# Synergy Valuation Concept Card: [Deal, course or case]

> A concept card for the M&A elective: how to estimate and value the synergies of an acquisition (cost synergies,
> revenue synergies, dis-synergies and the one-off costs to achieve them), how to compare their present value with the
> premium paid, how to find the walk-away price and the performance improvement a premium already assumes, and how to
> test the estimate before the board relies on it. It builds on mba/mba-growth-strategy-card (the acquisition value
> formula and the synergy trap), mba/mba-dcf-valuation-card (discounting, terminal value) and mba/mba-capm-wacc-card
> (the discount rate); read those first, because this card does not re-teach them. Source basis: Sirower (1997) on the
> synergy trap and the required performance improvement, the research on where merger gains come from (Bradley, Desai
> and Kim 1988; Healy, Palepu and Ruback 1992; Capron 1999; Houston, James and Ryngaert 2001), written up in original
> words. The examples use fictional companies with generic labels (Acquirer P and Target Q, the same deal as
> mba/mba-accretion-dilution-card). Replace every [bracketed] value and every row marked *Example*. This is a learning
> aid, not investment advice.

<!--
Guidance: How to use this card
- Read "The idea in plain language", then rebuild the synergy schedule of Worked example A in a spreadsheet.
- Value each synergy type on its own line with its own phase-in, probability and costs. A single "synergies" line
  hides the assumptions that matter.
- Compare the result with the premium plus deal costs, not with the price. The standalone value belongs to the
  target's shareholders already.
- Every number was computed in Python; Excel formulas are shown next to results.
- Related templates: mba/mba-mergers-acquisitions-guide, mba/mba-accretion-dilution-card, mba/mba-deal-structuring-card,
  mba/mba-corporate-strategy-card, mba/mba-growth-strategy-card, mba/mba-dcf-valuation-card, mba/mba-capm-wacc-card,
  mba/mba-decision-trees-card, mba/mba-negotiation-guide, mba/mba-formula-sheet, mba/mba-error-log,
  mba/mba-concept-flashcards, finance/valuation-report, finance/due-diligence-request-list,
  finance/quality-of-earnings-scope, finance/m-and-a-integration-100-day-plan, finance/investment-committee-memo,
  finance/impairment-test-memo.
-->

## Document control

<!-- Guidance: Record who owns each synergy line. In a live deal, a synergy without an owner is a hope. -->

| Field | Value |
|---|---|
| Deal, course or case | [Deal name or case] |
| Learner or analyst | [Your name] |
| Acquirer and target | [Acquirer P / Target Q (fictional) or your case] |
| Synergy case version | [Management, diligence-adjusted, board] |
| Owners of synergy lines | [Procurement lead, commercial lead, finance lead] |
| Reviewed by | [Learning team member, tutor or mentor] |
| Version | [0.1] |
| Last updated | YYYY-MM-DD |

## Contents

1. When to use it
2. The idea in plain language
3. Formulas and notation
4. Assumptions and limits
5. How managers use it in practice
6. Worked example A (fully solved): Acquirer P and Target Q
7. Worked example B (half solved): Acquirer M and Target N
8. Exercise C (unsolved)
9. Connections to other cards
10. Common mistakes and misconceptions
11. Self-test questions
12. My notes and next steps
13. Sources and further reading
14. Answer key
15. Revision history

## When to use it

<!-- Guidance: Use this card before any price is discussed. Once a number is on the table, synergy estimates tend to rise to justify it. -->

| Use it when | Use something else when |
|---|---|
| You must decide the highest price worth paying for a target | You need the target's standalone value (mba/mba-dcf-valuation-card) |
| A management synergy estimate must be challenged before a bid | You need the EPS effect of the synergies (mba/mba-accretion-dilution-card) |
| You compare bidders: who can pay most, and why | The buyer is a financial sponsor without operating synergies (mba/mba-lbo-model-card) |
| You set integration targets and track them after closing | You plan the integration itself (finance/m-and-a-integration-100-day-plan) |

## The idea in plain language

<!-- Guidance: One sentence first: synergies are the extra cash flows the combination creates that neither firm would create alone, valued like any project. -->

A target's market price, before rumours of a deal, is a fair estimate of what it is worth to its current owners. A
buyer that pays a premium above that price must earn the premium back from **synergies**: extra after-tax cash flows
that exist only because the firms combine. Synergies are a project, and are valued like one (mba/mba-npv-irr-card):
estimate the incremental cash flows, discount them at a rate that reflects their risk, subtract the investment needed
to obtain them.

