Firms HL and LL are identical except for their financial leverage ratios and the

Question

Firms HL and LL are identical except for their financial leverage ratios and the interest rates they pay on debt. Each has $18 million in invested capital, has $2.7 million of EBIT, and is in the 40% federal-plus-state tax bracket. Firm HL, however, has a debt-to-capital ratio of 60% and pays 12% interest on its debt, whereas LL has a 40% debt-to-capital ratio and pays only 9% interest on its debt. Neither firm uses preferred stock in its capital structure.

Calculate the return on invested capital (ROIC) for each firm. Round your answers to two decimal places.

ROIC for firm LL is   %
ROIC for firm HL is   %

Calculate the rate of return on equity (ROE) for each firm. Round your answers to two decimal places.

ROE for firm LL is    %
ROE for firm HL is    %

Observing that HL has a higher ROE, LL's treasurer is thinking of raising the debt-to-capital ratio from 40% to 60% even though that would increase LL's interest rate on all debt to 15%. Calculate the new ROE for LL. Round your answer to two decimal places.

%

Explanation / Answer

Total invested capital = 18million and tax is 40%

HL debt to capital ratio is 60%
Thus debt = 0.6*18 = 10.8
and equity = 18-10.8 = 7.2
and interest rate is 12% thus after tax cost of debt = d*(1-tax) = 12*(1-0.4) = 7.2
hence interest expense = 10.8*0.072 = 0.7776

LL debt to capital ratio is 40%
Thus debt = 0.4*18 = 7.2
and equity = 18-7.2 = 10.8
and interest rate is 9% thus after tax cost of debt = d*(1-tax) = 9*(1-0.4) = 5.4
hence interest expense = 7.2*0.054 = 0.3888

ROIC = net income / invested capital = EBIT - interest * (1-tax) / invested capital
HL = (2.7-0.7776 * (1-0.4)) / 18 = 0.06408 = 6.408%
LL = (2.7-0.3888 * (1-0.4)) / 18 = 0.07704 = 7.704%

ROE = net income / equity = EBIT - interest * (1-tax) / equity
HL = (2.7-0.7776 * (1-0.4)) / 7.2 = 0.1602 = 16.20%
LL = (2.7-0.3888 * (1-0.4)) / 10.8 = 0.1284 = 12.84%

LL's treasurer is thinking of raising the debt-to-capital ratio from 40% to 60% even though that would increase LL's interest rate on all debt to 15%.
LL debt to capital ratio is 60%
Thus debt = 0.6*18 = 10.8
and equity = 18-10.8 = 7.2
and interest rate is 15% thus after tax cost of debt = d*(1-tax) = 15*(1-0.4) = 9
hence interest expense = 10.8*0.09 = 0.972

ROE = net income / equity = EBIT - interest * (1-tax) / equity
LL = (2.7-0.972 * (1-0.4)) / 7.2 = 0.144 = 14.40%

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