Market-based and private company valuation - Private company...

Learning Outcomes

This article explains how to value private company interests using market-based evidence, including:

• understanding the conceptual difference between control and minority (non-controlling) interests and how these distinctions are embedded in observable market prices for public companies and transactions;
• distinguishing control premiums from discounts for lack of control (DLOC), and interpreting observed transaction premiums to infer appropriate DLOC estimates for minority interests;
• identifying when a valuation input (such as a guideline public multiple or M&A transaction price) reflects a controlling, minority, marketable, or non-marketable basis, and determining which adjustments are required to align it with the subject interest;
• performing step‑by‑step calculations to convert a control, marketable value into a minority, non‑marketable value (and vice versa) using the standard DLOC and discount for lack of marketability (DLOM) formulas tested at CFA Level 2;
• analyzing how combined DLOC and DLOM adjustments affect indicated equity value, emphasizing the correct multiplicative approach rather than simple addition of percentage discounts;
• evaluating practical scenarios commonly seen in exam vignettes to decide whether no adjustment, a single adjustment, or both control and marketability adjustments are necessary to produce a supportable private company valuation.

CFA Level 2 Syllabus

For the CFA Level 2 exam, you are required to understand market-based and private company valuation, with a focus on the following syllabus points:

• Recognizing when control or marketability adjustments are needed in private company valuation
• Explaining and calculating control premiums and discounts for lack of control (DLOC)
• Identifying circumstances requiring discounts for lack of marketability (DLOM)
• Evaluating how these adjustments affect private company valuations relative to public comparables

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.

Use the following vignette for Questions 1–4.

An analyst is valuing a 20% equity interest in Alpha Diagnostics, a private company. As part of the valuation:

• A guideline public company EV/EBITDA multiple is derived from several listed peers based on their current share prices (minority, marketable basis).
• A recent acquisition of 100% of a comparable public company was completed at a 25% premium to its unaffected share price one week before the deal announcement.
• The subject 20% interest in Alpha is in a private company with restrictive shareholder agreements and no plans for an IPO or sale in the near term.
• Empirical evidence and company‑specific factors suggest that a 30% discount for lack of marketability (DLOM) is appropriate for non‑marketable interests of similar private firms.

1. When the analyst uses the 25% takeover premium from the comparable acquisition, what is the main economic feature that this premium most directly reflects?
   1. The present value of expected acquisition-specific gains for the buyer only
   2. The value to the acquirer of obtaining control rights over the target’s decisions
   3. The increase in marketability from listing the target’s shares on an exchange
   4. The expected reduction in company‑specific risk after the acquisition
2. Suppose the analyst first values 100% of Alpha Diagnostics using a control‑basis multiple implied by the takeover transaction, then wants to value the 20% non‑controlling interest in Alpha (still assuming marketability). Which adjustment is most appropriate at this stage?
   1. Apply only a DLOM to reflect lack of liquidity
   2. Apply only a control premium to reflect the 20% stake
   3. Apply a DLOC to convert from control value to minority value
   4. Apply both DLOC and DLOM simultaneously
3. Based on the 25% control premium observed in the takeover transaction, what is the implied discount for lack of control (DLOC)?
   1. 20.0%
   2. 25.0%
   3. 31.3%
   4. 44.0%
4. The analyst ultimately needs a value for the 20% interest in Alpha that reflects both lack of control and lack of marketability. If the DLOC is 20% (from Question 3) and the DLOM is 30%, how should the combined discount be applied?
   1. Add the discounts: total discount = 20% + 30% = 50%
   2. Multiply the discounts: total discount = 1 – [(1 – 0.20)(1 – 0.30)]
   3. Take the larger of the two discounts: total discount = 30%
   4. Apply DLOC only, because the multiple already reflects marketability

Introduction

When valuing private companies, market-based methods often use transaction data or multiples from public companies. Unlike public companies, private firms’ shares may not include control rights or liquidity, which affects value. To ensure fair comparisons, analysts must adjust for control and marketability differences. These adjustments significantly impact the estimated value of the subject private company. A robust understanding of these principles is necessary for correct application in the CFA Level 2 exam and in professional practice.

Key Term: Controlling Interest
An ownership position with sufficient voting power to direct key corporate decisions, such as setting strategy, appointing and compensating management, determining dividends, and approving major transactions.

Key Term: Minority Interest
An ownership position representing less than 50% of voting shares, typically without power to direct company activities and therefore lacking unilateral control.

