Question

Firms HL and LL are identical except for their financial leverage ratios and the interest rates they pay on debt. Each has $17 million in invested capital, has $3.4 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 12% interest on its debt, whereas LL has a 30% 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 30% 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

Solution:
a.	ROIC for firm LL is 12.00%
	ROIC for firm HL is 12.00%
Working Notes:
	Return on invested capital (ROIC ) will be same both of the firm as both have same amount of invested capital, generate same amount of EBIT and are in same tax bracket.
	And
	Return on invested capital (ROIC ) = EBIT x ( 1 - tax rate)/Invested capital
	Return on invested capital (ROIC ) = $3,400,000 x ( 1 - 0.40)/$17,000,000
	Return on invested capital (ROIC ) = 0.1200
	Return on invested capital (ROIC ) = 12.00%
b.	ROE for firm LL is 14.57%
	ROE for firm HL is 17.87%
Working Notes:
	ROE for firm LL is 14.57%
	LL firm have 30% debt to capital ratio
	Total capital invested is $17,000,000
	Debt 30%     $17,000,000 x30% = $5,100,000
	Equity 70%    $17,000,000 x 70% = $11,900,000
	rate of interest on debt is 10%
	EBIT	$3,400,000
	Less: Interest	$510,000
	[10% x $5,100,000 debt =510,000]
	EBT	$2,890,000
	Less: Taxes @ 40%	$1,156,000
	[40% x $2,890,000]
	EAT	$1,734,000
	ROE for firm LL = EAT/Equity
	ROE for firm LL = $1,734,000 /$11,900,000
	ROE for firm LL = 0.1457142857
	ROE for firm LL = 14.57%
ROE for firm HL is 17.87%
	HL firm have 55% debt to capital ratio
	Total capital invested is $17,000,000
	Debt 55%     $17,000,000 x 55% = $9,350,000
	Equity 45%    $17,000,000 x 45% = $7,650,000
	rate of interest on debt is 12%
	EBIT	$3,400,000
	Less: Interest	$1,122,000
	[12% x   $9,350,000 debt = 1,122,000]
	EBT	$2,278,000
	Less: Taxes @ 40%	$911,200
	[40% x $2,278,000]
	EAT	$1,366,800
	ROE for firm HL = EAT/Equity
	ROE for firm HL = $1,366,800/$7,650,000
	ROE for firm HL = 0.17866667
	ROE for firm HL =17.87%
C.	New ROE for LL is 16.50%
Working Notes:
	New ROE for LL is 16.50%
	LL firm have 60% debt to capital ratio
	Total capital invested is $17,000,000
	Debt 60%     $17,000,000 x 60% = $10,200,000
	Equity 40%    $17,000,000 x 40% = $6,800,000
	rate of interest on debt is 15%
	EBIT	$3,400,000
	Less: Interest	$1,530,000
	[15% x $10,200,000]
	EBT	$1,870,000
	Less: Taxes @ 40%	$748,000
	[40% x $1,870,000]
	EAT	$1,122,000
	ROE for firm LL = EAT/Equity
	ROE for firm LL = $1,122,000 /$6,800,000
	ROE for firm LL = 0.16500
	ROE for firm LL = 16.50%
Please feel free to ask if anything about above solution in comment section of the question.