Problem #4: You have been hired by a new firm that is just being started. The CF

Question

Problem #4: You have been hired by a new firm that is just being started. The CFO wants to finance with 60% debt, but the president thinks it would be better to hold the percentage of debt in the capital structure (wd) to only 10%. Other things held constant, and based on the data below, if the firm uses more debt, by how much would the ROE change, i.e, what is ROENew - ROEold? Other Data Operating Data 60% 13% 10% 9% $4,000 Higher w Capital ROIC=EBIT(1- Tax rate Higher interest rate Lower wd Lower interest rate Capital 13.00% 35%

Explanation / Answer

ROIC = EBIT(1-T)/Capital = 13%

EBIT = 0.13*capital/(1-0.35) = 0.13 * 4000/0.65 = 800

ROE = net income/equity

with lower wd:

debt = 10% of 4000 = 400

interest = 9% 0f 400 = 36

equity = capital - debt = 4000 - 400 = 3600

net income = (EBIT-interest)*(1-T) = (800-36)*(1-.35) = (800-36)*0.65 = 496.6

ROEOld = net income/equity = 496.6/3600 = 13.8%

with higher wd:

debt = 60% of 4000 = 2400

interest = 13% 0f 2400 = 312

equity = capital - debt = 4000 - 2400 = 1600

net income = (EBIT-interest)*(1-T) = (800-312)*(1-.35) = (800-312)*0.65 = 317.2

ROENew = net income/equity = 317.2/1600 = 19.83%

ROENew - ROEOld = 19.83% - 13.8% = 6.03%

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