Business Plan (Q1, Q4)
Core Sections
- Executive Summary (1–2 pages): problem, solution, traction, TAM/SAM/SOM, ask.
- Opportunity: customer pain, value proposition, competition (5 Forces), differentiation.
- Market: size, growth, segments, personas.
- Go-to-Market: channels, pricing, positioning, sales motion.
- Operations: key resources, suppliers, partners, IP.
- Team: roles, gaps, advisors.
- Financials: 3–5 year projections, assumptions, break-even, unit economics.
- Risks & Mitigations: technical, market, regulatory.
- Milestones: roadmap with KPIs.
Useful Quant
TAM \(\approx\) population \(\times\) spend per user
Break-even quantity: \(Q_{BE}=\dfrac{FC}{P-VC}\)
Contribution margin: \(\text{CM}=P-VC\), \(\text{CM%}=\dfrac{P-VC}{P}\)
Break-even quantity: \(Q_{BE}=\dfrac{FC}{P-VC}\)
Contribution margin: \(\text{CM}=P-VC\), \(\text{CM%}=\dfrac{P-VC}{P}\)
FC=Fixed Cost, VC=Variable Cost per unit.
Segmentation, Targeting, Positioning (Q2, Q7, Q8, Q9)
Segmentation Bases
- Demographic
- Geographic
- Psychographic
- Behavioral
- Firmographic (B2B)
- Needs/Jobs-to-Be-Done
- Occasion/Usage
- Benefit sought
Good segments: measurable, substantial, accessible, differentiable, actionable.
Targeting Strategies
- Undifferentiated (mass)
- Differentiated (multi-segment)
- Concentrated (niche)
- Micromarketing (one-to-one)
Positioning
Choose a frame of reference, point(s) of difference, and reason to believe.
Template
“For [target], [brand] is the [frame of reference] that [point of difference] because [reason to believe].”
Perceptual maps visualize positions on attributes (e.g., price vs. quality).
Sales (Q3)
Pipeline
- Lead → MQL → SQL
- Discovery / Qualification (e.g., BANT)
- Demo / Proposal
- Negotiation
- Closed-Won / Closed-Lost
Key metrics: conversion rate, cycle length, ACV, win rate, churn.
Unit Economics
Customer Lifetime Value (stream): \(CLV=\sum_{t=1}^{T}\dfrac{(p_t-c_t) \cdot \Pr(\text{active}_t)}{(1+i)^t}\)
Constant margin \(m\), retention \(s\): \(CLV=\dfrac{m\,s}{1+i-s}\)
CAC payback (months): \(\dfrac{\text{CAC}}{\text{Monthly CM}}\)
Constant margin \(m\), retention \(s\): \(CLV=\dfrac{m\,s}{1+i-s}\)
CAC payback (months): \(\dfrac{\text{CAC}}{\text{Monthly CM}}\)
Forms of Business Ownership (Q5, Q6, Q22, Q23, Q25, Q28–Q30)
| Form | Liability | Taxation | Pros | Cons |
|---|---|---|---|---|
| Sole Proprietorship | Unlimited (personal) | Pass-through | Simple, full control | Unlimited liability, limited capital |
| General Partnership | Joint & several (general partners) | Pass-through | Shared skills/resources | Mutual liability, disputes |
| Limited Partnership (LP) | GP: unlimited; LP: limited to investment | Pass-through | Attracts investors | GP bears risk |
| LLP/LLC* | Limited | Pass-through (often) | Limited liability, flexible | More paperwork/fees |
| Corporation (C-Corp) | Limited | Entity taxed; dividends taxed | Capital access, perpetual life | Double taxation, regulation |
| Co-operative | Limited (usually) | Varies | Member-owned, patronage | Consensus decision-making |
| Franchise | Varies by contract | Pass-through (franchisee) | Brand & systems | Fees, less autonomy |
Financial Statements (Q10–Q11, Q26, Q33–Q35, Q45–Q46)
Balance Sheet
Assets \(=\) Liabilities \(+\) Equity
- Liquidity order: current vs. non-current items.
