Question

Firms ABC and XYZ are identical except for their use of debt and the interest rates they pay. ABC has more debt and must pay a higher interest rate. Based on the data as shown below, how much higher or lower will ABC's ROE be versus that of XYZ, i.e., what is ROEABC – ROEXYZ?

Applicable to Both Firms Firm ABC's & Data Firm XYZ's

Data Assets $3,000,000 (same for both )

Debt ratio 70%(ABC COMP.)

Debt ratio 20%(XYZ COM)

EBIT $500,000 (SAME)

Int. rate 12%(ABC COMP)

Int. rate 10% (XYZ)

Tax rate 35%(SAME)

Answer 1

Debt Ratio = Total Debt/Total Assets

Debt ratio for XYZ = 20%

=> Debt of XYZ = 20% of Total assets = 600,000

Equity of XYZ = Total Assets - Total Debt = 2,400,000

Debt ratio of ABC = 70%

=> Debt of ABC = 2,100,000

Equity of ABC = Total Assets - Total Debt = 900,000

EBIT is same for both the compnies = 500,000

Interest for ABC = 12% of toral debt of ABC = 252,000

PBT of ABC = EBIT - Interest = 248,000

Tax = 35%

PAT = PBT*(1 - tax rate) = 161,200

ROE of ABC = PAT/Equity of ABC = 17.911%

Equity of XYZ = Total Assets - Total Debt = 2,400,000

EBIT is same for both the compnies = 500,000

Interest for XYZ = 10% of toral debt of ABC = 60,000

PBT of ABC = EBIT - Interest = 440,000

Tax = 35%

PAT = PBT*(1 - tax rate) = 286,000

ROE of XYZ = PAT/Equity of XYZ = 11.917%

ROE of ABC is higher than ROE of XYZ by 5.994% points.