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for a) when calculating the cost of equity for WACC, the answer in the back calculates first the Elfus asset beta for the other activity which give 1.078 and then calculates the asset beta for the component through weightings of the equity portion.
however, when calculating the asset beta of the other activity (1.078), it already considers the 75% of the equity, then why is it that it weights again when it does 1.078*0.75 to calculate the asset beta of the component?When calculating the asset beta of other activities they are applying the asset beta formula in order to calculate the asset beta given that we know the equity beta. In the formula we use the MV of the equity and the MV of the debt x (1-T), and 1-T is 75% because the tax rate is 25%.
Calculating the component asset beta it is using the fact that the total asset beta is equal to the weighted average of the two individual asset betas (as I explain in my lectures), and the weighting is 75% / 25% due to the fact that 75% of the equity is ‘other activities’ and 25% is ‘component’ production’.
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