Analyst Dojo

Learning Module 8 of Equities 11–14% of the exam

Financial Statement Forecasting

7 lessons. About 43 minutes in cram mode, 196 minutes in full.

Start with lesson 1 Learn with Sensei Read the module summary Practice this module

Lessons

  1. 1
  2. 2
    Revenue models: historical, bottom-up and top-down

    explain 5 min cram, 22 min full

  3. 3
  4. 4
    Asset and financing models

    calculate 6 min cram, 28 min full

  5. 5
    Scenario analysis with probability weights

    interpret 5 min cram, 22 min full

  6. 6
  7. 7
    From the forecast model to an equity value

    calculate 8 min cram, 36 min full

What the exam expects you to do

  1. Explain the rationale, construction, and uses of financial statement forecast models in equity valuation.Why build a disaggregated model, and at what level of detail
  2. Evaluate the construction of an equity valuation model based on characteristics of the subject company.Model construction by company life cycle: from venture to decline
  3. Estimate and interpret the value of an equity security based on the outputs of a financial statement forecast model.Scenario analysis with probability weights

Module summary

The whole module on one sheet, organised by lesson: what to memorize, how the ideas fit together, the formulas and the key terms. No paragraphs, just what you need to revise.

How deeply to learn each part
Know the idea
Understand it in general. It frames other topics, but you will not calculate with it.
Use it
Understand it well enough to solve a question with it. Recognize when it applies.
Memorize
Learn it by heart. The exam will not give it to you.
1

Why build a disaggregated model, and at what level of detail

Known

MemorizeThe four areas of a model

AreaTypical inputsFeeds
Revenuemarket size, share, segments, demandincome
Expense or marginpricing power, materials and labor, marginsincome
Asset growth and efficiencyworking capital, fixed investmentnet investment
Financingdebt versus equity, tenor and typeFCFE, interest, WACC weights

Memory hook R-E-A-F: Revenue, Expenses, Assets, Financing. The first two make profit, the third spends it, the fourth pays for it.

Know it cold NOPAT=(Rev−COGS−SG&A−D&A)(1−t)NOPAT = (\text{Rev} - \text{COGS} - \text{SG\&A} - \text{D\&A})(1-t); FCFF=NOPAT−(Δworking capital+Δnet long-term assets)FCFF = NOPAT - (\Delta \text{working capital} + \Delta \text{net long-term assets}).

MemorizeWhen disaggregation matters

Memory hook Same growth everywhere = same answer as a constant growth model.

Know it cold Different growth rates across components (margins changing, payout changing, investment out of line with revenue) → build the model. More lines: richer story, but more error, noise and updating.

Key terms

  • disaggregated valuation model Memorize
  • static relationships among value drivers Know the idea
  • valuation narrative Know the idea
  • components growing at different rates Use it
  • payout ratio and dividend growth Use it
  • revenue model Memorize
  • expense or profit margin model Memorize
  • asset growth and efficiency model Memorize
  • financing model Memorize
  • net operating profit after taxes (NOPAT) Memorize
  • net investment Memorize
  • free cash flow to the firm (FCFF) Memorize
  • level of model detail Use it
  • consolidating line items Use it
  • uses of forecast models Know the idea
  • corporate restructuring Know the idea
  • leveraged buyout (LBO) Know the idea
The four areas of a disaggregated model
Disaggregated valuation modelforecast the statements, let cash flow come out
  • Revenue model Memorize market size, market share, segments, changes in demand; feeds income
  • Expense or profit margin model Memorize pricing power, materials and labor costs, efficiencies and margins; feeds income
  • Asset growth and efficiency model Memorize working capital and fixed investment; feeds net investment
  • Financing model Memorize mix of debt and equity, debt tenor and type; feeds FCFE, interest and the WACC weights
What a forecast model is used for
Uses of a forecast model
  • Estimate intrinsic value discount the free cash flow it produces
  • Update the value as news arrives quarterly results, a new product, a price change
  • What-if analysis scenarios, lesson 5
  • Link observable numbers to the share price quarterly sales, subscribers
  • Capture cost structure fixed versus variable costs, lesson 3
  • Plan funding for growth grow assets with sales and fund them consistently, lesson 4
  • Restructurings and leveraged buyouts acquisitions, disposals, debt-funded takeovers
  • Sensitivity analysis change one or more inputs, hold the rest