| Type | Examples | How reliable |
|---|---|---|
| Cost synergies | Purchasing scale, closing duplicate warehouses, offices and systems, shared overheads | Most reliable: within management's control, measurable in diligence |
| Revenue synergies | Cross-selling, entering each other's channels or countries, combined offers | Less reliable: depend on customers and competitors |
| Dis-synergies | Customers who leave because they will not buy from a competitor's owner, staff departures, price concessions | Often omitted, always present |
| Costs to achieve | Severance, systems migration, rebranding, retention bonuses, advisory costs of integration | Certain and front-loaded |
| Financial and tax effects | Use of tax losses, lower borrowing costs, tax structure | Check carefully: limited by tax rules and often already in standalone values |

The market seems to agree with this ranking. In a study of large bank mergers, Houston, James and Ryngaert (2001)
found that management's projected cost savings explained much of the market's valuation of the deals, while projected
revenue gains added little. Capron (1999) found that horizontal acquisitions create value both by cutting duplicated
assets and by redeploying resources between the firms, but that revenue gains need deliberate resource sharing.
Healy, Palepu and Ruback (1992) found improved operating returns after large US mergers driven by asset productivity.

Two facts make synergy valuation an exercise in discipline. First, the premium is paid at closing and in full, while
synergies arrive later, partly, and with costs. Sirower (1997) showed that a premium already implies a **required
performance improvement**: an annual increase in cash flow, starting now, that the combined firm must deliver just to
break even, often far above anything the business has achieved before. Second, competition among bidders raises the target's
share of the gains (Bradley, Desai and Kim 1988), and the winner of a contest is often the bidder who overestimated
most (the winner's curse behind Roll's 1986 hubris hypothesis). A walk-away price written down before bidding is the only protection.

## Formulas and notation

<!-- Guidance: Keep the probability on revenue synergies and the discount rate separate. Using both a haircut and a higher rate for the same risk double counts it. -->

**After-tax synergy cash flow in year $t$:**

$$
CF_t = \left(CS_t + p \cdot RS_t - DS_t - CTA_t\right)(1 - \tau) - \Delta NWC_t
$$

**Present value of net synergies** with a growing terminal value after year $T$ (recurring items only):

$$
PV_S = \sum_{t=1}^{T} \frac{CF_t}{(1 + r)^t} + \frac{1}{(1+r)^T} \cdot \frac{(CS_T + p \cdot RS_T - DS_T)(1-\tau)(1+g) - NWC_T \, g}{r - g}
$$

**Value to the acquirer, walk-away price and share of synergies kept:**

$$
NPV_A = PV_S - \Pi - F, \qquad \Pi = P - V_T, \qquad P_{\max} = V_T + PV_S - F, \qquad \kappa = \frac{NPV_A}{PV_S}
$$

**Required performance improvement** (Sirower's idea in a growing-perpetuity form): the after-tax synergy in year 1,
growing at $g$, whose present value equals the premium plus deal costs:

$$
RPI_1 = (\Pi + F)(r - g), \qquad RPI_1^{\text{pre-tax}} = \frac{RPI_1}{1 - \tau}
$$

| Symbol | Meaning | Unit |
|---|---|---|
| $CS_t$ | Pre-tax cost synergies in year $t$ | USD m |
| $RS_t$ | Pre-tax revenue synergies (contribution from extra revenue) if fully achieved | USD m |
| $p$ | Probability (or expected share) of revenue synergies achieved | 0 to 1 |
| $DS_t$ | Pre-tax dis-synergies (lost contribution) | USD m |
| $CTA_t$ | Pre-tax one-off costs to achieve | USD m |
| $\Delta NWC_t$, $NWC_T$ | Change in working capital to support extra revenue; its balance in year $T$ | USD m |
| $\tau$ | Tax rate | % |
| $r$ | Discount rate for synergies (the WACC of the business that produces them) | % |
| $g$ | Long-run growth of recurring synergies after year $T$ | % |
| $V_T$ | Target's standalone value (unaffected market value of equity) | USD m |
| $P$, $\Pi$, $F$ | Price paid for the equity; premium; deal costs | USD m |
| $P_{\max}$ | Walk-away price | USD m |
| $\kappa$ | Share of synergy value the acquirer keeps | % |
| $RPI_1$ | Required after-tax improvement in year 1 | USD m |