Key Term: Marketability
The ability to sell an ownership interest quickly and at a known, fair price in an organized and active market.

Key Term: Marketable Basis
A value indication that assumes the interest can be readily sold in a well‑functioning market (for example, listed public shares).

Key Term: Non‑marketable Basis
A value indication that assumes the interest cannot be readily sold, often due to lack of listing, a limited pool of buyers, or contractual transfer restrictions.

Key Term: Level of Value
The combination of assumptions about control (controlling vs minority) and marketability (marketable vs non‑marketable) supporting a particular value indication.

In practice, four common “levels of value” are distinguished:

• controlling, marketable (e.g., value implied by the sale of 100% of a public company);
• controlling, non‑marketable (e.g., 100% ownership of a private firm with no ready market);
• minority, marketable (e.g., trading price of a small block of public shares);
• minority, non‑marketable (e.g., small ownership stake in a private company with transfer restrictions).

Correctly identifying which level your starting evidence reflects—and which level your subject interest requires—is the basis for applying control and marketability adjustments correctly.

Adjustments for Control in Private Company Valuation

Valuing a private company often starts with public company comparables. However, the value indicated by public company prices usually reflects minority shareholdings with no control over company operations. Conversely, transactions involving entire companies or controlling interests include a premium for the ability to direct company decisions. If your valuation purpose concerns a minority interest (non-controlling), you may need to apply a discount for lack of control. If estimating a controlling interest, you may need to add a control premium.

Key Term: Control Premium
The additional amount paid over the market value of a minority interest, reflecting the value of decision-making authority and control rights.

Key Term: Discount for Lack of Control (DLOC)
A reduction in value applied to non-controlling interests to account for the absence of control, typically estimated using observed control premiums in acquisitions or by comparing control‑based versus minority‑based value estimates.

Why Control Has Value

Control allows an investor to:

• change management, strategy, and capital structure;
• alter payout policy (for example, increase dividends or initiate buybacks);
• sell or liquidate assets, or sell the entire company;
• change related‑party transactions or remove excess owner benefits.

If a company is poorly managed, or retains too much cash, a controlling owner can realize additional value by making changes. In such cases, control premiums (and hence implied DLOCs) can be substantial. If a company is already well‑run with shareholder‑friendly policies, the value of additional control may be small, and observed premiums may mainly reflect expected benefits for a particular buyer.

A control premium is visible in many merger and acquisition transactions for public firms, where acquirers often pay more per share than the pre-transaction trading price. This premium compensates for the acquirer’s new ability to influence strategy, dividends, management, and asset use. In private company valuation, if you start from a controlling-interest value and the subject interest lacks control, you must apply a DLOC to reflect the reduced rights and influence.

Calculating the Discount for Lack of Control

The DLOC is mathematically linked to observed control premiums. If the observed control premium is expressed as a proportion of the pre‑deal minority trading price:

For example, if the typical control premium is 25%:

This means a minority interest could be worth up to 20% less than a controlling interest, all else equal, when both interests are equally marketable.

You can move between control and minority values as follows:

• from control value to minority value (apply DLOC):
  $V_{\text{minority}} = V_{\text{control}} \times (1 - \text{DLOC})$
• from minority value to control value (apply control premium):
  $V_{\text{control}} = V_{\text{minority}} \times (1 + \text{Control Premium})$

The DLOC can also be inferred by comparing two valuations of the same company:

• one based on normalized earnings that assume control adjustments (control basis);
• one based on reported earnings without such adjustments (minority basis).

The gap between the two indicates the value impact of control-related changes.

Worked Example 1.1

Question: A controlling stake in a comparable company sold for a 30% premium over its unaffected market price. What is the implied discount for lack of control (DLOC) for valuing a minority interest?

Answer:
The DLOC is calculated as:

$$\text{DLOC} = 1 - \frac{1}{1 + 0.30} = 1 - \frac{1}{1.30} = 0.231 \text{ or } 23.1\%$$

Thus, the value of a non-controlling interest would be reduced by 23.1% compared to the controlling value, assuming both are equally marketable.

Control View Embedded in Market Evidence

It is essential to identify what view is embedded in your valuation input:

• Guideline public company method (GPCM):
  Multiples based on current trading prices generally reflect minority, marketable values (small public shareholders).

• Guideline transactions method (GTM):
  Multiples from acquisitions of entire companies reflect control, marketable values (assuming the target was public or otherwise readily saleable prior to the deal).

• Prior transaction method (PTM):
  Past trades in the subject company’s shares may reflect a variety of levels of value, depending on the deal terms (e.g., whether a controlling block was sold, any restrictions on resale).