Formulas

Intrinsic value from forecast FCFF Know the idea
IVt=∑i=1nFCFFt+i(1+WACC)i+E(Pt+n)(1+WACC)nIV_t = \sum_{i=1}^{n} \frac{FCFF_{t+i}}{(1 + WACC)^i} + \frac{E(P_{t+n})}{(1 + WACC)^n}
Quick example

Free cash flow to the firm of 40 and 44 in two years, a terminal value of 900 at the end of year 2, and a weighted average cost of capital of 10%. 40 ÷ 1.10 + 44 ÷ 1.10² + 900 ÷ 1.10² = 816.53, the value of the firm before subtracting debt.

On your calculator
  1. 944÷1.21=STO1 780.17 (year 2 flow and terminal value)
  2. 40÷1.1+RCL1= 816.53

STO store · RCL recall a stored number

  1. 944ENTER1.21÷ 780.17
  2. 40ENTER1.1÷+ 816.53

ENTER enter (on the HP, puts the number on the stack)

Intrinsic value from an EV/FCFF multiple Know the idea
IVt=FCFFt+1×EV multipletIV_t = FCFF_{t+1} \times \text{EV multiple}_t
Quick example

Next-year free cash flow to the firm of 50 and an enterprise value multiple of 14 times that cash flow give a firm value of 50 × 14 = 700.

On your calculator
  1. 50×14= 700
  1. 50ENTER14× 700

ENTER enter (on the HP, puts the number on the stack)

Dividend growth when the payout ratio changes Use it
gDPS=(1+gEPS)×PayouttPayoutt−1−1g_{DPS} = (1 + g_{EPS}) \times \frac{\text{Payout}_t}{\text{Payout}_{t-1}} - 1
Quick example

Earnings per share grow 5% while the payout ratio goes from 20% to 25%. Dividends per share grow 1.05 × 25 ÷ 20 − 1 = 31.25%.

On your calculator
  1. 1.05×0.25÷0.2−1= 0.3125
  1. 1.05ENTER0.25×0.2÷1− 0.3125

ENTER enter (on the HP, puts the number on the stack)

NOPAT Memorize
NOPAT=(Revenue−COGS−SG&A−D&A)(1−t)NOPAT = (\text{Revenue} - \text{COGS} - \text{SG\&A} - \text{D\&A})(1 - t)
Quick example

Revenue 200, cost of goods sold 110, selling, general and administrative expenses 40, depreciation and amortization 10, tax rate 30%. Operating profit is 40, so net operating profit after taxes is 40 × 0.70 = 28.

On your calculator
  1. 200−110−40−10=×0.7= 28
  1. 200ENTER110−40−10−0.7× 28

ENTER enter (on the HP, puts the number on the stack)

Net investment Memorize
Net investment=ΔWorking capital+ΔNet long-term assets\text{Net investment} = \Delta \text{Working capital} + \Delta \text{Net long-term assets}
Quick example

Working capital rises by 5 and net long-term assets by 8, so net investment is 5 + 8 = 13.

FCFF from NOPAT Memorize
FCFF=NOPAT−Net investmentFCFF = NOPAT - \text{Net investment}
Quick example

Net operating profit after taxes of 28 less net investment of 13 leaves free cash flow to the firm of 15.

On your calculator
  1. 28−13= 15
  1. 28ENTER13− 15

ENTER enter (on the HP, puts the number on the stack)

2

Revenue models: historical, bottom-up and top-down

Known

MemorizeThree revenue models

ModelBuilt fromSuits
Historicalpast growth, by segmentmature companies with stable products and competition
Bottom-upunits × revenue per unit (ASKs, stores, subscribers × ARPU)businesses with clear units of activity
Top-downmarket size × market share (units × price)firms whose market can be forecast from the economy

Memory hook History looks back; bottom-up counts units; top-down starts with the market.

Know it cold Store count plus same-store sales is bottom-up. Market share is top-down. Every forecast must name its units or its market.

