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EQ 6 – Private Company Valuation

Worked examples are fully visible. Check-yourself items are study aids you can reveal one at a time.

The mechanics of valuing a business do not change when the business is private. Discount expected cash flows at a rate that reflects their risk, or apply a multiple observed on comparable businesses, and you have a value. What changes is everything that feeds those mechanics: the reliability of the reported numbers, the availability of a market price to argue against, the composition of the shareholder base, and the ease with which a holder can turn a stake into cash. A private company valuation is therefore the same model run on materially worse inputs, with a set of deliberate corrections applied at each stage.

It helps to start by discarding the assumption that private means small or new. Very large and highly successful firms have stayed private from inception. India has the Tata Group. Europe has IKEA and ALDI. The United States has Cargill and Bechtel. Equally, a private company may be an early-stage venture with a handful of employees, or a failed business being wound up. The defining feature is not size but the absence of a public equity market, and the consequences that flow from that absence.

Public company valuation as the reference point

When an analyst values a listed company, several conveniences are taken for granted. Audited financial statements are prepared to a common standard and are equally available to everyone. A traded share price exists that aggregates the expectations of all market participants, so the analyst can compare an intrinsic value estimate against it and form a view on whether the shares are cheap or expensive. The perspective adopted is almost always that of an outside investor holding a small, non-controlling stake in freely traded shares. Listing rules reinforce all of this by imposing minimum shareholder numbers, minimum size or net worth thresholds, profitability tests and continuous reporting obligations.

Strip those conveniences away and the differences fall naturally into two groups: features of the company itself, and features of the specific ownership stake being valued.

Company-specific features

Life-cycle stage. Private companies cluster at the two ends of the corporate life cycle far more than listed companies do. Many are early-stage firms with minimal capital, few assets and few employees. Others are stable, mature going concerns. Some are in liquidation.
Size. Within a given industry, private firms tend to be smaller than their listed peers on revenue, assets or any other measure. Smaller scale usually justifies a higher required rate of return, because earnings are more variable: fewer product lines, fewer customers, less diversified end markets, thinner marketing, sales and distribution capability, and in some cases restricted growth prospects because access to capital is limited.
Disclosure quality. Reporting is often less complete and prepared to a less demanding standard than that applied to a listed issuer.
Overlap of ownership and management. Senior managers of private firms frequently hold controlling stakes. This sharply reduces the principal–agent problem that arises when owners and managers are separate people with separate incentives.

The overlap of ownership and management deserves emphasis because its effects run in both directions. Alignment gives managers direct control over strategy and lets them take a long-term view without pressure from outside investors chasing near-term share price gains. This is precisely the logic private equity firms exploit when they take an underperforming listed company private in order to restructure it, divest or bolt on business lines, and later sell the reorganised firm to another private buyer or back to the public market through an initial public offering. But the same alignment removes the external discipline that a market price and a dispersed shareholder register impose, which is exactly why the reported earnings of a private firm so often need correcting.

Family control is a special and very common case. In the German-speaking economies of Germany, Austria and Switzerland, the small and medium-sized enterprises known collectively as the Mittelstand are predominantly family owned and family managed. In Germany they account for over 90 percent of all companies, they employ approximately 58 percent of the workforce, and they produce over a third of everything the country sells domestically in goods and services. Many are globally competitive, export-oriented producers of niche capital goods and electronics. In developing markets, where legal, institutional and financial infrastructure is less established, family firms often draw on pooled capital from family and friends and on reinvested earnings, rely more heavily on trust and personal relationships, and operate in cultures where family members are more likely to keep running the business than to step back into a purely investor role. Succession from one generation to the next is one of the most frequent triggers for a private company valuation.

Stock-specific features

Illiquidity. This is the single most important stock-level difference. The pool of existing and potential buyers for a private stake is small, and that alone reduces the value of the shares relative to an otherwise identical listed company.
Concentration of control. Private companies typically have few shareholders, and control often rests with one investor or a small group. Concentrated control creates the possibility of corporate actions that benefit one group at the expense of another. Above-market executive compensation, or transactions with entities related to the controlling group struck at above-market prices, transfer value away from the non-controlling shareholders. Note that concentration of control can reasonably be classified as a company-level feature as well as a stock-level one.
Restrictions on sale. Shareholder agreements commonly restrict the right to sell, which further reduces the marketability of the interest.

The asymmetry between the two groups matters for the direction of the adjustment. Stock-specific features are almost uniformly negative for value. Company-specific features can cut either way: an early-stage private firm run by its founder may have growth prospects far beyond anything available among listed companies, while a subscale private firm competing in a mature industry against much larger listed rivals is at a straightforward disadvantage. The consequence is that the range of risk and return profiles among private companies is wider than among public companies, and the assumptions two analysts make about the same private company can diverge much further than they would for a listed one. That divergence depends on the purpose of the valuation, the perspective of the analyst, and how much reliable financial information exists.

Example 1 · Worked

Three short cases test whether a stated feature actually distinguishes a private company valuation from a public one.

1. Thunder Corporation is a small privately held household products company. Its shares are held by the original shareholders, none of whom works at the company. Senior management has run operations for the past decade and expects to stay on after any sale. Thunder has no access to public debt markets. Which of the following is the least likely source of valuation differences relative to a listed company: access to public debt markets, principal–agent issues, or company size?

