Question

Consider a company which has β equity = 1.5 and β debt = 0.4. Suppose that the risk-free rate of interest is 6%, the expected return on the market E ( r M ) = 15%, and that the corporate tax rate is 40%. If the company has 40% equity and 60% debt in its capital structure, calculate its weighted average cost of capital using both the classic CAPM and the taxadjusted CAPM.

Answer 1

1. WACC = 11.26% (using classical CAPM)

2. WACC = 11.22% (using tax-adjusted CAPM)

Step-by-step explanation:

The Weighted Average Cost of Capital (WACC) is the cost of capital of a firm where its equity and debt structure is proportionate.

The CAPM is two types, classic CAPM and tax-adjusted CAPM.

Classic CAPM Formula:

`r_E=r_f+\beta(E_(rM)-r_f)`

Tax adjusted CAPM Formula:

`r_E=r_f+\beta(E_(rM)-r_f)+T*r_f(\beta - 1)`

** same way for
`r_D`, cost of debt

Where

`r_E` is the cost of equity

`r_f` risk free rate

`\beta` is the volatility

`E_(rM)` is the market return

T is the tax rate

Also, formula for WACC is:

WACC =
`E(r_E)+D(r_D)(1-T)`

Where

E is percentage of equity of the firm

D is the percentage of debt in the firm

`r_E` is cost of equity

`r_D` is cost of debt

T is tax rate

Now, using classical CAPM Approach:

Cost of Equity:

`r_E=r_f+\beta(E_(rM)-r_f)\\r_E=0.06+1.5(0.15-0.06)\\r_E=0.195`

Cost of Debt:

`r_D=r_f+\beta(E_(rM)-r_f)\\r_D=0.06+0.4(0.15-0.06)\\r_D=0.096`

WACC:

`WACC=E*r_E+D*r_D(1-T)\\WACC=0.4(0.195)+0.6(0.096)(1-0.4)WACC=0.11256`

THus,

WACC = 11.26%

Using Tax adjusted CAPM:

Cost of Equity:

`r_E=r_f+\beta(E_(rM)-r_f)+T*r_f(\beta - 1)\\r_E=0.06+1.5(0.15-0.06)+(0.4)(0.06)(1.5-1)\\r_E=0.207`

Cost of Debt:

`r_D=r_f+\beta(E_(rM)-r_f)+T*r_f(\beta - 1)\\r_D=0.06+0.4(0.15-0.06)+0.4*0.06(0.4-1)\\r_D=0.0816`

Now, WACC:

`WACC=E(r_E)+D(r_D)(1-T)\\WACC=0.4(0.207)+0.6(0.0816)(1-0.4)\\WACC=0.112176`

Thus,

WACC = 11.22%