MemorizeComputations

CaseRule
Market and share both move(M₁ × s₁) ÷ (M₀ × s₀) − 1
Units and revenue per unit(1 + g_units)(1 + g_rev per unit) − 1

Memory hook "Share" or "market" means top-down; "per store", "per seat kilometer", "per user" means bottom-up.

Know it cold When both market and share move, compute both revenues and compare. Multiplying the two factors is exact; adding the growth rates is only an approximation.

Key terms

  • historical revenue model Memorize
  • mature company Use it
  • segment revenue growth Use it
  • bottom-up revenue model Memorize
  • available seat kilometers (ASKs) Use it
  • revenue per ASK Use it
  • capacity-based measures Use it
  • same-store sales growth Use it
  • subscribers and average revenue per user (ARPU) Use it
  • top-down revenue model Memorize
  • market growth and market share Use it
  • units sold and price per unit Use it
Three revenue models
Revenue modelthree ways to build the first line
  • Historical Memorize mature company: stable products, mix, footprint and competition
    • By segment Use it each segment at its own growth
  • Bottom-up Memorize units × revenue per unit
    • Available seat kilometers (ASKs) × revenue per ASK Use it airlines
    • Stores × sales per store Use it same-store sales + new stores
    • Subscribers × average revenue per user (ARPU) Use it acquisition and retention
  • Top-down Memorize market size × market share
    • Units × price by region Use it share change scales units

Formulas

Revenue from market size and share Use it
R=M×sgR=M1s1M0s0−1R = M \times s \qquad g_R = \frac{M_1 s_1}{M_0 s_0} - 1
Quick example

Market 312 → 330 (billions) at a constant 4.5% share. Revenue 14.04 → 14.85, growth 330 ÷ 312 − 1 = 5.77%. If the share also rose, growth would be higher.

On your calculator
  1. 330÷312−1= 0.0577
  1. 330ENTER312÷1− 0.0577

ENTER enter (on the HP, puts the number on the stack)

Revenue from units and revenue per unit Use it
R1=R0 (1+gunits)(1+grev per unit)R_1 = R_0\,(1 + g_{units})(1 + g_{\text{rev per unit}})
Quick example

Revenue 80.0; volume +5%, average price +2%. 80.0 × 1.05 × 1.02 = 85.68, growth 7.1%, not 7.0%: the cross term is real.

On your calculator
  1. 80×1.05×1.02= 85.68
  1. 80ENTER1.05×1.02× 85.68

ENTER enter (on the HP, puts the number on the stack)

Top-down revenue across regions Use it
R=∑iUnits soldi×Revenue per unitiUnits soldi=Market unitsi×siR = \sum_{i} \text{Units sold}_i \times \text{Revenue per unit}_i \qquad \text{Units sold}_i = \text{Market units}_i \times s_i
Quick example

Region A: market 1,000,000 units, share 10%, price 50. Region B: market 500,000 units, share 8%, price 80. Units sold are 100,000 and 40,000, so revenue is 5.0 million + 3.2 million = 8.2 million.

On your calculator
  1. 1000000×0.1×50=STO1 5000000
  2. 500000×0.08×80+RCL1= 8200000

STO store · RCL recall a stored number

  1. 1000000ENTER0.1×50×500000ENTER0.08×80×+ 8200000

ENTER enter (on the HP, puts the number on the stack)

3

Expense models: margins, itemization and operating leverage

Known

MemorizeThree expense models

ModelHowWatch out
Historicalregress expense changes on revenue changes: intercept = fixed, slope = variablechanges, not levels; mature firms only
Itemizationgive big costs their own line from as-reported statementsfuel and labor follow their own drivers
Direct marginassume gross or EBIT margincheck the implied expense growth

Memory hook History, Items, Margin: "HIM".

Know it cold Cost growth = a + b × revenue growth. Margin rises only if revenue outgrows costs. Implied COGS = (1 − margin) × revenue.

MemorizeFixed costs and margins

Memory hook Fixed costs give leverage: sales up, margin up faster; sales down, margin down faster.

Know it cold COGS = fixed + variable × revenue. Mix shifting toward a low-margin line lowers the total margin.

