(5 pts) A 30-year 6% semi-annual coupon bond has a tenor of 18 years and a yield

Question

(5 pts) A 30-year 6% semi-annual coupon bond has a tenor of 18 years and a yield to maturity of 7.2%. If the PAR value of the bond is $1000, what is the price of the bond today?

2. (5 pts) A 30-year 6% semi-annual coupon bond has a yield to maturity of 8.1% and a PAR value of $1000. If the current price is 84.0723% of PAR, what must be the tenor, in years?

3. (5 pts) A 30-year 6% semi-annual coupon bond has a PAR value of $1000 and a current price of 103.2121% of PAR. If the tenor of the bond is 14 years, what must the yield to maturity be?

Explanation / Answer

1) The price of a bond is the sum total of the expected cash flows from the bond, if it is held till maturity, the discount rate being the market interest rate of 7.2% p.a. (3.6% semi annual). The expected cash flows from the subject bonds are: *the maturity value of $1000, and *the semi-annual interest payments of $30, which are in the form of an annuity. Therefore, price of the bond = 1000/1.036^36+30*(1.036^36-1)/(0.036*1.036^36) $          879.99 Answer 2) Using the above formula and keeping the market number of years as the unknown quantity, we have 840.723 = 1000/1.0405^n+30*(1.0405^n-1)/(0.036*1.036^n), where n is the tenor in half years. The value of n can be found out by trial and error only, using different values for n. Using n = 26, RHS = 1000/1.0405^26+30*(1.0405^26-1)/(0.0405*1.0405^26) = $          833.09 Using n = 24, RHS = 1000/1.0405^24+30*(1.0405^24-1)/(0.0405*1.0405^24) = $          840.72 At n = 24, the value of RHS equals the price. Hence, tenor in years = 24/2 = 12 Years Answer 3) YTM is that discount rate which equates the cash flows from the bond with its price, if it is held till maturity (for 14 years). The cash flows are the maturity value of $1000 at EOY 5 and the semi-annual interest of $30 for 28 half years. The relevant discount rate has to be found by trial and error. Discounting with 2% (half year rate), PV of the cash flows = = 1000/1.02^28+30*(1.02^28-1)/(0.02*1.02^28) = $    1,212.813 Discounting with 3% (half year rate), PV of the cash flows = $    1,000.000 (When coupon rate equals the YTM, the bonds price is its face value) The value of the semi-annual interest rate lies between 2% and 3%. It is 2 + (1212.813-1032.121)/(1212.813-1000) = 2.849 % YTM = 2.849*2 = 5.698 % Answer

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