Synergy Case: Revenue and Cost

Step 1: Risk-Adjusted Run-Rate Synergies

Risk-Adjusted Run-Rate Synergy = Run-Rate Synergy × Probability of Realization

Revenue synergies: $20.0m × 50% (0.50) = $10.0m

Cost synergies: $15.0m × 75% (0.75) = $11.25m

Risk-adjusting a synergy estimate means multiplying the headline run-rate figure by the probability that it is actually captured. Interviewers expect you to apply a lower probability to revenue synergies than to cost synergies: cost savings (headcount overlap, procurement leverage) are largely within management's direct control, while revenue synergies depend on customer behavior and sales execution that the combined company cannot fully control. That is why the risk-adjusted cost synergy ($11.25m) is higher than the risk-adjusted revenue synergy ($10.0m) even though the raw run-rate estimates favor revenue ($20.0m vs. $15.0m).

Step 2: Phased (Ramped) Synergy Value by Year

Phased Synergy (Year N) = Risk-Adjusted Run-Rate Synergy × Ramp % (Year N)

Using the risk-adjusted run-rate synergies from Step 1 and the ramp schedule (30% / 65% / 100%):

Phasing exists because synergies are never captured on day one of a merger: systems need to be integrated, contracts renegotiated, and sales teams cross-trained. A ramp schedule reflects that reality instead of assuming the full run-rate synergy shows up immediately, which would overstate the near-term value of the deal.

Step 3: Converting Phased Revenue Synergies to EBITDA Impact

EBITDA Impact from Revenue Synergies (Year N) = Phased Revenue Synergy (Year N) × Gross Margin on Synergy Revenue (40%, or 0.40)

Unlike cost synergies, which drop straight to EBITDA, revenue synergies only contribute their gross margin to EBITDA — the incremental revenue still carries a cost of delivering it. Forgetting this conversion is one of the most common ways candidates overstate the EBITDA benefit of revenue synergies.

Step 4: Total Combined EBITDA Synergy by Year

Total EBITDA Synergy (Year N) = EBITDA Impact from Revenue Synergies (Year N) + Phased Cost Synergy (Year N)

This combined figure is what actually flows into the pro-forma income statement of the merged company. Notice that cost synergies dominate the total in every year — a pattern that holds in most real deals, which is exactly why deal teams and lenders tend to trust cost synergy estimates more than revenue synergy estimates when sizing a transaction.

Step 5: Present Value of Total Combined Synergies

NPV of Synergies = Sum over N = 1 to 3 of [Total EBITDA Synergy (Year N) / (1 + Discount Rate)^N]

Where: N = year number, Discount Rate = 10% (0.10), the WACC used to discount the synergy cash flows to present value.

Using the discount rate (10%) and the total EBITDA synergy figures from Step 4:

NPV of Synergies = $4.16m + $8.19m + $11.46m = $23.81m

Discounting matters because a dollar of synergy captured in Year 3 is worth less today than a dollar captured in Year 1 — the combined company has to wait longer for it, and that delay carries opportunity cost and execution risk that the discount rate captures. This $23.81m figure represents the maximum synergy value the acquirer should be willing to pay a premium for in the deal price; paying more than that for the same synergy assumptions destroys value for the acquirer's shareholders.

Final Results

• Risk-adjusted revenue synergy run-rate: $10.0m
• Risk-adjusted cost synergy run-rate: $11.25m
• Year 3 total EBITDA synergy: $15.25m
• NPV of total synergies (10% discount rate, 3-year horizon): $23.81m

This NPV feeds directly into the deal's purchase price negotiation: it caps how much of a synergy premium the acquirer can justify paying above the target's standalone value without destroying value for its own shareholders.

Would you like to explore how this NPV changes if integration costs are netted against the synergy stream, or if a terminal value beyond Year 3 is added?