Review of
Key
Concepts
Apr 29, 2025
CAPM - Cost of Equity
• Ke = Rf + BL (ERP)
• ERP = U.S. ERP + CRP (if sovereign rating below AAA)
• CRP = Default spread (stock / debt)
• BL = Bu [1+ (1-t)D/E ]
• Use market value D/E;
• D/E ≠ D/C; D/C = D/(D+E)
• Debt includes bank loans, lease liabilities, bonds;
• Equity includes NCI, preferred stock and common stock.
WACC
• WACC = WeKe + WpKp + WdKd(1 – t)
• Use market value weights
• Kd = 10-year fixed rate financing cost
• We =MVE / (MVE + MVP + MVD)
• Wp =MVP / (MVE + MVP + MVD)
• Wd =MVD / (MVE + MVP + MVD)
PV of Growing Annuity (PVGA)
• PV = CF1 / (r – g) [1 – (1+g/1+r)n ]
• CF1 = payment at the end of the first period;
• n = number of time periods;
• r = interest rate per period;
• g = annual growth rate.
ROIC, RIR and Growth
• ROIC = NOPAT/ Invested Capital
• Invested capital = BV of net OA = OWC + fixed assets
• Growth equation for NOPAT: g = RIR * ROIC
RIR = Net Investment / NOPAT
• Growth equation for Net Income:
g = Retention rate * ROE
Retention rate = 1 – Payout Ratio
Free Cash Flow to Firm (FCFF or FCF)
NOPAT = EBIT (1 –t)
Ways to calculate FCF:
• FCF = NOPAT + dep – CAPEX – Increase in OWC
• FCF = NOPAT – Increase in Invested Capital
• FCF = NOPAT (1 – RIR)
• FCF = NOPAT (1 – g/ROIC)
Key Value Driver Formula
• When a firm is in stable growth (to infinity):
• Intrinsic value of net OA = FCF 1 / (WACC – g)
= NOPAT1 (1 - g/RONIC)/(WACC - g)
2-stage FCF Model (high growth + stable
growth)
• Discount rate r = WACC
• High growth period of n years. EBIT grows at a constant rate gh .
• PVGA = FCF1/(r – gh)[1 - (1+gh/1+r)n]
• PVGA = NOPAT1(1 – gh/ROIC)/(r – gh)[1 – (1+gh/1+r)n]
• Stable growth period from Year n+1 to infinity. EBIT grows at a constant rate gs forever.
Use constant growth formula to estimate TVn.
• TVn = FCFn+1/(r – gs) = NOPATn+1(1 – gs/RONIC)/(r – gs)
• Intrinsic value of net OA = PVGA + PV of TVn
• PV of TVn = TVn/(1+r)n
DDM and FCFE
• When a firm pays out all excess cash as dividends that grow at a constant rate:
• Intrinsic value = D1/(Ke – g)
• Can be used to estimate total equity value or value per share.
• FCFE for valuation of banks:
• When capital ratio and/or ROE are changing:
• FCFE = Net Income – Increase in Common Equity
• In stable growth, when net income grows at a constant rate, and capital ratio and ROE
remain stable:
• Terminal value = NI1(1 - g/ROE)/(Ke – g)
Firm Value Vs. Equity Value
Balance sheet: Net OA + Non-OA = Debt + NCI + Equity
Firm Value = Net OA + Non-OA
Net OA = OWC + Fixed Assets (Net PPE, ROU Assets, Goodwill/Intangibles)
OWC = Current OA (AR, inventories etc.) – OL (AP etc.)
Debt = STD, LTD, and Lease Liabilities
DTL is an equity equivalent, not debt.
Valuation of Cross Holdings
• This applies to Minority Investments (on the asset side) and NCI (on the liability side)
• Estimate the MV of investments (shareholding below 50%) and add the value to the
intrinsic value of OA.
• Estimate the MV of NCI (arising from consolidation of non-wholly owned subsidiaries)
and subtract the value from the Firm Value.
Estimate Intrinsic Value per Share
Intrinsic value of the net operating assets
+ Cash
+ MV of investments (less than 50% owned) and other non-OA (if any)
= Intrinsic value of the firm
- MV of debts
- MV of NCI
= Intrinsic equity value (available to shareholders & options holders)
- MV of options issued by the firm
= Intrinsic equity value available to common shareholders
Divide by # of shares outstanding (including adjusted RSUs)
= Intrinsic value per share
Relative Valuation
• EV= MV of Equity + MV of debt + MV of NCI – Non-OA
• Commonly used multiples: P/E, P/B, PEG, P/S, EV/EBITDA, EV/EBIT, EV/Sales, FCF yield
• PEG Ratio= PE/Growth Rate; growth rate in %
• Unlevered FCF Yield (%)= FCFF/EV
• Levered FCF Yield (%) = FCFE / Market Cap
EV/EBIT vs P/E
• EV/EBIT is a capital structure neutral measure.
• P/E is affected by capital structure and non-operating assets.
• EBIT = Sales – depreciation – other operating expenses
• EBITDA – DA = EBIT
• (EBIT - interest expense + interest income)(1 – t) = Net Income
IPO Pricing
• The IPO price is determined after the book building exercise, which is a mechanism that
helps underwriters discover the appropriate price based on the demand for shares at the
end of the bidding process.
• An over-allotment option, also known as a green shoe, is a call option granted by the
issuer to the underwriters. This option allows the underwriters to purchase additional
shares from the issuer at the IPO price.
• Public float is calculated by dividing the shares held by the public by the total shares
outstanding, which includes both the shares held by the public and the shares held by
insiders.
Real Options
• Inputs for the Black Scholes Option Pricing Model:
• S = Current value of the underlying asset
• K = Strike price of the option
• t = Life to expiration of the option
• r = Risk-free interest rate corresponding to the life of the option
• σ = volatility of the value of the underlying asset
• y = dividend yield
Valuing Equity as a Call Option
• Need to consolidate all debts into a single zero coupon bond
• Option life (t) = years to maturity of this single zero, and Exercise price (K) = face value of
the single zero.
• To convert a coupon paying bond into a zero coupon bond: (i) face value of the zero =
sum of nominal cash flows of the coupon paying (all coupons + face value); (ii) years to
maturity of the zero = Macaulay duration of the coupon paying bond.
• To combine two zeros into one single zero: (i) face value of the single zero = sum of the
face values; (ii) years to maturity of the single zero = weighted average maturity using
face values as weights.
Value Investing
• Neutral bond/stock allocation (50% bonds and 50% equities).
• Dollar cost averaging.
• Graham number = square root of (22.5 x EPS x NAV)
• NCAV stock = stocks trading below the net current asset value.
• Stock represents fractional ownership of underlying businesses.
• Mr. Market: irrational or contradictory traits of the stock market and the risks of
following groupthink.
• Margin of Safety: buy a stock at a discount to its estimated value.
• Understand and develop your circle of competence.