Market-based and private company valuation - Venture capital...

Learning Outcomes

This article explains how to compare and apply market-based and income-based valuation approaches to private companies in typical CFA Level 2 exam settings, including:

• Distinguishing key features of public versus private company valuation inputs, data limitations, and implications for exam-style case vignettes.
• Detailing the venture capital (VC) method, including exit value estimation, target IRR selection, ownership calculation, option pools, and multi-round dilution mechanics.
• Explaining leveraged buyout (LBO) modeling, covering cash-flow projection, debt scheduling, exit multiple selection, and back-solving for purchase price and equity IRR.
• Describing how to incorporate control premiums and discounts for lack of marketability (DLOM) appropriately and avoid double-counting across methods.
• Comparing VC, LBO, discounted cash flow (DCF), and market multiple approaches and selecting the most appropriate method for different transaction types, ownership levels, and investor objectives.
• Linking private company discount rate estimation (expanded CAPM and build-up approaches) to the target return assumptions embedded in VC and LBO models.
• Interpreting how definitions of value (fundamental, fair market, investment value) influence model selection and adjustments in private company settings.
• Applying guideline public company and guideline transaction methods to value private companies and interpreting how control and marketability are reflected in observed multiples.
• Recognizing how normalized earnings and cash flows are derived for private firms and how they feed into VC, LBO, and conventional DCF valuations.
• Performing sensitivity analysis on VC and LBO assumptions (exit multiple, leverage, growth) and interpreting implications for pricing and risk.

CFA Level 2 Syllabus

For the CFA Level 2 exam, you are required to understand private company valuation and its application to VC and LBO transactions, with a focus on the following syllabus points:

• Contrast important public and private company features for valuation purposes.
• Describe uses of private business valuation and key areas of focus for analysts.
• Explain cash-flow estimation issues for private companies and normalized earnings.
• Explain factors that require adjustment when estimating the discount rate for private companies.
• Compare models used to estimate the required return to private company equity (CAPM, expanded CAPM, build-up approach).
• Explain income, market, and asset-based valuation approaches and select among them.
• Describe and apply the venture capital method and LBO modeling to value private companies.
• Evaluate the effects of control premiums and discounts for lack of marketability on private company values.
• Relate private company valuations to concepts of fundamental value, fair market value, and investment value in applied case vignettes.

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

A venture fund is considering a Series A investment in a private software firm. The firm is currently breakeven, but the VC expects rapid growth and an IPO in five years. The fund targets a 40% IRR and plans to invest alongside founders (no other investors today). Forecast year-5 revenue is $50 million and the VC uses a 4.0× EV/sales exit multiple based on comparable public SaaS firms, adjusted downward for higher risk.

1. Which valuation approach best describes the primary technique the VC is using in this situation?
   1. Pure income approach based on discounted FCFF with WACC from CAPM
   2. Market approach using guideline public company multiples with no discounting
   3. Hybrid VC method using a market-based exit multiple discounted at a target IRR
   4. Asset-based approach based on adjusted book value of net assets
2. The VC calculates a year-5 exit value of 200millionanddiscountsitat40200 million and discounts it at 40% to obtain a post-money valuation of approximately 200millionanddiscountsitat4018.6 million. If the VC invests $6 million in the Series A and assumes no future rounds, what ownership stake is required to meet its return target?
   1. 24%
   2. 29%
   3. 32%
   4. 40%
3. If the VC expects a follow-on Series B in year 2 that will give new investors 20% of the company at that time (post-money), what ownership percentage must the VC obtain at Series A to still hold the required stake at exit from Question 2?
   1. 29.0%
   2. 32.0%
   3. 36.3%
   4. 40.0%
4. The VC’s investment committee argues that an additional 25% DLOM should be applied to the post-money valuation because the shares are illiquid. Which response is most appropriate?
   1. Agree, because market-based exit multiples are based on liquid public companies
   2. Disagree, because the high target IRR already embeds a premium for illiquidity
   3. Agree, but only if the company will remain private and never exit
   4. Disagree, because DLOM should only be applied to minority interests

A buyout fund is evaluating a 100% acquisition of a mature manufacturing company through an LBO. The fund plans to finance 60% of the purchase price with debt and 40% with equity, target a five-year holding period, and exit by selling the business to a strategic buyer at a 7× EBITDA multiple. The transaction gives the fund full control.

1. In modeling this LBO, which input is most directly used to back-solve the maximum purchase price consistent with the fund’s target equity IRR?
   1. The control premium paid over the seller’s current market price
   2. The forecast of normalized net income under current capital structure
   3. The assumed exit EBITDA multiple and forecast EBITDA in year five
   4. The DLOM applied to the fund’s minority interest in the target
2. Relative to a DCF valuation using a standard WACC, which of the following is most accurate about the equity IRR in an LBO model?
   1. It will always be lower because of the higher financial risk
   2. It is directly comparable because both are calculated on unlevered cash flows
   3. It measures the return to equity holders given a specific leverage path and exit, not the fundamental value of the firm
   4. It is equivalent to the firm’s cost of equity estimated by CAPM
3. The deal team is debating whether they can justify paying a higher price than a strategic buyer that values the company using a fundamental DCF. Which statement is most accurate?
   1. The LBO fund can always outbid a strategic buyer because it uses more leverage
   2. A strategic buyer may be able to pay more because it can justify synergies that an LBO fund cannot realize
   3. The LBO fund should match the DCF value because IRR is always equal to the WACC
   4. The LBO fund will pay less because control premiums are not applied in LBOs
4. If the buyout uses 120millionofdebtand120 million of debt and 120millionofdebtand80 million of equity to finance a 200millionpurchase,andexitequityvalueinyear5ismodeledat200 million purchase, and exit equity value in year 5 is modeled at 200millionpurchase,andexitequityvalueinyear5ismodeledat240 million with no interim dividends, which best describes the equity investors’ money multiple?
   1. 1.2×
   2. 2.0×
   3. 2.5×
   4. 3.0×

Introduction

Private company valuation is required for M&A, buyouts, early-stage investing, estate and tax planning, shareholder disputes, and financial reporting. The process is affected by:

• Limited and lower-quality financial disclosure.
• Illiquidity and long expected holding periods.
• Concentrated ownership and often significant private benefits of control.
• Different viewpoints: minority versus controlling, financial versus strategic buyers.
• Heterogeneous objectives: growth capital, income, tax minimization, or litigation support.

Market-based and income-based approaches are commonly modified for these settings. Venture capital and leveraged buyout (LBO) models are specialized applications, each with characteristic inputs, assumptions, and adjustments. For Level 2, you must be able to follow these models in a case vignette, perform key calculations, and interpret the results.

Key Term: income approach
An income approach estimates value as the present value of expected future income or cash flows, discounted at a rate reflecting the required risk-adjusted return.

Key Term: market approach
A market approach values a business by reference to observed transaction multiples from sales of comparable companies or market trading data.

Key Term: asset-based approach
An asset-based approach estimates value as assets minus liabilities of the company, typically using adjusted fair values of individual assets and obligations.

Key Term: venture capital method
The venture capital method estimates the post-money value of a company by projecting a future exit value and discounting it at a high required rate of return.

Key Term: leveraged buyout (LBO) model
An LBO model projects future operating and cash-flow performance to determine the maximum purchase price that allows investors to achieve a required equity return using leveraged capital.

Key Term: internal rate of return (IRR)
IRR is the discount rate that sets the present value of an investment’s cash inflows equal to its cash outflows; private equity investors use it as the primary return metric.

Key Term: fundamental value
Fundamental value is the value of an asset to a fully informed investor with a complete understanding of its characteristics, based on fundamentals, independent of current market price.

Key Term: fair market value
Fair market value is the price at which a willing, informed, and able buyer and seller would transact, neither under compulsion, and both with reasonable knowledge of relevant facts.

Key Term: investment value
Investment value is the value of an asset to a particular buyer, incorporating that buyer’s specific expectations, required return, and potential synergies.

Because private company equity is illiquid and information asymmetry is high, VC and LBO investors often use target IRRs that are much higher than public equity required returns from CAPM. These target returns implicitly incorporate premiums for size, illiquidity, and company-specific risk, and are closer to an investment value concept for that specific investor than a pure fundamental value for a hypothetical diversified shareholder.

