Question

Morales Publishing's tax rate is 30%, its beta is 1.20, and it uses no debt. However, the CFO is considering moving to a capital structure with 30% debt and 70% equity. If the risk-free rate is 5.0% and the market risk premium is 6.0%, by how much would the capital structure shift change the firm's cost of equity? 1.53% 1.70% 2.16% 2.05% 1.87%

Answer 1

Solution:

Calculation of Cost of equity when the capital structure has only equity i.e., no debt:

As per the information given in the question we have:

Existing Beta = Unlevered Beta = β_U = 1.20 ( Since it uses no debt )

Risk free rate = 5.0 %    ; Market Risk Premium = 6.0 %

The Cost of equity of a firm β = 1.20, is calculated using the following formula:

Cost of equity = R_F + [ β * ( R_M - R_F ) ]

Where

R_F = Risk free rate of return   ; β = Beta ; ( R_M – R_F ) = Market risk Premium

As per the information given in the question we have

R_F = 5 %   ;      ( R_M – R_F )   = 6 %   ;   β = 1.20

Applying the above values in the formula we have

= 5 % + [ 1.20 * 6 % ]

= 5 % + 7.2 % = 12.20 %

Thus the cost of equity when the firm uses no debt = 12.20 %

Calculation of Cost of equity when the capital structure has debt and equity:

The CFO is considering moving to a capital structure with 30% debt and 70% equity.

Thus the existing Beta has to be adjusted for the same. The existing Beta has to be levered to include the debt.

The formula for calculating Levered Beta is

β_L = β_U * [ 1 + ((Debt /Equity ) * ( 1 – T)) ]

Where β_L = Levered Beta   ; β_U = Unlevered Beta

As per the information given in the question we have

β_U =1.20 ;   Debt /Equity = 3 0% / 70 % = 0.3 / 0.7 = 0.43    ;

T = 30 % = 0.30

Applying the above values in the formula we have

= 1.20 * [ 1 + ( 0.43 * ( 1 – 0.3 ) ) ]

= 1.20 * [ 1 + ( 0.43 * 0.7 ) ]

= 1.20 * [ 1 + 0.3010 ]

= 1.20 * 1.3010

=1.56

Thus the Levered Beta = 1.56

The Cost of equity of a firm when β = 1.56, is calculated using the following formula:

Cost of equity = R_F + [ β * ( R_M - R_F ) ]

Where

R_F = Risk free rate of return   ; β = Beta ; ( R_M – R_F ) = Market risk Premium

As per the information given in the question we have

R_F = 5 %   ;      ( R_M – R_F )   = 6 %   ;   β = 1.56

Applying the above values in the formula we have

= 5 % + [ 1.56 * 6 % ]

= 5 % + 9.36 % = 14.36 %

= 14.36 %

Thus the cost of equity when the firm uses 30 % debt and 70 % equity = 14.36 %

From the calculations made above, we already know that when the firm uses no debt the cost of equity = 12.20 %

Thus the capital structure shift changes the cost of equity by = 14.36 % - 12.20 % = 2.16 %

Thus the solution is Option 3 = 2.16 %