2. BOND VALUATION Dr. Rana Singh Associate Professor www.ranasingh.org

3. 2 CONTENTS Introduction Bond Returns coupon rate current yield spot interest rate yield to maturity yield to call Bond Prices Bond Pricing Theorems Bond Risks Bond Duration

4. 3 INTRODUCTION Bonds are Long-term fixed income securities. Debentures are also long-term fixed income securities. Both of these are debt securities. The two major categories of bonds are government bonds & corporate bonds. There are the two main features of bonds such as callability and convertibility.

5. 4 BOND RETURNS COUPON RATE:- It is the nominal rate of interest fixed and printed on the bond certificate. It is calculated on the face value of the bond. It is the rate at which interest is payable by the issuing company to the bondholder.

6. 5 BOND RETURNS (CONT….) CURRENT YIELD:- The current market price of a bond in the secondary market may differ from its face value. The current yield relates the annual interest receivable on a bond to its current market price. It can be expressed as follows:- Where I n = Annual Interest P o = Current market price current yield=I n /P o × 100

7. 6 BOND RETURNS (CONT….) SPOT INTEREST RATE :- Zero coupon bond is a special type of bond which does not pay annual interests. The return on this bond is in the form of a discount on issue of the bond. This type of bond is also called pure discount bond or deep discount bond. Spot interest rate is the annual rate of return on a bond that has only one cash inflow to the investor.

8. 7 BOND RETURNS (CONT….) YIELD TO MATURITY (YTM):- This is the most widely used measure of return on bonds. It may be defined as the compounded rate of return an investor is expected to receive from a bond purchased at the current market price and held to maturity. It is really the internal rate of return earned from holding a bond till maturity. YTM depends upon the cash outflow for purchasing the bond, that is, the cost or

9. 8 BOND RETURNS (CONT….) Current market price of the bond as well as the cash inflows from the bond, namely the future interest payments and the terminal principal repayment. YTM is the discount rate that makes the present value of cash inflows from the bond equal to the cash outflow for purchasing the bond. The relation between the cash outflow, the cash inflow and the YTM of a bond can be expressed as: MP = Ct TV (1 + YTM) t (1 + YTM) n

10. 9 BOND RETURNS (CONT….) Where :- MP = Current market price of the bond Ct = Cash inflow from the bond throughout the holding period. TV = Terminal cash inflow received at the end of the holding period.

11. 10 BOND PRICING THEOREMS The relation between bond prices and changes in the market interest rates have been stated by Burton G. Malkiel in the form of five general principles. These are known as Bond pricing theorems. The five principles are:- Bond prices will move inversely to market interest changes. Bond price variability is directly related to the term to maturity; which means, for a given change in the level of market interest rates, change in bond prices are greater for longer-term maturities.

12. 11 BOND PRICING THEOREMS(CONT…..) A bonds sensitivity to changes in market interest rate increases at a diminishing rate as the time remaining until its maturity increases. The price changes resulting from equal absolute increases in market interest rates are not symmetrical, i.e. for any given maturity, a decrease in market interest rate causes a price rise that is larger than the price decline that results from an equal increase in market interest rate.

13. 12 BOND PRICING THEOREMS (CONT…..) Bond price volatility is related to the coupon rate, which implies that the percentage change in a bonds price due to a change in the market interest rate will be smaller if its coupon rate is higher.

14. 13 BOND RISKS Two types of risk are associated with investment in bonds, namely default risk and interest rate risk. DEFAULT RISK:- Default risk refers to the possibility that a company may fail to pay the interest or principal on the stipulated dates. Poor financial performance of the company leads to such defaults.

15. 14 BOND RISKS (CONT…..) INTEREST RATE RISK:- The risk that an investment's value will change due to a change in the absolute level of interest rates. Such changes usually affect securities inversely and can be reduced by diversifying or hedging. Interest rate risk affects the value of bonds more directly than stocks, and it is a major risk to all bondholders. As interest rates rise, bond prices fall and vice versa.

16. 15 BOND DURATION Duration is the weighted average measure of a bonds life. The various time periods in which the bond generates cash flows are weighted according to the relative size of the present value of those flows. The formula for computing duration d is:- (t) (C t ) d= (1 + k) t C t (1 + k) t

17. 16 BOND DURATION (CONT…..) Where :- C t = Annual cash flow including interest & repayment of principal. n = Holding period. k = Discount rate which is the market interest rate. t = The time period of each cash flow.