Formula Sheet

Receipt value = shares per receipt × home price ÷ exchange rate

exchange rate

units of home currency per unit of the receipt's currency

Arbitrage keeps the receipt's market price close to this figure.

Related tool A1 Returns & Corporate Actions

Conversion value = conversion ratio × common share price

conversion ratio

common shares received per preferred share

Holders convert when this beats the call price or the value of staying preferred.

Related tool A1 Returns & Corporate Actions

Voting share = votes held ÷ total votes across all classes

A small economic stake can hold most of the votes, so compare the two.

Related tool A1 Returns & Corporate Actions

Total votes = shares × seats up for election

All the votes can go on one candidate, which helps a minority holder win a seat.

Related tool A1 Returns & Corporate Actions

Free float = shares issued − treasury shares − closely held shares

Closely held shares

stakes held by insiders, founders or governments

Tool A1 works from shares outstanding: free float = N × (1 − insider share).

Used in A1 Returns & Corporate Actions

Daily turnover = average daily volume ÷ free float

Measure against the float, not all shares, because locked-up shares can't trade.

Used in A1 Returns & Corporate Actions

Days = position ÷ (ADV × participation)

ADV

average daily volume

participation

share of daily volume you can take

Dividing by full daily volume ignores the limit on how much of the market you can be.

Used in A1 Returns & Corporate Actions

ADV = total volume ÷ trading days

ADV

average daily volume

Use trading days in the period, not calendar days.

Related tool A1 Returns & Corporate Actions

Turnover = annual volume ÷ shares

State the base: a question may set turnover on the free float, not on all shares.

Related tool A1 Returns & Corporate Actions

Percentage spread = (ask − bid) ÷ [(ask + bid) ÷ 2]

ask

lowest price a seller quotes

bid

highest price a buyer quotes

Measure against the midpoint. Half the spread is the distance from the midpoint to one side.

Related tool A1 Returns & Corporate Actions

Average price = Σ(shares at each price × that price) ÷ shares bought

An order larger than the depth at the best quote walks up the book and pays more on average.

Related tool A1 Returns & Corporate Actions

Gross proceeds = new shares × offer price

Existing shares sold by a founder raise no capital for the firm.

Related tool A1 Returns & Corporate Actions

Weight_i = (cap_i × float_i) ÷ Σ(cap × float)

cap

market cap of a constituent

float

share of its shares that trade freely

A large firm with a small float can carry less weight than a smaller firm that trades freely.

Related tool A1 Returns & Corporate Actions

Price return = (P₁ − P₀) ÷ P₀

P₀

price at the start

P₁

price at the end

It counts the price change only, so it understates what a holder of a dividend payer earned.

Used in A1 Returns & Corporate Actions

Total return = (P₁ − P₀ + D) ÷ P₀

P₀

price at the start

P₁

price at the end

D

dividends paid in the period

A price fall can still give a positive total return if the dividend is larger than the fall.

Related tool A1 Returns & Corporate Actions

R = (1 + r₁) × (1 + r₂) × … × (1 + r_T) − 1

R

return over the whole holding period

r_t

total return in period t

T

number of periods

Multiply, never add. Tool A1 links monthly returns, which assumes dividends are reinvested each month.

Used in A1 Returns & Corporate Actions

Total return = (1 + D ÷ P_d) × P₁ ÷ P₀ − 1

D

dividend per share

P_d

price at which the dividend buys more shares

P₀

price at the start

P₁

price at the end

The dividend buys extra shares, and those shares also earn the later price move.

Related tool A1 Returns & Corporate Actions

Return from dividends = total return − price return

Over several years this includes the return earned on reinvested dividends, so it is more than the sum of the yields.

Used in A1 Returns & Corporate Actions

Annualized return = (1 + R)^(1 ÷ n) − 1

R

return over the whole period

n

number of years

Dividing R by n ignores compounding and overstates the yearly rate of a gain.

Used in A1 Returns & Corporate Actions

Shares after = N × k; price, EPS and BVPS after = each one before ÷ k

N

shares outstanding

k

new shares per old share; below 1 for a reverse split

BVPS

book value per share

Market cap doesn't change. To measure a return across a split, adjust the old price by k as well.

Used in A1 Returns & Corporate Actions

Shares after = N × (1 + s); price, EPS and BVPS after = each one before ÷ (1 + s)

N

shares outstanding

s

stock dividend as a share of existing shares

It works like a small split: more shares, the same company, the same market cap.

Used in A1 Returns & Corporate Actions

Shares after = N − A ÷ P

N

shares outstanding

A

amount spent on the buyback

P

price paid per share

The higher the price paid, the fewer shares the same money retires.

Used in A1 Returns & Corporate Actions

EPS after = NI ÷ (N − A ÷ P)

NI

net income

N

shares outstanding

A

amount spent on the buyback

P

price paid per share

Net income is held flat, so EPS rises. A rise in EPS alone doesn't mean value was created.

Used in A1 Returns & Corporate Actions

BVPS after = (E − A) ÷ (N − A ÷ P)

E

book equity before the buyback

N

shares outstanding

A

amount spent on the buyback

P

price paid per share

BVPS rises if the shares are bought below book value per share, and falls if bought above it.

Used in A1 Returns & Corporate Actions

Ex-date = record date − (settlement days − 1) business days

Settlement days

business days from trade to settlement

The last day to buy and still get the dividend is the business day before the ex-date. Tool A1 skips weekends, not holidays.

Used in A1 Returns & Corporate Actions

Ex-date price = P − D

P

price before the ex-date

D

dividend per share

The fall in market cap equals the cash paid out, so holders are no better or worse off.

Related tool A1 Returns & Corporate Actions

V₀ = [Σ payout_t ÷ (1 + r)^t + TV ÷ (1 + r)^n] ÷ N

payout_t

cash the forecast can pay shareholders in year t

TV

next year's payout after the forecast ÷ (r − g)

r

required return on equity

n

number of years

N

shares outstanding

This is the case's estimate used by tools A2 and B1. It is only as good as the assumptions in the case.

Used in A2 Value Measures

Gap = P ÷ V − 1

P

price

V

estimated value

Above zero, the price is above the estimate. It's a gap against your assumptions, not proof of mispricing.

Used in A2 Value Measures

Gap = (V − P) ÷ P

P

price

V

estimated value

The same gap is a different percent of the value than of the price, so always state the base.

Related tool A2 Value Measures

Estimate − price = (true value − price) + (estimate − true value)

Part of any gap is the analyst's own error, which can be larger than the real mispricing.

Related tool A2 Value Measures

Annual return = (target ÷ price)^(1 ÷ n) − 1

n

number of years

The same rise earns less per year the longer the price takes to get there.

