skills/merger-model-builder/references/deep/model-math

# Model Math

## Table Of Contents
1. Equity purchase price
2. Transaction enterprise value
3. Sources and uses
4. Consideration mix
5. Shares issued and ownership
6. Purchase accounting
7. Financing effects
8. Synergy effects
9. Pro forma net income
10. EPS and accretion/dilution
11. Synergy breakeven

## Equity purchase price

If not explicitly provided:

```text
equity_purchase_price = offer_price * target_diluted_shares
```

Scenario `purchase_price_factor` scales the equity purchase price.

## Transaction enterprise value

```text
transaction_ev = equity_purchase_price + target_debt + other_debt_like_items - target_cash
```

Fees are shown in sources and uses but are not included in headline transaction EV unless specifically instructed.

## Sources and uses

Uses:

```text
cash_consideration
+ stock_consideration
+ other_consideration
+ target_debt_refinanced
+ transaction_fees
+ financing_fees
+ equity_issuance_fees
+ bridge_fees
+ debt_tender_premiums
```

Sources:

```text
new_debt
+ acquirer_cash_used
+ target_excess_cash_used
+ stock_consideration
+ other_consideration
```

Target excess cash used:

```text
max(target_cash - required_min_cash, 0)
```

only when `financing.use_target_cash` is true.

Hard failure: sources and uses must balance within tolerance.

## Consideration mix

```text
cash_consideration = equity_purchase_price * cash_percent
stock_consideration = equity_purchase_price * stock_percent
other_consideration = equity_purchase_price * other_percent + other_consideration_value
```

The mix must sum to 100% unless explicitly overridden.

## Shares issued and ownership

If an exchange ratio is provided:

```text
shares_issued = target_diluted_shares * exchange_ratio
```

If the deal is fixed-value stock consideration:

```text
shares_issued = stock_consideration / acquirer_share_price
```

Pro forma shares:

```text
pf_shares = acquirer_diluted_shares + shares_issued
```

Ownership:

```text
acquirer_ownership = acquirer_diluted_shares / pf_shares
target_ownership = shares_issued / pf_shares
```

## Purchase accounting

```text
fair_value_stepups = intangibles + ppe_step_up + inventory_step_up + other_fair_value_adjustments + deferred_revenue_adjustment
```

If DTL is not provided:

```text
deferred_tax_liability = max(fair_value_stepups, 0) * deferred_tax_rate
```

Identifiable net assets:

```text
identifiable_net_assets = target_book_equity - existing_goodwill + fair_value_stepups - deferred_tax_liability
```

Goodwill:

```text
goodwill = consideration_transferred + nci_fair_value + previously_held_interest_fair_value - identifiable_net_assets
```

If goodwill is negative, flag a bargain purchase review.

## Financing effects

```text
interest_expense = new_debt * debt_interest_rate
lost_cash_interest = (acquirer_cash_used + target_cash_used) * lost_cash_interest_rate
fee_amortization = financing_fees / fee_amortization_years
```

## Synergy effects

```text
revenue_synergy_contribution = revenue_synergies * revenue_synergy_margin
net_pre_tax_synergies = cost_synergies + revenue_synergy_contribution - dis_synergies
```

Scenario factors modify cost/revenue synergies, dis-synergies, and integration costs.

After-tax synergy contribution:

```text
after_tax_synergies = net_pre_tax_synergies * (1 - synergy_tax_rate)
```

## Pro forma net income

```text
pf_gaap_net_income =
  acquirer_net_income
+ target_net_income
+ after_tax_synergies
- after_tax_financing_drag
- after_tax_purchase_accounting_drag
- after_tax_integration_costs
- after_tax_transaction_fees
```

Adjusted net income adds back selected one-time or non-cash items only when explicitly specified:

- integration costs when `integration_costs_excluded_from_adjusted_eps` is true
- transaction fees when one-time transaction fees are excluded from adjusted EPS
- intangible amortization when `adjusted_eps_excludes_intangible_amortization` is true

## EPS and accretion/dilution

```text
pf_eps = pf_net_income / pf_diluted_shares
accretion_dilution = pf_eps / standalone_acquirer_eps - 1
```

Show GAAP and adjusted EPS separately.

## Synergy breakeven

For the primary period, run a no-synergy case and solve the pre-tax synergy required for adjusted EPS neutrality:

```text
required_pf_net_income = standalone_acquirer_eps * pf_shares
required_after_tax_synergy = required_pf_net_income - pf_adjusted_net_income_without_synergies
required_pre_tax_synergy = required_after_tax_synergy / (1 - tax_rate)
```

If required pre-tax synergy is negative, report zero.