## Assumptions and limits

<!-- Guidance: Use these in the limitations paragraph. The discount rate, the probability and the terminal value are the three assumptions faculty challenge most. -->

- **Discount rate.** Synergies carry the risk of the operations that produce them: use the target's (or the combined
  business's) WACC for cost synergies, not the acquirer's if they differ, and never the acquisition debt rate. Some
  practitioners add a premium to the rate for revenue synergies; if you do that, do not also apply a probability.
- **Terminal value.** Synergies in perpetuity are a strong assumption. Competitors copy cost advantages and customers
  bargain away gains; a fade (growth below inflation, or synergies that shrink after year 10) is often more honest.
  The terminal value is usually most of the total; test it.
- **Probability is a judgement.** Use evidence: the acquirer's track record, the share of customers that overlap,
  contracts and pilots. Document why you chose it.
- **Double counting.** Synergies already in the target's standalone plan, or in its share price through takeover
  speculation, must not be counted again.
- **Market power is not a synergy to plan on.** Gains from higher prices after removing a competitor are what merger
  control reviews; they can trigger remedies or a prohibition. Ask counsel; do not put them in the board case.
- **Diversification is not a synergy.** Combining two cash-flow streams lowers total volatility but not the market
  risk investors are paid for, so it does not lower the cost of capital (mba/mba-capm-wacc-card).
- **Tax synergies depend on rules.** Use of the target's tax losses after a change of control is limited in many
  jurisdictions; ask a tax adviser.

## How managers use it in practice

<!-- Guidance: Follow the steps in order. The baseline in step 1 is the one teams skip, and it is the one that prevents double counting. -->

1. **Fix the baseline**: both firms' standalone plans, so every synergy is incremental.
2. **Build bottom-up estimates** by line (sites, contracts, headcount, customers), each with an owner.
3. **Phase and cost each line**: when it starts, when it reaches run-rate, what it costs to achieve.
4. **Add dis-synergies**: customer overlap, key-person risk, price concessions.
5. **Assign probabilities** to revenue synergies and test cost synergies against diligence evidence.
6. **Discount** at the operating WACC, with a terminal value or a fade.
7. **Compare** with the premium and deal costs; set the walk-away price and the required performance improvement.
8. **Track after closing**: the same lines become integration targets (finance/m-and-a-integration-100-day-plan).

```mermaid
flowchart TD
    A["Fix standalone baselines of both firms"] --> B["Bottom-up synergy lines with owners"]
    B --> C["Phase-in, run-rate and costs to achieve per line"]
    C --> D["Add dis-synergies"]
    D --> E{"Revenue synergy evidence strong?"}
    E -- Yes --> F["Higher probability, documented"]
    E -- No --> G["Low probability or exclude"]
    F --> H["Discount at operating WACC with terminal value or fade"]
    G --> H
    H --> I["Present value of net synergies"]
    I --> J{"Present value above premium plus deal costs?"}
    J -- No --> K["Lower the price or walk away"]
    J -- Yes --> L["Set walk-away price and integration targets"]
    L --> M["Track synergies quarterly after closing"]
```

## Worked example A (fully solved): Acquirer P and Target Q

<!-- Guidance: Rebuild the schedule in a spreadsheet. Check your year 3 after-tax cash flow (45.47) before going further. -->

**Situation (*Example*, fictional).** Acquirer P offers a 30% premium for Target Q, a listed competitor with no debt,
60m shares at USD 22.50 (market value USD 1,350m), revenue USD 1,000m, EBIT USD 120m. The offer is USD 29.25 per share,
USD 1,755m in total; the premium is USD 405m (`=1350*30%`). Deal costs are USD 25m. Diligence produced:

- **Cost synergies:** run-rate USD 60m pre-tax (6% of Q's revenue: purchasing, two warehouses, overheads), 50% in
  year 1 and 100% in year 2, then growing 2% a year.
- **Dis-synergies:** customers who buy from both firms and want two suppliers will move part of their business: lost
  contribution USD 12m at run-rate, phased like the cost synergies.
- **Revenue synergies:** cross-selling of USD 100m of revenue at full run-rate (0 in year 1, 50 in year 2, 100 in year
  3, then growing 2%), at a 30% contribution margin, with working capital of 10% of the extra revenue. Probability of
  achievement 50%.
- **Costs to achieve:** USD 70m in year 1 and USD 30m in year 2, pre-tax.