Key terms

  • historical expense model Use it
  • regression of expense changes on revenue changes Use it
  • intercept as the fixed cost component Memorize
  • slope as the variable component Memorize
  • itemization of economically significant expenses Use it
  • standardized versus as-reported statements Know the idea
  • direct profit margin assumption Use it
  • implied expense growth Use it
  • gross margin Use it
  • product mix Use it
  • SG&A expenses Use it
  • fixed and variable costs Use it
  • operating leverage Use it
Three expense models
Expense or profit modelkeep costs coherent with revenue
  • Historical Memorize past growth, or regress expense changes on revenue changes
    • Intercept a Memorize fixed cost component
    • Slope b Memorize variable with revenue
  • Itemization Memorize model big costs the vendor data hide, from as-reported statements
  • Direct margin assumption Memorize assume the gross or operating margin; check the implied cost growth

Formulas

Expense growth from a regression Use it
ΔExpenset=a+b×ΔRevenuet\Delta \text{Expense}_t = a + b \times \Delta \text{Revenue}_t
Quick example

Intercept a = 0.010, slope b = 0.85, revenue growth 8%: 0.010 + 0.85 × 0.08 = 7.8%, so the margin rises.

On your calculator
  1. 0.85×0.08+0.01= 0.078
  1. 0.85ENTER0.08×0.01+ 0.078

ENTER enter (on the HP, puts the number on the stack)

Cost of sales implied by a gross margin Use it
COGSt+1=(1−mt+1)×Revenuet+1\text{COGS}_{t+1} = (1 - m_{t+1}) \times \text{Revenue}_{t+1}
Quick example

Revenue 400 → 432 (+8%), gross margin 30% → 32%. Cost of goods sold goes from 280 to 0.68 × 432 = 293.76: growth 4.9%.

On your calculator
  1. 432×0.68=÷280−1= 0.0491
  1. 432ENTER0.68×280÷1− 0.0491

ENTER enter (on the HP, puts the number on the stack)

Cost of sales with fixed and variable parts Use it
COGS=F+v×RevenueGross margin=1−COGS÷Revenue\text{COGS} = F + v \times \text{Revenue} \qquad \text{Gross margin} = 1 - \text{COGS} \div \text{Revenue}
Quick example

Fixed 100, variable 50% of revenue. Revenue 300: cost of goods sold 250, margin 16.7%. Revenue 360: cost 280, margin 22.2%.

On your calculator
  1. 0.5×360+100=÷360=+|-+1= 0.2222

+|- change sign

  1. 0.5ENTER360×100+360÷CHS1+ 0.2222

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

4

Asset and financing models

Known

MemorizeFinancing needs and FCFE

ItemFormula
Financing needsΔoperating assets − Δnon-debt liabilities − (net income − dividends)
FCFE (from net income)net income − net investment + Δdebt
FCFE (uses of cash)Δcash + dividends + buybacks − new shares
Net investmentΔoperating assets − Δnon-debt liabilities

Memory hook Spend, minus what suppliers fund, minus what profits keep = what must be raised.

Know it cold Need above zero: cash, then debt, equity last. Need below zero: add to cash, repay debt or buy back shares. Higher dividends raise the need.

MemorizeAsset model rules

Memory hook Grow it only if it is operating and it is cash.

Know it cold Assets = revenue growth means constant turnover (a = 0, b = 1). Asset regressions are weak: looser link, and assets come before the revenue. Do not grow marketable securities or impairments.

Key terms

  • asset model Memorize
  • asset-light and asset-heavy business models Know the idea
  • assets growing with revenue Use it
  • constant asset turnover Use it
  • regression of asset growth on revenue growth Use it
  • timing mismatch Know the idea
  • itemized asset forecast Use it
  • operating and cash-based line items Use it
  • non-operating assets Use it
  • financing model Memorize
  • financing needs Memorize
  • financing surplus Use it
  • sources and uses of financing Use it
  • free cash flow to equity (FCFE) Memorize
  • dividends and financing needs Use it
  • target debt ratio Use it
  • balancing figures Use it
Should this line grow with the forecast?
A balance sheet linetwo tests: does it arise from operations, and does it involve cash?
  • Both tests yes: grow it Memorize receivables, inventory, payables, net long-term operating assets, intangibles bought for cash
  • Not operating: do not grow it Memorize marketable securities and other non-operating assets; cash changes come from the financing model
  • No cash involved: do not forecast it Memorize a value change such as a goodwill impairment
Filling a gap or using a surplus
Financing needsthe sign decides what to do
  • Need above zero: money required Memorize
    • Cash draw it down, but not below a safe level
    • Debt check the debt ratio and the extra interest
    • Equity avoid unless the company has issued before
  • Need below zero: surplus Memorize
    • Cash add to the balance
    • Debt repay; check the debt ratio does not fall too low
    • Equity buy back shares or pay extra dividends