In exam vignettes, carefully identify which “definition of value” is relevant:

• Fundamental value for a diversified public investor or fairness opinion.
• Fair market value for tax, divorce, or shareholder disputes.
• Investment value for a specific VC or buyout fund with control and strategic plans.

The same company can have different values under these definitions; correctly recognizing the objective often determines which model and which adjustments are appropriate. For example:

• A fairness opinion in a going-private transaction is usually anchored on fundamental value to minority public shareholders, often ignoring buyer-specific synergies.
• A strategic acquirer’s valuation is closer to investment value because it includes synergies from combining operations and may justify paying more than fair market value.
• A VC fund’s valuation explicitly reflects its own hurdle rate and exit strategy, and therefore is an investment-value calculation, not a general fair market value.

Being clear about the valuation objective helps you decide:

• Which cash flows to forecast (status quo versus post-acquisition synergies).
• Which discount rate to use (diversified shareholder versus concentrated private-equity investor).
• Whether control premiums or discounts for lack of marketability (DLOMs) are appropriate.

These distinctions are very testable. A typical item set will describe several valuations of the same firm (for example, VC, LBO, and a strategic buyer’s DCF) and ask you to explain why they differ and which one is most relevant for a specific decision or stakeholder.

Valuation Approaches for Private Companies

Three general approaches are used to value private businesses: income, market, and asset-based methods. For the CFA exam, focus is on income and market approaches as they apply to VC investments and LBOs, but you should understand how all three relate.

• The income approach typically uses discounted cash flow (DCF) models such as free cash flow to the firm (FCFF) or free cash flow to equity (FCFE) to estimate enterprise or equity value. For private firms, these DCFs often start from normalized earnings rather than the most recent reported numbers.
• The market approach applies valuation multiples (for example, EV/EBITDA, P/E, EV/sales) from guideline public companies or completed transactions. When applying public-company multiples to a private firm, analysts must adjust for differences in risk, growth, and size.
• The asset-based approach is more commonly used for asset-heavy businesses and in liquidation or distress, and is rarely the primary method in VC or mainstream LBOs, although it can provide a floor value. It is also used for investment holding companies and real estate entities where market values of underlying assets are observable.

Within the market approach, private company practice recognizes three main methods:

Key Term: guideline public company method
The guideline public company method values a subject company using trading multiples from comparable publicly traded firms, usually reflecting minority, marketable interests.

Key Term: guideline transactions method
The guideline transactions method values a subject company using pricing multiples from completed M&A transactions in comparable companies, usually reflecting control-level, marketable interests including possible synergies.

Key Term: prior transaction method
The prior transaction method values a subject company using pricing information from recent transactions in the subject’s own shares or convertible securities, adjusted as needed for changes in conditions.

These methods are commonly referred to in the curriculum and are exam-relevant, especially when you need to decide whether a control premium or DLOM is already implicit in the multiples used.

Some nuances that often appear in item sets:

• Guideline public company multiples:
  • Reflect minority, marketable pricing.
  • Usually require upward adjustment (control premium) if the valuation objective is a controlling stake.
  • May require a size adjustment (lower multiple) when valuing a much smaller private firm.
• Guideline transaction multiples:
  • Often incorporate both control and expected synergies.
  • May overstate value for a purely financial buyer that cannot realize those synergies.
  • Should not be combined with a separate control premium, or control is double-counted.
• Prior transaction method:
  • Strongest when transactions are recent, arm’s length, and under similar conditions.
  • Requires judgment if the company has changed materially (new contracts, loss of key customer, large capex) since the prior deal.
  • Can be particularly useful for early-stage private companies where public comps are scarce.

Within the asset-based approach, you may see variants such as:

• Adjusted net asset value: restating balance sheet items to fair value (for example, revaluing real estate, recognizing unrecorded intangibles, writing down obsolete inventory).
• Orderly liquidation value: assuming assets are sold over time with some marketing effort.
• Forced liquidation value: assuming a rapid, distressed sale with steeper discounts.

On the exam, asset-based methods are most likely to be appropriate when:

• The business is not a going concern (for example, liquidation or break-up).
• The firm is an investment or holding company whose value is largely the market value of its assets.
• Operating earnings are too volatile or unreliable to support a meaningful DCF or multiple-based valuation.

From a model-selection standpoint:

• Income-based methods are preferred when detailed forecasts are available and the analyst wants a fundamental value benchmark (often for strategic buyers or fairness opinions).
• Market-based methods are used when there are reliable comparables and the main question is “What prices are similar assets trading at?”
• Asset-based methods are most relevant for holding companies, real estate vehicles, natural resource firms, or when the going-concern assumption is doubtful.

In practice, professional valuers often triangulate using more than one approach:

• A DCF provides a fundamental anchor.
• Guideline public or transaction multiples ensure results are broadly consistent with observed market pricing.
• Asset-based methods provide a floor value or liquidation benchmark.

A typical exam item will describe the company and the purpose of the valuation and then ask which approach (or combination) is most appropriate and why. Your answer should mention:

• Purpose of valuation (transaction pricing, litigation, tax, and so on).
• Premise (going concern versus liquidation).
• Level of value (control versus minority, marketable versus non-marketable).

Public vs Private Company Features Relevant for Valuation

In private company work, you frequently start from public-company data (market betas, trading multiples) and must adjust to reflect key differences:

• Size and diversification: Private companies tend to be smaller, with more concentrated product and geographic exposure. This implies higher business risk and therefore higher required returns than those suggested by large-cap public peers. Small-cap size premiums and specific company risk premiums often need to be added to a CAPM-based cost of equity.
• Information quality and transparency: Private firms often lack audited financials, have shorter reporting histories, and provide limited segment detail, increasing estimation uncertainty. Historical financials may be less reliable as a basis for trend analysis and forecasting.
• Corporate governance: Ownership is concentrated, boards may be less independent, and related-party transactions are more common. Weak governance or concentrated decision-making can increase the company-specific risk premium and may affect what a controlling buyer is willing to pay to implement improved governance.
• Liquidity: Public shares can be sold quickly at observable market prices; private shares are illiquid, with sale processes measured in months. This supports use of discounts for lack of marketability when valuing minority, non-marketable interests that cannot force an exit.
• Control: Transactions involving a change in control (strategic acquisitions, buyouts) often incorporate value from synergies and from the ability to alter strategy, financing, and payout policy. Minority interests lack these rights and typically are worth less on a per-share basis.
• Tax and legal form: Many private companies are tax pass-through entities (partnerships, S-corporations, LLCs). Analyst cash-flow forecasts often need to impute a corporate-level tax burden if the valuation is for a hypothetical diversified investor rather than the current owners.
• Key-person risk: Private firms are often highly dependent on founders or a few senior managers. Loss of these individuals could materially reduce value, justifying a higher specific risk premium.
• Access to capital markets: Private firms usually face higher financing costs and less flexibility in raising equity or debt. This affects sustainable growth rates and may constrain optimal capital structures.

These characteristics affect:

• Cash flows: For example, owner-managers may pay themselves above-market salaries or run personal expenses through the business. Normalized cash flows for a hypothetical buyer may differ significantly from reported results.
• Discount rates: Required returns should reflect higher risk due to size, concentration, and governance, versus the risk implied by public comparables.
• Premiums and discounts: Whether you need to apply a control premium, minority discount, or DLOM depends on both the nature of the interest being valued and what is already implicit in the method used.

Exam items often test whether you recognize that simply applying public-company P/E multiples to unadjusted private earnings, with no adjustment for size or control, is usually inappropriate. A good exam habit is to ask:

• What does the multiple represent (minority versus control, marketable versus non-marketable)?
• What does the subject interest represent?
• Do I need any conversions between levels of value (for example, adding a control premium or applying a DLOM), and am I double-counting anything?

Uses of Private Business Valuation

Exam vignettes can show private company valuations in different contexts:

• Transaction pricing (buy-side or sell-side M&A, VC, and LBO deals).
• Fairness opinions in going-private or related-party transactions.
• Tax and estate planning (transfers of minority interests, family businesses).
• Financial reporting (goodwill impairment testing, purchase price allocation).
• Shareholder litigation and disputes (squeeze-outs, dissenting shareholder actions).
• Management buyouts (MBOs) or leveraged recapitalizations.
• Collateral valuation for bank lending or covenant testing.