Recognizing these embedded assumptions allows you to decide whether to add a control premium, apply a DLOC, or make no control-related adjustment.

Worked Example 1.2

Question: A public comparable trades at an EV/EBITDA multiple of 8× based on its current share price. A recent acquisition of a similar public company occurred at an implied EV/EBITDA multiple of 10×. Assuming both companies are otherwise similar and the only systematic difference is control, what is the implied control premium and DLOC?

Answer:
The acquisition multiple (10×) versus the trading multiple (8×) reflects a 25% control premium:

$$\text{Control premium} = \frac{10 - 8}{8} = 0.25 = 25\%$$

The implied DLOC is:

$$\text{DLOC} = 1 - \frac{1}{1 + 0.25} = 1 - \frac{1}{1.25} = 0.20 = 20\%$$

Thus, a control‑basis valuation of a private company using a 10× multiple should be reduced by 20% to estimate the value of a minority interest, all else equal.

Adjustments for Marketability

Even after adjusting for control, private company shares typically cannot be readily sold on an open market. Lower liquidity and sometimes contractual transfer restrictions make these interests less desirable and less valuable than publicly traded securities.

Key Term: Discount for Lack of Marketability (DLOM)
A reduction applied to account for the difficulty or inability to quickly sell an interest at its appraised value due to limited or no market for the interest.

Empirical studies of restricted stock and pre-IPO transactions provide benchmarks for DLOM:

• Restricted stock studies: Compare prices of restricted shares (which cannot be freely traded for a period) with otherwise identical publicly traded shares.
• Pre‑IPO studies: Compare prices paid for private shares shortly before an IPO with the IPO price or immediate post‑IPO trading price.
• Option‑based models: Use the cost of put options (or synthetic equivalents) to estimate the value of liquidity protection.

The magnitude can vary significantly, often ranging from 10% to over 35%, depending on:

• expected holding period before liquidity;
• expected cash flows (for example, dividends) during the holding period;
• company‑specific risk and information quality;
• the presence of rights such as tag‑along, drag‑along, or contractual buyback features;
• the severity of contractual transfer restrictions.

A DLOM can apply to both controlling and minority interests whenever the shares are not readily tradable. However, in practice, minority interests in closely held firms typically warrant higher DLOMs than controlling interests, because the controller may have more realistic options for creating liquidity (e.g., selling the company).

Worked Example 1.3

Question: Suppose restricted shares of a public company, identical except for a one‑year trading restriction, trade at $30 when the company’s freely tradable shares trade at $40. What is the implied DLOM?

Answer:
The DLOM is the percentage reduction relative to the freely tradable price:

$$\text{DLOM} = \frac{40 - 30}{40} = \frac{10}{40} = 0.25 = 25\%$$

This suggests that, under similar risk and restriction conditions, a 25% DLOM might be appropriate when valuing non‑marketable interests.

Worked Example 1.4

Question: Suppose you value a private company’s minority interest at $2,000,000 based on public company comparables (no control or marketability adjustments included). If appropriate DLOC and DLOM are 20% and 30% respectively, what is the adjusted value?

Answer:
Start from the control/marketability basis reflected in the input and apply the discounts sequentially:

• Apply the DLOC:
  $2,000,000 × (1 − 0.20) = $1,600,000
• Apply the DLOM:
  $1,600,000 × (1 − 0.30) = $1,120,000
  The final adjusted value for the minority, non-marketable interest is $1,120,000.

Applying Both Adjustments

Both discounts may apply, especially when valuing a minority interest in a privately held firm without a ready market for its shares. The combined effect is multiplicative, not additive:

In Worked Example 1.4, the combined effect is:

Notice that:

• if you incorrectly added the discounts (20% + 30% = 50%), you would overstate the total reduction in value;
• the order of application (DLOC then DLOM, or DLOM then DLOC) does not change the final value because multiplication is commutative.

Exam Warning

Applying DLOC and DLOM as an additive (simply adding the percentages together) is incorrect. Always calculate them sequentially and use the multiplication rule to find the total discount. The exam frequently tests this distinction.

Worked Example 1.5

Question: You are valuing 100% of a private company using the guideline public company method. The public comparables’ trading multiples imply a value of $10 million on a minority, marketable basis. You believe a 20% control premium and a 25% DLOM are appropriate for the subject company. What is the value of a controlling, non‑marketable 100% interest?