Tax rate 25%; discount rate (Q's WACC) 8.5%; long-run growth 2%.

**Step 1. Synergy schedule (USD m).**

| *Example* line | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Cost synergies | 30.00 | 60.00 | 61.20 | 62.42 | 63.67 |
| Dis-synergies | -6.00 | -12.00 | -12.24 | -12.48 | -12.73 |
| Revenue synergies: extra revenue (full) | 0.00 | 50.00 | 100.00 | 102.00 | 104.04 |
| Revenue synergies: contribution at 50% probability | 0.00 | 7.50 | 15.00 | 15.30 | 15.61 |
| Costs to achieve | -70.00 | -30.00 | 0.00 | 0.00 | 0.00 |
| Pre-tax total | -46.00 | 25.50 | 63.96 | 65.24 | 66.54 |
| Less tax at 25% | 11.50 | -6.38 | -15.99 | -16.31 | -16.64 |
| Less working capital increase (expected) | 0.00 | -2.50 | -2.50 | -0.10 | -0.10 |
| After-tax cash flow | -34.50 | 16.63 | 45.47 | 48.83 | 49.81 |
| Discount factor at 8.5% | 0.9217 | 0.8495 | 0.7829 | 0.7216 | 0.6650 |
| Present value | -31.80 | 14.12 | 35.60 | 35.23 | 33.12 |

Excel: discount factor `=(1+8.5%)^-C1` with the year in row 1; present value of years 1 to 5
`=NPV(8.5%,C12:G12)` = **86.28**, with after-tax cash flows in C12:G12.

**Step 2. Terminal value.** Recurring after-tax synergies in year 5 = (63.67 - 12.73 + 15.61) x 0.75 = 49.91. Year 6
cash flow = 49.91 x 1.02 - 5.20 x 2% (extra working capital) = 50.80. Terminal value at the end of year 5 =
50.80 / (8.5% - 2%) = **781.57** (`=(49.908*1.02-5.202*2%)/(8.5%-2%)`), present value **519.78**
(`=781.57/(1+8.5%)^5`).

**Step 3. Total and components.**

| *Example* component | Present value (USD m) |
|---|---|
| Cost synergies | 658.81 |
| Dis-synergies | -131.76 |
| Revenue synergies at 50% probability (net of working capital) | 146.51 |
| Costs to achieve (after tax) | -67.50 |
| **Net synergies** | **606.06** |
| Memo: revenue synergies at 100% | 293.03 |

Check: 86.28 + 519.78 = 606.06. Excel for the total: `=NPV(8.5%,C12:G12)+H12/(1+8.5%)^5` with the terminal value in
H12.

**Step 4. Compare with the premium.**

| Item | Computation | Result | Excel formula |
|---|---|---|---|
| NPV to P's shareholders | 606.06 - 405 - 25 | 176.06 | `=606.06-405-25` |
| Share of synergy value kept by P | 176.06 / 606.06 | 29.05% | `=176.06/606.06` |
| Share paid away to Q's holders and advisers | 430 / 606.06 | 70.95% | `=430/606.06` |
| Walk-away price per Q share | 22.50 + (606.06 - 25) / 60 | 32.18 | `=22.5+(606.06-25)/60` |
| Walk-away premium | 581.06 / 1,350 | 43.04% | `=581.06/1350` |
| Required after-tax improvement, year 1 | (405 + 25) x (8.5% - 2%) | 27.95 | `=(405+25)*(8.5%-2%)` |
| Required pre-tax improvement, year 1 | 27.95 / 0.75 | 37.27 | `=27.95/(1-25%)` |
| As a share of Q's NOPAT (120 x 0.75 = 90) | 27.95 / 90 | 31.06% | `=27.95/90` |

The premium and deal costs require Q's after-tax operating profit to rise by about 31% from year 1 and keep growing, before
any cost of achieving it. P's cost synergies can do that at run-rate, but not in year 1.

