Question

As a firm takes on more debt, its probability of bankruptcy Other factors held constant, a firm whose earnings are relatively volatile faces a chance of bankruptcy. Therefore, when other factors are held constant, a firm whose earnings are relatively volatile should use debt than a more stable firm. When bankruptcy costs become more important, they the tax benefits of debt. Green Goose Automation Company currently has no debt in its capital structure, but it is considering using some debt and reducing its outstanding equity. The firm's unlevered beta is 1.05, and its cost of equity is 10.35%. Because the firm has no debt in its capital structure, its weighted average cost of capital (WACC) also equals 10.35%. The risk-free rate of interest (rRF) is 3%, and the market risk premium (RP) is 7%. Green Goose's marginal tax rate is 30%. Green Goose is examining how different levels of debt will affect its costs of debt and equity, as well as its WACC. The firm has collected the financial information that follows to analyze its weighted average cost of capital (WACC). Complete the following table. Before-Tax D/A E/A Bond Cost of Debt Levered Cost of Beta (b) D/E Ratio WACC Ratio Ratio Rating (ra) Equity (rs) 0.0 1.0 0.00 1.05 10.35% 10.35% _ 0.2 0.8 0.25 A 8.1% 11.61% 10.42% ВВB 0.4 0.6 0.67 8.5% 1.54 13.78% 0.6 0.4 1.50 В 10.9% 2.15 11.80% 0.8 0.2 C 13.9% 3.99 30.93%

Answer 1

Ans:- As a firm takes on more debt, its probability of bankruptcy increases.

Other factors held constant, a firm whose earnings are relatively less volatile faces a greater chance of bankruptcy.

Therefore when other factors are held constant, a firm whose earnings are relatively less volatile should use less debt than a more stable firm.

When bankruptcy costs become more important they reduce the tax benefits of debt.

(1) In this question, the D/E ratio is given by( D/A ratio/ E/A ratio)

D/E ratio = 0.8/0.2 = 4.0

(2) Unleveraged beta is given by the formula Leverage beta/( 1 + (1- tax rate) * D/E ratio). By this formula we can calculate the value of Leveraged beta.Unleveraged beta is given 1.05

1.05 = Leveraged Beta/ ( 1 + (1 - 0.30) * 0.25)

1.05 = Leveraged Beta/ 1.175

Leveraged Beta = 1.05*1.175 = 1.23375 = 1.23 (approx)

(3) weighted average cost of capital is given by the formula.

= Cost of equity* E/A+ Cost of debt * D/A * (1- tax rate)

= 13.78 % * 0.6 + 8.5% * 0.4 *(1 - 0.30)

= 0.1378 * 0.6 + 0.085 * 0.4 * (1 - 0.30) = 0.10648

= 10.648%

(4) we can find another Wacc in the table with the same formula.

= Cost of equity * E/A + Cost of debt * D/A * (1- tax rate)

= 30.93% * 0.2 + 13.9% * 0.8 * (1 -0.30)

=0.3093 * 0.2 + 0.139 * 0.8 * (1 - 0.30)

= 0.1397 *100 = 13.97%

(5) By the WACC formula we can also find the cost of equity if other variables are given.Lets assume of cost of equity be X, then through WACC formula.

WACC = cost of equity * E/A + Cost of debt * D/A * (1 - tax rate)

11.80% = X * 0.4 + 10.9% * 0.6 * (1 - 0.30)

0.1180 = X * 0.4 + 0.109 * 0.6 * (1 - 0.30)

0.1180 = X * 0.4 + 0.04578

0.1180 - 0.04578 = X*0.4   

0.07222/0.4 = X or cost of equity = 0.18055 = 18.055%

Note:- Pls give thumps up if this answer helps you.