Formulas

Asset growth from a regression Use it
%ΔAssett=a+b×%ΔRevenuet\%\Delta \text{Asset}_t = a + b \times \%\Delta \text{Revenue}_t
Quick example

Intercept a = 0.03, slope b = 0.40, revenue growth 5%: asset growth is 0.03 + 0.40 × 0.05 = 5.0%. "Assets grow with revenue" means a = 0 and b = 1.

On your calculator
  1. 0.4×0.05+0.03= 0.05
  1. 0.4ENTER0.05×0.03+ 0.05

ENTER enter (on the HP, puts the number on the stack)

Financing needs Memorize
Financing needs=ΔOperating assets−ΔNon-debt liabilities−ΔRetained earnings\text{Financing needs} = \Delta \text{Operating assets} - \Delta \text{Non-debt liabilities} - \Delta \text{Retained earnings}
Quick example

Operating assets rise 60 and non-debt liabilities 14. Net income is 35 and dividends 10, so retained earnings rise 25. Financing needs are 60 − 14 − 25 = 21: money is required.

On your calculator
  1. 60−14−35+10= 21
  1. 60ENTER14−35−10+ 21

ENTER enter (on the HP, puts the number on the stack)

FCFE from net income Memorize
FCFE=Net income−(ΔGross long-term assets−Depreciation)−ΔWorking capital+ΔDebtFCFE = \text{Net income} - (\Delta \text{Gross long-term assets} - \text{Depreciation}) - \Delta \text{Working capital} + \Delta \text{Debt}
Quick example

Net income 20, gross long-term assets +30, depreciation 10, working capital +5, debt +12. FCFE = 20 − (30 − 10) − 5 + 12 = 7.

On your calculator
  1. 20−30+10−5+12= 7
  1. 20ENTER30−10+5−12+ 7

ENTER enter (on the HP, puts the number on the stack)

FCFE from the uses of cash Memorize
FCFE=ΔCash+Dividends+Share repurchases−Share issuanceFCFE = \Delta \text{Cash} + \text{Dividends} + \text{Share repurchases} - \text{Share issuance}
Quick example

Cash rises 3, dividends are 6, buybacks 2 and new shares 4. FCFE = 3 + 6 + 2 − 4 = 7, the same company as the card above.

On your calculator
  1. 3+6+2−4= 7
  1. 3ENTER6+2+4− 7

ENTER enter (on the HP, puts the number on the stack)

5

Scenario analysis with probability weights

Known

MemorizeWeighted scenario value

StepRule
Value each scenariore-run the model to a firm and equity value
Floornegative equity value → 0 (limited liability)
WeightΣ p × value, probabilities sum to 1
Compareweighted value vs market capitalization

Memory hook Run, floor, weight, compare.

Know it cold Probabilities are subjective, not true; scenarios add narrative, not accuracy; update as news arrives.

MemorizeScenario or sensitivity?

Memory hook A scenario is a story; a sensitivity is a dial.

Know it cold Scenario: a coherent set of assumptions changes together. Sensitivity: chosen inputs change, all others held constant.

Key terms

  • scenario analysis Memorize
  • valuation narrative per scenario Know the idea
  • sensitivity analysis Memorize
  • subjective probabilities Use it
  • probability-weighted equity value Use it
  • negative equity value floored at zero Use it
  • limited liability Use it
  • comparison with market capitalization Use it
  • updating the model Know the idea
Scenario analysis against sensitivity analysis
Testing a valuation
  • Scenario analysis Memorize a story, with linked assumptions
    • Changes a whole set of linked assumptions, as a story
    • Output an equity value per scenario, then a weighted value
  • Sensitivity analysis Memorize a dial, one input at a time
    • Changes chosen inputs, all others held constant
    • Output how far value moves per input

Formulas

Probability-weighted equity value Use it
Equity value=∑sps×max⁡(Vs,0),∑sps=1\text{Equity value} = \sum_{s} p_s \times \max(V_s, 0), \qquad \sum_s p_s = 1
Quick example

Three scenarios: 90 (probability 35%), 60 (40%) and −20 (25%). The negative value counts as zero, so the weighted value is 0.35 × 90 + 0.40 × 60 + 0.25 × 0 = 55.5.