Related tool A2 Value Measures

Book value = assets − liabilities

It records past accounting, so it can sit far from what the assets would fetch today.

Related tool A2 Value Measures

BVPS = common equity ÷ shares outstanding

common equity

total equity less any preferred stock

BVPS

book value per share

Take preferred stock out first: its holders have a prior claim.

Used in A2 Value Measures

Market cap = price × shares outstanding

shares outstanding

shares issued less treasury shares

Treasury shares don't count. Market cap is the market's opinion at a moment, not a value estimate.

Used in A2 Value Measures

Net debt = debt − cash

A negative figure means net cash. Short-term investments count as cash.

Used in A2 Value Measures

EV = market cap + debt + preferred − cash

EV

enterprise value

preferred

preferred stock

Add minority interest too if the firm has it. EV isn't used for banks or insurers, whose debt is part of operations.

Used in A2 Value Measures

r = r_f + β × ERP

r

required return on equity

r_f

risk-free rate

β

beta, the share's sensitivity to the market

ERP

equity risk premium

A share plotting above this line has an expected return higher than the risk requires.

Used in A3 Required Return Builder

ERP = E(R_m) − r_f

E(R_m)

expected return on the market

r_f

risk-free rate

ERP

equity risk premium

If a question gives the market return, take off the risk-free rate before multiplying by beta.

Related tool A3 Required Return Builder

R_i − r_f = α + β × (R_m − r_f) + ε

R_i

the share's return

R_m

the market's return

r_f

risk-free rate

α

intercept

β

beta, the share's sensitivity to the market

ε

residual, with an expected value of zero

Tool A3 fits this on 120 months of excess returns. It describes the past; CAPM gives the forward-looking rate.

Used in A3 Required Return Builder

β = Cov(R_i, R_m) ÷ σ_m²

Cov(R_i, R_m)

covariance of the share with the market

σ_m²

variance of the market

Divide by the variance, not the standard deviation: square σ_m first.

Related tool A3 Required Return Builder

β = ρ × σ_i ÷ σ_m

ρ

correlation of the share with the market

σ_i

standard deviation of the share

σ_m

standard deviation of the market

A volatile share can have a low beta if little of its movement goes with the market.

Related tool A3 Required Return Builder

β_adj = ⅔ × β + ⅓

β

beta, the share's sensitivity to the market

It pulls a measured beta toward 1, because betas tend to drift that way over time.

Used in A3 Required Return Builder

r = r_f + b₁ × premium₁ + b₂ × premium₂ + … + b_k × premium_k

r_f

risk-free rate

b_k

the share's sensitivity to factor k

premium_k

the return premium on factor k

A negative loading lowers the return, as a growth share's value loading does.

Related tool A3 Required Return Builder

r = r_f + β × ERP + b_size × size premium + b_value × value premium

r_f

risk-free rate

β

beta, the share's sensitivity to the market

ERP

equity risk premium

b_size

the share's size loading

b_value

the share's value loading

Each premium is multiplied by its loading first. This is the multi-factor line in tool A3.

Used in A3 Required Return Builder

ERP = average equity return − average government bond return

ERP

equity risk premium

Strip out any one-way rise in the market P/E over the sample: it won't repeat.

Related tool A3 Required Return Builder

ERP = D₁ ÷ P + g − y

D₁

index dividends expected next year

P

index level

g

constant long-run growth rate

y

long-term government bond yield

Grow the dividend first: a question that gives the dividend just paid needs D₀ × (1 + g).

Related tool A3 Required Return Builder

ERP = [(1 + i) × (1 + rEg) × (1 + ΔPE) − 1] + Y − y

i

expected inflation

rEg

expected real EPS growth

ΔPE

expected yearly change in the market P/E

Y

expected income return

y

long-term government bond yield

Don't leave out the P/E change, and take off the bond yield: without it you have the equity return.

Related tool A3 Required Return Builder

r = yield on the firm's long-term debt + risk premium

r

required return on equity

A sense check when beta is unreliable: equity ranks behind debt, so r should sit above the bond yield.

Related tool A3 Required Return Builder

After-tax cost of debt = r_d × (1 − t)

r_d

pre-tax cost of debt

t

tax rate

Interest is tax deductible, which makes debt cheaper than its stated rate.

Used in A3 Required Return Builder

WACC = [E × r + D × r_d × (1 − t)] ÷ (E + D)

E

market value of equity

D

net debt

r

required return on equity

r_d

pre-tax cost of debt

t

tax rate

Use market weights, not book. Tool A3 floors net debt at zero. Tool C3 keeps it negative, so a net cash firm's WACC comes out above r.

Used in C3 DCF Lab

WACC = w_d × r_d × (1 − t) + (1 − w_d) × r_e

w_d

debt as a share of capital

r_d

pre-tax cost of debt

t

tax rate

r_e

required return on equity

A private firm has no market weights, so use a target or peer weight, or iterate from the value.

Used in E1 Private Company Valuation

WACC_t = [E_t × r + D_t × r_d × (1 − t)] ÷ (E_t + D_t)

E_t

equity value at the start of year t

D_t

net debt at the start of year t

r

required return on equity

r_d

pre-tax cost of debt

t

tax rate

This is what makes FCFF agree with FCFE when leverage changes. One constant WACC won't.

Used in F1 Model Reconciliation

Market size = units × average price; share = firm revenue ÷ market size

A change in share is a difference in percentage points, not a percent change.

Related tool B1 Industry Analyzer

Top-n share = revenue of the n largest firms ÷ total revenue

n

number of largest firms counted

It ignores how shares are spread inside the top group. In tool B1 the base is the peers' revenue, not the whole market.

Used in B1 Industry Analyzer

HHI = Σ(share in percent)²

HHI

Herfindahl-Hirschman index

Shares go in as whole percents. Two markets with the same four-firm share can have different indexes.

Related tool B1 Industry Analyzer

CAGR = (ending ÷ beginning)^(1 ÷ years) − 1

years

periods between the two figures, one less than the years listed

Five reported years span four periods of growth, so count the gaps, not the years.

Used in B2 Company Analyzer

Pretax ROIC = operating margin × revenue ÷ invested capital

Margins alone mislead when industries need very different amounts of capital.

Related tool B1 Industry Analyzer

Revenue growth = revenue ÷ last year's revenue − 1

Revenue is volume × price, so growth rates combine as (1 + a) × (1 + b) − 1, not a + b.

Used in B2 Company Analyzer

Gross margin = (revenue − cost of goods) ÷ revenue

It stops before operating expenses, so a good gross margin can hide heavy overheads.