Solution. Principal–agent issues. Thunder is small and cannot reach public debt markets, and both features genuinely affect its valuation relative to a listed peer. But ownership and management at Thunder are separate, exactly as they are at a typical listed company. The classic private company feature of owner and manager being the same person is absent, so the principal–agent dimension is not a point of difference here.

2. Sun and Moon Ltd. is owned and managed by five general partners. Two partners each hold 35 percent of the company and the remaining three each hold 10 percent. Every year an outside expert values each partner’s stake. Which factor explains why the per share value could differ across the partners: concentrated ownership, owner and manager overlap, or concentrated control?

Solution. Concentrated control. The two 35 percent holders can combine to form a 70 percent block and take effective control of the company. A 10 percent holder needs at least two of the other partners to agree before any control position exists. That difference in the ability to reach control attaches a different value to each unit of ownership. Concentrated ownership is not the answer, because the mere size of a partner stake is not what creates the gap. Owner and manager overlap is not the answer either, because every one of the five partners is involved in running the business, so the feature applies equally to all of them.

3. Privacy Group and PT Corp. are alike in size and business model. Both are majority family owned with heavy family involvement in management. The one material difference is that PT Corp. has publicly traded stock and Privacy Group has no public shareholders. Which factor most likely accounts for a significant valuation difference: owner and manager agency problems, illiquidity of shares, or concentrated control?

Solution. Illiquidity of shares. Shareholders in PT Corp. can sell into a liquid public market. Privacy Group shareholders cannot, and they bear the cost of that. Agency problems are unlikely to be severe at either company, because both are family owned and family managed, and the degree of control concentration is not materially different between the two. Liquidity is the one dimension on which the two firms genuinely part company.

Unlike a listed company, which is valued continuously by the market whether anyone asks for it or not, a private company gets valued because someone needs a number for a specific purpose. The purpose shapes the definition of value, the perspective adopted and the adjustments applied, so identifying it is the first step in any engagement. The reasons fall into three practice areas: transactions, compliance and litigation.

Transaction-related valuations

Transactions cover any event that changes the ownership or the financing of the business, and they are the largest single category.

Venture capital financing. Early-stage firms typically raise equity through a sequence of rounds, each tied to reaching a defined milestone. Because future cash flows at that stage are extremely uncertain, the valuation work is often informal and serves mainly as a starting point for negotiation between the company and prospective investors.
Private equity financing. These are growth or buyout transactions. Growth equity funds look for companies that can scale, and they usually take a minority position with the aim of expanding the business quickly. Buyout funds instead acquire majority control and create value by running the business more efficiently and by optimising the balance sheet. Both share the same objective: to exit at a higher valuation than the entry price.
Debt financing. Borrowers and lenders both value the business, to test whether operating cash flow will service existing debt and whether the firm can carry more borrowing in order to restructure, expand or acquire.
Initial public offering. The issuer, its investment banking advisers and prospective primary market investors all prepare valuations when a private company approaches the public equity market. An IPO commonly arises when an early-stage firm outgrows founder and venture capital funding, when a division or line of business is spun out of an existing listed group as a new company, or when a formerly listed business returns to public markets after a period of restructuring under private ownership.
Acquisitions and divestitures. Buying or selling a stand-alone company, a division or a product line is a routine strategy for development-stage and mature firms alike. The valuation may be prepared by the management of the target, by the buyer, or by investment banking advisers in the larger deals.
Bankruptcy. A firm operating under bankruptcy protection needs company-level and asset-level valuations to establish whether it is worth more as a going concern or in liquidation. Where the business remains viable, the valuation is central to restructuring an over-leveraged capital structure.
Share-based incentive compensation. Share-based payment is a transaction between the company and its employees, with accounting and tax consequences on both sides. Stock option grants, restricted stock grants and employee stock ownership plan transactions all require a share value, and for a private company that value has to be appraised rather than observed.

Compliance and litigation valuations

Compliance valuations are those required by law or regulation. Under financial reporting, investment firms need recurring valuations for performance measurement, and any company that has made an acquisition needs them for goodwill impairment testing. Divisions of listed companies are themselves valued using private company techniques. Under tax reporting, corporate restructurings, transfer pricing and property tax matters generate valuation requirements, as do individual matters such as estate and gift taxation in jurisdictions that levy them.

Litigation valuations support legal proceedings: damages claims, lost profits, shareholder disputes and divorce. Litigation may involve a public or a private company, and some disputes run purely between shareholders with no effect at the corporate level at all.

Each practice area demands a different skill set, which is why valuation professionals tend to specialise. Transaction work draws in investment bankers. Compliance work requires detailed command of the relevant accounting or tax rules. Litigation work requires the ability to present and defend an opinion in a legal setting. The purpose also drives the applicable standard of value: the fair market value used for financial or tax reporting can differ substantially from the investment value that a specific acquirer would place on the same business if that acquirer expects synergies from combining it with an existing operation.

The three areas of focus

Whatever the purpose, an analyst applying a standard enterprise-level free cash flow to the firm model to a private company has to make three categories of adjustment. They map neatly onto the numerator, the denominator and the result.

The familiar enterprise discounted cash flow model. Private company adjustments enter through the numerator, the discount rate, and a final adjustment to the resulting value.

