Your firm's debt ratio is only 5.00%,but the new CFO thinks that more debt should be employed.She wants to sell bonds and use the proceeds to buy back and retire common shares so the percentage of common equity in the capital structure (w_c)= 1 - w_d.Other things held constant,and based on the data below,if the firm increases the percentage of debt in its capital structure (w_d)to 60.0%,by how much would the ROE change,i.e. ,what is ROE_New - ROE_Old? Do not round your intermediate calculations. A) 14.95% B) 19.17% C) 17.59% D) 21.64% E) 14.42%

Question

Quizplus · Accepted Answer

The formula for calculating the new ROE after changing the debt ratio is:

ROEnew = ROEold + (ROEold - rS1U1B0) x (wS1U1B1dS1U1B0 - wS1U1B1cS1U1B0)

where:
ROEold = Previous Return on Equity
rS1U1B0 = Cost of Equity
wS1U1B1dS1U1B0 = New Percent of Debt
wS1U1B1cS1U1B0 = Old Percent of Debt

ROEold can be calculated as:
ROEold = Net Income / Total Equity
ROEold = $300,000 / $6,000,000
ROEold = 5.00%

rS1U1B0 can be calculated as:
rS1U1B0 = Risk-free rate + Beta x Market Risk Premium
rS1U1B0 = 3.00% + 1.20 x 6.00%
rS1U1B0 = 10.20%

Plugging in the values, we get:

ROEnew = 5.00% + (5.00% - 10.20%) x (60.0% - 5.00%)
ROEnew = 17.59%

Therefore, the answer is C, and the new ROE after changing the debt ratio would be 17.59% which is an increase of 12.59% from the original ROE of 5.00%.

Your Firm's Debt Ratio Is Only 5