Used in B2 Company Analyzer

EBIT margin = EBIT ÷ revenue

EBIT

earnings before interest and tax

Compare this across firms with different debt, because interest and tax come later.

Used in B2 Company Analyzer

Net margin = net income ÷ revenue

The first DuPont factor. Debt and tax both affect it.

Used in B2 Company Analyzer

DOL = contribution ÷ operating profit

DOL

percent change in operating profit per percent change in sales

contribution

sales less variable costs

High fixed costs raise DOL, so a small rise in sales lifts profit by much more.

Related tool B2 Company Analyzer

Days of receivables = receivables ÷ (revenue ÷ 365)

Rising days can mean looser credit terms, which absorbs cash even when sales are growing.

Used in B2 Company Analyzer

Days of inventory = inventory ÷ (cost of goods ÷ 365)

Use cost of goods, not revenue, because inventory is carried at cost.

Used in B2 Company Analyzer

Days of payables = payables ÷ (cost of goods ÷ 365)

Longer days free up cash, but paying past the agreed terms can't last.

Used in B2 Company Analyzer

Cycle = days of inventory + days of receivables − days of payables

Payables come off, because suppliers fund that part of the cycle.

Used in B2 Company Analyzer

Capex to revenue = capex ÷ revenue

A firm that must reinvest more for the same growth is worth less.

Used in B2 Company Analyzer

Capex to depreciation = capex ÷ depreciation

Above 1 the asset base is growing; below 1 for long, it may be wearing out.

Used in B2 Company Analyzer

ROE = net income ÷ equity

Check the base. Tool B2 lets you choose year-end or average equity, and tool B3 uses opening equity.

Used in B2 Company Analyzer

ROA = net income ÷ total assets

It equals net margin × asset turnover: the return before leverage.

Used in B2 Company Analyzer

Asset turnover = revenue ÷ total assets

Revenue earned on each unit of assets.

Used in B2 Company Analyzer

Leverage = total assets ÷ equity

More leverage lifts ROE, but shareholders carry more risk for it.

Used in B2 Company Analyzer

ROE = net margin × asset turnover × leverage

Compare each factor across years to see which one moved ROE.

Used in B2 Company Analyzer

ROE = tax burden × interest burden × EBIT margin × asset turnover × leverage

It only splits net margin into three, so the answer is the same ROE.

Used in B2 Company Analyzer

Tax burden = net income ÷ pretax income

A higher figure means less tax. It equals 1 − t.

Used in B2 Company Analyzer

Interest burden = pretax income ÷ EBIT

A higher figure means less interest. Net interest income can push it above 1.

Used in B2 Company Analyzer

Debt to equity = debt ÷ equity

Check whether lease liabilities are in debt before comparing firms.

Used in B2 Company Analyzer

Debt to capital = debt ÷ (debt + equity)

Unlike debt to equity, this can't go above 100% while equity is positive.

Related tool B2 Company Analyzer

EBITDA = EBIT + depreciation

EBITDA

earnings before interest, tax, depreciation and amortization

It ignores the capital spending that depreciation stands for, so it isn't free cash flow.

Used in B2 Company Analyzer

Net debt to EBITDA = net debt ÷ EBITDA

Years of EBITDA needed to repay net debt. Negative means more cash than debt.

Used in B2 Company Analyzer

Interest cover = EBIT ÷ net interest expense

It has no meaning when the firm earns more interest than it pays.

Used in B2 Company Analyzer

Revenue_t = revenue_(t−1) × (1 + growth)

Tool B3 fades growth toward the long-run rate over the forecast.

Used in B3 Forecast Builder

Real growth = (1 + nominal) ÷ (1 + inflation) − 1

Taking inflation off the nominal rate is only an approximation.

Used in B3 Forecast Builder

Receivables = revenue × days ÷ 365; inventory and payables = cost of goods × days ÷ 365

Hold days steady and the balances grow with sales, which absorbs cash.

Used in B3 Forecast Builder

PP&E_t = PP&E_(t−1) + capex − depreciation

PP&E

property, plant and equipment, net

Tool B3 sets depreciation as a share of opening net PP&E.

Used in B3 Forecast Builder

Interest_t = (debt_(t−1) − cash_(t−1)) × interest rate

Tool B3 uses opening balances to avoid a circular model. Some questions use average debt instead, so read the stem.

Used in B3 Forecast Builder

EPS = revenue × margin × (1 − t) ÷ shares

margin

pretax margin

t

tax rate

Buybacks change the share count, so forecast shares as well as earnings.

Related tool B3 Forecast Builder

Equity_t = equity_(t−1) + net income − FCFE

FCFE

free cash flow to equity, all paid out

This is what keeps the forecast on clean surplus, so the models agree in tool F1.

Used in B3 Forecast Builder

Stable capex = PP&E × depreciation rate + PP&E × g

PP&E

net property, plant and equipment at the end of the forecast

g

constant long-run growth rate

Net PP&E has to grow with the business, or the terminal flow is overstated.

Used in B3 Forecast Builder

Implied value = forecast EPS × target P/E

Pair the multiple with the right year's EPS, and compare the result with the price.

Related tool B3 Forecast Builder

NIM = net interest income ÷ (loans + securities)

NIM

net interest margin

The spread earned after paying depositors and lenders.

Used in B2 Company Analyzer

Cost to income = operating expenses ÷ (net interest income + fee income)

Lower is better. Credit losses are left out, so read it beside the provision.

Used in B2 Company Analyzer

Provision = opening loans × credit cost ratio

credit cost ratio

provision as a share of loans

Loan losses are a bank's main swing factor, so stress this ratio first.

Used in F1 Model Reconciliation

Capital ratio = equity ÷ risk-weighted assets

risk-weighted assets

loans + securities × their risk weight, in the sample banks

Regulators set the floor, which limits what a bank can pay out.

Used in F1 Model Reconciliation

Payout = net income − change in required equity

It is what is left after holding the capital the business needs. Free cash flow says little about these firms.

Used in F1 Model Reconciliation

Loss ratio = claims ÷ premiums

Read which premiums a question gives: the loss ratio and expense ratio can sit on different bases.

Used in B2 Company Analyzer

Expense ratio = underwriting expenses ÷ premiums

The share of premiums spent on writing the business.

Used in B2 Company Analyzer

Combined ratio = loss ratio + expense ratio

Below 100% means underwriting made a profit before investment income.

Used in B2 Company Analyzer

V₀ = D₀ × (1 + g) ÷ (r − g)

D₀

dividend just paid

g

constant long-run growth rate

r

required return on equity

It needs r above g. If the question gives D₁, don't grow it again.

Used in C1 DDM Lab

V₀ = D₁ ÷ (r − g)

D₁

dividend expected next year

g

constant long-run growth rate

r

required return on equity

The value is dated one year before the dividend on top. The same rule sets where a terminal value sits.