Cash flow and earnings adjustments. For a listed company, financial statements prepared under generally accepted accounting principles are equally accessible to every analyst. For a private company, the analyst must first identify and correct balance sheet and income statement items that reflect private ownership rather than the underlying economics of the business, in order to arrive at normalised earnings. These corrections change the numerator.
Discount rate and rate of return adjustments. Market prices for the debt and equity of a private firm do not exist, so the assumptions behind the capital asset pricing model frequently fail. Required returns have to be estimated and then adjusted. These changes affect the denominator.
Valuation discount or premium. Once numerator and denominator are corrected, the stake itself must be considered. A buyer acquiring control gains something a minority holder does not have; a minority holder in an unquoted company bears illiquidity that a public market investor does not. Either consideration is applied to the value that the model produces.

Figure 1: Where a private company valuation departs from a public one

The model itself is unchanged. What is added is a correction stage before the model runs, a correction stage inside the discount rate, and a correction stage after the model produces a number.

Example 2 · Worked

Three questions on classifying a valuation task and locating the adjustment it requires.

1. Jun Nakatami is interviewing at a firm that covers several private business valuation areas and wants to know which practice area handles valuations of share-based payments to employees. Which is it?

Solution. Transactions. A share-based payment to an employee is an issuance of securities, and therefore a transaction between the company and that employee. The issuer needs a value at which to record it.

2. Mohammad al Mollabi covers listed consumer discretionary stocks and has been asked to value a privately held company in the same sector. Which adjustments will he most likely need to make relative to his usual public company work: cash flow adjustments only, discount rate adjustments only, or both?

Solution. Both. The numerator has to be normalised and the denominator has to be re-estimated. Neither correction substitutes for the other.

3. Aliya Chandra is a senior executive at a family-owned firm whose compensation package includes personal use of company assets. In a discounted cash flow valuation of that firm, does this fact primarily affect the numerator, the denominator, or the valuation discount or premium?

Solution. The numerator. Personal use of company assets runs through the income statement as an expense of the business, so it distorts reported earnings. Correcting it is an earnings normalisation, which is a numerator adjustment.

Private companies generally have a shorter run of financial history, apply less demanding accounting standards, and mix personal with business expenses because the owner and the manager are frequently the same person. The starting material is therefore weaker than it is for a listed company, and the analyst has to repair it before using it.

The assurance ladder

Not all financial statements carry the same weight. An audit provides the highest level of assurance. Reviewed financial statements come with an opinion letter containing representations and limited assurances from the accountant, based on a less thorough examination than an audit. Compiled financial statements are the most basic level of all and carry no auditor opinion letter. Reviewed and compiled statements almost always need adjustment before they can be used in a valuation.

What normalisation means here

Analysts use the term normalised earnings in a general sense to mean earnings stripped of cyclicality, seasonality and one-off revenue or expense items. In private company valuation it carries a wider meaning. It covers those items, but it also covers persistent anomalies that arise from private ownership and that prevent any direct comparison with a listed peer. The objective is to arrive at a baseline that can support a forecast of what the business would earn under new ownership, run efficiently at arm’s length.

The critical distinction is between a one-time event and an ongoing distortion. An owner might contribute a property to the company, or take a single large distribution that reduces assets and income. Those are one-off. Ongoing distortions usually arise from related-party transactions. A related party transaction is one between parties that share economic or other interests. An arm’s length transaction is one between independent parties each acting in their own self-interest, and it is recorded at or close to fair market value. Two families of private company transactions routinely fail the arm’s length test:

Transactions between the company and its controlling owners, most often involving compensation or non-operating assets.
Transactions between separate private entities that share the same controlling shareholders, covering goods, services, financing, or the use of intangible property such as licences and cost-sharing arrangements.

The adjustments run through the income statement in a predictable pattern. Revenue may need repricing where sales between affiliates are not at market terms. Cost of goods sold may need the same treatment. Operating expenses commonly carry related-party compensation and the cost of real estate or other assets used on non-market terms. Depreciation and amortisation may be distorted by asset values or ownership arrangements. Taxes must then be recalculated on the adjusted taxable income. Dividends and distributions may need adjustment where an owner-manager takes value out of the business in a form a listed company would not use.

Above-market compensation is the most common item and the easiest to see, because it reduces both taxable income and tax expense. Excessive employee benefits belong in the same category. Personal expenses charged to the company, assets held for personal use, and excess entertainment all need reconciling. Personal residences, aircraft and luxury or excessive personal use of company vehicles are frequent culprits. Life insurance and loans to shareholders merit review whenever they appear.

The correction does not always run in the same direction. Where a private company reports thin profits or losses, expenses may be understated and income overstated, because an active owner-manager is taking less than the market rate of compensation for the work being done. Normalising in that case reduces earnings.

Where more than one shareholder is involved, or where several private companies share the same owners, the analyst must also consider transfers of value that never appear in either set of financial statements. Above-market compensation or expenses can hand a controlling shareholder a disproportionate return at the expense of the others. A private company that buys inventory, uses assets or receives services from an affiliated company at below fair market value will look more profitable than it would if it dealt with an independent third party.

Real estate: a recurring special case

Real estate used by a private business is the classic ongoing distortion. Where a private company owns the property it occupies, many analysts separate the real estate from the operating business. That means removing the revenues and expenses associated with the property from the income statement, and then adding a market rental charge for the use of the space. The resulting earnings figure describes the business operations excluding the real estate, and the property itself becomes a non-operating asset of the entity. The separation is justified because the operating business and the property have different risk profiles and different growth expectations, so blending them into one cash flow stream and one discount rate misprices both.

