Equity Investments A: Valuation Models

• Topic 01

  Equity Valuation in Practice

  42 questions
• Topic 02

  DCF Valuation: FCFF and FCFE Models

  42 questions
• Topic 03

  DDM Advanced Applications

  39 questions
• Topic 04

  Market-Based Valuation Multiples

  42 questions
• Topic 05

  Residual Income Valuation

  42 questions
• Topic 06

  Private Company Valuation

  42 questions
• Topic 07

  Real Option Valuation

  36 questions
• Topic 08

  Sum-of-the-Parts Valuation

  42 questions
• Topic 09

  ESG Integration in Equity Valuation

  42 questions

A few questions from this unit, with the answer and a full explanation. The complete bank is available when you start practising.

1. A private company valuation under ASC 820 is required for a venture capital fund's financial reporting. The company has recently completed a Series B at $25/share (preferred). The fund holds Series A preferred at a conversion price of $10/share. Common shares trade in informal secondary transactions at $8/share. Using a waterfall analysis, what is the fair value of the Series A preferred?

   • A
     Fair value of Series A = $25/share because the most recent round (Series B) sets the market price for all equity
   • B
     Fair value of Series A = $8/share because the secondary market common price is the observable Level 2 benchmark for all share classes
   • C
     The fair value of Series A preferred lies between the common value ($8) and the Series B price ($25), depending on liquidation preference terms; an option pricing model (Black-Scholes or binomial) should be used to allocate total equity value across classes
     Correct answer
   • D
     Fair value of Series A = $25/share because preferred shareholders rank senior to common and must be valued at the most recent round price
   Explanation

   In a venture-backed company with multiple share classes (preferred with liquidation preferences, anti-dilution, participation rights), fair value cannot be assigned uniformly across classes. The option pricing model approach (OPM) or probability-weighted expected return method (PWERM) is required to allocate total equity value. The total equity value is bounded by: (1) The Series B implied total equity value (most recent transaction price as a calibration point for total enterprise value); (2) The common secondary market price (reflects the residual equity value after preferred claims). Series A preferred sits between the two: it has priority over common (higher than $8 common) but junior to Series B preferred (with potentially higher liquidation preference). A Black-Scholes or binomial OPM treats each share class as an option on the total firm value with different strike prices (liquidation preferences) and maturities (expected IPO/exit), producing a fair value for Series A between $8 and $25 depending on the preference structure.

2. What is a key limitation of applying the Black-Scholes-Merton (BSM) model to real options, compared to financial options?

   • A
     BSM cannot be used for real options because real options do not have a specified exercise price
   • B
     BSM gives exact results for real options whereas it only gives approximate results for financial options
   • C
     The volatility input (σ) is unobservable for real assets and must be estimated using proxies such as comparable company equity volatility or commodity price volatility
     Correct answer
   • D
     BSM cannot be applied to real options because the risk-free rate is not an appropriate discount rate for project cash flows
   Explanation

   Financial options: σ is the standard deviation of the traded stock price — directly observable from market prices or implied volatility surfaces.

   Real options: The underlying asset is a project or business, which is not publicly traded. There is no direct market price to compute historical or implied volatility. Proxies must be used:

   • Volatility of comparable publicly traded companies
   • Volatility of the relevant commodity price (e.g., oil price volatility for an oil project)
   • Monte Carlo simulation of project cash flows

   This estimation uncertainty means BSM gives an approximation, not a precise value, for real assets. Other limitations include: real assets cannot be continuously traded (no delta hedging), and project cash flows may not follow geometric Brownian motion.

3. A cement manufacturer emits 2 million tonnes of CO₂ per year and faces a carbon price of $50 per tonne. The company's marginal tax rate is 25%. What is the annual after-tax FCFF reduction from carbon costs?

   • A
     $37.5 million
   • B
     $75 million
     Correct answer
   • C
     $50 million
   • D
     $150 million
   Explanation

   Annual carbon cost = 2 million tonnes × $50/tonne = $100 million

   This reduces EBIT by $100 million. The after-tax FCFF impact = Carbon cost × (1 – tax rate) = $100m × (1 – 0.25) = $75 million.

   The pre-tax cost ($100m) reduces EBIT; the tax deductibility offsets 25% of this, so the net after-tax free cash flow reduction is $75m. This is directly analogous to how any operating cost reduces FCFF by cost × (1 – t). The full $100m would be the answer if the company were tax-exempt.