“As an M&A analyst, you are tasked with valuing the expected synergies in a proposed acquisition — risk-adjusting them for realization probability, taxing them appropriately, discounting them to present value — and using that figure to judge whether the price your company is paying for those synergies is actually justified.”
As an M&A analyst, you are tasked with valuing the expected synergies in a proposed acquisition — risk-adjusting them for realization probability, taxing them appropriately, discounting them to present value — and using that figure to judge whether the price your company is paying for those synergies is actually justified.
Task: determine whether the risk-adjusted, after-tax present value of the deal's expected synergies exceeds the acquisition premium your company is paying to capture them.
Your company is acquiring a target and expects the following synergies and deal terms.
| Line Item | Value |
|---|---|
| Gross Revenue Synergies (fully phased-in run-rate) | $50.0m per year |
| Revenue Synergy Ramp — Year 1 / Year 2 / Year 3 | 40% / 70% / 100% |
| Revenue Synergy Realization Probability | 60% (0.60) |
| Gross Cost Synergies (fully phased-in run-rate) | $30.0m per year |
| Cost Synergy Ramp — Year 1 / Year 2 / Year 3 | 50% / 100% / 100% |
| Cost Synergy Realization Probability | 90% (0.90) |
| One-Time Cost to Achieve (incurred in Year 1) | $40.0m |
| Tax Rate | 25% (0.25) |
| Synergy Discount Rate | 12% (0.12) |
| Terminal Growth Rate (Year 4 onward) | 2% (0.02) |
| Acquisition Premium Attributed to Synergies | $200.0m |
Risk-Adjusted Synergy = Gross Run-Rate Synergy × Ramp % × Realization Probability
Using this formula, compute the risk-adjusted revenue and cost synergies separately for each of the three years.
After-Tax Synergy Cash Flow = [(Risk-Adjusted Revenue Synergies + Risk-Adjusted Cost Synergies) × (1 - Tax Rate)] - [One-Time Cost to Achieve × (1 - Tax Rate), in the year incurred]
Using this formula, compute the net after-tax synergy cash flow for each of the three years.
Terminal Value = [Year 3 Cash Flow × (1 + Terminal Growth Rate)] / (Discount Rate - Terminal Growth Rate)
Using this formula, compute the terminal value of the synergy cash flows as of the end of Year 3.
PV of Synergies = Σ [Year t Cash Flow / (1 + Discount Rate)^t] + [Terminal Value / (1 + Discount Rate)^3]
Using this formula, compute the present value of the synergies and compare it to the acquisition premium attributed to them.
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