Example 3 · Worked

Cheryl Xin is the sole shareholder and chief executive of Fyt for Life, Inc. (FLI), a producer and distributor of outdoor fitness products aimed at a young, active customer base. Dev Khan is a private equity analyst assessing a purchase of FLI. He identifies the following facts about the most recent fiscal year.

Xin was paid SGD 1.5 million for the year. Khan’s compensation consultant considers SGD 500,000 the appropriate normalised expense for a chief executive of a company like FLI. Compensation sits within selling, general and administrative expenses.
Certain corporate assets, specifically a ranch property and a condominium, are in Khan’s view not required for core operations. Expenses relating to them for the year were SGD 400,000, made up of SGD 300,000 of operating costs such as upkeep, property taxes and insurance recorded in SG&A, plus SGD 100,000 of depreciation. All other asset balances, cash included, are believed to be at the level operations require.
FLI carried debt of SGD 2,000,000 at an interest rate of 7.5 percent, below what would be considered an optimal level of borrowing. Because reported interest expense does not represent an optimal charge, Khan works with operating income after taxes, an earnings measure that excludes interest expense entirely.

FLI operating income after taxes, as reported

Line item, year to 31 December (SGD)	As reported
Revenue	50,000,000
Cost of sales	30,000,000
Gross profit	20,000,000
Selling, general and administrative	5,000,000
EBITDA	15,000,000
Depreciation and amortisation	1,000,000
EBIT	14,000,000
Pro forma tax at 17 percent	2,380,000
Operating income after tax	11,620,000

1. Identify the adjustments Khan should make to the reported figures in order to estimate normalised operating income after taxes.

Solution. Two adjustments, affecting three lines.

Compensation. SG&A carries SGD 1,500,000 of chief executive pay where SGD 500,000 is the market rate under professional management. Reduce SG&A by SGD 1,500,000 − SGD 500,000 = SGD 1,000,000.

Non-operating assets. The ranch and the condominium are not required by the business, so the expenses associated with them are removed as if the assets had been sold. Two lines move: SG&A falls by a further SGD 300,000, and depreciation and amortisation falls by SGD 100,000.

2. Construct the pro forma statement of normalised operating income after taxes.

Solution. SG&A becomes 5,000,000 − 1,000,000 − 300,000 = SGD 3,700,000, so EBITDA rises to 20,000,000 − 3,700,000 = SGD 16,300,000. Depreciation and amortisation becomes 1,000,000 − 100,000 = SGD 900,000, giving EBIT of 16,300,000 − 900,000 = SGD 15,400,000. Tax at 17 percent is 0.17 × 15,400,000 = SGD 2,618,000, leaving operating income after taxes of SGD 12,782,000.

FLI operating income after tax, normalised

Line item, year to 31 December (SGD)	As adjusted
Revenue	50,000,000
Cost of sales	30,000,000
Gross profit	20,000,000
Selling, general and administrative	3,700,000
EBITDA	16,300,000
Depreciation and amortisation	900,000
EBIT	15,400,000
Pro forma tax at 17 percent	2,618,000
Operating income after tax	12,782,000

Normalisation lifted after-tax operating income by SGD 12,782,000 − SGD 11,620,000 = SGD 1,162,000, which is the SGD 1,400,000 of pre-tax expense removed (SGD 1,000,000 of compensation, SGD 300,000 of property operating cost and SGD 100,000 of depreciation), net of tax at 17 percent.

3. Suppose instead that Xin takes no salary at all and receives the SGD 1.5 million as a dividend, with all reported figures otherwise unchanged. How would FLI’s earnings have to be normalised?

Solution. Normalised earnings would fall. The income statement would then carry no chief executive compensation expense at all, yet a buyer would have to pay someone to do the job. The appropriate charge is the same SGD 500,000 market rate, and it must be deducted. Paying the same total amount as a dividend rather than as salary does not make the position cost-free; it merely moves the cost off the income statement, and the normalisation puts it back.

4. Suppose FLI’s products are manufactured in a building owned by Xin’s family, and FLI records no expense for using it. How should Khan treat this?

Solution. Add a market rental charge, which reduces normalised earnings. The fact that FLI does not own the building is irrelevant: an arm’s length occupier would pay rent, so a market-determined rental rate belongs in the normalised income statement. Restating the balance sheet alone would not fix an income statement that omits a real cost of operations.

Example 4 · Worked

Chandra Consolidated is a family-owned private group with two principal operating units. Chandra Holdings is a long-established commercial property company. Chandra Shops, founded only recently, runs luxury retail stores. Chandra Holdings owns several office buildings in major business centres across India. Seeing growing demand for luxury goods among urban white-collar workers, and an opportunity to use ground floor space that is poorly suited to corporate leases, the family set up Chandra Shops to run luxury retail stores in that space.

Chandra Shops pays directly for operating expenses other than rent. There is no formal agreement between the two units and no payment passes between them for the use of the retail space.

1. How should an analyst normalise the earnings of the two Chandra businesses in respect of the retail space?

Solution. Paying only the non-rent operating costs badly understates the true opportunity cost of occupying the space. Chandra Shops reports no rental expense, and Chandra Holdings reports no rental revenue from that floor area, so both sets of accounts are wrong in opposite directions.

The analyst should establish the market cost of comparable retail leases in the same business centres and add that market rental charge as a recurring expense in the income statement of Chandra Shops. The identical amount should appear as rental income in the income statement of Chandra Holdings. The transfer is internal to the group, so consolidated earnings do not change, but the earnings of each unit do.