Answer:
The starting point ($10 million) is minority, marketable. To reach a controlling, non‑marketable level of value:

• Step 1 – Add a control premium:
  Control value (marketable) = $10,000,000 × (1 + 0.20) = $12,000,000
• Step 2 – Apply a DLOM to reflect lack of marketability:
  Controlling, non‑marketable value = $12,000,000 × (1 − 0.25) = $9,000,000
  The indicated value of the controlling, non‑marketable 100% interest is $9,000,000.

Determining When to Adjust

The key is to compare:

• the basis of your valuation input (control vs minority, marketable vs non‑marketable), and
• the basis required for the subject interest.

Key Term: Discount for Lack of Control (DLOC)
(revisited)
Applied when the valuation input reflects a control view and the subject interest is non‑controlling, all else equal.

Key Term: Discount for Lack of Marketability (DLOM)
(revisited)
Applied when the valuation input reflects a marketable basis and the subject interest is less marketable (for example, interests in a private firm).

General guidelines:

• Use a control premium (or remove a DLOC) when valuing a controlling interest and the base value reflects a minority view (e.g., public trading multiples).
• Apply a DLOC when the subject interest is non-controlling and the base value reflects control (e.g., guideline transactions method using whole‑company acquisitions).
• Apply a DLOM whenever the interest lacks access to a liquid market—this is common in private company equity, even for controlling interests.
• If both control and marketability differ from the benchmark transaction, both adjustments are typically necessary.

A useful way to think about this is the “levels of value” grid:

In exam vignettes, carefully identify:

• whether comparables are public trading multiples (minority, marketable);
• whether observed transactions involve 100% acquisitions (control, marketable);
• whether the subject interest is minority vs controlling, and private vs public.

Worked Example 1.6

Question: You are valuing a 15% equity interest in a private company for which the guideline public company method yields $5 million (control, fully marketable basis is stated by the appraiser). If DLOC is 18% and DLOM is 22%, what is the estimated value of the minority, non-marketable interest?

Answer:
Given that the $5 million reflects a control, marketable basis:

• Apply DLOC:
  $5,000,000 × (1 − 0.18) = $4,100,000
• Apply DLOM:
  $4,100,000 × (1 − 0.22) = $3,198,000
  The estimated value of the 15% minority, non-marketable interest is $3,198,000.

In a different scenario, if the $5 million had been explicitly described as a minority, marketable value (for example, directly capitalizing public trading prices), you would not apply a DLOC; you would apply only the DLOM to reach a minority, non‑marketable basis.

Summary

When using market-based valuation for private companies, always evaluate whether adjustments for control and marketability are necessary. Control premiums and DLOC address voting and decision rights, while DLOM corrects for liquidity disparities. Properly identifying the level of value embedded in your inputs, and aligning it with the subject interest, is critical.

For CFA Level 2 purposes, you should be able to:

• interpret control premiums and infer corresponding DLOCs;
• decide when no adjustment, only DLOC, only DLOM, or both are appropriate;
• apply the correct multiplicative formula for combined discounts;
• trace step‑by‑step movements between minority/marketable and control/non‑marketable levels of value.

Correct application of these factors ensures fair, comparable values for private company interests, consistent with CFA Level 2 requirements.

Key Point Checklist

This article has covered the following key knowledge points:

• Control premiums reflect the value of decision rights and are typically observed in whole‑company acquisitions; DLOC is the corresponding discount to move from control to minority value.
• DLOC and control premiums are mathematically linked: $\text{DLOC} = 1 - \frac{1}{1 + \text{Control Premium}}$.
• DLOM adjusts value for illiquidity or transfer restrictions and is typically estimated using restricted stock studies, pre‑IPO studies, or option‑based models.
• DLOM can apply to both minority and controlling interests whenever the interest is less marketable than the benchmark used for valuation.
• Combined DLOC and DLOM discounts are applied sequentially and multiplicatively; total discount $= 1 - [(1 - \text{DLOC})(1 - \text{DLOM})]$.
• Market‑based valuation inputs (public trading multiples vs M&A transactions) embed different levels of value; you must align these with the subject interest by applying appropriate discounts or premiums.
• Exam questions often test whether you can correctly diagnose when no adjustment, a single adjustment, or both control and marketability adjustments are required.

Key Terms and Concepts

• Controlling Interest
• Minority Interest
• Marketability
• Marketable Basis
• Non‑marketable Basis
• Level of Value
• Control Premium
• Discount for Lack of Control (DLOC)
• Discount for Lack of Marketability (DLOM)