Chartered Financial Analyst Level 2

Explanation

Step 1: Calculate Initial EPS

• Earnings = $45,000,000
• Shares outstanding = 4,500,000
• Initial EPS = $45,000,000 / 4,500,000 =$10.00

Step 2: Calculate Interest Expense

• Debt raised = $25,000,000
• After-tax cost of debt = 7%
• Interest expense = $25,000,000 × 7$1,750,000

Step 3: Calculate New Earnings

• New earnings = Initial earnings - Interest expense
• New earnings = $45,000,000 -$1,750,000 = $43,250,000

Step 4: Calculate New Shares Outstanding

• Shares repurchased = 250,000
• New shares outstanding = 4,500,000 - 250,000 = 4,250,000

Step 5: Calculate New EPS

• New EPS = $43,250,000 / 4,250,000 =$10.176 ≈ $10.2

Verification:

• The company is paying $100 per share to repurchase shares
• Earnings yield = $10 /$100 = 10%
• Cost of debt = 7%
• Positive spread of 3% explains why EPS increases from $10.00 to$10.20

Therefore, the EPS after repurchase will be closest to $10.2.