Question

Assume that Rf= 6 percent and the market risk premium (Km -Rf ) is 7.0 percent. Compute Kj for the following betas, using Formula 11A-2.

a. 0.6

b. 1.3

c. 1.9

Short answer

1. The Kj for beta 0.6 is 10.42%
2. The Kj for beta 1.3 is 15.1%
3. The Kj for beta 1.9 is 19.3%

Step-by-step solution

Meaning of Cost of Equity

Cost of equity refers to a return that an investor must expect from the company for his investment, which is the cost for the company.

Computation of Kj if the beta is 0.6

$\begin{array}{rcl}{\mathit{K}}_{\mathbf{j}}& \mathbf{=}& {\mathit{R}}_{\mathbf{f}}\mathbf{+}\mathit{\beta }\mathbf{(}{\mathit{K}}_{\mathbf{m}}\mathbf{-}{\mathit{R}}_{\mathbf{f}}\mathbf{)}\\ & \mathbf{=}& \mathbf{6}\mathbf{\%}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{6}\mathbf{\times }\left(7\%\right)\\ & \mathbf{=}& \mathbf{6}\mathbf{\%}\mathbf{+}\mathbf{4}\mathbf{.}\mathbf{2}\mathbf{\%}\\ & \mathbf{=}& \mathbf{10}\mathbf{.}\mathbf{42}\mathbf{\%}\\ & & \end{array}$

Computation of Kjif the beta is 1.3

$\begin{array}{rcl}{\mathit{K}}_{\mathbf{j}}& \mathbf{=}& {\mathit{R}}_{\mathbf{f}}\mathbf{+}\mathit{\beta }\mathbf{(}{\mathit{K}}_{\mathbf{m}}\mathbf{-}{\mathit{R}}_{\mathbf{f}}\mathbf{)}\\ & \mathbf{=}& \mathbf{6}\mathbf{\%}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{\times }\left(7\%\right)\\ & \mathbf{=}& \mathbf{6}\mathbf{\%}\mathbf{+}\mathbf{9}\mathbf{.}\mathbf{1}\mathbf{\%}\\ & \mathbf{=}& \mathbf{15}\mathbf{.}\mathbf{1}\mathbf{\%}\\ & & \end{array}$

Computation of Kjif the beta is 1.9

$\begin{array}{rcl}{\mathit{K}}_{\mathbf{j}}& \mathbf{=}& {\mathit{R}}_{\mathbf{f}}\mathbf{+}\mathit{\beta }\mathbf{(}{\mathit{K}}_{\mathbf{m}}\mathbf{-}{\mathit{R}}_{\mathbf{f}}\mathbf{)}\\ & \mathbf{=}& \mathbf{6}\mathbf{\%}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{9}\mathbf{\times }\left(7\%\right)\\ & \mathbf{=}& \mathbf{6}\mathbf{\%}\mathbf{+}\mathbf{13}\mathbf{.}\mathbf{3}\mathbf{\%}\\ & \mathbf{=}& \mathbf{19}\mathbf{.}\mathbf{3}\mathbf{\%}\\ & & \end{array}$