Question

Firms HL and LL are identical except for their leverage ratios and the interest rates they pay on debt. Each has $25 million in invested capital, has $5 million of EBIT, and is in the 40% federal-plus-state tax bracket. Firm HL, however, has a debt-to-capital ratio of 55% and pays 11% interest on its debt, whereas LL has a 20% debt-to-capital ratio and pays only 10% 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. 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 %
3. Observing that HL has a higher ROE, LL's treasurer is thinking of raising the debt-to-capital ratio from 20% 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. ROIC for firm LL 12%

ROIC for firm HL 12%

B. ROE for firm LL 13.5%

ROE for firm HL 18.6%

C. New ROE for firm LL 16.5%

Step-by-step explanation:

A. Calculation to determine the return on invested capital (ROIC) for each firm

Using this formula

ROIC=EBIT(1-T)/Total Invested Capital

Let plug in the formula

ROIC=$5 million(1-.40)/$25 million

ROIC=$5 million*.60/$25 million

ROIC=$3 million/$25 million

ROIC=0.12*100

ROIC=12% for both firms

Therefore the return on invested capital (ROIC) for each firm is:

ROIC for firm LL is 12%

ROIC for firm HL is 12%

B. Calculation to determine the rate of return on equity (ROE) for each firm.

Calculation for ROE for firm LL

First step is to calculate the Debt

Debt=$25 million*20%

Debt=$5 million

Second step is to calculate the Debt Interest

Debt Interest=$5 million*10%

Debt Interest=$500,000

Third step is to calculate the EBIT of firm LL

EBIT of firm LL=$5 million- $500,000

EBIT of firm LL=$4,500,000

Fourth step is to calculate Tax owed

Tax owed =$4,500,000*40%

Tax owed =$1,800,000

Fifth step is to calculate the Net income of firm LL

Net income of firm LL=$4,500,000-$1,800,000

Net income of firm LL=$2,700,000

Sixth step is to calculate the Equity for firm LL

Equity for firm LL=$25million-$5 million

Equity for firm LL=$20 million

Now let calculate the ROE using this formula

ROE=Net income /Equity

Let plug in the formula

ROE=$2,700,000/$20 million*100

ROE=13.5%

Calculation for ROE for firm HL

First step is to calculate the Debt

Debt=$25 million*55%

Debt=$13,750,000

Second step is to calculate the EBIT of firm HL

EBIT of firm HL=$5 million-[(55%*$25 million)*11%]

EBIT of firm HL=$5 million-($13,750,000*11%)

EBIT of firm HL=$5 million-$1,512,500

EBIT of firm HL=$3,487,500

Third step is to calculate the Tax owed

Tax owed =$3,487,500*40%

Tax owed =$1,395,000

Fourth step is to calculate the Net income of firm HL

Net income of firm HL=$3,487,500-$1,395,000

Net income of firm HL=$2,092,500

Fifth step is to calculate the Equity for firm HL

Equity for firm HL=$25million- $13,750,000

Equity for firm HL=$11,250,000

Now let calculate the ROE using this formula

ROE=Net income /Equity

ROE=$2,092,500/$11,250,000*100

ROE=18.6%

Therefore the rate of return on equity (ROE) for each firm is:

ROE for firm LL is 13.5%

ROE for firm HL is 18.6%

C. Calculation to determine the new ROE for LL

First step is to calculate the debt

Debt=$25 million*60%

Debt=$15 million

Second step is to calculate the Debt Interest

Debt Interest=$15 million*15%

Debt Interest=$2,250,000

Third step is to calculate the EBIT of firm LL

EBIT of firm LL=$5 million- $2,250,000

EBIT of firm LL=$2,750,000

Fourth step is to calculate the Tax owed

Tax owed =$2,750,000*40%

Tax owed =$1,100,000

Fifth step is to calculate the Net income of firm LL

Net income of firm LL=$2,750,000-$1,100,000

Net income of firm LL=$1,650,000

Sixth step is to calculate the Equity for firm LL

Equity for firm LL=$25million-$15 million

Equity for firm LL=$10 million

Now let calculate the New ROE using this formula

ROE=Net income /Equity

Let Plug in the formula

ROE=$1,650,000/$10 million*100

ROE=16.5%

Therefore the new ROE for LL is 16.5%