1. **Problem Statement:** Calculate the portfolio standard deviation for a portfolio consisting of Chaga PLC and Toga PLC with given weights and standard deviations under different correlation coefficients: +1.00, 0.00, and -1.00. 2. **Formula:** The portfolio standard deviation $\sigma_p$ is given by: $$\sigma_p = \sqrt{w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_1 \sigma_2 \rho}$$ where $w_1, w_2$ are weights, $\sigma_1, \sigma_2$ are standard deviations, and $\rho$ is the correlation coefficient. 3. **Given Data:** - $w_1 = 0.42$, $\sigma_1 = 0.18$ - $w_2 = 0.58$, $\sigma_2 = 0.11$ 4. **Calculations:** **a. For $\rho = +1.00$:** $$\sigma_p = \sqrt{(0.42)^2 (0.18)^2 + (0.58)^2 (0.11)^2 + 2 \times 0.42 \times 0.58 \times 0.18 \times 0.11 \times 1}$$ Calculate each term: $$= \sqrt{0.1764 \times 0.0324 + 0.3364 \times 0.0121 + 2 \times 0.42 \times 0.58 \times 0.18 \times 0.11}$$ $$= \sqrt{0.0139 + 0.00407 + 0.0193} = \sqrt{0.03727} = 0.1931$$ **b. For $\rho = 0.00$:** $$\sigma_p = \sqrt{0.0139 + 0.00407 + 0} = \sqrt{0.01797} = 0.1340$$ **c. For $\rho = -1.00$:** $$\sigma_p = \sqrt{0.0139 + 0.00407 - 0.0193} = \sqrt{-0.00133}$$ Since variance cannot be negative, this means the portfolio standard deviation is zero or very close to zero due to perfect negative correlation: $$\sigma_p = 0$$ 5. **Assumptions of Modigliani & Miller (1958) Model:** - No taxes - No bankruptcy costs - Symmetric information - Investors and firms can borrow at the same risk-free rate - No transaction costs - Homogeneous expectations 6. **Capital Structure Data for Tibul PLC:** The data shows that as the debt to assets ratio increases, the share price and earnings per share increase, while the price to earnings ratio and WACC decrease, indicating a beneficial effect of moderate leverage on firm value and cost of capital.