Valuation Principles: formula sheet

Key formulas

Future value (single sum)

FV = PV × (1 + r)ⁿ

r is the rate per period and n is the number of periods. Match them (e.g. half-yearly rate with half-yearly periods).

Present value (single sum)

PV = FV ÷ (1 + r)ⁿ

This is discounting. Higher r or longer n gives lower PV.

Periodic rate for compounding m times a year

Periodic rate = Annual rate ÷ m; periods = years × m

Use this when the question says half-yearly, quarterly or monthly compounding.

PV of ordinary annuity

PV = C × [1 − (1 + r)⁻ⁿ] ÷ r

C is the cash flow at the end of each period. The PV sits one period before the first cash flow.

FV of ordinary annuity

FV = C × [(1 + r)ⁿ − 1] ÷ r

Value is at the time of the last payment.

Annuity due adjustment

Annuity due value = Ordinary annuity value × (1 + r)

Applies to both PV and FV. Each payment is one period earlier.

PV of perpetuity

PV = C ÷ r

First cash flow is one period from now. r must be a rate per period of the cash flow.

PV of growing perpetuity

PV = C₁ ÷ (r − g)

C₁ is the next period's cash flow. Valid only when r > g.

Effective annual rate

EAR = (1 + Annual rate ÷ m)ᵐ − 1

More frequent compounding gives a higher EAR for the same stated rate.

CAPM (cost of equity)

Ke = Rf + β × (Rm − Rf)

Rf is the risk-free rate, Rm the expected market return. (Rm − Rf) is the market risk premium.

After-tax cost of debt

Kd (after tax) = Kd × (1 − T)

T is the tax rate. Use the interest rate on the debt, not the coupon of an old issue if market yield differs.

WACC

WACC = (E ÷ V) × Ke + (D ÷ V) × Kd × (1 − T)

E = market value of equity, D = market value of debt, V = E + D.

Capital weights

E ÷ V and D ÷ V, where V = E + D

The weights must add up to 1 (or 100%).

FCFF from net income

FCFF = Net income + Non-cash charges + Interest × (1 − t) − Fixed capital investment − Increase in working capital

t is the tax rate. Interest is added back after tax because FCFF is before payments to lenders.

FCFF from EBIT

FCFF = EBIT × (1 − t) + Depreciation − Capex − Increase in working capital

Use the increase in non-cash working capital. A decrease adds to cash flow.

FCFE from FCFF

FCFE = FCFF − Interest × (1 − t) + Net borrowing

Net borrowing = new debt raised − debt repaid.

FCFE from net income

FCFE = Net income + Depreciation − Capex − Increase in working capital + Net borrowing

Interest is already deducted in net income, so do not subtract it again.

Firm value (FCFF)

Firm value = Σ FCFFt ÷ (1 + WACC)^t + Terminal value ÷ (1 + WACC)^n

Equity value = Firm value − Debt + Cash (net debt deducted).

Equity value (FCFE)

Equity value = Σ FCFEt ÷ (1 + ke)^t + Terminal value ÷ (1 + ke)^n

ke is the cost of equity.

Terminal value (Gordon growth)

TVn = CFn+1 ÷ (r − g) = CFn × (1 + g) ÷ (r − g)

Valid only when g < r. r is WACC for FCFF and ke for FCFE.

WACC

WACC = E/V × ke + D/V × kd × (1 − t)

Weights use market values of equity and debt.

Gordon growth model

P₀ = D₁ ÷ (r − g)

Valid only when r > g and growth is constant forever. D₁ is next year's dividend.

Next dividend from last dividend

D₁ = D₀ × (1 + g)

If the question gives the dividend just paid (D₀), grow it by one year first.

General DDM

P₀ = Σ Dₜ ÷ (1 + r)ᵗ, for t = 1 to ∞

Value is the present value of all expected dividends.

Terminal value at end of year n

Pₙ = Dₙ₊₁ ÷ (r − g₂)

Used in multi-stage models. Dₙ₊₁ = Dₙ × (1 + g₂). Discount Pₙ back by (1 + r)ⁿ.

Two-stage model value

P₀ = Σ Dₜ ÷ (1 + r)ᵗ (t = 1 to n) + Pₙ ÷ (1 + r)ⁿ

High-growth dividends plus discounted terminal value.

Implied growth or return

r = D₁ ÷ P₀ + g

Rearranged Gordon model: expected dividend yield plus growth.

Sustainable growth rate

g = ROE × retention ratio

Retention ratio = 1 − dividend payout ratio. Used to estimate g.

Price to earnings (P/E)

P/E = Market price per share ÷ Earnings per share (EPS)

Equivalent to market capitalisation ÷ net profit. Trailing uses past 12 months EPS; forward uses expected EPS.

Price to book (P/B)

P/B = Market price per share ÷ Book value per share

Book value per share = shareholders' equity ÷ number of shares. Preferred for banks and financials.