The purpose of valuation influences which definition of value is relevant:

• Fundamental value is most relevant for public markets and long-term investors.
• Fair market value is often mandated in tax and legal contexts.
• Investment value is most relevant for strategic buyers and financial sponsors (VC and LBO funds) evaluating a specific transaction.

Two additional dimensions are also important:

• Premise of value: Going concern versus liquidation or orderly disposition of assets. Asset-based approaches are more consistent with a liquidation premise; income and market approaches typically assume going concern.
• Level of value: Control versus minority, and marketable versus non-marketable. This affects whether you start from control-level cash flows, apply control premiums, or apply DLOMs.

Recognizing all three—purpose, premise, and level of value—is often the key to answering “which method is most appropriate?” exam questions. When multiple methods are presented in an item set, you are often expected to:

• Identify which methods are conceptually aligned with the stated purpose and level of value.
• Comment on whether inputs (multiples, discount rates) are consistent with that level.
• Explain differences in values across methods in terms of assumptions, not “who is right.”

Cash-Flow Estimation Issues for Private Firms

Before applying a DCF or VC/LBO model, the analyst typically estimates normalized earnings or cash flow, adjusting for:

• Non-recurring revenues or expenses: One-off legal settlements, asset sales, restructuring charges, unusually large bad debt write-offs, or pandemic-related subsidies.
• Discretionary expenses: Above- or below-market owner salaries, family payroll, owner perks (cars, travel, club memberships), and charitable contributions not required for the business.
• Related-party transactions and transfer pricing: Non-arm’s-length revenues or costs with affiliates, such as below-market rent charged by a related real estate entity, or above-market prices paid to a related supplier.
• Non-operating assets and income: Excess real estate, portfolio investments, or idle cash that do not contribute to operating cash flows; these should be valued separately and added to the operating business value.
• Maintenance versus growth capex: Private firms may underinvest (to boost reported profit) or overinvest (for tax or personal reasons). You must estimate sustainable maintenance capex consistent with normalized operations.
• Owner financing choices: Private firms might have suboptimal capital structures (too little or too much debt) for tax or control reasons. When valuing on a control basis, you may adjust capital structure and re-estimate WACC.

Failure to normalize can bias both income-based valuations and multiples (for example, EBITDA), and thereby distort VC or LBO model outputs.

Analysts also face forecasting challenges:

• Limited historical data and poor accrual quality increase the risk that reported earnings do not map cleanly into cash flows.
• For cyclical or project-based businesses, recent years may not be representative; you must adjust to mid-cycle margins and normalize working capital swings.
• For high-growth startups, historicals may be irrelevant; forecasts rely on business plans, market growth, and competitive dynamics rather than time-series extrapolation.
• For tax pass-through entities, entity-level tax expense may be low; when valuing equity for a diversified investor, you often impute a corporate-level tax burden in the cash flows.

A simple illustration: suppose a founder-managed company reports $2 million of pre-tax income, but pays the founder$1.2 million salary where a market CEO would cost $600,000. Normalized pre-tax income for a controlling buyer is:

This higher normalized base feeds directly into FCFF/FCFE projections and any multiples based on earnings.

Another common adjustment in private-company exams is for excess or deficient owner compensation. Under a minority, non-controlling valuation, you would typically leave above-market compensation unchanged (because the minority investor cannot change it). Under a control valuation, you adjust to market-level compensation, because a controller can reset pay.

From a DCF standpoint, these normalized earnings usually feed into free cash flow metrics:

• Free cash flow to the firm (FCFF), which belongs to all capital providers.
• Free cash flow to equity (FCFE), which belongs only to equity holders.

Typical formulas (using notation from corporate finance readings) are:

or equivalently:

and

where:

• $\text{FCInv}$ is investment in fixed capital.
• $\text{WCInv}$ is investment in working capital.

In private company valuation these formulas are applied to normalized inputs rather than raw reported numbers. Note also that:

• Dividends and share repurchases are uses of FCFE, but they do not determine the level of FCFE.
• Changes in leverage mainly affect FCFE via net borrowing and future interest expense; FCFF is unaffected by financing choices.

Level 2 questions sometimes test whether you mistakenly equate net income or EBITDA with free cash flow. Both are poor proxies because they ignore some of the adjustments above (capex, working capital, taxes, and net borrowing).

In practice, analysts often use a hybrid of bottom-up (firm- or segment-specific drivers) and top-down (macro and industry trends) approaches to build cash-flow projections that are internally consistent with the firm’s strategic position. This forecast work underpins both traditional FCFF/FCFE DCF models and the simplified cash-flow assumptions embedded in VC and LBO methods.

Venture Capital Valuation

Venture capital (VC) valuation focuses on potential high-growth, high-risk investments. VC investors seek large returns to compensate for high failure rates and illiquidity. Instead of detailed yearly cash-flow forecasts many years into the future, they typically target a desired exit value based on the company’s future earnings or revenues at the time of sale or IPO, and then discount that exit value at a high required IRR.

Key Term: pre-money valuation
Pre-money valuation is the value of a company immediately before a new investment round; it equals post-money valuation minus the amount of new equity invested.

Key Term: post-money valuation
Post-money valuation is the value of a company immediately after a new investment round; it equals the amount invested divided by the investor’s required ownership share.

Key Term: exit multiple
An exit multiple is a valuation multiple (such as EV/EBITDA, EV/sales, or P/E) applied to forecasted financial metrics at the planned exit date to estimate terminal (exit) value.

Key Term: option pool
An option pool is a block of shares or options reserved for future grants to employees and management, typically expressed as a percentage of the company’s fully diluted equity.

Why the VC Method Is Used

The VC method is particularly suited to early-stage companies because:

• Operating histories are short, and current cash flows are often negative or negligible.
• Uncertainty about medium-term cash flows is extreme, making multi-year DCFs unreliable.
• Investor returns are dominated by the outcome at a single major liquidity event (trade sale, IPO, or occasionally secondary sale), not by interim dividends.
• Failure rates are high; many portfolio companies may be written down to zero, so the winners must generate very high multiples.

The valuation question in VC is therefore framed as:

• Given an assumed exit valuation and holding period, what ownership stake does the VC need today (and at exit) to achieve its target IRR?
• Given a target ownership stake, what pre-money valuation is consistent with the VC’s required return?

The VC method is essentially an investment value framework from the fund’s point of view: it asks, “What price and ownership make sense given our hurdle rate?” rather than “What is the fundamental value to a diversified shareholder?”

Target IRRs vary by stage, reflecting risk:

• Seed and very early stage: often 40–70% per year.
• Early stage: roughly 30–50% per year.
• Later stage or growth equity: more like 20–35% per year.

These target IRRs must compensate not only for the risk in one company but also for:

• High probability of total loss in other portfolio companies.
• Illiquidity and long holding periods.
• Fund-level fees and carried interest.

In practice, VC funds also rely on staged financing. Rather than committing all the capital up front, they invest in rounds tied to milestones (for example, product prototype, first revenue, regulatory approval). This gives the investor a real option to abandon if the company underperforms, which partially explains why high target IRRs are still consistent with positive expected value.

On the exam, when you see a very high discount rate and a focus on a single exit value rather than detailed annual cash flows, you are almost certainly looking at a VC-method calculation, even if the vignette does not use that label.

Structure of the Venture Capital Method

A single-round VC method for a new investment typically proceeds through the following steps:

• Step 1 – Estimate exit value:
  Project the company’s value at a future exit event (for example, strategic sale or IPO) using a benchmark multiple applied to forecasted financials at exit (revenue, EBITDA, or earnings). This step uses the market approach.

  For example, if forecast year-5 revenue is $50 million and an appropriate EV/sales multiple is 4.0×, exit enterprise value (EV) is:

  $$\text{Exit EV} = 4.0 \times 50 = 200\ \text{million}$$

  If the company is expected to have net debt of $10$ million at exit, exit equity value is $190$ million.

• Step 2 – Select target return (IRR):
  VCs use a target rate of return (“hurdle rate”), often 30–70% for early-stage investments and 20–35% for later-stage deals, to reflect high business risk, failure probability, and illiquidity. The IRR is applied over the planned holding period (for example, five to seven years).

• Step 3 – Discount exit value to today:
  The estimated exit equity value is discounted back to present using the VC’s target IRR to obtain the post-money valuation for the entire company:

  $$\text{Post-money value} = \frac{\text{Exit equity value}}{(1 + r_{\text{target}})^T}$$

  where $r_{\text{target}}$ is the VC’s target IRR and $T$ is the number of years to exit.

