interest rate

change and economic activity.

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Yield Curve

Generally it is upward sloping , indicating that longterm rates are greater than the short term rates.

YTM

Maturity

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Yield Curve

y Can we have an inverted yield curve?

y Or a Flat Yield Curve?YTM

Maturity

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Thank You

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Bond Valuation 1

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