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Taylor Warfield · Lesson 4 Email + Formulas Cheat Sheet
Quant, Formulas & Mental Math
Every formula from the cheat sheet + the K/M/B/T trick to eliminate zero errors — the #1 mistake Bain interviewers see.
K/M/B/T Math Trick Profit Formulas Investment Operations Market Share Finance
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The K/M/B/T Trick — Cut Math Errors by 50%
Lesson 4
The #1 mistake Bain interviewers see
Botching zeroes in large-number calculations. Answers to "What is 100,000 × 10,000?" ranged from 1 million to 1 trillion in real interviews. The fix is simple: stop writing out zeroes entirely. Use letters instead.
Step 1 — Memorise the four letters
K
Thousand
1,000
M
Million
1,000,000
B
Billion
1,000,000,000
T
Trillion
1,000,000,000,000
Step 2 — Memorise the multiplication rules
K × K
=
M
M × K
=
B
K × K × K
=
B
B × K
=
T
M × M
=
T
K × K × K × K
=
T
Step 3 — Apply it: worked examples
Example 1 — from Taylor's email: 100,000 × 10,000
①
Convert: 100,000 × 10,000 → 100K × 10K
②
Split numbers and letters: (100 × 10) × (K × K)
③
Solve separately: 1,000 × M
✓
= 1,000M = 1B
Example 2 — market sizing: 330M population × $50K avg spend
①
Write in letters: 330M × 50K
②
Split: (330 × 50) × (M × K)
③
Solve: 16,500 × B
✓
= 16,500B = $16.5T
Example 3 — revenue calc: 5M customers × $200 avg price × 12 months
①
Write: 5M × 200 × 12 (200 and 12 are just numbers, no letter)
②
Combine numbers: 5 × 200 × 12 = 12,000 → so 12,000M
③
Simplify: 12,000M = 12B
✓
= $12B annual revenue
How to use this in the interview room
Write K, M, B, T on your scratch paper from the very start. Every time you write a number, convert it immediately. Say the letters out loud as you calculate — "330M times 50K equals M times K which is B, so 16,500B which is 16.5 trillion." This narrates your logic to the interviewer while protecting you from zero errors.
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Profit Formulas
10 formulas
Profit
Revenue – Costs
Revenue
Quantity × Price
Costs
Total Variable Costs + Fixed Costs
Total Variable Costs
Quantity × Variable Cost
Profit (expanded)
[(Price – Variable Cost) × Quantity] – Fixed Costs
Contribution Margin
Price – Variable Cost
How much each unit sold contributes toward covering fixed costs and generating profit
Breakeven Quantity
Fixed Costs ÷ Contribution Margin
The number of units you must sell before profit = $0
Breakeven Revenue
Breakeven Quantity × Price
Profit Margin
(Profit ÷ Revenue) × 100%
Denominator is Revenue — this is margin, not markup. A $30 profit on $100 revenue = 30% margin.
Cost Margin
(Cost ÷ Revenue) × 100%
Profit Margin + Cost Margin = 100%
The diagnostic tree — use this when profits are falling
Start top-down: Revenue side or cost side? If revenue: is it price or volume? If cost: is it fixed or variable? Narrow systematically before proposing solutions. Never jump to recommendations before you've identified the root cause.
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Investment Formulas
3 formulas
ROI
(Profit ÷ Initial Investment) × 100%
Return on Investment — how much you get back relative to what you put in
Payback Period
Initial Investment ÷ Profit Per Year
How many years until the investment pays for itself. Used in M&A and market entry cases.
CAGR
(Ending Value ÷ Beginning Value)^(1/Years) – 1
Compounded Annual Growth Rate — the smoothed annual growth rate over a period. Used to describe market or revenue growth.
When these show up in cases
ROI and Payback Period appear in M&A, Market Entry, and Investment cases — especially when the interviewer asks "how long until this investment pays off?" CAGR appears in growth cases when describing historical or projected market growth: "The market has been growing at a CAGR of 8% over the past five years."
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Operations Formulas
2 formulas
Output
Rate × Time
Used in operations and efficiency cases. E.g. a factory producing 500 units/hour for 8 hours = 4,000 units output.
Utilization
(Actual Output ÷ Maximum Possible Output) × 100%
How efficiently a resource is being used. A factory running at 70% utilization has headroom to grow without new capex.
Operations cases — what to watch for
If a client is losing money but revenue looks fine, check utilization — they may be carrying underused assets (factories, stores, staff) that are inflating fixed costs. Low utilization = high fixed cost per unit = margin compression.
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Market Share Formulas
3 formulas
Market Size
Total Customers × Average Annual Spend Per Customer
The demand-side approach to market sizing. Used as your final step after estimating the number of buyers and their spend.
Market Share
(Company Revenue ÷ Total Market Revenue) × 100%
What percentage of total market spending flows to our client. Useful for benchmarking competitive position.
Relative Market Share
Company Revenue ÷ Revenue of Largest Competitor
A ratio, not a percentage. A score above 1.0 means you are the market leader. Used in BCG matrix analysis.
Market sizing in interviews — the approach
Always build market size bottom-up in interviews: start with population → filter to addressable segment → estimate frequency → estimate average spend → multiply. State each assumption aloud, round aggressively, then sanity-check your final number. The K/M/B/T trick is essential here to avoid zero errors.
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Finance Formulas
7 formulas
Gross Profit
Revenue – Cost of Goods Sold (COGS)
Profit before operating expenses (salaries, rent, marketing). The "raw" margin from producing and selling the product.
Operating Profit
Gross Profit – Operating Expenses
Also called EBIT (see below). Profit from core business operations before interest and tax.
Net Profit
Revenue – All Expenses
The "bottom line" — what's left after every cost, including interest payments and taxes.
EBIT ¹
= Operating Profit ²
Earnings Before Interest and Taxes. Used to compare operating performance across companies with different capital structures.
EBITDA ³
EBIT + Depreciation + Amortization
The most common profitability metric in M&A. Strips out non-cash charges to show true cash-generating ability.
Inventory Turnover ⁴
Cost of Goods Sold ÷ Average Inventory
How many times inventory is sold and replenished in a period. Higher = more efficient. Retail and operations cases.
Days of Inventory ⁵
365 ÷ Inventory Turnover
Average number of days inventory sits before being sold. Lower = leaner, faster-moving supply chain.
1 EBIT = Earnings Before Interest and Taxes.
2 EBIT and Operating Profit are used interchangeably, but are only the same if the company has no non-operating income or expenses.
3 EBITDA = Earnings Before Interest, Taxes, Depreciation, and Amortization.
4 Inventory Turnover measures how many times a company sells through and replenishes its inventory over a given period.
5 Days of Inventory measures the average number of days inventory sits before it's sold.
What interviewers expect you to know
At a minimum: Gross Profit, Operating Profit, Net Profit, and EBITDA — and the difference between them. In M&A cases, acquisition price is typically expressed as a multiple of EBITDA (e.g. "the target is trading at 12x EBITDA"). Know that EBITDA strips out depreciation and amortization because those are non-cash charges that distort the true cash earnings of a business.