• Step 4 – Determine ownership share at exit and today:
  If the VC invests an amount $I$ today and requires IRR $r_{\text{target}}$ for $T$ years, the future value of the investment is:

  $$\text{Future value of investment} = I(1 + r_{\text{target}})^T$$

  The investor’s required ownership percentage at exit is:

  $$\text{Required ownership at exit} = \frac{I(1 + r_{\text{target}})^T}{\text{Exit equity value}}$$

  In simpler questions without future rounds or option-pool complications, we can directly compute required current ownership as:

  $$\text{VC ownership \%} = \frac{\text{Investment}}{\text{Post-money value}}$$

  and the pre-money valuation as:

  $$\text{Pre-money value} = \text{Post-money value} - \text{Investment}$$

Key Term: ownership dilution
Ownership dilution is the reduction in an existing investor’s percentage ownership of a company that occurs when new shares are issued in later financing rounds or for option exercises.

Correctly mapping between ownership “today” and ownership “at exit” is critical in multi-round structures, because dilution from later investors and option pools can be substantial. Many Level 2 questions revolve around this mapping.

Worked Example 1.1

An investor targets a required IRR of 40%. They estimate the company will be sold in five years for $100 million based on projected earnings and a benchmark P/E. What is the maximum post-money value today? If the investor plans to invest$4 million in this round and there will be no further financing, what ownership share is required?

Answer:
The post-money value is the present value of the $100 million exit at a 40% IRR over five years:

$$\text{Post-money} = \frac{100}{(1.40)^5} \approx \frac{100}{5.378} \approx 18.6\ \text{million}$$

The required ownership percentage based on the dollars invested is:

$$\text{Ownership} = \frac{4}{18.6} \approx 21.5\%$$

The implied pre-money valuation is:

$$\text{Pre-money} = \text{Post-money} - \text{Investment} \approx 18.6 - 4 = 14.6\ \text{million}$$

Relative to a conventional DCF with a much lower discount rate, this VC-method valuation is likely to be lower, because the 40% IRR embeds high risk and illiquidity.

Exam tip: if a question gives you the exit value, target IRR, and investment amount, you can compute either the post-money valuation (by discounting the exit value) or the required ownership (by growing the investment to exit and dividing by exit value). Make sure you identify which one the question is asking for.

Multi-Round Financing and Dilution

In practice, high-growth startups often raise multiple rounds (Series A, B, C...). Existing investors are diluted when new shares are issued. VC method calculations must therefore distinguish between:

• Ownership required at exit to achieve the target IRR.
• Ownership required today, after accounting for expected dilution from future rounds and option pools.

A common exam pattern is:

• Compute the required exit ownership from the exit value and target IRR.
• Work backwards through expected financing rounds to find the required ownership immediately after the current round.

For a single future round, if future investors are expected to receive a fraction $f$ of the post-money equity in that round, earlier holders will collectively own $(1 - f)$. If the VC needs to own $p_{\text{exit}}$ at exit and no other dilution occurs, its post-current-round ownership $p_0$ must satisfy:

With multiple future rounds, you multiply through:

where $f_i$ is the post-money percentage sold in round $i$. Exam questions may ask you to compute this backward step explicitly.

A subtle point: these percentages are usually on a fully diluted basis (including all shares, options, and convertibles that are expected to be in-the-money at exit). If a vignette provides both basic and fully diluted share counts, use the fully diluted base when linking percentage ownership to dollar value at exit.

Worked Example 1.2

A VC invests in a startup today (Series A) and expects a Series B in two years that will take 25% of the company’s equity at that time. The VC targets owning 15% of the company at exit in year 5 to achieve its IRR based on the projected exit value. What ownership percentage does the VC need immediately after its Series A investment?

Answer:
Let $x$ be the VC’s ownership right after Series A. After Series B, the VC and existing shareholders are diluted to 75% of the company (because the new Series B investors will own 25%). The VC’s ownership at exit (assuming no further dilution) will be:

$$\text{Ownership at exit} = x \times 0.75$$

Setting this equal to the target of 15%:

$$x \times 0.75 = 0.15 \Rightarrow x = \frac{0.15}{0.75} = 0.20 = 20\%$$

The VC must own 20% immediately after Series A to still hold 15% after the Series B dilution.

Worked Example 1.3 – Multi-Round VC with Target IRR

Consider a VC planning a Series A investment of $5 million today. The VC targets a 35$150 million at exit, based on an EV/sales multiple applied to forecast revenue.

The VC expects a Series B in year 2 that will give new investors 25% of the company at that time (post-money). There is no additional dilution after Series B. What ownership percentage must the VC negotiate at Series A to meet its return target?

Answer:
First compute the future value of the $5 million investment at the target IRR over five years:

$$\text{Future value of investment} = 5 \times (1.35)^5 \approx 5 \times 4.482 \approx 22.41\ \text{million}$$

The VC must own a fraction of the exit value equal to:

$$\text{Required ownership at exit} = \frac{22.41}{150} \approx 14.9\%$$

After Series B dilution:

$$\text{VC ownership at exit} = x \times 0.75$$

Set this equal to the required exit ownership:

$$x \times 0.75 = 0.149 \Rightarrow x = \frac{0.149}{0.75} \approx 0.199 \approx 19.9\%$$

So the VC must negotiate about a 20% ownership stake post-Series A, anticipating dilution from the future Series B round.

A typical exam variation is to give you the required Series A ownership percentage and the expected dilution, then ask you to compute the implied IRR or the implied exit value.

Option Pools and Ownership Calculations

In early rounds, VCs commonly require the company to create or expand an option pool to incentivize management. Crucially, the pool is often specified as a percentage of post-money fully diluted equity, but created out of the pre-money ownership—diluting founders more than the new investor.

Exam vignettes may describe:

• A target post-money option pool percentage.
• Whether the pool is included in “fully diluted” when calculating the VC’s ownership.
• Whether the pool expansion is assumed to come from founders only or pro rata from all existing holders.

You must carefully follow the wording; misinterpreting the pool mechanics is a common source of exam errors.

Worked Example 1.4 – Effect of an Option Pool

A startup has 1,000,000 founder shares outstanding before Series A. A VC offers to invest $4 million at a$6 million pre-money valuation, and requires a 15% employee option pool on a post-money, fully diluted basis. Pool shares will be issued out of founders’ holdings (i.e., the VC is not diluted by the pool creation). What are the post-money ownership percentages of founders, VC, and the option pool?

Answer:
First compute post-money valuation:

$$\text{Post-money} = \text{Pre-money} + \text{Investment} = 6 + 4 = 10\ \text{million}$$

The VC’s ownership fraction based on dollars invested is:

$$\text{VC \%} = \frac{4}{10} = 40\%$$

The option pool must be 15% of fully diluted post-money equity. Let total fully diluted shares be $N$. Then:

• VC holds $0.40N$.
• Option pool holds $0.15N$.
• Founders hold the remaining $0.45N$.

Thus, on a percentage basis:

• VC: 40%.
• Option pool: 15%.
• Founders: 45%.

The founders’ stake falls from 100% pre-money to 45% post-money. Even though the VC owns 40% of the company economically, the requirement that the entire 15% pool come out of founders’ shares means the founders, not the VC, bear all of the pool dilution.

In some deals, the term sheet will say that the pool is “included in the pre-money valuation.” This usually means that the option pool must exist before the VC’s percentage is calculated. Economically, this reduces the founders’ effective pre-money per-share price compared with the headline valuation. On the exam, if you are given both a target pool size and a pre-money valuation, read carefully to see whether the pool is assumed to be created pre-money or post-money; the founders’ dilution can differ materially.

Security Design and IRR Measurement

Most VC investments are structured as preferred equity (often convertible preferred), with features such as:

• Liquidation preferences (for example, 1× non-participating preferred, giving the VC the right to receive its invested capital back before common shareholders).
• Participating preferred with caps (allowing the VC to receive preference plus share pro rata in remaining proceeds).
• Anti-dilution protection (full ratchet or weighted-average adjustments to conversion price if future rounds are down-rounds).
• Redemption rights or protective provisions.

These terms determine how exit proceeds are allocated across securities. In principle, the VC’s IRR should be computed based on actual cash flows to the specific security held (dividends, liquidation proceeds, conversion into common at IPO), not simply its percentage ownership of the company’s headline exit value.