2. The family is considering selling a minority interest in Chandra Shops to a business partner with more experience in luxury retail. What effect does normalisation have on the valuation of Chandra Shops?

Solution. It lowers it. Under-reporting rent flatters the retail business, so normalised earnings for Chandra Shops fall once the market rental charge is imposed, and its valuation falls with them. The mirror image applies to Chandra Holdings: its normalised earnings rise and so does its value. Unless the family normalises the costs of the retail company and the revenues of the real estate company to reflect a proper rental transfer, it will sell a stake in Chandra Shops at a price built on earnings the business never really produced.

Two general points close this section. First, the effect of transactions between related entities must be considered for private company valuations, and the same issue arises at some listed companies too. Second, all the adjustments that apply to public companies apply here as well: inventory accounting methods, depreciation assumptions, and decisions to capitalise rather than expense a cost all remain live questions in a private company valuation.

Normalising earnings fixes the historical base. Turning that base into a forecast of cash flow raises a second set of problems. Two cash flow definitions carry over unchanged from public company valuation:

Free cash flow to the firm (FCFF) is cash flow at the enterprise level, available to debt holders and equity holders together.
Free cash flow to equity (FCFE) is cash flow available to shareholders only, and it values equity directly.

Three challenges are specific to private companies: the nature of the interest being valued, the sheer width of the range of possible futures, and the involvement of management in producing the forecast.

The interest being valued drives the assumptions

A listed company valuation is nearly always performed from the standpoint of a non-controlling shareholder. For a private company, the equity interest being appraised and the intended use of the appraisal jointly determine the appropriate definition of value. The cash flow assumptions that belong in a valuation of the entire equity of a business, where the buyer can change compensation, capital structure and distribution policy, are not the assumptions that belong in a valuation of a small minority stake whose holder can change nothing.

Uncertainty wide enough to need scenarios

For a mature business, cash flow projections rest on a band of growth and profitability assumptions and a single forecast is defensible. For many private companies the range of outcomes is too wide for that. Over a single forecast period a privately held firm may go public, be acquired, continue as a private operator, or fail. An early-stage company may face a proof of concept milestone or a regulatory approval on which the entire business depends. In those cases the appropriate method is scenario analysis: value the firm under each outcome, weight by the probability of that outcome, and discount.

Figure 2: A two-stage scenario tree for a regulatory approval

Only the upper path survives to a second decision point. The two paying outcomes each carry a joint probability of 0.80 × 0.40 = 0.32, and the remaining 0.36 of probability weight attaches to outcomes worth nothing.

Example 5 · Worked

Nano Beta S.r.L. is a private Italian biotech firm developing nanoparticles designed to overcome the limitations of conventional cancer treatment and drug resistance. It is seeking approval from the European Medicines Agency for a novel immunotherapy approach, expecting preliminary approval in one year and final approval in two. A venture capital analyst has built the scenario tree in Figure 2. The company is assumed to be worth nothing if the product is not approved. The weighted average cost of capital is 15 percent and each surviving scenario is modelled as a constant growth perpetuity.

Broad applicability. The therapy is applied to several widespread forms of cancer. Annual FCFF is expected to be EUR 200 million growing in perpetuity at 5 percent.
Limited applicability. Efficacy proves narrow and the therapy is used only for a few rare cancer types. Annual FCFF is expected to be EUR 50 million growing at 2 percent.

1. Solve for firm value at t = 2 under each scenario.

Solution. Apply the constant growth perpetuity, with next period cash flow equal to current cash flow grown one period.

Broad applicability: EUR 200 million × 1.05 ÷ (0.15 − 0.05) = EUR 210 million ÷ 0.10 = EUR 2.1 billion.
Limited applicability: EUR 50 million × 1.02 ÷ (0.15 − 0.02) = EUR 51 million ÷ 0.13 = EUR 392,307,692.

2. Calculate the probability-weighted firm value at t = 2 and the value today.

Solution. Each paying branch requires preliminary approval and then that specific final outcome, so its probability is 0.80 × 0.40 = 0.32. Both branches share the same joint probability.

Weighted value at t = 2 = (0.32 × EUR 2.1 billion) + (0.32 × EUR 392,307,692) = EUR 672,000,000 + EUR 125,538,462 = EUR 797,538,462.

Discount two years at the 15 percent WACC:
EUR 797,538,462 ÷ (1.15)² = EUR 797,538,462 ÷ 1.3225 = EUR 603,053,657.

The product line is worth approximately EUR 603 million today. Notice that the two scenarios differ not only in the level of operating cash flow but in the assumed growth rate, and the growth assumption does much of the work: a fourfold difference in annual cash flow, EUR 200 million against EUR 50 million, becomes a difference of more than five times in value, because the broad case also carries the higher perpetual growth rate.

3. Researchers now believe preliminary approval is less likely but that broad applicability is more likely if approval is obtained. The analyst cuts the probability of preliminary approval from 80 percent to 60 percent, raises broad applicability from 40 percent to 60 percent, and cuts limited applicability from 40 percent to 20 percent. How does the estimated value change?

Solution. The scenario values at t = 2 are unchanged. Only the weights move. Broad applicability now carries 60% × 60% = 36% against 32% before, while limited applicability falls to 60% × 20% = 12% against 32% before.

