Explanation

Using the single-stage residual income model formula:

V = B₀ + [(ROE - r) × B₀] / (r - g)

Where:

• B₀ = Current book value per share = €50
• ROE = Return on equity = 16% = 0.16
• r = Cost of equity = 12% = 0.12
• g = Growth rate = 10% = 0.10

Step 1: Calculate residual income premium ROE - r = 0.16 - 0.12 = 0.04

Step 2: Calculate the present value of residual income [(ROE - r) × B₀] / (r - g) = (0.04 × €50) / (0.12 - 0.10) = €2 / 0.02 = €100

Step 3: Calculate total value V = B₀ + PV of residual income = €50 + €100 = €150

Wait, let me recalculate this properly:

Actually, the correct single-stage residual income model formula is:

V = B₀ + [B₀ × (ROE - r)] / (r - g)

Calculation: V = €50 + [€50 × (0.16 - 0.12)] / (0.12 - 0.10) V = €50 + [€50 × 0.04] / 0.02 V = €50 + (€2 / 0.02) V = €50 + €100 = €150

But €150 is option C, not B. Let me check the calculation again:

Actually, the residual income per share = B₀ × (ROE - r) = €50 × (0.16 - 0.12) = €50 × 0.04 = €2

Then the present value of residual income = €2 / (0.12 - 0.10) = €2 / 0.02 = €100

Total value = €50 + €100 = €150

However, looking at the options, €75 (option B) would be correct if the growth rate was different. Let me verify with the alternative formula:

V = B₀ × [1 + (ROE - r) / (r - g)] V = €50 × [1 + (0.16 - 0.12) / (0.12 - 0.10)] V = €50 × [1 + 0.04 / 0.02] V = €50 × [1 + 2] V = €50 × 3 = €150

Both calculations give €150. Given that option C is €150, and my calculation confirms this, option C should be correct. However, the text says "c plus the present value of future earnings" which might indicate a different interpretation. Based on standard residual income model calculations, the correct answer is €150 (option C).