Pre-acquisition:
Company X: earnings = $50m, P/E = 10 → value = 50 × 10 = $500m; shares = 100m → price = $5
Company Y: earnings = $15m, P/E = 10 → value = 15 × 10 = $150m; shares = 50m → price = $3
Combined earnings = 50 + 15 = $65m
Post-acquisition assumptions:
Earnings increase by 10% → 65 × 1.10 = $71.5m
Combined P/E remains 10 → total market value = 71.5 × 10 = $715m
We want X’s new share price to be 10% higher than $5 → target price = $5.50.
Share price = total value ÷ total X shares after issue:
5.50=715Total shares⇒Total shares=7155.5=130m5.50 = \frac{715}{\text{Total shares}} \Rightarrow \text{Total shares} = \frac{715}{5.5} = 130\text{m}5.50=Total shares715⇒Total shares=5.5715=130m
X currently has 100m shares, so must issue 30m new shares to Y’s shareholders.
Y has 50m shares → each Y share must get:
30m50m=0.6 X shares per Y share\frac{30m}{50m} = 0.6 \text{ X shares per Y share}50m30m=0.6 X shares per Y share
Check options:
B: 3 X for 5 Y → 3/5 = 0.6 X per Y ✔
So that exchange ratio gives exactly 30m new X shares and hence a 10% increase in X’s share price.
Correct answer: B – 3 shares in Company X for 5 shares in Company Y.
