(c) The investment portfolio of Mapeni Limited consists of shares in five companies operating in different industries.
(i) Compute the expected return from the market (Rm).
(ii) Calculate the beta coefficient for the portfolio (βp)
(iii) Determine the equation for the security market line.
(b) From casual observation, the optimal debt level is simply 10% debt, 90% equity since it has the lowest cost of debt (Kd). The examiner did not give the corporate tax rate but even if a 30% rate is assumed, the answer won‟t change. The Kd at various debt levels would be as follows:
The best gearing is 10% debt, 90% equity since Kd is lowest. However, this does not represent the optimal gearing (mix of debt and equity) at which point the overall cost of capital should be lowest and value of the firm maximized.
(c) (i)Expected market return ERM = (10 x 0.10) + (12 x 0.2) + (13 x 0.4) + (16 x 0.2) +
(17 x 0.10) = 13.5%
(iii) the security market line (SML) is in form of regression equation Y = a + bx Where Y = required returns of a security/ portfolio
a = Y intercept = risk free rate (Rf) 8% b = gradient = Beta factor
x = excess returns above risk free rate = ERM – Rf
Y = 8% + (13.5 – 8) B
for any portfolio j, required returns Rj = Rf + (ERM – Rf) Bj
= 0.08 + 0.055 Bj OR
Y = 0.08 + 0.055 B (SMC equation) For our portfolio,
Rj = 0.08 + 0.055 x 1.80 = 0.179 = 17.9%