At Level 2, however, exam questions on the VC method typically abstract from detailed security features and assume that the investor’s return is proportional to its ownership stake in total equity value at exit. You should still recognize qualitatively that:

• Liquidation preferences protect downside (raising IRR in low or moderate exit scenarios).
• Conversion into common at high exits can make the VC’s payoff more closely resemble that of ordinary equity.
• Preferred structures mean that naïvely multiplying percentage ownership by exit equity value may overstate or understate true economic returns in some scenarios.

If a vignette explicitly mentions liquidation preferences and competing classes of stock (for example, one series is “out of the money” at the modeled exit value), you may be asked to comment qualitatively on which series is likely to realize higher IRR or whether common shareholders receive anything.

Inputs and Adjustments in VC Valuation

In VC valuation, two important exam points are:

• High discount rates:

  • High target IRRs implicitly account for:
  • High probabilities of total failure or very low exits.
  • Illiquidity and long holding periods.
  • Company-specific risks (management execution, technology, competition, regulatory risk).

• Choice and adjustment of multiples:

  • Benchmark exit multiples are often derived from public comparables but may be:
  • Discounted for smaller size and higher risk (for example, using a lower EV/sales than public SaaS peers).
  • Adjusted for differences in growth prospects, margins, and capital intensity.
  • Selected based on the most relevant metric at exit: revenue for early-stage, EBITDA or earnings for later-stage.

When applying an EV-based multiple, you must:

1. Estimate exit enterprise value using the multiple.
2. Subtract forecast net debt and other senior claims at exit to derive equity value.
3. Use this equity value as the basis for the VC method.

Ignoring net debt can materially overstate equity value for a capital-intensive startup.

In more advanced practice (beyond typical Level 2 questions), VCs may model multiple scenarios (pessimistic, base, optimistic) with different exit valuations and probabilities, and compute an expected value or risk-adjusted IRR. On the exam, you could be given multiple exit scenarios with associated probabilities and asked to compute an expected exit value before discounting at the target IRR.

Given the extreme uncertainty, VC valuations are approximate and scenario-based. In item sets, you may be asked to compare a VC-method valuation with a DCF or market-multiple valuation and comment on why they differ and which is more decision-relevant for a given investor.

Worked Example 1.5 – VC Method vs DCF Comparison

A later-stage VC fund is considering investing in a profitable private firm expected to grow at 20% for five years and then at 4% perpetually. A conventional FCFE DCF valuation using a required return of 12% produces an equity value of $80 million. The fund, however, targets a 25$150 million in five years.

1. Using the VC method, what post-money valuation does the fund imply?
2. Conceptually, why might the VC’s indicative valuation differ from the DCF value?

Answer:

• The VC method post-money value is:

$$\text{Post-money} = \frac{\text{Exit value}}{(1 + r_{\text{target}})^T} = \frac{150}{(1.25)^5}$$

$(1.25)^5 \approx 3.052$, so:

$$\text{Post-money} \approx \frac{150}{3.052} \approx 49.1\ \text{million}$$

The VC method therefore implies a post-money valuation of about $49$ million, substantially below the $80$ million DCF estimate.

• The DCF value of $80$ million reflects a diversified shareholder’s required return of 12% and assumes:
• Stable access to capital markets.
• Liquid secondary markets and the ability to trade at or near fair value.
• Diversification across many investments so that company-specific risk is largely diversified away.
• Under those assumptions, a 12% required return is sufficient compensation for risk, so the DCF can support a higher value. The VC’s 25% target IRR instead embeds:
• A significant illiquidity premium and compensation for the inability to exit at will.
• A portfolio-level view that several investments may fail, so winners must generate higher multiples.
• A focus on a single 5-year exit event, ignoring cash flows beyond year 5 that are captured in the DCF’s terminal value.

Leveraged Buyout (LBO) Approaches

LBOs involve acquiring a company primarily with debt, and repaying that debt with the company’s future cash flows. The financial sponsor (private equity fund) aims to maximize return on equity by optimizing capital structure, improving operations, and timing the exit.

Key Term: management buyout (MBO)
A management buyout is a type of leveraged buyout in which the existing management team participates as buyers, often alongside a private equity sponsor.

Key Term: enterprise value (EV)
Enterprise value is the total value of the firm’s operating assets, equal to the market value of equity plus net debt (and other non-equity claims), and is independent of capital structure.

Key Term: money multiple
Money multiple (or multiple of invested capital) is the ratio of total cash returned to equity investors (including exit and interim distributions) to total equity invested.

LBO investors typically acquire control (often 100% equity), so the valuation is on a controlling, marketable basis. The LBO model is not primarily intended to estimate fundamental value; instead, it asks:

• Given assumptions about operations, leverage, and exit multiple, what equity IRR will we earn at a given purchase price?
• Alternatively, what is the maximum price we can pay and still achieve our target IRR?

The LBO framework is therefore an investment-value tool, just like the VC method, but applied to more mature, cash-generating companies.

Characteristics of Attractive LBO Candidates

Conceptually, the best LBO targets share several features:

• Stable, predictable cash flows and earnings.
• Moderate capital expenditure needs and limited working capital swings.
• Established, defensible market positions with some pricing power.
• Tangible asset base that can support secured debt (for example, property, plant, equipment, receivables).
• Opportunities for operational improvement (margin expansion, cost reductions).
• Non-core or underperforming divisions that can be divested to reduce debt.
• Capable management team willing to stay and be incentivized with equity.

Companies with highly volatile cash flows or extreme cyclicality are difficult to finance at high leverage levels because lenders require assurance that interest and principal can be serviced through downturns. An exam vignette may explicitly note “cyclical earnings” or “volatile operating cash flow” and ask whether the company is suitable for an LBO; your answer should tie back to debt service capacity.

Another practical consideration is asset intensity. Businesses with meaningful tangible assets (manufacturing, industrials, some business services) are easier to finance with secured loans than asset-light businesses where most value resides in intangibles (for example, early-stage tech). The latter may still attract growth equity but are less typical LBO candidates.

Steps in an LBO Valuation

An LBO model typically includes:

• Step 1 – Project operating performance and cash flows:
  Estimate revenue, margins, capital expenditures, and working capital needs over the holding period (commonly five years). From this, derive free cash flow available for debt service and distributions. Many models focus on EBITDA and EBIT as key drivers and treat capital expenditure and working capital as percentages of sales or depreciation.

  For debt modeling, the key cash-flow metric is often cash flow available for debt service (CFADS)—cash that can be used to pay interest and principal after operating needs and necessary investments. A simple approximation is:

  $$\text{CFADS} \approx \text{EBITDA} - \text{Cash taxes} - \text{Capex} - \Delta \text{Working capital}$$

• Step 2 – Build the sources and uses at closing:
  Determine how the acquisition is financed (debt tranches and equity contribution) and how much of the purchase price goes to equity sellers, transaction fees, and refinancing of existing debt. This produces an entry enterprise value and equity value.

  Typical “sources” include new debt, equity from the fund, and possibly management co-investment. “Uses” include purchase of equity, repayment of existing debt, fees, and sometimes cash added to the balance sheet. Conceptually:

  $$\text{Total sources} = \text{Total uses}$$

  and equity invested is the residual after subtracting debt sources from total uses.

• Step 3 – Model debt schedules:
  For each debt tranche, simulate interest expense, mandatory amortization, and optional repayments, reflecting typical LBO structures (term loans, high-yield bonds, mezzanine debt). Include any “cash sweep” using excess cash to repay debt faster.

• Step 4 – Estimate exit value:
  Apply a market multiple (typically EV/EBITDA) to forecast EBITDA in the exit year to estimate enterprise value at exit. Subtract net debt at exit to obtain exit equity value. In many exam questions, all debt is assumed to be repaid by exit.

• Step 5 – Calculate equity returns and maximum purchase price:
  Given the upfront equity invested and the equity value realized at exit (including any interim dividends or recapitalizations), compute the equity IRR and money multiple. Alternatively, back-solve for the purchase price that produces the required IRR.

Key Term: mezzanine debt
Mezzanine debt is subordinated debt (often with warrants or PIK features) used in LBOs, sitting between senior debt and equity in the capital structure, with higher yield and looser covenants.