Used in C1 DDM Lab

V₁ = V₀ × (1 + g)

g

constant long-run growth rate

In this model the value grows at g, so V₁ also equals D₂ ÷ (r − g).

Related tool C1 DDM Lab

r = D₀ × (1 + g) ÷ P₀ + g

D₀

dividend just paid

g

constant long-run growth rate

P₀

price today

The return splits into a forward dividend yield and a capital gain at rate g.

Used in C1 DDM Lab

V₀ = D ÷ r

D

constant dividend

r

required return on equity

The Gordon model with g = 0.

Related tool C1 DDM Lab

V₀ = Σ D_t ÷ (1 + r)^t + P_n ÷ (1 + r)^n

D_t

dividend in year t

P_n

expected sale price in year n

r

required return on equity

n

number of years

If P_n is itself a Gordon value, the answer matches Gordon: the holding period doesn't change the value.

Used in C1 DDM Lab

V₀ = Σ D_t ÷ (1 + r)^t + V_n ÷ (1 + r)^n

D_t

dividend in year t, grown at each stage's rate

V_n

terminal value at the end of the last stage

r

required return on equity

n

number of years

A three-stage model adds a middle stage of growth. Discount the terminal value over n years, not n + 1.

Used in C1 DDM Lab

V_n = D_n × (1 + g_L) ÷ (r − g_L)

D_n

dividend in the last year of the forecast

g_L

long-run growth rate

r

required return on equity

Grow the last dividend one year at the long-run rate, not at the high rate.

Used in C1 DDM Lab

V₀ = [D₀ × (1 + g_L) + D₀ × H × (g_S − g_L)] ÷ (r − g_L)

D₀

dividend just paid

g_S

short-term growth at the start of the fade

g_L

long-run growth rate

H

half the length of the fade, in years

r

required return on equity

H is half the fade. It's an approximation, closest when the fade is short or the gap small.

Used in C1 DDM Lab

r = (D₀ ÷ P₀) × [(1 + g_L) + H × (g_S − g_L)] + g_L

D₀

dividend just paid

P₀

price today

g_S

short-term growth at the start of the fade

g_L

long-run growth rate

H

half the length of the fade, in years

At H = 0 it collapses to the Gordon return.

Used in C1 DDM Lab

V₀ = Σ D_t ÷ (1 + r)^t + V_n ÷ (1 + r)^n, with V_n an H-model value on D_n

D_t

dividend in year t of the first stage

V_n

H-model value at the end of the first stage

r

required return on equity

n

number of years

The H-model gives a value dated at the end of the first stage, so discount it back n years.

Used in C1 DDM Lab

PVGO = P₀ − E₁ ÷ r

P₀

price today

E₁

EPS expected next year

r

required return on equity

Negative PVGO can mean new investment earns under r, or that the market thinks E₁ won't last.

Used in C1 DDM Lab

P₀ ÷ E₁ = 1 ÷ r + PVGO ÷ E₁

P₀

price today

E₁

EPS expected next year

r

required return on equity

A no-growth firm's leading P/E is just 1 ÷ r. The rest is what is paid for growth.

Related tool C1 DDM Lab

g = (r × P₀ − D₀) ÷ (P₀ + D₀)

r

required return on equity

P₀

price today

D₀

dividend just paid

Taking r − D₀ ÷ P₀ treats the dividend just paid as next year's. If D₁ is given, g = r − D₁ ÷ P₀.

Used in C1 DDM Lab

V₀ = D ÷ r_p

D

fixed preferred dividend

r_p

required yield on the preferred share

A fixed dividend forever. If r_p rises, value falls by a set proportion, whatever the dividend.

Used in C1 DDM Lab

g = b × ROE

b

retention ratio, the share of earnings kept

ROE

return on equity

The growth a firm can fund from its own earnings. Tool C1 uses the latest year's ROE and retention.

Used in C1 DDM Lab

b = 1 − DPS ÷ EPS

DPS

dividend per share

EPS

earnings per share

Tool C1 floors b at zero, so a dividend above EPS gives no sustainable growth.

Used in C1 DDM Lab

b = (NI − dividends − buybacks) ÷ NI

NI

net income

When a firm returns cash through buybacks, b has to reflect all the cash paid out.

Related tool C1 DDM Lab

g = b × net margin × asset turnover × leverage

b

retention ratio, the share of earnings kept

Solve it for any term: to hold g when margin falls, retention or leverage must rise.

Related tool C1 DDM Lab

FCFF = NI + NCC + Int × (1 − t) − FCInv − WCInv

NI

net income

NCC

non-cash charges

Int

interest expense

t

tax rate

FCInv

fixed capital investment (capex)

WCInv

working capital investment

Net non-cash charges take off any non-cash gain. In tool C2, NCC is depreciation.

Used in C2 Free Cash Flow Bridge

FCFF = EBIT × (1 − t) + Dep − FCInv − WCInv

EBIT

earnings before interest and tax

t

tax rate

Dep

depreciation

FCInv

fixed capital investment (capex)

WCInv

working capital investment

EBIT is before interest, so there is no interest to add back.

Used in C2 Free Cash Flow Bridge

FCFF = EBITDA × (1 − t) + Dep × t − FCInv − WCInv

EBITDA

EBIT plus depreciation

t

tax rate

Dep

depreciation

FCInv

fixed capital investment (capex)

WCInv

working capital investment

EBITDA is already before depreciation, so only depreciation's tax saving is added.

Used in C2 Free Cash Flow Bridge

FCFF = CFO + Int × (1 − t) − FCInv

CFO

cash from operations

Int

interest expense

t

tax rate

FCInv

fixed capital investment (capex)

CFO has already taken off working capital, so don't subtract WCInv again.

Used in C2 Free Cash Flow Bridge

FCFE = FCFF − Int × (1 − t) + net borrowing

Int

interest expense

t

tax rate

Net borrowing

new debt less repayments

Borrowing adds to FCFE and leaves FCFF alone. FCFE lifted by debt can't last.

Used in C2 Free Cash Flow Bridge

FCFE = NI + NCC − FCInv − WCInv + net borrowing

NI

net income

NCC

non-cash charges

FCInv

fixed capital investment (capex)

WCInv

working capital investment

Net borrowing

new debt less repayments

Interest is already out of net income, so nothing is added back. A share issue is left out.

Used in C2 Free Cash Flow Bridge

FCFE = CFO − FCInv + net borrowing

CFO

cash from operations

FCInv

fixed capital investment (capex)

Net borrowing

new debt less repayments

A net repayment is negative net borrowing, so it comes off.