Price to sales (P/S)

P/S = Market capitalisation ÷ Revenue (or price per share ÷ sales per share)

Useful when earnings are negative. Ignores margins, so compare only within the same industry.

Enterprise value (EV)

EV = Market capitalisation + Total debt + Preference capital + Minority interest − Cash and cash equivalents

Some texts use net debt (debt − cash). Know that EV is the value of the whole operating business.

EV/EBITDA

EV/EBITDA = Enterprise value ÷ EBITDA

Capital-structure neutral. Equity value = EV − net debt (and other claims).

PEG ratio

PEG = P/E ÷ Expected annual EPS growth rate (in % points)

Growth is entered as a number, so 20% growth means divide by 20. A PEG near or below 1 is often read as reasonable, but this is only a rule of thumb.

Implied value from peer multiple

Implied price = Peer multiple × Company's metric per share

For EV multiples: Implied EV = Peer multiple × EBITDA, then subtract net debt and divide by shares.

Net asset value

NAV = Value of assets − Value of liabilities

Use fair values where available. NAV per share = NAV ÷ number of shares.

Replacement cost comparison

Market value of firm ÷ Replacement cost of assets

A ratio below 1 suggests the market values the firm below the cost of rebuilding its assets.

Sum-of-the-parts equity value

Equity value = Σ (segment values) + non-operating assets − net debt and other claims

Value each segment with a method suited to it.

Residual income

RI = Net income − (Cost of equity × Beginning book value of equity)

The deduction is the equity charge.

Residual income valuation

Equity value = Book value now + PV of future residual incomes

Discount residual incomes at the cost of equity.

Economic Value Added

EVA = NOPAT − (WACC × Invested capital)

NOPAT is net operating profit after tax. Positive EVA means value creation.

Quick revision

• Present value = future value ÷ (1 + r)ⁿ.
• A perpetuity's value = cash flow ÷ r.
• A growing perpetuity's value = next year's cash flow ÷ (r − g), valid only when r > g.
• FCFF is discounted at WACC and gives firm value; subtract debt to reach equity value.
• FCFE is discounted at cost of equity and gives equity value directly.
• WACC = weights of equity and debt times their costs, with debt cost taken after tax.
• Gordon growth model: value = D1 ÷ (ke − g), where D1 is next year's dividend.
• Terminal value often forms a large share of DCF value, so it is sensitive to assumptions.
• P/E = price ÷ earnings per share; compare it only with similar companies.
• EV includes debt, so EV multiples are compared with firm-level measures like EBITDA, not with per-share earnings.
• Asset-based methods value assets less liabilities and may ignore future earning power.
• Read each question for the exact rate, period and cash flow before calculating.

Common mistakes

• Using the annual rate with half-yearly or quarterly periods. Fix: Divide the rate by m and multiply the years by m before any calculation.
• Adding cash flows from different years without discounting. Fix: Bring each cash flow to the same date first, then add.
• Using Rm instead of (Rm − Rf) in the beta term. Fix: Write Rf + β × (Rm − Rf). Beta multiplies only the premium.
• Using pre-tax cost of debt in WACC. Fix: Always multiply Kd by (1 − T) unless the question says the rate is already after tax.
• Discounting FCFF at the cost of equity, or FCFE at WACC. Fix: FCFF belongs to all capital providers, so use WACC. FCFE belongs to shareholders, so use cost of equity.
• Forgetting to subtract debt after valuing with FCFF. Fix: FCFF gives firm value. Subtract net debt (and other claims) to get equity value before dividing by shares.
• Using D₀ directly in the Gordon formula. Fix: Read the wording. Just paid or last year's dividend means D₀, so multiply by (1 + g). Expected next year means D₁.
• Applying the Gordon formula when g is greater than or equal to r. Fix: Always check r > g first. If not, the constant growth model cannot be used.
• Dividing EV by net profit or P/E-style EPS, or price by EBITDA. Fix: EV pairs with EBITDA (before interest). Price or market cap pairs with EPS or net profit.
• Treating the EV/EBITDA result as the share price. Fix: Peer multiple × EBITDA gives EV. Subtract net debt, then divide by number of shares.

Exam tips

• Read the compounding frequency and timing words (end of year, beginning of year, forever) before touching the formula.
• For perpetuity questions, check whether the cash flow given is the next one or the current one when growth is involved.
• Know the direction rules: higher rate lowers PV and raises FV; longer time lowers PV and raises FV.
• Conceptual options often test that a riskier cash flow needs a higher discount rate and so has a lower present value.
• Wrong answers cost marks in this exam, so use the direction and size checks to remove options before guessing.
• Questions usually give numbers and ask for one step, such as Ke or after-tax Kd. Do not compute more than needed.
• Watch for 'after-tax' and 'pre-tax' wording in options. The trap is the pre-tax answer.
• Remember which rate goes with which cash flow: WACC with FCFF, Ke with FCFE and dividends.