1. **Problem 1a:** Calculate the value of a bond with face value RM1000, coupon rate 10%, maturity 15 years, and required return 13%. 2. **Formula:** The bond price is the present value of coupons plus the present value of face value: $$P = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$$ where $C$ is annual coupon, $r$ is required return, $F$ is face value, $n$ is years to maturity. 3. **Calculate coupon:** $C = 1000 \times 0.10 = 100$ 4. **Calculate present value of coupons:** Use the formula for annuity present value: $$PV_{coupons} = C \times \frac{1 - (1+r)^{-n}}{r} = 100 \times \frac{1 - (1+0.13)^{-15}}{0.13}$$ Calculate: $$1+0.13=1.13$$ $$1.13^{-15} = \frac{1}{1.13^{15}} \approx 0.1660$$ So, $$PV_{coupons} = 100 \times \frac{1 - 0.1660}{0.13} = 100 \times \frac{0.834}{0.13} \approx 100 \times 6.415 = 641.5$$ 5. **Calculate present value of face value:** $$PV_{face} = \frac{1000}{(1.13)^{15}} = 1000 \times 0.1660 = 166.0$$ 6. **Bond value:** $$P = 641.5 + 166.0 = 807.5$$ --- 7. **Problem 1b:** Compare the bond in (a) with a zero-coupon bond selling for RM150, face value RM1000, maturity 15 years. 8. **Calculate yield to maturity (YTM) of zero-coupon bond:** $$150 = \frac{1000}{(1 + r)^{15}} \Rightarrow (1 + r)^{15} = \frac{1000}{150} = 6.6667$$ Take 15th root: $$1 + r = 6.6667^{1/15}$$ Calculate: $$\ln(6.6667) \approx 1.8971$$ $$\frac{1.8971}{15} = 0.1265$$ $$1 + r = e^{0.1265} \approx 1.135$$ So, $$r = 0.135 = 13.5\%$$ 9. **Compare prices:** The bond in (a) is priced at RM820, which is higher than the calculated value RM807.5, indicating a slightly lower yield than 13%. The zero-coupon bond has a yield of 13.5%. 10. **Recommendation:** If Amanda requires 13% return, the bond in (a) is priced close to her required return but offers lower yield than zero-coupon bond (13.5%). The zero-coupon bond is cheaper but riskier due to no periodic coupons. If Amanda prefers steady income, choose bond (a); if she prefers higher yield and can wait, zero-coupon bond is better. --- 11. **Problem 2a i:** Calculate current value of stock with dividend RM2, growth 8%, required return 16%. 12. **Formula (Gordon Growth Model):** $$P_0 = \frac{D_1}{r - g}$$ where $D_1 = D_0 (1+g) = 2 \times 1.08 = 2.16$ 13. **Calculate:** $$P_0 = \frac{2.16}{0.16 - 0.08} = \frac{2.16}{0.08} = 27$$ 14. **Problem 2a ii:** Value of stock in 5 years: 15. **Calculate dividend in 5 years:** $$D_5 = D_0 (1+g)^5 = 2 \times 1.08^5 = 2 \times 1.4693 = 2.9386$$ 16. **Calculate price in 5 years:** $$P_5 = \frac{D_6}{r - g} = \frac{D_5 (1+g)}{r - g} = \frac{2.9386 \times 1.08}{0.08} = \frac{3.173}{0.08} = 39.66$$ --- 17. **Problem 2b:** Check if stock priced at RM10 is fairly priced given dividend next year RM1, growth 5%, cost of capital 10%. 18. **Calculate intrinsic value:** $$P_0 = \frac{D_1}{r - g} = \frac{1}{0.10 - 0.05} = \frac{1}{0.05} = 20$$ 19. **Compare:** Market price RM10 is less than intrinsic value RM20, so the stock is undervalued and a good buy. **Final answers:** - 1a: Bond value = RM807.5 - 1b: Recommend zero-coupon bond for higher yield or bond (a) for steady income - 2a i: Stock value = RM27 - 2a ii: Stock value in 5 years = RM39.66 - 2b: Stock is undervalued at RM10, intrinsic value RM20