Key Term: cash sweep
A cash sweep is a provision requiring that excess free cash flow, after required expenses and capex, be used to repay outstanding debt, accelerating deleveraging.

In exam questions, the LBO model is heavily simplified: you usually see one or two debt tranches, no mandatory cash sweep other than “all FCF is used to repay debt,” and a single exit year with an assumed EV/EBITDA multiple.

Conceptually, note the distinction between:

• Firm value (EV), which would be estimated by a DCF using FCFF and WACC.
• Equity IRR in an LBO, which is computed from equity cash flows given a specified leverage path and exit value.

An LBO does not by itself provide a statement about fundamental EV; it gives a price ceiling for that particular financial sponsor.

Worked Example 1.6 – Simple LBO IRR Calculation

A buyout fund models $5 million annual cash flow (after interest and taxes but before debt principal repayments) for five years. It expects to sell the business for 6× EBITDA at exit, with$20 million EBITDA and all debt repaid by year five. What equity IRR does a $50 million equity investment imply if the exit equity value is$120 million (6 × $20m) and there are no dividends before exit?

Answer:
The cash flows to equity are:

• Year 0: $50 million outflow (equity investment).
• Years 1–4: $5 million each year.
• Year 5: $5 million +$120 million = $125 million.

The equity IRR is the rate $r$ that solves:

$$-50 + \frac{5}{(1 + r)^1} + \frac{5}{(1 + r)^2} + \frac{5}{(1 + r)^3} + \frac{5}{(1 + r)^4} + \frac{125}{(1 + r)^5} = 0$$

Solving by financial calculator or spreadsheet yields an IRR of approximately 59%.
This high IRR reflects both leverage (all debt is gone by exit) and the low entry price relative to the exit equity value.

Debt Capacity, Covenants, and Lender View

Although exam questions largely focus on the equity investor, it is helpful to remember that debt capacity constrains the amount of leverage in an LBO. Lenders typically impose:

• Maximum leverage ratios (for example, total debt/EBITDA ≤ 4.0× or 5.0×).
• Minimum interest coverage ratios (for example, EBITDA/interest ≥ 2.5–3.0×).
• Occasionally, minimum fixed-charge coverage or debt service coverage ratios.
• Limits on additional indebtedness or asset sales.

Thus, even if higher leverage would boost equity IRR, the sponsor may be limited by what banks and bond investors are willing to underwrite. A vignette might present different financing structures and ask which is more realistic given covenants and business risk.

If a company’s projected cash flow barely covers interest expense, the lender is likely to cap leverage at a lower multiple, which in turn constrains the maximum purchase price or lowers expected equity IRR.

From the lender’s standpoint, key questions include:

• Is CFADS sufficient to cover interest and scheduled principal with a margin of safety?
• How cyclical is EBITDA, and how would coverage look in a downturn?
• What collateral is available in the event of default?

These considerations shape the amount, tenor, and pricing of LBO debt and thus indirectly influence equity returns.

Key LBO Model Inputs and Sensitivities

Key assumptions that drive LBO results include:

• Leverage levels:
  Starting and ending debt-to-equity or debt-to-EBITDA ratios. Higher leverage amplifies equity IRR but increases financial risk and the probability of distress. Lenders typically impose maximum leverage ratios and minimum interest coverage covenants that limit how much debt can be raised.

• Operating performance:
  Revenue growth, EBITDA margins, and capital-expenditure intensity. Even modest improvements in margins or working capital efficiency can significantly raise free cash flow and accelerate deleveraging. Conversely, a small shortfall in EBITDA growth can dramatically reduce IRR when leverage is high.

• Exit assumptions:
  Exit timing and the exit EV/EBITDA multiple. A higher assumed exit multiple directly increases exit equity value and IRR; assuming multiple expansion (exit multiple > entry multiple) can be aggressive and is often stress-tested. A conservative model usually assumes flat or slightly lower exit multiples.

• Target IRR and holding period:
  LBO funds often target 20–30% IRR for core deals, higher for turnarounds or emerging markets. Holding periods typically range from 3 to 7 years; longer holding periods make IRR more sensitive to interim cash flows and less to exit timing, while shorter holding periods increase the importance of the entry/exit multiple differential.

Exam questions frequently involve sensitivity analysis: how does the IRR change if the exit multiple falls, or if EBITDA growth is slower than expected? Intuitively:

• The more leverage, the more sensitive IRR is to any assumption that affects equity value at exit.
• If no dividends are paid during the holding period, IRR is especially sensitive to the exit multiple and exit timing.

Worked Example 1.7 – Back-Solving Maximum Equity Investment

A buyout fund targets a 25% equity IRR over a five-year holding period. It is evaluating a company with forecast EBITDA of $15 million at exit. The fund assumes a 7× EV/EBITDA exit multiple, no net debt at exit, and no interim dividends. What is the maximum equity investment it can make today?

Answer:
First compute the forecast exit equity value (since there is no net debt):

$$\text{Exit equity value} = 7 \times 15 = 105\ \text{million}$$

With no interim cash flows, the equity IRR equation is:

$$-\text{Equity investment} + \frac{105}{(1 + 0.25)^5} = 0$$

Solving for the maximum equity investment:

$$\text{Equity investment} = \frac{105}{(1.25)^5} \approx \frac{105}{3.052} \approx 34.4\ \text{million}$$

Paying more than $34.4$ million would reduce the IRR below 25% under these assumptions.

In an actual LBO, part of the purchase price would be financed with debt, but from the equity investor’s standpoint, the key figure is how much equity can be invested for a given exit equity value and target IRR.

Worked Example 1.8 – LBO IRR Sensitivity to Exit Multiple

Assume the same company as in Example 1.7 is acquired with $30$ million of equity and $70$ million of debt (total enterprise value $100$ million). All debt is fully repaid by year 5 using free cash flow. There are no interim dividends.

1. What is the equity IRR if the exit multiple remains at 7× EBITDA (exit equity = $105$ million)?
2. What is the equity IRR if the exit multiple compresses to 6× EBITDA (exit equity = $90$ million)?

Answer:

• With no net debt at exit and no interim distributions, the IRR is determined by:

$$-30 + \frac{105}{(1 + r)^5} = 0$$

So:

$$(1 + r)^5 = \frac{105}{30} = 3.5 \Rightarrow 1 + r = 3.5^{1/5}$$

$3.5^{1/5} \approx 1.28$, so $r \approx 28\%$.

• If the exit multiple compresses to 6×, exit equity value is $90$ million:

-30 + \frac{90}{(1 + r)^5} = 0 \Rightarrow (1 + r)^5 = \frac{90}{30} = 3 $ $3^{1/5} \approx 1.245$, so $r \approx 24.5\%$. This illustrates how sensitive LBO returns can be to relatively modest changes in the exit multiple, especially over short holding periods.

Comparing Equity IRR and Money Multiple

For private equity investors, both IRR and money multiple are important:

• IRR emphasizes the timing of cash flows; earlier distributions boost IRR.
• Money multiple focuses on total value creation; it is less sensitive to exact timing as long as the holding period is similar.

Using the “Test Your Knowledge” LBO scenario: investing $80$ million of equity and receiving $240$ million in year 5 implies a money multiple of:

The corresponding IRR would be the 5-year annualized rate that turns 1 into 3:

On the exam, you may not be required to compute IRR from a money multiple directly, but recognizing that a 3× multiple over five years is consistent with roughly mid-20s IRR helps you sanity-check answers.

A common error is to equate the LBO equity IRR with the company’s cost of equity from CAPM. They measure different things:

• Cost of equity from CAPM: required return for a diversified investor holding the stock at current leverage, with no assumption about exit.
• LBO equity IRR: realized or targeted return for a concentrated investor who controls leverage, cash flows, and exit timing.

Financial vs Strategic Buyers

When comparing LBO sponsors with strategic buyers (operating companies), remember:

• Strategic buyers may realize synergies (cost savings, cross-selling, technology, tax benefits) and thus can justify paying a higher price than a financial sponsor, all else equal.
• LBO funds add value primarily through:
  • Financial engineering (leveraging and deleveraging).
  • Operational improvements (margin enhancement, working capital management).
  • Governance changes and management incentives.
• Strategic buyers may use a lower discount rate (reflecting synergies and diversification), while LBO sponsors require higher equity IRRs due to concentrated risk and leverage.

