1. **Problem Statement:** Calculate the value of a bond issued by City Development Corporation Ltd. with a face value of Tk. 5,000, a 6-year maturity, a 12% annual coupon rate payable semiannually, and cost of capital at (a) 10% and (b) 14%. Determine if an investor should buy the bond. 2. **Formula and Explanation:** The bond price is the present value of all future coupon payments plus the present value of the face value at maturity. Coupon payment per period: $$C = \frac{12\%}{2} \times 5000 = 0.06 \times 5000 = 300$$ Number of periods: $$n = 6 \times 2 = 12$$ Present value of coupons: $$PV_{coupons} = C \times \frac{1 - (1 + r)^{-n}}{r}$$ Present value of face value: $$PV_{face} = 5000 \times (1 + r)^{-n}$$ Where $r$ is the semiannual cost of capital rate. 3. **Calculations:** (a) For 10% annual cost of capital, semiannual rate: $$r = \frac{10\%}{2} = 0.05$$ $$PV_{coupons} = 300 \times \frac{1 - (1 + 0.05)^{-12}}{0.05} = 300 \times 8.8633 = 2658.99$$ $$PV_{face} = 5000 \times (1 + 0.05)^{-12} = 5000 \times 0.5568 = 2784.00$$ Bond value = $$2658.99 + 2784.00 = 5442.99$$ (b) For 14% annual cost of capital, semiannual rate: $$r = \frac{14\%}{2} = 0.07$$ $$PV_{coupons} = 300 \times \frac{1 - (1 + 0.07)^{-12}}{0.07} = 300 \times 7.5361 = 2260.83$$ $$PV_{face} = 5000 \times (1 + 0.07)^{-12} = 5000 \times 0.4360 = 2180.00$$ Bond value = $$2260.83 + 2180.00 = 4440.83$$ 4. **Interpretation:** - At 10% cost of capital, bond value (5442.99) is above face value (5000), so the bond is attractive. - At 14% cost of capital, bond value (4440.83) is below face value, so the bond is less attractive. **Final answer:** - Bond value at 10% cost of capital: Tk. 5442.99 - Bond value at 14% cost of capital: Tk. 4440.83 An investor should buy the bond if their required return is 10% but not if it is 14%.