- Working capital: \(WC=CA-CL\); Current ratio: \(CR=\dfrac{CA}{CL}\).
Income Statement
Revenue \(-\) COGS \(=\) Gross Profit
\(-\) OpEx \(=\) EBIT
\(-\) Interest/Taxes \(=\) Net Income
\(-\) OpEx \(=\) EBIT
\(-\) Interest/Taxes \(=\) Net Income
Margins: Gross, Operating, Net.
Cash Flow
- Operating (CFO), Investing (CFI), Financing (CFF).
- Free Cash Flow: \(FCF=EBIT(1-T)+\text{Dep/Amort}-\Delta NWC-\text{Capex}\).
Common Ratios
ROA \(=\dfrac{NI}{Avg\,Assets}\), ROE \(=\dfrac{NI}{Avg\,Equity}\)
Quick ratio \(=\dfrac{CA-Inventory}{CL}\)
Debt-to-Equity \(=\dfrac{Total\,Debt}{Equity}\)
Quick ratio \(=\dfrac{CA-Inventory}{CL}\)
Debt-to-Equity \(=\dfrac{Total\,Debt}{Equity}\)
Opportunity Cost (Q12, Q24)
Cost of the next-best forgone alternative.
Along a PPF, OC of 1 more unit of \(X\) in terms of \(Y\): \(\text{OC}_{X}=\dfrac{\Delta Y}{\Delta X}\).
Business Production Decision-Making (Q13)
- Output rule: produce where \(MR=MC\) (if price \(\ge\) shutdown condition).
- Short run: at least one input fixed; Long run: all inputs variable.
- Capacity & bottlenecks; learning curves; economies vs. diseconomies of scale.
Short-Run Cost Graphs & Functions (Q14–Q18, Q15–Q16)
Definitions
\(TC=TFC+TVC\),\quad \(ATC=\dfrac{TC}{Q}=AFC+AVC\)
\(AFC=\dfrac{TFC}{Q}\),\quad \(AVC=\dfrac{TVC}{Q}\)
\(MC=\dfrac{dTC}{dQ}=\dfrac{dTVC}{dQ}\)
\(AFC=\dfrac{TFC}{Q}\),\quad \(AVC=\dfrac{TVC}{Q}\)
\(MC=\dfrac{dTC}{dQ}=\dfrac{dTVC}{dQ}\)
Graph Facts (U-shapes)
- \(MC\) cuts \(AVC\) and \(ATC\) at their minima.
- When \(MC < ATC\), \(ATC\) falls; when \(MC > ATC\), \(ATC\) rises (same for \(AVC\)).
- \(AFC\) declines as \(Q\) rises (spreading effect).
Shutdown & Break-Even
- Shutdown (SR): produce 0 if \(P < \min AVC\).
- Break-even: \(P = \min ATC\).
- Profit: \(\pi = TR-TC=Q(P-ATC)\).
Market Structure (Q19–Q20, Q31–Q32)
| Structure | # Firms | Product | Entry Barriers | Price Power | LR Profit |
|---|---|---|---|---|---|
| Perfect Competition | Many | Homogeneous | None | Price taker (\(P=MR=AR\)) | Zero (normal) |
| Monopolistic Competition | Many | Differentiated | Low | Some (non-price) | Zero (due to entry) |
| Oligopoly | Few | Either | High | Interdependent | Can persist |
| Monopoly | One | Unique | Very high | Price maker | Can persist |
Organizational Innovation (Unit 2 Appendix) (Q27, Q41–Q43)
Types
- Product vs. Process
- Business model
- Position (brand/market)
- Paradigm
- Incremental vs. Radical
- Architectural vs. Component
Structures & Methods
- Ambidexterity (explore and exploit).
- Stage-gate / lean experimentation (MVP, build-measure-learn).