**Step 5. Sensitivities (NPV to P, USD m).**

| *Example* change | NPV |
|---|---|
| Base case | 176.06 |
| Revenue synergies at 0% probability | 29.55 |
| Revenue synergies at 100% | 322.58 |
| Only 80% of cost synergies achieved | 44.30 |
| Only 60% of cost synergies achieved | -87.46 |
| Cost synergy phase-in one year late: 0 in year 1, 30 in year 2, the base path from year 3 (value lost 39.85) | 136.21 |

**Chart.** The value bridge from synergies to NPV:

```vega-lite
{
  "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
  "description": "Acquirer P and Target Q (fictional): present value of synergy components, premium and deal costs, USD m",
  "width": "container",
  "height": 260,
  "data": {
    "values": [
      {"item": "1 Cost synergies", "value": 658.81, "kind": "Synergy"},
      {"item": "2 Dis-synergies", "value": -131.76, "kind": "Synergy"},
      {"item": "3 Revenue synergies (50%)", "value": 146.51, "kind": "Synergy"},
      {"item": "4 Costs to achieve", "value": -67.50, "kind": "Synergy"},
      {"item": "5 Net synergies", "value": 606.06, "kind": "Subtotal"},
      {"item": "6 Premium", "value": -405.00, "kind": "Paid away"},
      {"item": "7 Deal costs", "value": -25.00, "kind": "Paid away"},
      {"item": "8 NPV to acquirer", "value": 176.06, "kind": "Subtotal"}
    ]
  },
  "mark": "bar",
  "encoding": {
    "x": {"field": "item", "type": "nominal", "title": null, "axis": {"labelAngle": -30}},
    "y": {"field": "value", "type": "quantitative", "title": "Present value (USD m)"},
    "color": {"field": "kind", "type": "nominal", "title": "Type"}
  }
}
```

**Conclusion (*Example*).** At a 30% premium the deal creates about USD 176m for P's shareholders on expected
synergies, but P keeps only 29% of the synergy value it creates. The case rests on cost synergies: if only 60% arrive,
the deal destroys value. The walk-away price is USD 32.18 per share; in a contest, P should not follow a rival above
it. Because value depends on execution, consider paying part in stock to share the risk (mba/mba-accretion-dilution-card
shows the EPS effect of each mix) and tie integration targets to the cost synergy lines.

## Worked example B (half solved): Acquirer M and Target N

<!-- Guidance: Fill each [ ] before checking the answer key. Keep the same order as example A. -->

**Situation (*Example*, fictional).** Acquirer M considers Target N, market value USD 800m, at a 25% premium. Cost
synergies USD 20m pre-tax in year 1 and USD 40m a year from year 2, flat forever (no growth). Costs to achieve
USD 50m in year 1. No revenue synergies or dis-synergies. Tax 25%, discount rate 9%, no deal costs.

| Item | Computation | Result |
|---|---|---|
| After-tax cash flows, years 1 to 5 | (20 - 50) x 0.75; 40 x 0.75 | -22.50; 30.00 each year from year 2 |
| Present value of years 1 to 5 | `=NPV(9%,-22.5,30,30,30,30)` | 68.52 |
| Terminal value at the end of year 5 | 30 / 9% | [ ] |
| Present value of terminal value | Terminal value / 1.09^5 | [ ] |
| Present value of net synergies | Sum | [ ] |
| Premium | 25% x 800 | [ ] |
| NPV to M | Net synergies - premium | [ ] |
| Required after-tax improvement in year 1 (no growth) | Premium x 9% | [ ] |

Question: what share of the synergy value does M keep, and what is the walk-away premium as a percentage?

## Exercise C (unsolved)

<!-- Guidance: Build this one from a blank sheet. No answer key: defend your assumptions, especially the probability and the fade. -->

Corvane Robotics, a growth-stage warehouse-robotics company, considers acquiring a fictional software company
("Target W") whose fleet-management software would run Corvane's robots and those of other makers. Target W's
standalone value is USD 240m; the seller asks for USD 330m. Corvane's team estimates:

- Cost synergies: USD 4m a year pre-tax from year 1 (shared cloud and support), growing 3%.
- Revenue synergies: software attached to 40% of new robot sales, adding USD 25m of contribution a year at run-rate
  from year 3 (30% in year 1, 70% in year 2), growing 5% to year 7 and 3% after.
- Dis-synergies: other robot makers who use Target W's software may switch away: lost contribution of USD 6m a year
  from year 2.
- Costs to achieve: USD 15m in year 1. Tax 25%. Discount rate 12% (growth-company WACC).

1. Value the net synergies with an explicit probability on the revenue synergies of your choice, and justify it.
2. Compute the NPV at the asking price, the walk-away price and the required performance improvement.
3. Which single assumption drives the answer? Show a one-way sensitivity.
4. Would you structure part of the price as an earn-out (see mba/mba-deal-structuring-card)? On which metric?

