Bond Value Bd8F8E

1. Problem: Calculate the value of a bond with semiannual interest payments and different required rates of return. 2. Formula: The value of a bond is the present value of its coupon payments plus the present value of its face value at maturity. 3. Important rules: - Coupon payment = (Coupon rate \times Face value) / Number of periods per year - Number of periods = Years to maturity \times Number of periods per year - Discount rate per period = Required annual rate / Number of periods per year 4. Given: Face value = Tk. 1000, Coupon rate = 8%, Years to maturity = 10, Interest paid semiannually. 5. Calculate coupon payment: $$\text{Coupon payment} = \frac{8\% \times 1000}{2} = 40$$ 6. Number of periods: $$10 \times 2 = 20$$ 7. Calculate bond value for each required rate of return: (i) Required rate = 6% annual, semiannual rate = 3% $$\text{Bond value} = 40 \times \frac{1 - (1 + 0.03)^{-20}}{0.03} + 1000 \times (1 + 0.03)^{-20}$$ Calculate: $$40 \times 14.8775 + 1000 \times 0.5537 = 595.1 + 553.7 = 1148.8$$ (ii) Required rate = 8% annual, semiannual rate = 4% $$\text{Bond value} = 40 \times \frac{1 - (1 + 0.04)^{-20}}{0.04} + 1000 \times (1 + 0.04)^{-20}$$ Calculate: $$40 \times 13.5903 + 1000 \times 0.4564 = 543.6 + 456.4 = 1000$$ (iii) Required rate = 12% annual, semiannual rate = 6% $$\text{Bond value} = 40 \times \frac{1 - (1 + 0.06)^{-20}}{0.06} + 1000 \times (1 + 0.06)^{-20}$$ Calculate: $$40 \times 11.4699 + 1000 \times 0.3118 = 458.8 + 311.8 = 770.6$$ 8. Interpretation: - When required rate is less than coupon rate (6% < 8%), bond sells at a premium (1148.8 > 1000). - When required rate equals coupon rate (8%), bond sells at par value (1000). - When required rate is greater than coupon rate (12% > 8%), bond sells at a discount (770.6 < 1000). Final answers: (i) Bond value = Tk. 1148.8 (premium) (ii) Bond value = Tk. 1000 (par value) (iii) Bond value = Tk. 770.6 (discount)