1. BOND VALUATION All bonds have the following characteristics: 1. A maturity date- typically 20-25 years. 2. A coupon rate- the rate of interest that the issuing company pays to the holder. 3. A face value- usually $1000 or $5000.

2. BOND VALUATION The value of a bond is the sum of the present value of the annual interest payments plus the present value of the face value; Where; interest = coupon rate x face value r = discount rate n = years to maturity

3. BOND VALUATION Where 1/(1+r) = discount rate

4. BOND VALUATION EXAMPLE Find the value of a 20 year, 10%, $1000 face value bond. The interest payment is given by:.10 x $1000 = $100/year THE FORMULA IS: PV = PV = $100(6.145) + $1000(.386) = $614.50 + $386 = $1000

5. BOND VALUATION if the coupon rate is 8%, then the formula for the value of the bond is; PV = $80(6.145) + $1000(.386) = $877.60 THE BOND SELLS AT A DISCOUNT

6. BOND VALUATION if the coupon rate is 12%, then the formula for the value of the bond is; PV = $120(6.145) + $1000(.386) = $1123.40 THE BOND SELLS AT A PREMIUM

7. BOND THEOREMS In this section we will look at the relationship between changes in bond prices and changes in term to maturity, coupon rate, and discount rates (market yields).

8. 7 1/4 %, due 1995, $1000 Face 8/8 10 3/8 %, due 1995, $1000 Face 8/8

9. 7 1/4 %, due 1995, $1000 Face 8/8 10 3/8 %, due 1995, $1000 Face 8/8

10. Change in Bond Prices Price of 7 1/4 bond fell by $3.75 or.42% Price of 10 3/8 bond fell by $5.00 or.48% When market yields fall unexpectedly, the prices of financial assets rise and vice-versa Theorem I

11. Consider two Bonds with 12% coupon of equal risk, one 5 year term, the other 15 year term

12. in 5 year bond is :in 15 year bond is : in 5 year bond is : in 15 year bond is : If yields fall to 11%:

13. Theorem II Holding coupon rate constant, for a given change in market yields, percentage changes in bond prices are greater the longer the term to maturity.

15. in 15 year bond is : in 10 year bond is : (% change in 15 - % change in 10)

16. in 5 year bond is : (% change in 10 - % change in 5)

17. Theorem III The percentage price changes described in Theorem II increase at a decreasing rate as N increases. - Slopes are percentage changes.

18. Consider: 12%, 8 year, $1000 coupon bond If yields move from 12% to 14%, price falls to 907. = If yields fall to 10%, price is 1107 =

19. Theorem IV Holding N constant and starting from same market yield, equal yield changes up or down do not result in equal percentage price changes. A decrease in yield increases prices more than an equal increase in yield decreases prices. Price changes are asymmetric with respect to changes in yield.

21. in 12% coupon = in 10% coupon = Theorem V Holding N constant and starting from the same yield,the greater the coupon rate, the smaller the percentage change in price for a given change in yield.

22. DURATION AND BOND PRICES The relationship between duration and the expected percentage price change expected from a change in market yield is closely approximated by: % P 0 = -DUR Percentage price changes accompanying the change in market yields between August 8th and August 10th can be estimated:

23. % = -5.6409 X = -.41% = -5.3366 X % = -.49%

24. ESTIMATING INTEREST RATE ELASTICITY E = -DUR E = == =