Question

Firms HL and LL are identical except for their financial leverage ratios and the interest rates they pay on debt. Each has $23 million in invested capital, has $3.45 million of EBIT, and is in the 25% federal-plus-state tax bracket. Firm HL, however, has a debt-to-capital ratio of 50% and pays 12% interest on its debt, whereas LL has a 25% 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: % ROIC for firm HL: % Calculate the rate of return on equity (ROE) for each firm. Round your answers to two decimal places. ROE for firm LL: % ROE for firm HL: % Observing that HL has a higher ROE, LL's treasurer is thinking of raising the debt-to-capital ratio from 25% 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. %

Answer 1

(a) HL: Total Invested Capital = $ 23 million, EBIT = $ 3.45 million, Tax Rate = t = 25%, Debt-to-Capital Ratio = 50% and Interest Rate = 12 %

Net Operating Profit After-Tax = NOPAT = EBIT x (1-Tax Rate) = 3.45 x (1-0.25) = $ 2.5875 million

ROIC = (NOPAT / Invested Capital) x 100 = (2.5875/23) x 100 = 11.25 %

Debt = 50% of Invested Capital = 0.5 x 23 = $ 11.5 million and Equity = 50% of Invested Capital = 0.5 x 23 = $ 11.5 million

LL:

Total Invested Capital = $ 23 million, EBIT = $ 3.45 million, Tax Rate = t = 25%, Debt-to-Capital Ratio = 25% and Interest Rate = 9 %

Net Operating Profit After-Tax = NOPAT = EBIT x (1-Tax Rate) = 3.45 x (1-0.25) = $ 2.5875 million

ROIC = (NOPAT / Invested Capital) x 100 = (2.5875/23) x 100 = 11.25 %

Debt = 25 % of Invested Capital = 0.25 x 23 = $ 5.75 million and Equity = 75% of Invested Capital = 0.75 x 23 = $ 17.25 million

(b) HL: EBIT = $ 3.45 million

Interest Expense = Debt x Interest Expense = 11.5 x 0.12 = $ 1.38 million

PBT (Profit Before Tax) = 3.45 - 1.38 = $ 2.07 million

Tax Expense = PBT x Tax Rate = 2.07 x 0.25 = $ 0.5175 million

Net Income = PBT - Tax Expense = 2.07 - 0.5175 =$ 1.5525 million

Equity Value = $ 11.5 million

ROE = (1.5525 / 11.5) x 100 = 13.5 %

LL:

EBIT = $ 3.45 million

Interest Expense = Debt x Interest Expense = 5.75 x 0.09 = $ 0.5175 million

PBT (Profit Before Tax) = 3.45 - 0.5175 = $ 2.9325 million

Tax Expense = PBT x Tax Rate = 2.9325 x 0.25 = $ 0.733125 million

Net Income = PBT - Tax Expense = 2.9325  - 0.733125 = $ 2.199375 million

Equity Value = $ 17.25 million

ROE = (2.199375 / 17.25) x 100 = 12.75 %

(c) New Debt Level = 60% of Invested Capital = 0.6 x 23 = $ 13.8 million, New Equity Value = 23 - 13.8 = $ 9.2 million, New Interest Rate = 15 %

EBIT = $ 3.45 million

Interest Expense = 0.15 x 13.8 = $ 2.07 million

PBT = EBIT - Interest Expense = 3.45 - 2.07 = $ 1.38  million

Tax Expense = PBT x Tax Rate = 1.38 x 0.25 = $ 0.345  million

Net Income = 1.38 - 0.345 = $ 1.035 million

Equity Value = $ 9.2 million

ROE = (1.035 / 9.2) x 100 = 11.25 %