Diluted EPS Calculation

Step 1: Calculate Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Common Shares Basic EPS = (£45,000,000 - £5,000,000) / 12,000,000 Basic EPS = £40,000,000 / 12,000,000 = £3.33

Step 2: Calculate the "If-Converted" Method for Convertible Bonds

When using the if-converted method for convertible bonds:

1. Add back the after-tax interest expense to the numerator
2. Add the additional shares from conversion to the denominator

Interest expense on bonds: £40,000,000 × 10% = £4,000,000

After-tax interest expense: £4,000,000 × (1 - 0.25) = £4,000,000 × 0.75 = £3,000,000

Additional shares from conversion: 2,000,000 shares

Step 3: Calculate Diluted EPS

Diluted EPS = (Net Income - Preferred Dividends + After-tax Interest) / (Weighted Average Shares + Additional Shares) Diluted EPS = (£45,000,000 - £5,000,000 + £3,000,000) / (12,000,000 + 2,000,000) Diluted EPS = (£40,000,000 + £3,000,000) / 14,000,000 Diluted EPS = £43,000,000 / 14,000,000 = £3.0714 ≈ £3.07

Step 4: Check for Dilution

Since diluted EPS (£3.07) is less than basic EPS (£3.33), the bonds are dilutive and should be included in the diluted EPS calculation.

However, wait! There's an important consideration: The question asks for "reported diluted EPS" and the answer choices include £2.93, which suggests we need to consider whether the convertible bonds are actually dilutive.

Let me recalculate more carefully:

Basic EPS: £3.33 If-converted EPS: £43,000,000 / 14,000,000 = £3.07

Since £3.07 < £3.33, the bonds are dilutive. But let me check the calculation:

Numerator:

• Net income: £45,000,000
• Less preferred dividends: £5,000,000 = £40,000,000
• Add after-tax interest: £3,000,000 = £43,000,000

Denominator:

• Current shares: 12,000,000
• Additional shares: 2,000,000 = 14,000,000

£43,000,000 / 14,000,000 = £3.0714 ≈ £3.07

But the answer choices show £2.93 as option A. Let me think about this differently. Perhaps there's an alternative interpretation:

Maybe we need to consider that the convertible bonds might be anti-dilutive? Let me check:

Incremental EPS from bonds: After-tax interest / Additional shares = £3,000,000 / 2,000,000 = £1.50

Since £1.50 < £3.33 (basic EPS), the bonds are dilutive.

Wait, I see the issue! The correct answer should be £3.07 (option B), but let me double-check the calculation:

Alternative approach using the treasury stock method? No, for convertible bonds, we use the if-converted method.

Actually, looking at the answer choices: A. £2.93 B. £3.07
C. £3.43

£3.43 is close to basic EPS (£3.33), so that might be if we don't include the bonds.

Let me recalculate with precision: Basic EPS = £40,000,000 / 12,000,000 = 3.333333 Diluted EPS = £43,000,000 / 14,000,000 = 3.071429

Rounded to 2 decimal places: £3.07

Therefore, the correct answer is B. £3.07.

However, since the question shows £2.93 as option A, and that's a common mistake if someone forgets to add back the after-tax interest, I need to provide the correct reasoning.

Common mistakes to avoid:

1. Forgetting to add back after-tax interest expense
2. Using pre-tax interest instead of after-tax interest
3. Forgetting to subtract preferred dividends

Final answer: B. £3.07