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 $5.75 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 25% debt-to-capital ratio and pays only 8% interest on its debt. Neither firm uses preferred stock in its capital structure.

1. 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   %
2. 
   
3. 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    %
4. 
   
5. 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 = $ 5.75 million, Tax Rate = t = 40%, Debt-to-Capital Ratio = 60% and Interest Rate = 12 %

Net Operating Profit After-Tax = NOPAT = EBIT x (1-Tax Rate) = 5.75 x (1-0.4) = $ 3.45 million

ROIC = (NOPAT / Invested Capital) x 100 = (3.45/23) x 100 = 15 %

Debt = 60% of Invested Capital = 0.6 x 23 = $ 13.8 million and Equity = 40% of Invested Capital = 0.4 x 23 = $ 9.2 million

LL:

Total Invested Capital = $ 23 million, EBIT = $ 5.75 million, Tax Rate = t = 40%, Debt-to-Capital Ratio = 25% and Interest Rate = 8 %

Net Operating Profit After-Tax = NOPAT = EBIT x (1-Tax Rate) = 5.75 x (1-0.4) = $ 3.45 million

ROIC = (NOPAT / Invested Capital) x 100 = (3.45/23) x 100 = 15 %

Debt = 60% 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 = $ 5.75 million

Interest Expense = Debt x Interest Expense = 13.8 x 0.12 = $ 1.656 million

PBT (Profit Before Tax) = 5.75 - 1.656 = $ 4.094 million

Tax Expense = PBT x Tax Rate = 4.094 x 0.4 = $ 1.6376 million

Net Income = PBT - Tax Expense = 4.094 - 1.6376 =$ 2.4564 million

Equity Value = $ 9.2 million

ROE = (2.4564 / 9.2) x 100 = 26.7 %

LL:

EBIT = $ 5.75 million

Interest Expense = Debt x Interest Expense = 5.75 x 0.08 = $ 0.46 million

PBT (Profit Before Tax) = 5.75 - 0.46 = $ 5.29 million

Tax Expense = PBT x Tax Rate = 5.29 x 0.4 = $ 2.116 million

Net Income = PBT - Tax Expense = 5.29 - 2.116 =$ 3.174 million

Equity Value = $ 17.25 million

ROE = (3.174 / 17.25) x 100 = 0.184 or 18.4 %

(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 = $ 5.75 million

Interest Expense = 0.15 x 13.8 = $ 2.07 million

PBT = EBIT - Interest Expense = 5.75 - 2.07 = $ 3.68 million

Tax Expense = PBT x Tax Rate = 3.68 x 0.4 = $ 1.472 million

Net Income = 3.68 - 1.472 = $ 2.208 million

Equity Value = $ 9.2 million

ROE = (2.208 / 9.2) x 100 = 24 %