Answer: €5.40.

## Explanation This is a fixed income valuation problem for a preferred stock with a maturity date (making it similar to a bond). The key information: - **Par value**: €55 - **Intrinsic value (current price)**: €75 - **Maturity**: 5 years - **Required rate of return**: 7.2% - **Dividend payment frequency**: Semiannual Since this is a preferred stock with a maturity, we can value it using the bond pricing formula: \[ P = \frac{C}{r} \times \left[1 - \frac{1}{(1+r)^n}\right] + \frac{FV}{(1+r)^n} \] Where: - P = Current price = €75 - C = Semiannual dividend (what we need to find) - r = Semiannual required return = 7.2%/2 = 3.6% = 0.036 - n = Number of semiannual periods = 5 years × 2 = 10 periods - FV = Par value = €55 Rearranging the formula to solve for C: \[ C = \frac{P - \frac{FV}{(1+r)^n}}{\frac{1}{r} \times \left[1 - \frac{1}{(1+r)^n}\right]} \] First, calculate the present value of the par value: \[ \frac{€55}{(1.036)^{10}} = \frac{€55}{1.4243} = €38.62 \] Then calculate the annuity factor: \[ \frac{1}{0.036} \times \left[1 - \frac{1}{(1.036)^{10}}\right] = 27.7778 \times \left[1 - 0.7021\right] = 27.7778 \times 0.2979 = 8.275 \] Now solve for C: \[ C = \frac{€75 - €38.62}{8.275} = \frac{€36.38}{8.275} = €4.396 \] This is the **semiannual** dividend, which is approximately €4.40. However, looking at the options: - A: €3.96 - B: €4.40 - C: €5.40 Our calculation gives €4.396 ≈ €4.40, which corresponds to option B. **Wait, let me double-check the calculation:** Actually, I made an error in the interpretation. The question asks for the **semiannual dividend**, and my calculation gave €4.40. But let me verify with the exact calculation: 1. PV of par value: €55 / (1.036)^10 = €55 / 1.4243 = €38.62 2. Present value of dividends: €75 - €38.62 = €36.38 3. Annuity factor: (1 - 1/1.036^10) / 0.036 = (1 - 0.7021) / 0.036 = 0.2979 / 0.036 = 8.275 4. Semiannual dividend: €36.38 / 8.275 = €4.396 ≈ €4.40 This matches option B. However, I need to check if there's a different approach. **Alternative approach using financial calculator logic:** - N = 10 (5 years × 2) - I/Y = 3.6 (7.2%/2) - PV = -75 (price paid today, negative as outflow) - FV = 55 (par value received at maturity) - Compute PMT = ? Using the TVM formula: PMT = [PV - FV/(1+r)^n] / [1/r × (1 - 1/(1+r)^n)] This gives the same result: €4.396 ≈ €4.40 Therefore, the correct answer is **B. €4.40**. **Why not C (€5.40)?** This would be too high and would imply a much higher current price than €75 given the 7.2% required return. **Why not A (€3.96)?** This would be too low and would imply a lower current price than €75 given the 7.2% required return.