Used in C2 Free Cash Flow Bridge

FCFE = EBIT × (1 − t) − Int × (1 − t) + Dep − FCInv − WCInv + net borrowing

EBIT

earnings before interest and tax

Int

interest expense

t

tax rate

Dep

depreciation

FCInv

fixed capital investment (capex)

WCInv

working capital investment

Net borrowing

new debt less repayments

Tool C2 reaches this in two steps: EBIT to FCFF, then FCFF to FCFE.

Used in C2 Free Cash Flow Bridge

FCFE = EBITDA × (1 − t) + Dep × t − Int × (1 − t) − FCInv − WCInv + net borrowing

EBITDA

EBIT plus depreciation

Dep

depreciation

Int

interest expense

t

tax rate

FCInv

fixed capital investment (capex)

WCInv

working capital investment

Net borrowing

new debt less repayments

Tool C2 reaches this in two steps: EBITDA to FCFF, then FCFF to FCFE.

Used in C2 Free Cash Flow Bridge

WCInv = change in (receivables + inventory − payables)

WCInv

working capital investment

Cash and short-term debt stay out: one is the result, and the other is financing.

Used in C2 Free Cash Flow Bridge

FCInv = ending net PP&E − beginning net PP&E + depreciation

FCInv

fixed capital investment (capex)

PP&E

property, plant and equipment

If assets were sold, take the proceeds off capex to get net investment.

Related tool C2 Free Cash Flow Bridge

t = tax ÷ pretax income

t

tax rate

Tool C2 uses the year's own effective rate, so all four routes reach the same FCFF.

Used in C2 Free Cash Flow Bridge

FCFF = EBIT × (1 − t) − (FC rate + WC rate) × increase in sales

FC rate

net fixed investment as a share of the increase in sales

WC rate

working capital investment as a share of the increase in sales

t

tax rate

Investment is net of depreciation here, so don't add depreciation back as well.

Related tool C2 Free Cash Flow Bridge

FCFE = NI − (1 − DR) × (FCInv − Dep + WCInv)

NI

net income

DR

share of net investment funded by debt

FCInv

fixed capital investment (capex)

Dep

depreciation

WCInv

working capital investment

Equity funds only the part of net investment that debt doesn't.

Related tool C2 Free Cash Flow Bridge

Firm value = FCFF₀ × (1 + g) ÷ (WACC − g)

FCFF₀

free cash flow to the firm, latest year

g

constant long-run growth rate

WACC

weighted average cost of capital

FCFF belongs to all capital providers, so discount at WACC, then take off net debt.

Used in C3 DCF Lab

Equity value = FCFE₀ × (1 + g) ÷ (r − g)

FCFE₀

free cash flow to equity, latest year

g

constant long-run growth rate

r

required return on equity

FCFE is already after debt service, so discount at r and don't subtract debt.

Used in C3 DCF Lab

Value = Σ CF_t ÷ (1 + k)^t + TV ÷ (1 + k)^n

CF_t

FCFF or FCFE in year t

k

WACC for FCFF, r for FCFE

TV

terminal value at the end of year n

n

number of years

Match the rate to the flow. FCFF at r, or FCFE at WACC, is the classic error.

Used in C3 DCF Lab

Equity value = firm value − net debt

Add assets that FCFF leaves out, such as a surplus property, before dividing by shares.

Used in C3 DCF Lab

Value per share = equity value ÷ shares

Use firm value less net debt first if you started from FCFF.

Used in C3 DCF Lab

Terminal value share = PV of terminal value ÷ total value

PV

present value

A high share means the estimate hangs on the r − g spread you assumed.

Used in C3 DCF Lab

g = (r × V − F₀) ÷ (V + F₀)

r

required return on equity

V

the price or terminal value to explain

F₀

latest free cash flow

Use it to test an exit multiple: if g comes out above long-run economic growth, the multiple is too high.

Related tool C3 DCF Lab

TV_n = CF_(n+1) ÷ (k − g)

CF_(n+1)

flow in the first year after the forecast

k

WACC for FCFF, r for FCFE

g

constant long-run growth rate

Discount it back n years. In tool C3, the flow comes from a stable year built by the forecast.

Used in C3 DCF Lab

TV_n = EV/EBITDA × EBITDA_n, or P/E × net income_n

EBITDA_n

EBITDA in the last forecast year

net income_n

net income in the last forecast year

An EV multiple gives firm value for FCFF. A P/E gives equity value for FCFE.

Used in C3 DCF Lab

Equity charge = r × B

r

required return on equity

B

book equity at the start of the year

Use opening book value. Interest is already in net income, so only equity is charged.

Used in C4 Residual Income Lab

RI = NI − r × B

RI

residual income

NI

net income

r

required return on equity

B

book equity at the start of the year

A firm can report a profit and still have negative RI if ROE is below r.

Used in C4 Residual Income Lab

RI = (ROE − r) × B

ROE

return on equity

r

required return on equity

B

book equity at the start of the year

The drivers of RI are the size of the book and the spread over r.

Related tool C4 Residual Income Lab

NOPAT = EBIT × (1 − t)

NOPAT

net operating profit after tax

t

tax rate

Interest stays out, because WACC already prices the debt.

Used in C4 Residual Income Lab

EVA = NOPAT − WACC × capital

EVA

economic value added

WACC

weighted average cost of capital

capital

equity + debt − cash

EVA charges for all capital; residual income charges for equity only.

Used in C4 Residual Income Lab

MVA = market value of the firm − capital

MVA

market value added

market value of the firm

equity at market + net debt

capital

equity + debt − cash, at book

It looks at the whole firm, not just the equity.

Used in C4 Residual Income Lab

V₀ = B₀ + B₀ × (ROE − r) ÷ (r − g)

B₀

book value today

ROE

return on equity

r

required return on equity

g

constant long-run growth rate

If ROE equals r, new equity earns only its cost and the value is book value.

Used in C4 Residual Income Lab

V₀ = B₀ + Σ RI_t ÷ (1 + r)^t + RI_(T+1) ÷ [(r − g) × (1 + r)^T]

B₀

book value today

RI_t

residual income in year t

T

last forecast year

r

required return on equity

g

constant long-run growth rate

Book value is the opening balance, so RI recognizes value earlier than a dividend model.

Used in C4 Residual Income Lab

V₀ = B₀ + Σ RI_t ÷ (1 + r)^t + RI_T ÷ [(1 + r − ω) × (1 + r)^(T−1)]

B₀

book value today

RI_t

residual income in year t, summed to T − 1

RI_T

residual income in the last forecast year

ω

persistence: 0 for none, 1 for all of it forever

r

required return on equity

T

last forecast year

The last term also holds year T's own RI, so the sum stops one year earlier.