Weighted value at t = 2 = (0.36 × EUR 2.1 billion) + (0.12 × EUR 392,307,692) = EUR 756,000,000 + EUR 47,076,923 = EUR 803,076,923.

Value today = EUR 803,076,923 ÷ 1.3225 = EUR 607,241,530.

That is an increase of approximately EUR 4.2 million. The large fall in the probability of getting through the first gate is almost exactly offset by the shift in weight towards the far more valuable of the two surviving outcomes.

Management involvement in the forecast

Managers of a private company know far more about it than any outside analyst. Either management prepares the cash flow forecast with input from the appraiser, or the appraiser prepares it and consults management as required. Neither arrangement is neutral. An analyst should be alert to the direction in which management incentives push the forecast: values tend to be overstated where goodwill impairment testing is at stake, and understated where the exercise supports the grant of incentive stock options. The analyst should also check that the projections make adequate provision for the capital the business will need in future, since forecasts prepared by operators frequently understate reinvestment requirements.

Public company valuation uses observed market prices for debt and equity to weight the cost of capital, and it uses the capital asset pricing model to obtain the cost of equity. Both starting points are recalled below, because the private company adjustments are defined relative to them.

Weights are the proportions of debt and equity in the target capital structure, measured at market value.

The cost of debt entering the WACC is after tax, because interest is deductible against taxable income.

The capital asset pricing model. A single premium, scaled by beta, is added to the risk-free rate.

Neither market prices nor the assumptions behind the CAPM survive the move to a private company intact. Where a beta is needed, the usual route is to take betas of comparable listed companies and adjust them so that they match the leverage of the private firm, a procedure set out later in this lesson. Four further issues arise.

Size premiums

Size premiums are applied to private company discount rates far more often than to public company discount rates, and the effect is to produce a small size discount in the resulting value. The practice needs care. Size premium estimates are usually derived from public company data on the smallest market capitalisation segments, and part of the excess return observed in those segments reflects financial or operating distress rather than size as such. If the company being valued is small but sound, importing a premium estimated on a distressed sample overstates its required return.

Debt availability and the cost of debt

Estimating debt capacity correctly is a persistent problem. A private company generally has less access to debt financing than a comparable listed company. Reduced access pushes the firm towards equity funding, and because equity is more expensive than debt, that pushes the weighted average cost of capital up. On top of that, a smaller private company may face greater operating risk, which raises the cost of the debt it can obtain. Both effects work in the same direction, and both must be reflected when a WACC is being built for an FCFF valuation.

The acquisition context

The rule established for acquisitions elsewhere in the curriculum is that the cost of capital used to evaluate a target should reflect the target’s own capital structure and the riskiness of the target’s cash flows. The buyer’s cost of capital is irrelevant. When a large, mature company acquires a small, risky one, the buyer will normally have the lower cost of capital, and using it would produce a higher valuation. From the seller’s point of view that would be very welcome, and that is precisely the problem: the buyer would then be paying the seller for value the buyer itself brings to the transaction in the form of cheaper capital.

Projection risk

Less is known about the operations and the business model of a private company than about those of a comparable listed company, and that ignorance introduces genuine uncertainty into the projections. It can justify a higher required return. A related point is that private company management often has less experience in forecasting financial performance, so the projections handed to the analyst may be excessively optimistic or excessively pessimistic. Any discount rate adjustment made for projection risk or for inexperience in forecasting is unavoidably a matter of judgement, and it should be labelled as such rather than presented as a measured quantity.

Why a lower WACC can be bad news for the buyer

A private company financed with less debt than is optimal has a WACC above the level it could achieve. Recapitalising it lowers the WACC and raises the calculated value. If a private equity buyer prices its offer off the optimal, lower WACC, it pays the seller today for a change the seller never made and that the buyer will have to execute itself after completion. Value moves from buyer to seller for nothing given in return. The same arithmetic works in reverse for the seller: agreeing a price built on the existing, suboptimal capital structure hands the improvement to the buyer for free. Which WACC is correct depends on what is being appraised, and the answer for a sale of the whole company is generally the optimal structure, since any competent acquirer both could and would establish it.

Whether the CAPM is the right tool for a private company at all is a fair question. Two objections carry weight. First, a small firm with little prospect of listing or of being bought by a listed company may simply not be comparable to the public companies from which market-based beta estimates are drawn. Second, beta measures non-diversifiable risk on the assumption that investors hold well-diversified portfolios, and buyers and sellers of private businesses routinely violate that assumption, since much of their wealth sits in the one company. An undiversified owner is exposed to the total risk of the business, not just its market risk, and arguably deserves a higher premium than beta alone suggests.

Both objections are addressed by modifying rather than abandoning the model. Two alternatives are used.

The expanded CAPM

The expanded CAPM keeps the beta-scaled market premium and adds two further premiums, one for small size and one for company-specific risk.

The company-specific premium is the most subjective element in the whole exercise. It is set on the basis of industry and company analysis together with a review of comparable listed companies, which in this context are usually called guideline public companies. Dependence on a single key individual, customer concentration and litigation exposure are typical justifications for it.

The build-up approach

The build-up approach constructs the required return as a stack of premiums added to the risk-free rate, with no beta anywhere in the calculation.