Strategic buyers may realize synergies through cost cuts or revenue enhancements that an LBO sponsor cannot capture, while LBO sponsors may be able to use higher leverage or more efficient capital structures to create value. Both may compete in auctions, but their reservation prices and preferred structures differ.

Thus, in competitive auctions, either strategic or financial buyers could be the highest bidder depending on:

• The magnitude and realizability of the synergies.
• The amount of leverage the sponsor can prudently deploy.
• The fund’s required IRR given its risk appetite and investor promises.

For exam purposes, you should recognize that an LBO price is an investment-value ceiling for the financial sponsor (given its target IRR), while a strategic acquirer’s DCF with synergies may justify a higher investment value.

Discount Rates for Private Company Valuations

For many private company valuations (particularly outside pure VC modeling), analysts explicitly estimate the required return on equity using extended forms of CAPM or build-up models.

Key Term: expanded CAPM
Expanded CAPM extends the traditional CAPM by starting with a peer-based beta and then adding explicit premiums for size, industry, country, and company-specific risks.

Key Term: build-up approach
The build-up approach estimates the required return on equity by starting with a base equity risk premium for large public companies and adding premiums for size and company-specific risks without using beta.

Key Term: country risk premium (CRP)
Country risk premium is the additional return demanded by investors for exposure to the economic, political, and currency risks of a specific country, often estimated from sovereign yield spreads.

In symbol form, the expanded CAPM can be written as:

where:

• $r_e$ = required return on equity.
• $r_f$ = risk-free rate.
• $\beta_{\text{peer}}$ = beta estimated from comparable public companies.
• ERP = broad equity risk premium (for the relevant market).
• SP = size premium (often higher for small, illiquid firms).
• IP = industry risk premium (if needed).
• SCRP = specific company risk premium (governance, customer concentration, management risk, and so on).

The build-up approach omits beta and instead starts from the expected return on a large-cap market portfolio:

This reflects the idea that a market-cap-weighted index is dominated by large firms; the ERP plus the risk-free rate approximates the required return on a “typical” large public company.

Both models are consistent with the income approach: the higher the risk (size, country, firm-specific), the higher the discount rate, and the lower the present value of a given stream of cash flows.

Qualitative and Quantitative Drivers of SCRP

Analysts consider both qualitative and quantitative factors when specifying the specific company risk premium:

• Qualitative factors (higher SCRP if worse):

  • Weak corporate governance or opaque financial reporting.
  • Customer or supplier concentration (few key relationships).
  • Geographic concentration in volatile or emerging markets.
  • Highly specialized or intangible asset base that may be hard to redeploy.
  • Dependence on a small number of key executives or founders.

• Quantitative factors (higher SCRP if more aggressive):

  • High operating leverage (fixed-cost structure).
  • High financial leverage (debt ratios).
  • Volatile historical earnings and cash flows.
  • Cyclical exposure and sensitivity to macro conditions.

For companies with material emerging-markets exposure, a country risk premium is added. One common approach is:

• Use the sovereign yield spread between the emerging market’s government bonds and a developed-market benchmark.

• Adjust for relative volatility between the country’s equity and bond markets:

  $$\text{CRP} = \text{sovereign yield spread} \times \left( \frac{\sigma_{\text{equity}}}{\sigma_{\text{bond}}} \right)$$

This CRP is then added (possibly scaled by the firm’s exposure to that market) to the ERP in the expanded CAPM.

An alternative framing, sometimes called the country-spread model, expresses the equity risk premium for an emerging market as:

where $\lambda$ captures the firm’s exposure to the local economy (for example, proportion of revenue or assets in that country).

For multinational firms operating mostly in developed markets, global CAPM variants may be used, but for typical private-company exam questions, applying an explicit CRP to an otherwise standard model is sufficient.

For Level 2 purposes, you should be able to:

• Calculate a private company’s cost of equity using expanded CAPM or build-up inputs.
• Comment on the reasonableness of the resulting required return relative to the target IRR used in a VC or LBO model.
• Recognize that VC/LBO hurdle rates often exceed expanded CAPM outputs to reflect illiquidity and portfolio-level risk (for example, failure rates and fund economics).

Worked Example 1.9 – Expanded CAPM for a Private Company

A small private manufacturing firm in an emerging market is being valued. The following inputs are provided:

• Risk-free rate (local currency government bond): 4%.
• Global developed-market ERP: 5%.
• Peer-group beta (from public comparables): 1.2.
• Size premium (for small companies): 3%.
• Specific company risk premium: 2%.
• Sovereign yield spread versus developed benchmark: 2%.
• Volatility ratio $\sigma_{\text{equity}} / \sigma_{\text{bond}} = 1.5$.

Estimate the required return on equity using an expanded CAPM with a country risk premium.

Answer:
First compute the country risk premium:

$$\text{CRP} = 2\% \times 1.5 = 3\%$$

The effective equity risk premium for this market is:

$$\text{ERP}_{\text{total}} = \text{ERP}_{\text{developed}} + \text{CRP} = 5\% + 3\% = 8\%$$

Now apply the expanded CAPM:

$$r_e = r_f + \beta_{\text{peer}} \times \text{ERP}_{\text{total}} + \text{SP} + \text{SCRP}$$ $$r_e = 4\% + 1.2 \times 8\% + 3\% + 2\% = 4\% + 9.6\% + 3\% + 2\% = 18.6\%$$

The required return on equity for this private firm is approximately 18.6%, significantly higher than typical large-cap public equity returns because of size, country, and firm-specific risk.

In VC and some LBO contexts, investors often bypass these formulas and instead specify a target IRR directly. Conceptually, that target IRR should be broadly consistent with the risks captured by expanded CAPM or build-up models, but it also reflects portfolio-level considerations (such as expected loss rates and fund economics). For example, if expanded CAPM produces a 19% cost of equity, a VC fund targeting 30–40% IRRs is implicitly layering on additional premiums for illiquidity, stage risk, and diversification limitations.

Premiums and Discounts in Private Company Valuation

Adjustments for control and marketability are needed to reflect unique characteristics of private firms and the specific interest being valued.

Key Term: control premium
A control premium is an amount a buyer is willing to pay above the pro rata value of shares to gain a controlling interest and the ability to direct company decisions (for example, strategy, dividend policy, compensation).

Key Term: discount for lack of marketability (DLOM)
A DLOM is a reduction in value applied to private company equity to reflect the additional risk and cost arising from the inability to quickly sell shares at fair value.

Key Term: minority discount
A minority discount is a reduction in value applied to a non-controlling equity interest to reflect the absence of control over key corporate decisions; it is conceptually the inverse of a control premium.

Control vs Minority, Marketable vs Non-Marketable

Conceptually:

• Guideline public company multiples usually reflect minority, marketable interests (trading prices of non-controlling shares but in liquid markets).
• A strategic or financial buyer acquiring control may pay a control premium over the implied pro rata equity value. Part of this premium may reflect genuine control rights (ability to change strategy and payout); part may reflect buyer-specific synergies.
• A minority investor in a private firm owns an interest that is non-controlling and non-marketable, often requiring both:
  • A minority discount (to adjust from control to non-control, if starting from control-level values).
  • A DLOM (to adjust for lack of liquidity).

In LBOs and many VC deals:

• The investor typically acquires or collectively holds control and actively influences decisions, and ultimately plans to exit into a liquid market or strategic sale.
• The valuation (post-money or enterprise value) is usually on a controlling, marketable basis.
• Consequently, additional control premiums are generally not added to LBO or VC valuations; they are embedded in the transaction structure and the use of control-based cash flows.

Linking Control Premiums and Minority Discounts

Suppose the pro rata value of equity based on public trading prices (minority, marketable) is $100$ per share. If control transactions in the sector occur at a 25% premium, the implied control value is:

The implied minority discount relative to the control value is:

This relationship is often used to move between control and minority value levels, depending on the purpose of the valuation. Algebraically:

You should be comfortable going in either direction:

• From minority to control: multiply by $(1 + \text{control premium})$.
• From control to minority: multiply by $(1 - \text{minority discount})$.

DLOM Considerations

Empirical estimates of DLOM draw on:

• Restricted stock studies: comparing prices of restricted shares with otherwise identical publicly traded shares.
• Pre-IPO studies: comparing private transaction prices with IPO prices shortly thereafter.

