Foundations
Available offline
101 of 101 formulas
Rule of 72
Investment and growth
Years to double ≈ 72 / growth rate (%)
Doubling in 3 years needs about 26% a year, in 5 years about 15%, in 7 years about 10%.
Available seat-km (ASK)
Industry metricsAirlines
Seats available × Distance flown (km)
Capacity measure.
Load factor
Industry metricsAirlines
Seats sold / Seats available
RASK and CASK
Industry metricsAirlines
RASK = Revenue / ASK; CASK = Total cost / ASK
Profitability per unit of capacity is RASK minus CASK; fuel is usually the largest cost.
Airline revenue
Industry metricsAirlines
Average fare × Load factor × Seats per flight × Flights
Yield
Industry metricsAirlines
Passenger revenue / (Passengers × km)
Break-even volume
Break-even and contribution
Fixed costs / Contribution margin per unit
Units needed to cover fixed costs.
Example: Price 50,000 VND, variable cost 30,000 VND, fixed costs 200 million VND: 200m / 20,000 = 10,000 units.
Break-even revenue
Break-even and contribution
Fixed costs / Contribution margin ratio
Revenue needed to cover fixed costs.
Large numbers
Mental-math shortcuts
Work in powers of ten (thousand 10³, million 10⁶, billion 10⁹), then add the unit
Write the zeros down; most case errors are a missing zero.
CASA ratio
Industry metricsBanking
(Current + savings deposits) / Total deposits
A higher share means cheaper funding.
Cost-to-income ratio
Industry metricsBanking
Operating expenses / Operating income
Lower is more efficient.
Net interest margin
Industry metricsBanking
(Interest income − Interest expense) / Interest-earning assets
The core profitability measure of a bank.
Practise with this case:Sen Bank: doubling revenue in a cashless boomNon-performing loan ratio
Industry metricsBanking
Non-performing loans (overdue more than 90 days) / Total loans
A net version subtracts provisions first.
Spread
Industry metricsBanking
Average lending rate − Average deposit rate
Compound annual growth rate
Investment and growth
(End value / Start value)^(1 / years) − 1
The steady yearly rate that links two values.
Example: From 100 to 150 in three years: 1.5^(1/3) − 1 ≈ 14.5% a year.
Calendarisation
LTM and calendarisation
Restate figures to the same calendar year before comparing companies
Needed when companies have different fiscal year-ends.
Cost of equity (CAPM)
Valuation (IB)
Cost of equity = Risk-free rate + Beta × (Market return − Risk-free rate)
Contribution margin per unit
Break-even and contribution
Price − Variable cost per unit
What each sale adds towards covering fixed costs.
Example: A ride-hailing platform keeps 16,000 VND of an 80,000 VND fare and spends 6,000 VND per ride: contribution is 10,000 VND.
Practise with this case:Đi Cùng: should we match Xanh SM's prices?Contribution margin ratio
Break-even and contribution
(Price − Variable cost) / Price
The same idea as a percentage of price.
Total cost
Core formulas
Total cost = Fixed costs + Variable cost per unit × Units
Always separate fixed from variable: they react differently when volume changes.
Elements:
Interest coverage
Credit statistics
EBITDA / Interest expense
Higher is safer. A stricter version subtracts capex from EBITDA first.
DCF enterprise value
Valuation (IB)
EV = Σ PV(free cash flows) + PV(terminal value)
Terminal value is often most of the total, so test how sensitive the result is to it.
Debt to total capitalisation
Credit statistics
Debt / (Debt + Preferred stock + Non-controlling interest + Equity)
Dividend yield
Return ratios
Annualised dividend per share / Share price
EBITDA margin
Margins
EBITDA / Revenue
Operating profit before depreciation and amortisation.
EBIT (operating) margin
Margins
EBIT / Revenue
Operating profit after depreciation and amortisation.
Average order value
Industry metricsE-commerce and marketplaces
GMV / Orders
Conversion and repeat rate
Industry metricsE-commerce and marketplaces
Conversion = Orders / Visits; Repeat rate = Returning buyers / All buyers
GMV and take rate
Industry metricsE-commerce and marketplaces
Platform revenue = GMV × Take rate
GMV is the value of goods traded, not the platform's revenue.
Practise with this case:Đi Cùng: should we match Xanh SM's prices?Entry economics
Market sizing and entry
Market size × Achievable share × Contribution margin ratio − Fixed costs
A quick test of whether entry can make money at a realistic share.
Elements:
Equity contribution
LBO and returns
Equity / Total sources of funding
In leveraged buyouts this is often around 25–40%.
Equity value from EV
Valuation (IB)
Equity value = EV − Net debt − Preferred stock − Non-controlling interest
Belongs to shareholders only, so pair it with net income and EPS.
Enterprise value
Valuation (IB)
EV = Equity value + Total debt + Preferred stock + Non-controlling interest − Cash
Belongs to all capital providers, so pair it with metrics before interest: revenue, EBITDA, EBIT.