Analysts reach for it when comparable public companies are unavailable or when their comparability is doubtful, which is exactly the situation in which a borrowed beta would be least trustworthy. Because the equity risk premium enters unscaled, the model implicitly assumes a beta of one. An industry risk premium, which may be positive or negative, is often included in place of the beta adjustment. The consequence is worth stating plainly: if the true beta of the business exceeds one, the build-up approach will produce a lower required return than the expanded CAPM even though it appears to contain more premiums, and if the true beta is below one it will produce a higher one.

Example 6 · Worked

Dev Khan must choose a discount rate for FLI. Chief executive Xin explored various sources of debt financing to run FLI at a lower overall cost of capital, but the company has operated with very little debt. Analysis of listed companies in the industry produced several guideline public companies. Khan settles on the following estimates.

FLI discount rate inputs

Input	Estimate
Risk-free rate	3.8%
Equity risk premium	5%
Beta from listed comparables	1.1
Small stock premium	3%
Company-specific risk premium	1%
Industry risk premium (build-up only)	0%
Pre-tax cost of debt	7.5%
Debt to total capital, comparable companies	20%
Debt to total capital, optimal for FLI	10%
Debt to total capital, FLI actual	2%
Combined corporate tax rate	17%

The small stock premium reflects FLI’s smaller size and less diversified operations relative to the listed comparables. The company-specific premium of 1 percent reflects the key role of Xin herself; no other unusual risk was identified. No industry factor was judged material, hence the zero industry premium. The optimal debt ratio of 10 percent sits below the 20 percent observed at the comparables because FLI is smaller and riskier as a stand-alone business.

1. Calculate FLI’s required return on equity using the CAPM.

Solution. r_e = 3.8% + 1.1 × 5.0% = 3.8% + 5.5% = 9.30%.

2. Calculate FLI’s required return on equity using the expanded CAPM.

Solution. Add the small stock and company-specific premiums to the CAPM result.

FLI expanded CAPM: required return on equity

Component	Rate
Risk-free rate	3.8%
CAPM equity risk premium (1.1 beta × 5.0%)	5.5%
Small stock premium	3.0%
Company-specific risk adjustment	1.0%
Indicated required return on equity	13.3%

The result is 13.3%.

3. Calculate FLI’s required return on equity using the build-up method.

Solution. Sum the premiums on top of the risk-free rate, with no beta adjustment applied to the equity risk premium.

FLI build-up method: required return on equity

Component	Rate
Risk-free rate	3.8%
Equity risk premium	5.0%
Small stock premium	3.0%
Industry risk premium	0.0%
Company-specific risk adjustment	1.0%
Indicated return on equity	12.8%

The result is 12.8%. Since beta of 1.1 is close to one, any industry risk adjustment would be small in magnitude, which is consistent with setting it to zero here.

4. Discuss the choice of capital structure weights for FLI’s WACC.

Solution. For a valuation connected with a possible sale of FLI, optimal capital structure weights are appropriate, because an acquirer would be both able and motivated to move the company to its optimum. FLI currently carries less debt than is optimal, so its WACC today is higher than it needs to be. Note the second point though: the debt weight observed at large listed comparables may itself exceed what is optimal for FLI. Large listed firms have far better access to public debt markets, and FLI’s small size raises its risk relative to them. Both factors raise FLI’s cost of debt relative to a large listed peer and therefore lower its optimal debt weight.

5. Calculate the WACC using FLI’s current capital structure and a 13 percent cost of equity.

Solution. The after-tax cost of debt is 7.5% × (1 − 0.17) = 7.5% × 0.83 = 6.225%.

FLI WACC: current capital structure

Component	Value
Pre-tax cost of debt r	7.5%
Tax rate complement (1 − t)	0.83
After-tax cost of debt r_d	6.225%
Weight w_d	0.02
Weighted cost of debt	0.1%
Cost of equity r_e	13.0%
Weight w_e	0.98
Weighted cost of equity	12.7%
WACC	12.9%

Carrying the arithmetic without intermediate rounding, 0.02 × 6.225% + 0.98 × 13.0% = 0.1245% + 12.74% = 12.9% to one decimal place. With only 2 percent of capital in debt, the WACC sits almost on top of the cost of equity.

6. Calculate the WACC using FLI’s optimal capital structure and the same 13 percent cost of equity.

Solution. The optimal structure carries a higher proportion of the cheaper financing, so the WACC falls.

FLI WACC: optimal capital structure

Component	Value
Pre-tax cost of debt r	7.5%
Tax rate complement (1 − t)	0.83
After-tax cost of debt r_d	6.225%
Weight w_d	0.10
Weighted cost of debt	0.62%
Cost of equity r_e	13.0%
Weight w_e	0.90
Weighted cost of equity	11.7%
WACC	12.3%

That is 0.10 × 6.225% + 0.90 × 13.0% = 0.6225% + 11.7% = 12.3%. Rounded figures are used throughout this example.

Figure 3: Building FLI’s required return on equity

The build-up staircase ends 0.5 percentage points below the expanded CAPM line for one reason only: the expanded CAPM scales the 5.0 percent equity risk premium by a beta of 1.1, adding 5.5 percent instead of 5.0 percent. The industry premium, the extra term the build-up approach offers, contributes nothing here.

Reading the results together

Six numbers now describe the same company, and a candidate must be able to explain every gap between them.