## Connections to other cards

<!-- Guidance: Follow the link that matches your next question. -->

- mba/mba-growth-strategy-card: the acquisition value formula, build, borrow or buy, and the synergy trap introduced in
  the core.
- mba/mba-dcf-valuation-card: standalone value, terminal value checks, discount-rate consistency.
- mba/mba-capm-wacc-card: the discount rate for synergies; why diversification does not lower it.
- mba/mba-accretion-dilution-card: the EPS effect of the same synergies and how payment form shares their risk.
- mba/mba-mergers-acquisitions-guide: the whole deal process and the Northfield mini-case.
- mba/mba-deal-structuring-card: earn-outs and contingent payments when synergies are uncertain.
- mba/mba-decision-trees-card: valuing staged integration choices and options to abandon.
- mba/mba-negotiation-guide: using the walk-away price as a reservation price.
- mba/mba-corporate-strategy-card: the better-off and parenting tests behind any synergy claim.

## Common mistakes and misconceptions

<!-- Guidance: Check your model against this list before you present. Items 1, 2 and 5 are the ones boards most often miss. -->

1. **Comparing synergies with the price instead of the premium.** The standalone value is not yours to create.
2. **Ignoring costs to achieve and phase-in.** Run-rate synergies from day 1 overstate value, often by a lot.
3. **Leaving out dis-synergies.** Overlapping customers and departing staff are predictable.
4. **Double counting risk.** A probability haircut plus a higher discount rate for the same uncertainty.
5. **Synergies in perpetuity at full strength,** without asking whether competitors will erode them.
6. **Using the acquirer's WACC or the cost of acquisition debt** instead of the operating risk of the synergies.
7. **Counting diversification or market power as synergies.**
8. **Synergies already in the target's plan or price,** counted again.
9. **A top-down percentage** ("5% of combined costs") with no lines, owners or evidence.
10. **Letting the estimate rise with the price** during an auction.

## Self-test questions

<!-- Guidance: Answer in writing from memory, then check the key. Repeat after two days and after a week. -->

1. An after-tax synergy of USD 30m a year forever, no growth, at 9%: what is its present value?
2. Pre-tax cost synergies of USD 40m a year forever, no growth, tax 25%, discount rate 10%: present value?
3. A buyer pays a USD 300m premium. The discount rate is 9% and synergies would grow 2% a year. What after-tax
   synergy in year 1 does the premium require? What pre-tax amount at a 25% tax rate?
4. Why should revenue synergies usually receive a larger haircut than cost synergies? Cite evidence.
5. Why is applying both a probability and a higher discount rate to revenue synergies a mistake?
6. Give three examples of dis-synergies.
7. Why do competitive auctions tend to transfer synergies to the target's shareholders?
8. Why are costs to achieve part of the synergy valuation and not only of the integration budget?
9. Cost synergies arrive one year later than planned. Explain why value falls even if the run-rate is unchanged.
10. Why should synergies be discounted at the operating WACC rather than at the interest rate on acquisition debt?

## My notes and next steps

<!-- Guidance: This section is yours. Update it after each case or model review. -->

| Item | My entry |
|---|---|
| Synergy line I find hardest to estimate | [ ] |
| Probability I used for revenue synergies and why | [ ] |
| Mistakes logged in mba/mba-error-log | [Date and short description] |
| Flashcards added in mba/mba-concept-flashcards | [ ] |
| Next review date | YYYY-MM-DD |

## Sources and further reading

<!-- Guidance: Primary works for each idea on the card. Venues and years were checked against bibliographic records. -->