On your calculator
  1. 0.35×90=STO1 31.5
  2. 0.4×60+RCL1= 55.5

STO store · RCL recall a stored number

  1. 0.35ENTER90×0.4ENTER60×+ 55.5

ENTER enter (on the HP, puts the number on the stack)

6

Model construction by company life cycle: from venture to decline

Known

MemorizeValuation focus by stage

StageMetricValue driverTerminal valueHistory
Start-upsalesmarket potentialP/S × horizon revenue ÷ ROIlittle or none
Growthcash flow for high growthsustainable growth and marginsP/E × horizon earnings ÷ ROIlimited
Matureearnings and cash flow for stable growthsustainable profitsconstant growth or peer multiplelong
Declinecash flow to return capitallong-run margins after declinegoing concern vs distress, weightedlong

Memory hook Sales, then earnings, then steady cash, then survival.

Know it cold Start-up value is post-money. Pre-money = post-money − new equity; stake = new equity ÷ post-money. ROI = (1 + IRR)^n.

MemorizeDistress and control

Memory hook Weight it, do not bend the rate.

Know it cold Value = going-concern value × (1 − p) + distress sale value × p, with the sale value discounted to today. Financial investor: value as run; activist with a plan: value the plan as a scenario.

Key terms

  • areas of valuation focus Know the idea
  • development stage Use it
  • data availability Know the idea
  • analyst perspective Know the idea
  • company life cycle stages Memorize
  • start-up valuation Use it
  • price-to-sales (P/S) terminal value Use it
  • return on investment (ROI) Use it
  • internal rate of return (IRR) Use it
  • venture capital (VC) Use it
  • post-money valuation Memorize
  • pre-money valuation Memorize
  • fractional ownership Memorize
  • growth-phase valuation Use it
  • earnings multiple terminal value Use it
  • firms in decline Use it
  • financial distress Use it
  • cash flow adjustments Know the idea
  • denominator issues Know the idea
  • terminal value and horizon issues Know the idea
  • going-concern value Memorize
  • distress sale value Memorize
  • probability of distress Memorize
  • financial investor Use it
  • strategic investor Use it
  • activist investor Use it
Valuation focus by life-cycle stage
Company life cyclestages vary widely in length
  • Start-up Memorize metric: sales · driver: market potential · history: little or none
    • Terminal value P/S × revenue at the horizon
  • Growth Memorize metric: cash flow to fund high growth · driver: sustainable growth and margins · history: limited
    • Terminal value P/E × earnings at the horizon
  • Mature Memorize metric: earnings and cash flow for stable growth · driver: sustainable profits · history: long
    • Terminal value constant growth or peer multiple
  • Decline Memorize metric: cash flow to return capital · driver: long-run margins after decline · history: long
    • Terminal value weight going concern against distress
What to adjust for a firm in decline
Valuation of a firm in decline
  • Cash flows Know the idea customers and suppliers leave, assets are impaired; timing uncertain
  • Discount rate Know the idea cost of debt jumps with default risk; required return on equity becomes unstable
  • Terminal value and horizon Know the idea a going concern is no longer certain; healthy peers' multiples distort
Who holds the shares
Shareholder typecontrol changes how the company is run
  • Financial investor Use it no influence: value as currently run
  • Strategic investor Use it control to combine or reshape
  • Activist investor Use it minority or majority stake; pushes a plan: model it as a scenario

Formulas

Value from cash flows and a terminal value Know the idea
IVt=∑i=1nE(CFt+i)(1+r)i+E(Pt+n)(1+r)nIV_t = \sum_{i=1}^{n} \frac{E(CF_{t+i})}{(1 + r)^i} + \frac{E(P_{t+n})}{(1 + r)^n}
Quick example

Expected cash flows of 10 and 12, a terminal value of 200 at the end of year 2, required return 12%. 10 ÷ 1.12 + (12 + 200) ÷ 1.12² = 177.93.