- Open innovation, alliances, IP strategy.
Diffusion (Rogers)
- Innovators → Early adopters → Early majority → Late majority → Laggards.
- Adoption drivers: relative advantage, compatibility, complexity, trialability, observability.
Supply, Demand & Market Equilibrium (Q47–Q49)
Basics
Demand: \(Q_d = f(P, Y, P_s, tastes, \dots)\)
Supply: \(Q_s = g(P, input\;costs, tech, \dots)\)
Supply: \(Q_s = g(P, input\;costs, tech, \dots)\)
Equilibrium: set \(Q_d(P^*)=Q_s(P^*)\) to solve \(P^*, Q^*\).
Elasticities
Price elasticity (point): \(\varepsilon_d=\dfrac{dQ}{dP}\cdot\dfrac{P}{Q}\)
Arc elasticity: \(\varepsilon_d=\dfrac{\Delta Q}{\Delta P}\cdot\dfrac{\bar P}{\bar Q}\)
Cross-price: \(\varepsilon_{xy}=\dfrac{\%\Delta Q_x}{\%\Delta P_y}\), Income: \(\eta=\dfrac{\%\Delta Q}{\%\Delta Y}\)
Arc elasticity: \(\varepsilon_d=\dfrac{\Delta Q}{\Delta P}\cdot\dfrac{\bar P}{\bar Q}\)
Cross-price: \(\varepsilon_{xy}=\dfrac{\%\Delta Q_x}{\%\Delta P_y}\), Income: \(\eta=\dfrac{\%\Delta Q}{\%\Delta Y}\)
Elastic demand: \(|\varepsilon_d| > 1\); Inelastic: \(|\varepsilon_d| < 1\).
Policy (taxes/controls)
- Specific tax \(t\) creates wedge \(P_b-P_s=t\), reduces \(Q\).
- Incidence falls more on the side that is less elastic.
- DWL (approx.): \(\frac{1}{2}\,t\,\Delta Q\).
- Price ceiling < \(P^*\) → shortage; floor > \(P^*\) → surplus.
Perfect Competition, Monopolistic Competition, Oligopoly & Monopoly (Q21, Q36–Q40, Q44, Q50)
Perfect Competition
- Price taker: \(P=MR=AR\).
- Profit max: produce where \(P=MC\) (if \(P\ge \min AVC\)).
- Long run: entry drives \(P=\min ATC\), zero economic profit.
Monopolistic Competition
- Many firms, differentiated products.
- SR: \(MR=MC\) at \(Q\), set \(P\) from demand; LR: entry shifts demand until \(P=ATC>MC\) (excess capacity).
Oligopoly
- Few firms; strategic interdependence.
- Game-theory ideas: Cournot (quantities), Bertrand (prices), Stackelberg (leader/follower).
- Concentration: \(HHI=\sum s_i^2\) (shares in % units).
Monopoly (also Q44, Q50)
- Choose \(Q\) where \(MR=MC\); set \(P\) on demand at that \(Q\).
- Markup rule (iso-elastic demand): \(\dfrac{P-MC}{P}=\dfrac{1}{|\varepsilon_d|}\) ⇒ \(P=\dfrac{|\varepsilon_d|}{|\varepsilon_d|-1}MC\).
- Allocative inefficiency: \(P>MC\); DWL triangle between \(Q_M\) and \(Q^*\).
- Price discrimination (1st/2nd/3rd degree) can increase output and reduce DWL.
Quick Symbols & Identities
\(TR=P\cdot Q,\; AR=\dfrac{TR}{Q},\; MR=\dfrac{dTR}{dQ}\)
Profit: \(\pi=TR-TC=Q(P-ATC)\)
Learning curve (example): \(C(Q)=aQ^{b},\; b<0\) for learning effects.
Profit: \(\pi=TR-TC=Q(P-ATC)\)
Learning curve (example): \(C(Q)=aQ^{b},\; b<0\) for learning effects.