Answer: £2.93.

## 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**