On your calculator
  1. 212÷1.2544=STO1 169.01
  2. 10÷1.12+RCL1= 177.93

STO store · RCL recall a stored number

  1. 212ENTER1.2544÷ 169.01
  2. 10ENTER1.12÷+ 177.93

ENTER enter (on the HP, puts the number on the stack)

Venture capital method Use it
IVt=Expected revenuet+n×P/S(1+r)n=Expected revenuet+n×P/SROIIV_t = \frac{\text{Expected revenue}_{t+n} \times P/S}{(1 + r)^n} = \frac{\text{Expected revenue}_{t+n} \times P/S}{ROI}
Quick example

Revenue of 40 at the horizon, a price-to-sales multiple of 3 and a target return of 10 times the money: 40 × 3 ÷ 10 = 12.0, the post-money value.

On your calculator
  1. 40×3÷10= 12
  1. 40ENTER3×10÷ 12

ENTER enter (on the HP, puts the number on the stack)

ROI and IRR Use it
ROI=(1+IRR)nROI = (1 + IRR)^n
Quick example

A target IRR of 30% a year for 4 years means an ROI of 1.30⁴ = 2.8561 times the original investment.

On your calculator
  1. 1.3y^x4= 2.8561

y^x power

  1. 1.3ENTER4y^x 2.8561

ENTER enter (on the HP, puts the number on the stack) · y^x power

Pre-money valuation Memorize
Pre-money=Post-money−New equity\text{Pre-money} = \text{Post-money} - \text{New equity}
Quick example

A post-money value of 80 with 20 of new equity means a pre-money value of 80 − 20 = 60.

Fractional ownership Memorize
Fractional ownership=New equityPost-money\text{Fractional ownership} = \frac{\text{New equity}}{\text{Post-money}}
Quick example

New equity of 20 into a post-money value of 80 buys 20 ÷ 80 = 25% of the company.

On your calculator
  1. 20÷80= 0.25
  1. 20ENTER80÷ 0.25

ENTER enter (on the HP, puts the number on the stack)

Growth-phase value from an earnings multiple Use it
IVt=Net incomet+n×P/EROIIV_t = \frac{\text{Net income}_{t+n} \times P/E}{ROI}
Quick example

Net income of 8 at the horizon, a price-to-earnings multiple of 12 and a target return of 4 times the money: 8 × 12 ÷ 4 = 24.0.

On your calculator
  1. 8×12÷4= 24
  1. 8ENTER12×4÷ 24

ENTER enter (on the HP, puts the number on the stack)

Value with a probability of distress Memorize
IVt=Going-concern value×(1−pdistress)+Distress sale value×pdistressIV_t = \text{Going-concern value} \times (1 - p_{distress}) + \text{Distress sale value} \times p_{distress}
Quick example

A going-concern value of 100, a 20% chance of distress and a distress sale worth 30 today: 0.80 × 100 + 0.20 × 30 = 86.

On your calculator
  1. 0.2×30=STO1 6
  2. 0.8×100+RCL1= 86

STO store · RCL recall a stored number

  1. 0.2ENTER30×0.8ENTER100×+ 86

ENTER enter (on the HP, puts the number on the stack)

7

From the forecast model to an equity value

Known

MemorizeFrom model to equity value

StepFormula
FCFFNOPAT − net investment
Growthreinvestment rate × return on capital = (1 − FCFF ÷ NOPAT) × NOPAT ÷ prior capital
Terminal valueFCFF × (1 + g) ÷ (WACC − g)
Equity valuepresent value at WACC of FCFF and terminal value − market value of debt
Checkterminal value ÷ EBIT (or EBITDA, revenue) vs peers

Memory hook Cash, grow, cap, discount, subtract.

Know it cold FCFF goes with WACC and a firm-level multiple; subtract debt only at the end. Compare total equity value with market capitalization.

MemorizeChoosing the terminal value

Memory hook Stable and positive: grow it. Still growing fast: multiply it.

Know it cold Constant growth needs positive FCFF and stable fundamentals at the horizon. High growth or negative FCFF: a peer multiple of final-year revenue or earnings.

