1. **Problem statement:** We have bonds with a face value of Rs 1000, 10 years to maturity, an 11% annual coupon, current price Rs 1175, callable in 5 years at 109% of face value. We need to find: a) Yield to Maturity (YTM) b) Yield to Call (YTC) c) Which yield investors might expect and why. 2. **Formulas and rules:** - Coupon payment $C = 0.11 \times 1000 = 110$ Rs annually. - Yield to Maturity (YTM) is the interest rate $r$ that satisfies: $$ 1175 = \sum_{t=1}^{10} \frac{110}{(1+r)^t} + \frac{1000}{(1+r)^{10}} $$ - Yield to Call (YTC) is the interest rate $r_c$ that satisfies: $$ 1175 = \sum_{t=1}^{5} \frac{110}{(1+r_c)^t} + \frac{1090}{(1+r_c)^5} $$ - The call price is 109% of face value: $1090$ Rs. 3. **Calculating Yield to Maturity (YTM):** We solve for $r$ in: $$ 1175 = 110 \times \frac{1 - (1+r)^{-10}}{r} + \frac{1000}{(1+r)^{10}} $$ Using trial or financial calculator approximation: - At $r=8\%$, present value is approximately 1175, so YTM $\approx 8\%$. 4. **Calculating Yield to Call (YTC):** We solve for $r_c$ in: $$ 1175 = 110 \times \frac{1 - (1+r_c)^{-5}}{r_c} + \frac{1090}{(1+r_c)^5} $$ Using trial or financial calculator approximation: - At $r_c=7\%$, present value is close to 1175, so YTC $\approx 7\%$. 5. **Which yield might investors expect?** Since the bond is callable in 5 years at a premium, if interest rates fall, the issuer may call the bond, so investors expect to earn the lower yield to call (7%). If rates stay high, they get the YTM (8%). Usually, investors consider the yield to call as the expected yield because of the call risk. **Final answers:** - Yield to Maturity $\approx 8\%$ - Yield to Call $\approx 7\%$ - Investors expect to earn the Yield to Call because the bond may be called early, limiting their return.