Used in C4 Residual Income Lab

V₀ = B₀ + Σ RI_t ÷ (1 + r)^t + (P_T − B_T) ÷ (1 + r)^T

B₀

book value today

RI_t

residual income in year t

P_T

expected price at the horizon

B_T

expected book value at the horizon

r

required return on equity

T

last forecast year

A wasting asset has no RI after its life ends, and closing book can overstate what holders get.

Related tool C4 Residual Income Lab

g = r − B₀ × (ROE − r) ÷ (P₀ − B₀)

r

required return on equity

B₀

book value today

ROE

return on equity

P₀

price today

It's the growth of residual income, not of earnings. A result above economic growth means the single stage model doesn't fit.

Used in C4 Residual Income Lab

Value from residual income = 1 − B₀ ÷ V₀

B₀

book value today

V₀

equity value from the model

The higher it is, the more of the value rests on forecasts and not on the balance sheet.

Used in C4 Residual Income Lab

Closing equity = opening equity + net income − dividends − buybacks

Items that bypass net income break it, and the models stop agreeing unless they're restored.

Used in C4 Residual Income Lab

RI = comprehensive income − r × B

r

required return on equity

B

book equity at the start of the year

Use this when a loss goes straight to equity and bypasses net income.

Related tool C4 Residual Income Lab

Value per share = adjusted multiple × company's per-share figure

per-share figure

EPS, book value per share or sales per share

The multiple and the figure must be on the same basis. A peer P/S ignores a lower margin.

Used in D1 Multiples & Comps

Value per share = (adjusted EV/EBITDA × EBITDA − net debt) ÷ shares

An EV multiple gives firm value, so take off net debt before dividing by shares.

Used in D1 Multiples & Comps

Value per share = dividend per share ÷ adjusted yield

Yield runs the other way: a higher yield means a lower price.

Used in D1 Multiples & Comps

Premium = company multiple ÷ peer multiple − 1

For a yield, flip it to peer yield ÷ company yield − 1, so the premium is still measured on price.

Used in D1 Multiples & Comps

Adjusted multiple = benchmark × (1 − risk discount) × (1 + growth premium)

benchmark

the peers' central multiple

The steps multiply one after the other. For a yield, divide the benchmark by the two factors.

Used in D1 Multiples & Comps

Trailing P/E = P₀ ÷ E₀

P₀

price today

E₀

EPS for the year just ended

On last year's EPS. Not meaningful when EPS is negative or near zero.

Used in D1 Multiples & Comps

Leading P/E = P₀ ÷ E₁, with E₁ = E₀ × (1 + g)

P₀

price today

E₁

EPS expected next year

E₀

EPS for the year just ended

g

EPS growth expected next year

On next year's EPS, so it's lower than the trailing P/E when earnings are growing.

Used in D2 Justified Multiples

EPS = net income ÷ average shares

EPS

earnings per share

Average shares fit a flow earned over the year. Restate past EPS after a split before comparing.

Used in D1 Multiples & Comps

Sales per share = revenue ÷ shares

Tool D1 uses the year-end share count here, and a financial firm's top line in place of revenue.

Used in D1 Multiples & Comps

P/B = price ÷ book value per share

Above 1 means the market expects returns above r, or values assets that book leaves out.

Used in D1 Multiples & Comps

Tangible BVPS = (common equity − goodwill) ÷ shares

common equity

total equity less preferred stock

Take preferred out as well as goodwill, or the figure is too high.

Related tool D1 Multiples & Comps

P/S = price ÷ sales per share

It works when earnings are negative, but says nothing about margins. A bank's top line stands in for sales.

Used in D1 Multiples & Comps

P/CF = price ÷ [(net income + depreciation and amortization) ÷ shares]

This simple cash flow ignores working capital, so it can miss a sharp rise in receivables.

Related tool D1 Multiples & Comps

P/FCFE = price ÷ FCFE per share

FCFE

free cash flow to equity

The tightest cash measure, but it moves with borrowing and capex timing.

Related tool D1 Multiples & Comps

Dividend yield = dividend per share ÷ price

It leaves out buybacks, and a high yield with a payout above earnings may not last.

Used in D1 Multiples & Comps

Earnings yield = EPS ÷ price

Unlike P/E it stays meaningful with negative or tiny EPS, and a higher yield means cheaper.

Related tool D1 Multiples & Comps

EV/EBITDA = enterprise value ÷ (EBIT + depreciation)

It suits firms with different debt or heavy depreciation. Not used for banks or insurers.

Used in D1 Multiples & Comps

EV/sales = enterprise value ÷ revenue

Pair EV with revenue, not market cap, so the top and bottom match.

Used in A2 Value Measures

(EV + lease liabilities) ÷ (EBITDA + operating part of lease payments)

operating part

lease payments less the interest on the lease liability

Keep both sides on one basis: leases in EV need EBITDA struck before the lease cost.

Related tool D1 Multiples & Comps

P₀ ÷ E₁ = (1 − b) ÷ (r − g)

1 − b

payout ratio

r

required return on equity

g

constant long-run growth rate

The narrower the r − g spread, the more a small change moves the multiple.

Used in D2 Justified Multiples

P₀ ÷ E₀ = (1 − b) × (1 + g) ÷ (r − g)

1 − b

payout ratio

r

required return on equity

g

constant long-run growth rate

The extra (1 + g) is there because the multiple sits on the smaller, earlier EPS.

Used in D2 Justified Multiples

P₀ ÷ B₀ = (ROE − g) ÷ (r − g)

ROE

return on equity

r

required return on equity

g

constant long-run growth rate

Above 1 only when ROE is above r. It equals 1 + (ROE − r) ÷ (r − g).

Used in D2 Justified Multiples

P₀ ÷ S₀ = net margin × (1 − b) × (1 + g) ÷ (r − g)

S₀

sales per share, latest year

1 − b

payout ratio

r

required return on equity

g

constant long-run growth rate

It is net margin × the justified trailing P/E.

Used in D2 Justified Multiples

P₀ ÷ CF₀ = FCFE₀ × (1 + g) ÷ (r − g) ÷ CF₀

CF₀

cash flow per share, latest year

FCFE₀

FCFE per share, latest year

r

required return on equity

g

constant long-run growth rate

A firm that must reinvest more converts less cash flow to FCFE, so it deserves a lower P/CF.

Related tool D2 Justified Multiples

P₀ ÷ E₁ = (1 − b) ÷ (r − b × ROE)

1 − b

payout ratio

r

required return on equity

b

retention ratio, the share of earnings kept

ROE

return on equity

With ROE below r, keeping more earnings lowers the multiple: growth destroys value.

