Consider a 4 coupon bond with a face value of 10000 It matur

Consider a 4% coupon bond with a face value of $10000. It matures in 5 years, and pays annual coupons (a total of five coupons). Estimate the price of the bond for a discount rate of 2%, 4% and 6%. What can you conclude from your answer?

Solution

Issue price: Discount rate 2% Par value of Bonds 10000 Annual interest (10000*4%) 400 Annuity factor for 5 years at 2% 4.7135 Present value factor f for 5th year 0.9057 Present value of interest 1885.4 Present value of maturity 9057 Issue price 10942.4 Discount rate 4%; Par value of Bonds 10000 Annual interest (10000*4%) 400 Annuity factor for 5 years at 4% 4.4518 Present value factor f for 5th year 0.8219 Present value of interest 1780.72 Present value of maturity 8219 Issue price 9999.72 Discount rate 6% Par value of Bonds 10000 Annual interest (10000*4%) 400 Annuity factor for 5 years at 6% 4.2124 Present value factor f for 5th year 0.7473 Present value of interest 1684.96 Present value of maturity 7473 Issue price 9157.96 Hence, it can be concluded that: When the market rate is lower than stated rate, the bonds will be issued at premium. When the market rate is equal to stated rate, the bonds are issued at par value. When the market rate is higher than stated rate, the bonds are issued at discount.