1. 1 Bond Valuation Issuer (Seller) Investors (Buyers) $ $$ Bond Contract

2. 2 How much should you pay ?  Bond Value = ? Par C C C C C 1 2 4123n Buy the bond today

3. 3 Value of Bond today = C (PVIFA i, n ) + Par (PVIF i, n ) Bond Value C = Coupon Payment = coupon rate x par Par value or Face Value = $1,000 Par C C C C C 1 2 4123n

4. 4 An example You buy bond with $1,000 par value, Coupon rate 9% paid once per year, 5 years until maturity. Assume interest rate is 3%. What is the value of this bond? 1,000 90 90 90 90 90 Vb =+ PAR x PVIF i, n C x PVIFA i, n + 1,000 x PVIF 3%,5 90 x PVIFA 3%,5 1,274.77

5. 5 Find value of bond with $1,000 par value, Coupon rate 15% paid once per year, 4 years until maturity Vb = C (PVIFA i,n ) + Par (PVIF i,n ) $ 1,158.49 $ 1,000 $ 870.61 Bond Price = 10% = 15% = 20% If interest Bond sold at Premium Bond is sold at Par Bond sold at Discount Price-Yield relationship

6. 6 Semiannual coupon payment Coupon per period = coupon per year ÷ 2 Find value of bond with 10% coupon rate paid semiannually, 10 years maturity. Interest rate is 6% Bond Value = C (PVIFA i/2,nx2 ) + Par (PVIF i/2,nx2 ) Coupon per period = 10% x 1,000 ÷ 2= 50 Vb = 50 (14.8775) + 1,000 (0.5537) Vb = 50 (PVIFA 3%, 20 ) + 1,000 (PVIF 3%, 20 ) Vb = 1,297.57

7. 7 Finding the interest rate (YTM) = coupon per year + [(par – price) ÷ n] (par + price) ÷ 2 ***coupon per year = coupon rate x par ***par = $1,000 ***price = market price ***n = number of years

8. 8 Finding the interest rate (YTM) = coupon per year + [(par – price) ÷ n] (par + price) ÷ 2 ***coupon per year = 10% x 1000 = $ 100 ***par = $1,000 ***price = $ 850 ***n = 5 years

9. 9 Finding the interest rate (YTM) = $ 100 + [(1,000 – 850) ÷ 5] (1,000 + 850) ÷ 2 ***coupon per year = 10% x 1000 = $ 100 ***par = $1,000 ***price = $ 850 ***n = 5 years

10. 10 Finding the interest rate (YTM) = $ 100 + [(1,000 – 850) ÷ 5] (1,000 + 850) ÷ 2 = $ 100 + 30 925 = 0.1405 = 14.05 %

11. 11 Finding the interest rate (YTM) = $ 160 + [(1,000 – 1,100) ÷ 10] (1,000 + 1,100) ÷ 2 ***coupon per year = 16% x 1000 = $ 160 ***par = $1,000 ***price = $ 1,100 ***n = 10 years

12. 12 Finding the interest rate (YTM) = $ 160 + [(1,000 – 1,100) ÷ 10] (1,000 + 1,100) ÷ 2 = $ 160 - 10 1,050 = 0.1429 = 14.29 %

13. 13 Exercise 1. A corporate bond with a coupon rate of 7% matures in 4 years. Its price is currently $1,150. - Calculate the current yield on this bond - Calculate the yield to maturity on this bond

14. 14 Current Yield Formula The current yield refers simply to the annual payment (coupon) divided by the price. Y c = R/P where Y c is the current yield, R is the annual coupon payment in dollars, P is the market price.

15. 15 Current Yield Example Market price of 5-years treasury bond is $1,020. the bond is paying a coupon of $50 per year. Find the current yield. Y c = 50 1020 Y c = 0.049 or 4.9%

16. 16 Comparing bond value & market price If the market price of Bond < Bond Value Then the Bond is “Cheap” Bond is Undervalued (Underpriced) Investors will buy the Bond Demand > Supply Price will increase

17. 17 Comparing bond value & market price If the market price of Bond > Bond Value Then the Bond is “Expensive” Bond is Overvalued (Overpriced) Investors will sell the Bond Demand < Supply Price will decrease

18. 18 A bond will have a higher price if: Interest rate (yield) is …………….(higher/lower) Coupon rate, payment is …………….(higher/lower) Maturity is ……….(longer/shorter)