Related tool D2 Justified Multiples

g = r − (1 − b) ÷ (P/E)

r

required return on equity

1 − b

payout ratio

Payout ÷ P/E is the dividend yield, which is r − g. Don't mistake that yield for growth.

Used in D2 Justified Multiples

g = [P/E × r − (1 − b)] ÷ [P/E + (1 − b)]

r

required return on equity

1 − b

payout ratio

Trailing needs this longer form, because g also sits in the (1 + g) on top.

Used in D2 Justified Multiples

ROE = g + P/B × (r − g)

r

required return on equity

g

constant long-run growth rate

The return the market must expect for a given P/B to be fair.

Related tool D2 Justified Multiples

V_n = leading P/E × E_(n+1), or trailing P/E × E_n

E_n

EPS in the horizon year

E_(n+1)

EPS in the year after the horizon

A leading multiple goes on the year after the horizon, and its value still sits at year n.

Used in D2 Justified Multiples

PEG = P/E ÷ g in percent

g in percent

5% growth divides by 5

Divide by 5, not 0.05. Tool D1 uses trailing P/E and tool D2 leading. It ignores risk and how long growth lasts.

Used in D1 Multiples & Comps

Normalized EPS = sum of EPS over the years ÷ number of years

Restate old EPS for any split first. It ignores any change in the size of the firm.

Used in D1 Multiples & Comps

Normalized EPS = average ROE × current book value per share

It reflects the firm's size today, which makes it better than a plain average for a growing cyclical.

Used in D1 Multiples & Comps

Underlying income = NI − gains × (1 − t) + charges × (1 − t)

NI

net income

t

tax rate

Add back in full any charge with no tax relief, such as a goodwill impairment.

Related tool D1 Multiples & Comps

Unexpected earnings = reported EPS − expected EPS

The size alone says little until it's scaled by how much the firm usually misses.

Used in D1 Multiples & Comps

SUE = (reported EPS − expected EPS) ÷ standard deviation of surprises

SUE

standardized unexpected earnings

A noisy company's large miss can count for less than a steady firm's small one. Price plays no part.

Used in D1 Multiples & Comps

Relative strength = price ÷ index

A level has no meaning alone, so compare it over time.

Used in D1 Multiples & Comps

Change = (end price ÷ end index) ÷ (start price ÷ start index) − 1

Above zero means the share beat the index, even if its price fell.

Used in D1 Multiples & Comps

P/E = a + b₁ × growth + b₂ × payout + b₃ × beta

a

regression intercept

b₁, b₂, b₃

regression coefficients

growth, payout

entered in percent, not as decimals

Stay inside the sample's ranges. Tool D2 fits it across peers, and the inputs are often correlated.

Used in D2 Justified Multiples

Mean = Σx ÷ n

x

each peer's multiple

n

number of peers

One very high multiple can drag it up, and it overstates a group's P/E.

Used in D1 Multiples & Comps

Median = the middle peer, or the mean of the middle two

It resists outliers, so it's the default benchmark in tool D1.

Used in D1 Multiples & Comps

Harmonic mean = n ÷ Σ(1 ÷ x)

n

number of peers

x

each peer's multiple

It always sits at or below the arithmetic mean. It needs every value above zero.

Used in D1 Multiples & Comps

Weighted harmonic mean = 1 ÷ Σ(w ÷ x)

w

each peer's weight, with the weights adding to 1

x

each peer's multiple

With market cap weights on P/E, this is total market cap ÷ total earnings: the portfolio's true P/E.

Used in D1 Multiples & Comps

Net charge = costs capitalized in the year − amortization of past costs

Reverse the amortization as well, or you charge the old costs twice.

Used in D1 Multiples & Comps

Adjusted net income = net income − net charge × (1 − t)

t

tax rate

Divide by average shares for adjusted EPS. Comparing firms needs one accounting policy first.

Used in D1 Multiples & Comps

Normalized EBIT = reported EBIT + owner pay above market + personal expenses + other items

other items

one-off items

A controlling buyer can reset owner pay, so these adjustments count only on a control basis.

Used in E1 Private Company Valuation

Normalized EBIT = reported EBIT + other items

other items

one-off items

A minority holder can't change owner pay, so only one-off items come out.

Used in E1 Private Company Valuation

Normalized net income = reported net income + adjustments × (1 − t)

adjustments

normalized EBIT less reported EBIT

t

tax rate

Higher pretax income bears more tax, so the adjustment goes in after tax.

Used in E1 Private Company Valuation

r = r_f + ERP + size premium + company premium

r_f

risk-free rate

ERP

equity risk premium

A beta of 1 is implied. It suits a private firm with no peer beta to borrow.

Used in E1 Private Company Valuation

r = r_f + β × ERP + size premium + company premium

r_f

risk-free rate

β

beta, the share's sensitivity to the market

ERP

equity risk premium

With a beta below 1, this comes out below the build-up rate on the same inputs.

Used in E1 Private Company Valuation

Value = FCF₁ ÷ (r − g) = FCF₀ × (1 + g) ÷ (r − g)

FCF₀

normalized free cash flow, year just ended

FCF₁

next year's flow

r

required return on equity

g

constant long-run growth rate

Tool E1 capitalizes FCFE at the equity rate. Stable growth only: use a DCF if growth will change.

Used in E1 Private Company Valuation

Excess earnings = normalized EBIT × (1 − t) − WC × r_wc − FA × r_fa

t

tax rate

WC

working capital

r_wc

required return on working capital

FA

fixed assets

r_fa

required return on fixed assets

Tangible assets take their return first. What is left belongs to the intangibles.

Used in E1 Private Company Valuation

Intangibles = excess earnings × (1 + g) ÷ (r_i − g)

r_i

required return on intangibles, above the rate for tangible assets

g

constant long-run growth rate

Grow the excess one year first, and use the higher rate for intangibles.

Used in E1 Private Company Valuation

Equity value = working capital + fixed assets + intangibles − net debt

Firm value adds the three assets back together, then net debt comes off.

Used in E1 Private Company Valuation

Equity value = multiple × (1 − size discount) × EBITDA − net debt

EBITDA

normalized with no control adjustment

Public peers trade on minority prices, so don't use control-adjusted earnings. On a P/E, no net debt comes off.

Used in E1 Private Company Valuation

Equity value = deal multiple × control EBITDA − net debt

control EBITDA

EBITDA a controlling buyer would have

Deals are purchases of control, so no further premium goes on.

Used in E1 Private Company Valuation

Adjusted net assets = book equity + fair value adjustment

It equals assets at fair value less liabilities, so the book value of a revalued property plays no part.