- Bradley, M., Desai, A., and Kim, E. H. (1988). Synergistic gains from corporate acquisitions and their division
  between the stockholders of target and acquiring firms. *Journal of Financial Economics*, 21(1), 3-40.
- Healy, P. M., Palepu, K. G., and Ruback, R. S. (1992). Does corporate performance improve after mergers? *Journal of
  Financial Economics*, 31(2), 135-175.
- Roll, R. (1986). The hubris hypothesis of corporate takeovers. *The Journal of Business*, 59(2), 197-216.
- Sirower, M. L. (1997). *The Synergy Trap: How Companies Lose the Acquisition Game*. Free Press.
- Capron, L. (1999). The long-term performance of horizontal acquisitions. *Strategic Management Journal*, 20(11),
  987-1018.
- Eccles, R. G., Lanes, K. L., and Wilson, T. C. (1999). Are you paying too much for that acquisition? *Harvard
  Business Review*, 77(4).
- Houston, J. F., James, C. M., and Ryngaert, M. D. (2001). Where do merger gains come from? Bank mergers from the
  perspective of insiders and outsiders. *Journal of Financial Economics*, 60(2-3), 285-331.
- Andrade, G., Mitchell, M., and Stafford, E. (2001). New evidence and perspectives on mergers. *Journal of Economic
  Perspectives*, 15(2), 103-120.
- Textbooks (by name only): Koller, T., Goedhart, M., and Wessels, D., *Valuation*; Bruner, R. F., *Applied Mergers and
  Acquisitions*; Damodaran, A., *Damodaran on Valuation*.
- Open resource: OpenStax, *Principles of Finance* (2022), free online at https://openstax.org, for discounting and
  growing perpetuities (check the licence on the book page).

## Answer key

<!-- Guidance: Check only after writing your own answers. Note why a wrong answer was wrong, not only the right one. -->

**Worked example B.** Terminal value = 30 / 9% = **333.33** (`=30/9%`); present value 333.33 / 1.09^5 = **216.64**
(`=333.33/(1+9%)^5`). Present value of net synergies = 68.52 + 216.64 = **285.17**. Premium = **200.00**
(`=800*25%`). NPV to M = **85.17**. Required after-tax improvement = 200 x 9% = **18.00** a year (USD 24.00 pre-tax).
M keeps 85.17 / 285.17 = 29.9% of the synergy value; the walk-away premium is 285.17 / 800 = 35.6%.

**Self-test.**

1. 30 / 0.09 = **USD 333.33m** (`=30/9%`).
2. 40 x 0.75 / 0.10 = **USD 300m** (`=40*(1-25%)/10%`).
3. 300 x (9% - 2%) = **USD 21.0m** after tax in year 1, or 21.0 / 0.75 = **USD 28.0m** pre-tax.
4. Revenue synergies depend on customers and competitors, take longer and need investment; cost synergies are within
   management's control. Houston, James and Ryngaert (2001) found that the market valued projected cost savings in bank
   mergers but gave little value to projected revenue gains.
5. Both adjustments price the same uncertainty, so the value is cut twice. Use expected cash flows at the operating
   rate, or a risk-adjusted rate on a best estimate, not both.
6. Customers who move part of their business to keep two suppliers; key staff who leave; price cuts to retain
   customers; disruption to sales during systems migration; loss of partners who compete with the acquirer.
7. Each bidder will pay up to its own walk-away price; competition pushes the winning bid toward the second-highest
   bidder's value, raising the target's share of the gains (Bradley, Desai and Kim 1988), and the winner is often the
   most optimistic bidder (Roll 1986).
8. Synergies do not exist without them: they are the investment in the synergy project. Leaving them out overstates
   the NPV and the walk-away price.
9. Value depends on when cash arrives, not only on the run-rate: each synergy dollar that slips is received later
   (worth less after discounting), and the synergies of the slipped years are lost for good. In example A a phase-in
   one year late (0 in year 1 and 30 in year 2 instead of 30 and 60, the same path from year 3) loses USD 39.85m of
   present value: 22.5 / 1.085 + 22.5 / 1.085^2 after tax.
10. The synergies carry the operating risk of the business; the debt rate reflects the lender's lower, contractually
    protected risk. Using it would overstate value (mba/mba-capm-wacc-card).

## Revision history

<!-- Guidance: Add a row when you change a synergy line, a probability or the discount rate. -->

| Version | Date | Author | Change summary |
|---|---|---|---|
| 0.1 | YYYY-MM-DD | [Your name] | Card set up from the template |
| 0.2 | YYYY-MM-DD | [Your name] | *Example:* Diligence-adjusted synergy case, dis-synergies added |

## Standard and licence note

Structure aligned with the synergy valuation taught in leading international MBA mergers and acquisitions electives,
based on the published research cited above (Sirower 1997 for the required performance improvement; Bradley, Desai and
Kim 1988; Healy, Palepu and Ruback 1992; Capron 1999; Houston, James and Ryngaert 2001), summarised in original words.
The text, the fictional deals, all numbers and all questions are original; no textbook or case text is copied. The
template is independent and not affiliated with or endorsed by any business school or publisher. Check your own
syllabus and current sources before you rely on it. Template licence: MIT.