Example: Shares bought for USD 345m plus USD 60m of net debt: EV = USD 405m.
Practise with this case:TailWorks and VetNest: a pet retailer buys vet clinicsEV / EBIT
Valuation (IB)
Enterprise value / EBIT
Useful when depreciation differs a lot between companies.
EV / EBITDA
Valuation (IB)
Enterprise value / EBITDA
The most common multiple; largely independent of capital structure and tax.
EV / Sales
Valuation (IB)
Enterprise value / Revenue
For companies that are not yet profitable.
Free-cash-flow yield
Return ratios
(Cash from operations − Capex) / Market capitalisation
Gross margin
Margins
(Revenue − Cost of goods sold) / Revenue
How efficiently the company makes or buys what it sells.
Simple growth
Investment and growth
(End value − Start value) / Start value
Growth over a single period.
Revenue per occupied bed
Industry metricsHealthcare
Revenue / Occupied beds
Bed occupancy
Industry metricsHealthcare
Beds occupied / Beds available
Hospital revenue
Industry metricsHealthcare
Patients × Revenue per patient (split inpatient and outpatient)
Average daily rate (ADR)
Industry metricsHotels
Room revenue / Rooms sold
Average length of stay
Industry metricsHotels
Room nights / Guest stays
Occupancy
Industry metricsHotels
Rooms sold / Rooms available
Practise with this case:Yamabuki Ryokan: riding Japan's tourism wave — or not?RevPAR
Industry metricsHotels
ADR × Occupancy = Room revenue / Rooms available
The industry's headline metric: it combines price and utilisation.
Implied value from a multiple
Valuation (IB)
Implied value = Chosen multiple × Target's metric
Make sure the multiple and the metric match (EV with EBITDA, equity with net income).
Combined ratio
Industry metricsInsurance
Loss ratio + Expense ratio
Below 100% means an underwriting profit, before investment income.
Expense ratio
Industry metricsInsurance
Operating expenses / Premiums earned
Loss ratio
Industry metricsInsurance
Claims paid / Premiums earned
IRR
LBO and returns
The discount rate at which the NPV of the cash flows equals zero
Private-equity buyers commonly look for returns around 20%.
Leverage
Credit statistics
Total debt / EBITDA
How many years of EBITDA the debt represents.
Last twelve months (LTM)
LTM and calendarisation
Last fiscal year + Current year-to-date − Prior year-to-date
Gives the most recent full-year view.
Profit margin
Core formulas
Margin = Profit / Revenue
A percentage, so it compares across years and companies of different sizes.
Cost-plus price
Pricing
Price = Unit cost × (1 + Markup %)
Markup is measured on cost; margin is measured on price — do not mix them.
Maximum price for a target
M&A and synergies
Standalone value + Value of synergies − Integration and retention costs
Paying above this hands the seller more than all the value the deal creates.
Elements:
Practise with this case:Hanul Thermal and Wärmewerk: buying the channelFixed cost per unit
Industry metricsManufacturing and energy
Total fixed costs / Units produced
When volume falls, fixed cost per unit rises — this is operating leverage.
Practise with this case:Kessler Präzisionsteile: a flat market that isn'tPlant revenue
Industry metricsManufacturing and energy
Capacity × Utilisation × Price
Capacity utilisation
Industry metricsManufacturing and energy
Actual output / Maximum capacity
Compare demand with effective (not nominal) capacity.
Practise with this case:Kessler Präzisionsteile: three lines, two too many?Market size (demand side)
Market sizing and entry
Target customers × Units per customer per period × Price
Top-down estimate from the buyers.
Elements:
Practise with this case:Coffee cups sold per day in Ho Chi Minh CityMarket size (supply side)
Market sizing and entry
Number of outlets or plants × Output per outlet × Price
Bottom-up estimate from the sellers; a good cross-check.
Elements:
Practise with this case:Bubble tea sales in SingaporeMOIC (cash-on-cash)
LBO and returns
Equity value at exit / Equity invested
Ignores timing; read it together with IRR.
Net debt
Valuation (IB)
Total debt − Cash and equivalents
Net leverage
Credit statistics
Net debt / EBITDA
Net margin
Margins
Net income / Revenue
After interest and taxes.
Payback period
Break-even and contribution
Initial investment / Net cash flow per period
How long until the investment is recovered; compare with the client's hurdle.
Example: SAR 150m invested for SAR 16.8m a year: about 8.9 years.
Practise with this case:Marah Parks: will the tourism boom double us?Percentages as fractions
Mental-math shortcuts
20% = ÷5; 25% = ÷4; about 33% = ÷3; 10% = move the decimal point
P / E
Valuation (IB)
Share price / Diluted EPS = Equity value / Net income
For mature companies with stable earnings.
