1. **Problem Statement:** Calculate the price of a debenture with principal Shs 1,000, term 20 years, semi-annual payments, for market interest rates 20%, 16%, and 12%. 2. **Formula Used:** The price of a debenture (bond) is the present value of its future cash flows, which include the semi-annual coupon payments and the principal repayment at maturity. Price = Present Value of Coupons + Present Value of Principal Where: - Coupon Payment = Principal \times Coupon Rate per period - Number of periods = Term \times 2 (because semi-annual) - Market interest rate per period = Annual market rate / 2 3. **Assumption:** Since coupon rate is not given, we assume the coupon rate equals the market rate for each case to calculate price (price equals par). If coupon rate differs, price calculation would differ. Here, we calculate price assuming coupon rate equals market rate. 4. **Calculations:** For each market rate $r$, semi-annual rate $i = \frac{r}{2}$, number of periods $n = 20 \times 2 = 40$. Coupon payment $C = 1000 \times i$. Price $P = C \times \frac{1 - (1 + i)^{-n}}{i} + 1000 \times (1 + i)^{-n}$. **Case 1: Market rate 20%** $i = 0.20 / 2 = 0.10$ $C = 1000 \times 0.10 = 100$ Calculate present value of coupons: $$PV_{coupons} = 100 \times \frac{1 - (1 + 0.10)^{-40}}{0.10}$$ Calculate present value of principal: $$PV_{principal} = 1000 \times (1 + 0.10)^{-40}$$ Calculate powers: $(1 + 0.10)^{-40} = (1.10)^{-40} \approx 0.02209$ So, $$PV_{coupons} = 100 \times \frac{1 - 0.02209}{0.10} = 100 \times \frac{0.97791}{0.10} = 100 \times 9.7791 = 977.91$$ $$PV_{principal} = 1000 \times 0.02209 = 22.09$$ Price: $$P = 977.91 + 22.09 = 1000$$ **Case 2: Market rate 16%** $i = 0.16 / 2 = 0.08$ $C = 1000 \times 0.08 = 80$ $(1 + 0.08)^{-40} = (1.08)^{-40} \approx 0.04632$ $$PV_{coupons} = 80 \times \frac{1 - 0.04632}{0.08} = 80 \times \frac{0.95368}{0.08} = 80 \times 11.9209 = 953.67$$ $$PV_{principal} = 1000 \times 0.04632 = 46.32$$ Price: $$P = 953.67 + 46.32 = 999.99 \approx 1000$$ **Case 3: Market rate 12%** $i = 0.12 / 2 = 0.06$ $C = 1000 \times 0.06 = 60$ $(1 + 0.06)^{-40} = (1.06)^{-40} \approx 0.09722$ $$PV_{coupons} = 60 \times \frac{1 - 0.09722}{0.06} = 60 \times \frac{0.90278}{0.06} = 60 \times 15.0463 = 902.78$$ $$PV_{principal} = 1000 \times 0.09722 = 97.22$$ Price: $$P = 902.78 + 97.22 = 1000$$ 5. **Explanation:** Since coupon rate equals market rate in each case, the price equals the principal (par value) 1000 Shs. --- **Note:** For 4.b) explanation of four factors influencing share price is not solved here as per instructions to solve only first question. **Final Answer:** Price of debenture for each market rate is approximately 1000 Shs.