Factors increasing DLOM include:

• Longer expected holding periods before an exit.
• Greater uncertainty about exit timing and valuation.
• Restrictions on transfer (for example, shareholder agreements, rights of first refusal).
• Smaller company size and limited information disclosure.

In exam settings, you will usually be given an estimated DLOM percentage and asked to apply it appropriately, not to derive it.

DLOM tends to be smaller (or even zero) when:

• The interest being valued is controlling and the controller can initiate a sale or IPO in the near term.
• The company is already in a sale process or has a credible exit path, shortening the expected illiquidity period.

Exam Warning on Double-Counting

Exam warning: Discounts and premiums must not be added or subtracted without evaluating whether the subject interest already embeds control or marketability features. For example:

• If you value equity using a DCF model based on control-level cash flows (for example, assuming optimal capital structure and payout policy), the resulting equity value is at a control level. Applying a separate control premium would double-count control. If the discount rate already includes a premium for illiquidity, adding a DLOM may also double-count illiquidity.
• If guideline transaction multiples are based on acquisitions of whole companies (control transactions), applying an additional control premium is inappropriate.
• If a VC model uses a very high target IRR to reflect illiquidity and failure risk, adding a separate DLOM to the post-money valuation is typically inconsistent.

On the exam, carefully identify:

• The nature of the interest being valued (minority versus control, marketable versus non-marketable).
• The basis of the inputs (public trading multiples, control transaction multiples, or explicit control-level cash flows).
• Whether any control or marketability adjustments are already implicit in the method, cash flows, and discount rate.

A simple diagnostic for exam questions:

• Are the cash flows control-based (assuming optimal policies) or status quo?
• Is the discount rate derived for a diversified public investor (no illiquidity premium) or a private equity investor (with implicit illiquidity premiums)?
• Are the multiples drawn from minority trades or control acquisitions?

A simple diagnostic for exam questions:

• Are the cash flows control-based (assuming optimal policies) or status quo?
• Is the discount rate derived for a diversified public investor (no illiquidity premium) or a private equity investor (with implicit illiquidity premiums)?
• Are the multiples drawn from minority trades or control acquisitions?

Answering these questions usually reveals whether additional premiums or discounts are appropriate.

Worked Example 1.10 – Applying Control Premium and DLOM

An analyst values a private company’s equity at $80$ million using a DCF model that reflects control-level cash flows (assumes optimal capital structure and payout policy) and a discount rate based on an expanded CAPM without any explicit illiquidity premium. The analyst believes:

• A controlling interest in comparable public companies trades at a 30% control premium over their minority trading prices.
• A 20% DLOM is appropriate for a non-marketable interest.

How should the analyst estimate the value of a 30% non-controlling, non-marketable interest in the company, starting from the $80$ million control value?

Answer:
The $80$ million DCF estimate reflects a controlling interest. We must adjust to:

• Remove control (apply a minority discount).
• Then apply DLOM to reflect non-marketability.

The implied minority discount corresponding to a 30% control premium is:

$$\text{Minority discount} = 1 - \frac{1}{1 + 0.30} = 1 - \frac{1}{1.30} \approx 23.1\%$$

Step 1: Move from control to minority, marketable value:

$$\text{Minority, marketable value} = 80 \times (1 - 0.231) \approx 80 \times 0.769 \approx 61.5\ \text{million}$$

Step 2: Apply DLOM to reflect non-marketability:

$$\text{Minority, non-marketable value} = 61.5 \times (1 - 0.20) = 61.5 \times 0.80 = 49.2\ \text{million}$$

Step 3: Compute the value of a 30% interest:

$$\text{Value of 30\% interest} = 0.30 \times 49.2 \approx 14.8\ \text{million}$$

This stepwise approach avoids double-counting and aligns the valuation with the nature of the interest being appraised.

Note that it would not be appropriate to apply a control premium to the $80$ million control-level value, or to add an additional illiquidity premium to the discount rate without adjusting the DLOM. On the exam, when you see both discount-rate adjustments and DLOMs being discussed, think carefully about whether they are alternative ways of capturing the same risk.

Comparing Approaches: VC, LBO, and Conventional Methods

The venture capital method, LBO modeling, and conventional DCF/multiple approaches all combine income and market viewpoints but differ in emphasis and purpose.

Key points by method:

• VC method:

  • Best suited for early-stage, high-risk companies with limited historical data.
  • Relies heavily on exit scenarios and target IRRs, with simplified cash-flow treatment.
  • Less granular annual cash-flow modeling; more emphasis on multiples and dilution.
  • Often yields lower valuations than a conventional DCF due to higher required returns.
  • Reflects investment value to the VC fund, not necessarily fair market value.

• LBO model:

  • Best suited for mature, cash-flow-generating businesses.
  • Explicitly models capital structure and debt repayment (investment value to the sponsor).
  • Used to determine what price financial buyers can pay, not necessarily fundamental value.
  • IRR depends on leverage path, operational improvements, and exit multiple; it is not equivalent to the firm’s cost of equity from CAPM.

• Traditional DCF / relative valuation:

  • Useful for strategic buyers, minority investors, or fairness opinions.
  • Often provides a fundamental value benchmark against which VC or LBO pricing can be compared.
  • Uses discount rates from CAPM/expanded CAPM or build-up models, assuming diversified investors.
  • Depending on the multiples used (guideline public vs guideline transactions), may reflect minority or control levels of value.

In many exam vignettes, you will be asked to interpret differing values from these methods and explain which method is most relevant for a specific investor (for example, VC fund vs strategic acquirer vs minority shareholder). You should:

• Identify which assumptions differ (growth, discount rate, leverage, exit multiple).
• Relate each method to its core valuation concept (fundamental, fair market, or investment value).
• Comment on potential biases (optimistic exit multiples, aggressive synergies, understated risk premiums).
• Recognize when an additional control premium or DLOM is inappropriate because the method already reflects control or illiquidity.

A common structure in an item set is:

• A strategic buyer’s DCF including synergies → highest value (investment value with synergies).
• A fairness opinion DCF for minority shareholders → lower value (fundamental/fair market).
• An LBO model → a “maximum price” for the buyout fund given its IRR hurdle.
• A VC-style exit-multiple valuation → a still lower value for a high-risk early-stage investment.

The correct answer often hinges on matching the valuation to the decision-maker’s standpoint and the legal or practical constraints in the scenario.

Key Point Checklist

This article has covered the following key knowledge points:

• Distinguish income, market, and asset-based valuation approaches for private firms and recognize data limitations versus public companies.
• Explain how differences in size, governance, liquidity, and disclosure between public and private firms affect both cash-flow forecasts and discount rates.
• Describe guideline public company, guideline transactions, and prior transaction methods within the market approach and relate them to control vs minority levels of value.
• Apply the venture capital method using exit multiples, target IRR, and pre-/post-money valuation, including multi-round financing and dilution from future rounds and option pools.
• Understand how security design (preferred stock, liquidation preferences) conceptually affects VC cash flows, while exam problems typically abstract to proportional equity stakes.
• Build and interpret a simplified LBO model to determine maximum purchase price, exit equity value, equity IRR, and money multiple, and perform sensitivity analysis to leverage, growth, and exit multiples.
• Explain how expanded CAPM and build-up approaches are used to estimate private company discount rates, including size, industry, company-specific, and country risk premiums.
• Adjust private company values for control premiums, minority discounts, and marketability discounts while avoiding double-counting across methods, cash flows, and discount rates.
• Relate VC and LBO target IRRs to the risk characteristics of the investment and to more traditional required return estimates from CAPM-based models.
• Compare and select among VC, LBO, DCF, and market-multiple approaches for different transaction types, ownership levels (control vs minority), and investor objectives (financial vs strategic buyers).
• Link normalized earnings and free cash flow estimation (FCFF/FCFE) to private company valuation in both DCF and PE-style models.

Key Terms and Concepts

• income approach
• market approach
• asset-based approach
• venture capital method
• leveraged buyout (LBO) model
• internal rate of return (IRR)
• fundamental value
• fair market value
• investment value
• guideline public company method
• guideline transactions method
• prior transaction method
• pre-money valuation
• post-money valuation
• exit multiple
• option pool
• ownership dilution
• management buyout (MBO)
• enterprise value (EV)
• money multiple
• mezzanine debt
• cash sweep
• expanded CAPM
• build-up approach
• country risk premium (CRP)
• control premium
• discount for lack of marketability (DLOM)
• minority discount