The income-statement cascade
Margins
Revenue − COGS = Gross profit; − SG&A = EBITDA; − D&A = EBIT; − Interest = Pre-tax income; − Tax = Net income
Knowing which line moved tells you where to look.
Break-even volume loss for a price rise
Pricing
Maximum share of volume you can lose = 1 − (Old contribution per unit / New contribution per unit)
If fewer customers than this leave, the price rise pays off.
Example: Contribution rises from USD 2.50 to 3.50 per wash: you can lose up to 1 − 2.5/3.5 ≈ 29% of washes.
Practise with this case:FreshFold Laundromat: is $4 too cheap?Profit
Core formulas
Profit = Revenue − Costs
The root of every profitability tree.
Elements:
Discounting one cash flow
Valuation (IB)
PV = Cash flow / (1 + discount rate)^t
Like-for-like (same-store) growth
Industry metricsRetail and consumer
(This year's sales − last year's sales) / last year's sales, for stores open over a year
Separates real growth from growth bought with new stores; also compare it with inflation.
Store revenue
Industry metricsRetail and consumer
Visitors × Conversion rate × Average basket
Traffic, conversion and basket move for different reasons.
Sales density
Industry metricsRetail and consumer
Revenue / Selling area (m²)
Inventory turnover
Industry metricsRetail and consumer
COGS / Average inventory
Revenue
Core formulas
Revenue = Units sold × Price per unit
Splits a revenue change into a volume effect and a price effect.
Elements:
Revenue (customer view)
Core formulas
Revenue = Customers × Purchase frequency × Average order value
Useful for retail, food and services, where traffic and basket size behave differently.
Elements:
Return on assets
Return ratios
Net income / Average total assets
Return on equity
Return ratios
Net income / Average shareholders' equity
Return on investment
Investment and growth
(Gain − Investment) / Investment
Ignores timing; use payback or IRR when timing matters.
Return on invested capital
Return ratios
EBIT × (1 − tax rate) / Invested capital
Round early
Mental-math shortcuts
Use round inputs (e.g. 360 days, 50% of adults)
Estimates are judged on approach, not decimals.
Elements:
MRR and ARR
Industry metricsSaaS
Monthly or annual recurring revenue
The base of most SaaS metrics.
SaaS LTV (shortcut)
Industry metricsSaaS
ARPU × Gross margin % / Churn rate
LTV / CAC
Industry metricsSaaS
LTV / CAC
A common rule of thumb treats 3 or more as healthy.
Net revenue retention
Industry metricsSaaS
(Starting recurring revenue + Upsell − Churn − Downgrades) / Starting recurring revenue
Above 100% means revenue from existing customers grows even after losses.
CAC payback
Industry metricsSaaS
CAC / (Monthly revenue per customer × Gross margin %)
Often considered good when under about 12 months.
Order-of-magnitude check
Mental-math shortcuts
If a result is 10× away from a known benchmark, recheck the assumptions
Elements:
Market share
Market sizing and entry
Company revenue / Total market revenue
Use the same basis (value or volume) on both sides.
Share price
Valuation (IB)
Equity value / Fully diluted shares outstanding
ARPU
Industry metricsTelecom and subscriptions
Revenue / Average subscribers
Customer acquisition cost
Industry metricsTelecom and subscriptions
Sales and marketing spend / New customers
Churn rate
Industry metricsTelecom and subscriptions
Subscribers lost in the period / Average subscribers
Expected customer lifetime ≈ 1 / annual churn.
Practise with this case:Nabd Fitness: a leaky bucket in a booming marketCustomer lifetime value
Industry metricsTelecom and subscriptions
Contribution per period summed (and discounted) over the expected lifetime − Acquisition cost
Example: ARPU 200,000 VND a month, cost to serve 80,000: contribution 120,000 a month, or 1.44m a year. With 25% annual churn the customer stays about 4 years: about 5.8m before discounting; minus a 1m acquisition cost leaves about 4.8m.
Synergy logic
M&A and synergies
Value(A + B) > Value(A) + Value(B)
The deal only makes sense if combining creates value neither has alone.
Elements:
Value of synergies
M&A and synergies
Present value of synergy cash flows − Cost to achieve them
A quick version: annual synergy × a (lower, risk-adjusted) multiple.
Practise with this case:An Phú Bank and QuickPay: paying for the QR boomTerminal value — exit multiple
Valuation (IB)
Final-year EBITDA × Exit multiple
Multiple taken from comparable companies.
Terminal value — perpetuity growth
Valuation (IB)
Final-year FCF × (1 + g) / (WACC − g)
g is usually set at about 2–4%, close to long-run nominal economic growth.
Unlevered free cash flow
Valuation (IB)
EBIT × (1 − tax rate) + D&A − Capex − Change in net working capital
The cash a business generates for all capital providers.
WACC
Valuation (IB)
WACC = E/V × Cost of equity + D/V × Cost of debt × (1 − tax rate), where V = E + D
The discount rate for unlevered cash flows.