Key terms

  • six-step valuation process Memorize
  • reading an assumption table Use it
  • margin direction Use it
  • investment intensity Use it
  • FCFF from forecast statements Use it
  • FCFE from forecast statements Use it
  • choosing FCFF over FCFE Use it
  • constant growth terminal value Memorize
  • sustainable growth rate of FCFF Memorize
  • reinvestment rate Memorize
  • return on capital Memorize
  • implied terminal multiple Use it
  • present value at the weighted average cost of capital (WACC) Use it
  • firm value Use it
  • market value of debt Use it
  • total equity value Memorize
  • comparison with market capitalization Use it
  • terminal value for a high-growth company Use it
From forecast to equity value
Six stepssome summaries merge steps 2 and 3, giving five
  • 1. Gather historical statements
  • 2. Forecast the income statement Memorize revenue, expenses, margins
  • 3. Forecast the balance sheet Memorize assets and financing
  • 4. Compute free cash flow to the firm (FCFF) and to equity (FCFE)
  • 5. Estimate the terminal value constant growth or a multiple
  • 6. Discount and subtract debt present value at WACC − market value of debt

Formulas

Sustainable growth rate of FCFF Memorize
FCFF SGRt+n=(1−FCFFt+nNOPATt+n)×NOPATt+nBook value of total capitalt+n−1FCFF\,SGR_{t+n} = \left(1 - \frac{FCFF_{t+n}}{NOPAT_{t+n}}\right) \times \frac{NOPAT_{t+n}}{\text{Book value of total capital}_{t+n-1}}
Quick example

Free cash flow to the firm 30, net operating profit after taxes 40, capital at the start of the year 250. Reinvestment rate 1 − 30 ÷ 40 = 25%, return on capital 40 ÷ 250 = 16%, so growth is 0.25 × 0.16 = 4.0%.

On your calculator
  1. 30÷40=+|-+1=×40÷250= 0.04

+|- change sign

  1. 1ENTER30ENTER40÷−40×250÷ 0.04

ENTER enter (on the HP, puts the number on the stack)

Terminal firm value (constant growth) Memorize
Firm valuet+n=FCFFt+n×(1+FCFF SGRt+n)WACC−FCFF SGRt+n\text{Firm value}_{t+n} = \frac{FCFF_{t+n} \times (1 + FCFF\,SGR_{t+n})}{WACC - FCFF\,SGR_{t+n}}
Quick example

Final-year free cash flow to the firm of 30, growth of 4.0% and a weighted average cost of capital of 9%: 30 × 1.04 ÷ (0.09 − 0.04) = 624.

On your calculator
  1. 30×1.04÷(0.09−0.04)= 624
  1. 30ENTER1.04×0.09ENTER0.04−÷ 624

ENTER enter (on the HP, puts the number on the stack)

Implied terminal multiple Use it
Implied multiple=Terminal firm valueEBITt+n\text{Implied multiple} = \frac{\text{Terminal firm value}}{EBIT_{t+n}}
Quick example

A terminal firm value of 624 against final-year operating profit (EBIT) of 52 implies 624 ÷ 52 = 12.0 times EBIT. Compare that with peers.

On your calculator
  1. 624÷52= 12
  1. 624ENTER52÷ 12

ENTER enter (on the HP, puts the number on the stack)

Equity value from forecast FCFF Memorize
IVt=[∑i=1nFCFFt+i(1+WACC)i+E(Pt+n)(1+WACC)n]−MVDebtIV_t = \left[\sum_{i=1}^{n} \frac{FCFF_{t+i}}{(1 + WACC)^i} + \frac{E(P_{t+n})}{(1 + WACC)^n}\right] - MV_{Debt}
Quick example

Free cash flows of 10 and 12, a terminal value of 200 at the end of year 2, a weighted average cost of capital of 10% and debt of 50: 10 ÷ 1.10 + (12 + 200) ÷ 1.10² − 50 = 134.30.

On your calculator
  1. 212÷1.21=STO1 175.21
  2. 10÷1.1+RCL1−50= 134.30

STO store · RCL recall a stored number

  1. 212ENTER1.21÷ 175.21
  2. 10ENTER1.1÷+50− 134.30

ENTER enter (on the HP, puts the number on the stack)

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