Used in E1 Private Company Valuation

DLOC = 1 − 1 ÷ (1 + control premium)

DLOC

discount for lack of control

The premium is on the minority value and the discount on the control value. Strip out any synergy in the premium.

Used in E1 Private Company Valuation

Total discount = 1 − (1 − DLOC) × (1 − DLOM)

DLOC

discount for lack of control

DLOM

discount for lack of marketability

Discounts multiply, because each comes off what the one before leaves. Adding them overstates the total.

Used in E1 Private Company Valuation

Value = equity value × holding × (1 − DLOC) × (1 − DLOM)

holding

share of the firm held

DLOC

discount for lack of control

DLOM

discount for lack of marketability

Take the pro rata share first, then step down through each discount.

Used in E1 Private Company Valuation

Value = equity value × holding × (1 − DLOM)

holding

share of the firm held

DLOM

discount for lack of marketability

A marketable minority value has no control in it, so no DLOC comes off.

Used in E1 Private Company Valuation

Control value = marketable minority value ÷ (1 − DLOC)

DLOC

discount for lack of control

Undo a discount by dividing. Multiplying by (1 + control premium) gives the same answer when DLOC comes from that premium.

Used in E1 Private Company Valuation

Segment value = segment EBIT × EV/EBIT

EV/EBIT

the multiple for that segment's own peers

Give each segment the multiple of its own industry, not the group's.

Used in E2 Sum-of-the-Parts

Head office value = yearly head office cost × multiple

A cost no segment bears still has to be paid every year, so it comes off as a lump.

Used in E2 Sum-of-the-Parts

Enterprise value = Σ segment values − capitalized head office costs

Leaving the head office out overstates the group.

Used in E2 Sum-of-the-Parts

Value per share = (enterprise value − net debt) ÷ shares

The segments are valued on EBIT, so they're worth enterprise value: net debt still has to come off.

Used in E2 Sum-of-the-Parts

Discount = (value per share − price) ÷ value per share = 1 − price ÷ value per share

Measured on the value, not the price. A gap may reflect weak segments, not only the group structure.

Used in E2 Sum-of-the-Parts

Segment return = segment EBIT ÷ segment assets

This one is pretax, so don't compare it with a group ROA on net income.

Used in E2 Sum-of-the-Parts

Share = segment's asset growth ÷ all segments' asset growth

Set beside segment returns, it shows whether capital is going where the returns are.

Used in E2 Sum-of-the-Parts

Implied multiple = (market EV − value of the other segments) ÷ remaining segment's EBIT

market EV

market cap + net debt

A low result suggests the market is paying little for that part of the group.

Related tool E2 Sum-of-the-Parts

Tax = larger of (sale price − tax basis) and zero × t

tax basis

the segment's cost for tax

t

tax rate

A loss earns no tax credit here. Net proceeds = sale price − this tax.

Used in E2 Sum-of-the-Parts

Value per share = (EV − segment value − net debt + net proceeds) ÷ shares

EV

sum-of-the-parts enterprise value

The tax on the gain is the leak: a sale at the segment's value still loses it.

Used in E2 Sum-of-the-Parts

EPS = [NI − (segment EBIT − interest gained) × (1 − t)] ÷ average shares

NI

net income

interest gained

interest saved or earned on the proceeds in a full year

t

tax rate

A full year on the new shape, with the one-off gain left out.

Used in E2 Sum-of-the-Parts

Value per share = (equity value − stranded cost × head office multiple) ÷ shares

stranded cost

head office cost the departing segment no longer helps carry

Holders keep both parts, so only the stranded cost comes off the total.

Used in E2 Sum-of-the-Parts

EPS = [NI − (segment EBIT + stranded cost) × (1 − t)] ÷ average shares

NI

net income

stranded cost

head office cost the departing segment no longer helps carry

t

tax rate

No cash comes in, so there's no interest gained to offset the lost EBIT.

Used in E2 Sum-of-the-Parts

Repurchase price = price × (1 + premium)

premium

premium paid over the market price

A tender offer usually pays above market, so the same money retires fewer shares.

Used in E3 Payout & Leverage Effects

Income forgone = amount × r_d × (1 − t), or amount × after-tax yield on cash

r_d

pre-tax cost of the new debt

t

tax rate

Debt costs interest and spent cash stops earning, so neither is free.

Used in E3 Payout & Leverage Effects

EPS after = (NI − income forgone) ÷ (N − shares repurchased)

NI

net income

N

shares outstanding

Take the cost of the funding off the top as well as the shares off the bottom.

Used in E3 Payout & Leverage Effects

EPS rises if EPS ÷ repurchase price > after-tax funding cost

EPS ÷ repurchase price

the earnings yield at the price paid

A rise in EPS isn't a rise in value: the firm's risk moves too.

Used in E3 Payout & Leverage Effects

Value per share after = (market value of the shares − amount) ÷ shares left

Only a purchase below what the shares are worth adds value for those who stay.

Used in E3 Payout & Leverage Effects

Net debt to EBITDA after = (debt − cash + amount) ÷ EBITDA

Cash paid out and new debt raise net debt by the same amount.

Used in E3 Payout & Leverage Effects

FCFE after = CFO − capex + net borrowing − income forgone

CFO

cash from operations

Net borrowing

new debt less repayments

The cost of the funding carries on each year, after the payout itself is done.

Used in E3 Payout & Leverage Effects

r_e after = [(1 − w_d) × r_e + w_d × r_d − w_d after × r_d] ÷ (1 − w_d after)

r_e

cost of equity before

w_d

debt weight before

w_d after

debt weight after

r_d

pre-tax cost of debt

The pre-tax blend is held still, so more debt moves risk onto equity without changing the firm's own risk.

Used in E3 Payout & Leverage Effects

Target dividend = EPS × target payout

Dividends paid on this rule swing with earnings, so few firms follow it exactly.

Used in E3 Payout & Leverage Effects

D₁ = D₀ + (EPS × target payout − D₀) × adjustment factor

D₀

dividend just paid

adjustment factor

1 ÷ years taken to close the gap

Only part of the gap to target closes each year, which keeps dividends smooth.

Used in E3 Payout & Leverage Effects

Coverage = net income ÷ dividends

Dividends are paid in cash, so earnings cover alone doesn't show a dividend is safe.

Used in E3 Payout & Leverage Effects

Coverage = (CFO − capex) ÷ dividends

CFO

cash from operations

Below 1 with rising debt is a classic sign the dividend is being borrowed.

Used in E3 Payout & Leverage Effects

Gap = model value − anchor value

anchor value

the payout value of the forecast at the required return

Models on the same forecast and rate should agree, so a gap points to a difference in assumptions.

Used in F1 Model Reconciliation