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Bonds and Their Valuation

Key features of bonds Bond valuation Measuring yield Assessing risk

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What is a bond?

A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.

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Par value (face value) Coupon rate Coupon payment Maturity date

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Key Features of a Bond

Face Value Face value is called par value. A

bond is generally issued at a par value of taka 100 or 1000 and interest is paid on face value.Face amount of the bond, which is paid at maturity

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Interest rate/ Coupon Interest Rate stated interest rate (generally fixed)

paid by the issuer. Interest rate is fixed and known to the

bondholders. Interest is also called coupon rate. It is a rate mentioned on the certificate. Multiply by par to get taka payment of

interest

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Maturity A bond is issued for a specified

period of time. It is paid repaid on maturity. Issue date – when the bond was

issued.

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Present Value of Cash Flows as Rates Change

Bond Value = PV of coupons + PV of par

Bond Value = PV annuity + PV of lump sum

Remember, as interest rates increase present values decrease

So, as interest rates increase, bond prices decrease and vice versa

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Perpetual Bond:

Bonds which will never mature are known as perpetual bonds.

In case of perpetual bond, there is no maturity or terminal value, the value of the bonds would simply be discounted value of the infinite stream of interest flows.

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Example: A bond will pay tk 70 interest

annually. What would be its value if the required rate of return is 8%. What would be the value of the bond?

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Discount Rate Value of Bond

4 1750

5 1400

6 1166.67

7 1000

8 875

9 777.78

10 700

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If the interest rate is 7%, the value of the bond will be tk. 1,000 and if it is 9% the value will be tk. 777.78.

Thus, value of the bond will decrease as the interest rate increase.

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Yield to Maturity

We have so far assumed that the bond’s required rate of return is given for calculating its value.

We may be required rate to calculate the required rate of return when the bond’s price and cash flows are known. This rate is also known as yield to maturity (YTM) or internal rate of return

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Bond maturity and interest Rate Risk: The value of the bond depends upon the

interest rate. As the interest changes, the value of a

bond also varies. There is an inverse relationship between the value of the bond and interest rate.

The value will decline when the interest rate rises and vice-versa.

Interest rates have the tendency of rising or falling in practice. Thus, investors investing their funds in bonds are exposed to risk from increasing or falling interest rates.

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Interest Rate

Value of 5 year bond

Value of 10 year bond

Value of perpetual bond

4 1134 1244 1750

5 1087 1155 1400

6 1042 1073 1167

7 1000 1000 1000

8 961 933 875

9 922 871 778

10 886 816 700

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Example: The value of a 5 year bond comes down to

960.51 from 1,000 when interest rate is assumed to rise from 7% to 8%, resulting in a loss of 39.49 to the bondholder.

At 7% interest rate, values of all three bonds are same, tk.1000. When interest rate rises to say 8%, 5 year bond falls to 961, 10 year bond to 933 and perpetual bond further to 875.

Similarly, the value of long term bond will fluctuate (increase) more when rates fall below 7 percent.

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The differential value response to interest rates changes between short and long term bond will always be true.

Two bonds have different exposure to interest ate risk- the one with longer maturity is exposed to greater degree of risk from increasing interest rates

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Behavior of Bond Price When the market required rate of return

is more than the stated coupon rate, the price of the bond will be less than its face value. Such a bond is said to be selling at a discount from face value. The amount by which the face value exceeds the current price is the bond discount.

If a bond sells at a discount, then P0<Par and YTM > Coupon Rate

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When the market required rate of return is less than the stated coupon rate, the price of the bond will be more than its face value. Such a bond is said to be selling at a premium over face value. The amount by which the current price exceeds the face value is the bond premium.

If a bond sells at a premium, then P0>Par and YTM<Coupon Rate

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When the market required rate of return equals the stated coupon rate, the price of the bond will equal its face value. Such a bond is said to be selling at par.

If a bond sells at par, then P0 =Par and YTM= Coupon Rate.

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If interest rates rise so that the market required rate of return increases, the bond’s price will fall. If interest rate falls, the bond’s price will increase. In short, interest rates and bond prices move n opposite directions.

For a given change in market required return, the price of a bond will change by a greater amount, the longer its maturity.

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Bond Prices: Relationship Between Coupon and Yield

If YTM = coupon rate, then par value = bond price

If YTM > coupon rate, then par value > bond price Why? Selling at a discount, called a discount bond

If YTM < coupon rate, then par value < bond price Why? Selling at a premium, called a premium bond

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Zero Coupon Bonds A bond that pays no interest but sells at

a deep discount from its face value; it provides compensation to investors in the form price appreciation.

In other words, a bond that pays no coupons at all must be offered at a price much lower than its face value. Such bonds are called zero coupon bonds.

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Why buy a bond that pays no interest?

The buyer of such a bond does receive a return. This return consists of the gradual increase (appreciation) in the value of the security from its original, below face value purchase price until it is redeemed at face value on its maturity date.

Value of Bond= (Face value) /(1+kd)^n

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