FLI cost of capital estimates

Estimate	Basis	Result
Cost of equity	CAPM	9.3%
Cost of equity	Expanded CAPM	13.3%
Cost of equity	Build-up approach	12.8%
Cost of equity adopted	Judgement	13.0%
WACC	FLI actual debt ratio	12.9%
WACC	FLI optimal debt ratio	12.3%

Expanded CAPM against CAPM, a gap of 4.0 percentage points. The size premium of 3 percent accounts for the majority of it and the company-specific premium for the remaining 1 percent. The industry risk premium plays no part, because it does not appear in either model.
Build-up against expanded CAPM, a gap of 0.5 percentage points the other way. The build-up approach contains one extra term, the industry premium, but that term was set to zero. The difference therefore comes entirely from the absence of a beta adjustment. Beta of 1.1 adds 0.5 percent to the expanded CAPM result. There is no difference in the assumed market return between the two models, which is a common trap in the answer choices.
Optimal WACC against actual WACC, a gap of 0.6 percentage points. This gap exists because FLI carries less debt than is optimal, not more. It creates the acquisition problem set out in the reveal above: pricing off the lower, optimal WACC transfers value to the seller for a capital structure change that the buyer will have to make itself.

A public company valuation normally assumes an exchange of liquid shares between a non-controlling buyer and a non-controlling seller. A private company valuation may assume neither. The stake may confer control, or it may confer none, and in either case the shares cannot readily be sold. Both differences are handled after the model has produced a value, by moving between levels of value.

The levels of value

The highest possible value indication for a business is its investment value to a strategic buyer, an acquirer able to capitalise on synergies. Such a buyer intends to use a controlling stake to raise revenue or cut costs beyond what current expectations imply. The highest bidder for a private firm is typically the investor who sees the greatest synergy potential and who is also able and willing to carry the execution risk of realising it.

A financial buyer may still pay a premium for control, but it is a smaller one. Such a buyer either cannot identify synergies, or can identify them but lacks the operational or management expertise to capture them, or has too little appetite for the risk involved. Financial buyers include investors looking to bring in a synergistic buyer or partner later, and existing minority shareholders who would benefit from control of the business as it currently runs.

Below those two sits the value of a non-controlling interest that is readily marketable, which is broadly the price at which shares of comparable listed companies trade. Below that again sits the non-controlling, non-marketable interest, which is what a minority holder in a private company actually owns.

Figure 4: The levels of value

Moving down the ladder is a discount and moving up is a premium. The marketable minority level is the one an observed public market price describes, which is why comparable company multiples land there and have to be adjusted in both directions depending on what is being valued.

The application of these premiums and discounts is fact specific and depends heavily on whether the valuation forms part of a competitive bidding process, so estimates vary a great deal between practitioners. Part of the variation comes from the difficulty of finding genuinely comparable data with which to quantify a discount. The rest comes from differences of interpretation over the size of the shareholding and how the remaining shares are distributed, the relationship between the parties, the laws protecting minority shareholders in the relevant jurisdiction, and how closely a minority investor is aligned with the controlling shareholder.

The single most important practical consideration is the timing of a potential liquidity event. An interest in a private company that is actively pursuing an IPO or a strategic sale can reasonably be valued with modest discounts. An interest in a private company that pays no dividends and has no prospect of any liquidity event at all requires much larger ones.

Discount for lack of control

A discount for lack of control (DLOC) is a deduction from the pro rata share of the value of 100 percent of an equity interest, reflecting the absence of some or all of the powers of control. Lacking control matters because the holder cannot appoint directors, officers or management, and therefore cannot distribute cash, buy or sell assets, arrange financing, or influence any other corporate action that would affect the value of the investment, the timing of distributions and the eventual return.

The effect on value is nonetheless uncertain, and a DLOC is not automatic. What supports one is the existence of disproportionate returns, meaning that controlling shareholders raise their own returns through above-market compensation and similar actions that reduce what is left for minority holders. A private company preparing for an IPO or a strategic sale is less likely to have a controlling group behaving that way, although pre-IPO investors do sometimes retain a concentration of control relative to ordinary shareholders.

Data for estimating a lack of control discount are thin and interpretations differ widely. For interests in operating companies, control premium data drawn from acquisitions of public companies are commonly used, and the same factors that inform a control premium inform the discount. The two are linked by a simple identity.

A control premium is expressed on the minority value; the discount is expressed on the control value. They are not the same number.

Example 7 · Worked

Andrea Miceli is valuing a non-controlling minority interest in Everfloat Ltd., a private UK company whose shares have not traded recently. She estimates the unadjusted value of Everfloat at GBP 1.65 billion and uses data on similar listed companies to estimate a control premium of 15 percent.

Calculate Everfloat’s DLOC and its adjusted value.

Solution. DLOC = 1 − (1 ÷ 1.15) = 1 − 0.8696 = 0.130, or 13.0 percent.

Adjusted value = GBP 1.65 billion × (1 − 0.13) = GBP 1.4355 billion.

Note that a 15 percent control premium does not translate into a 15 percent minority discount. Applying the premium to the smaller base gives a smaller absolute adjustment when read as a discount from the larger base.

Whether a DLOC applies at all depends on the perspective embedded in the valuation, and this is where candidates most often go wrong. A discounted cash flow value is generally accepted as a controlling interest value if the cash flows and the discount rate were themselves estimated on a controlling interest basis. If control cash flows were not used, or the discount rate does not reflect an optimal capital structure, then the resulting value already reflects a lack of control and applying a DLOC on top of it would double count.

Discount for lack of marketability

A discount for lack of marketability (DLOM) is a deduction from the value of an ownership interest reflecting the relative absence, compared with a listed company, of a liquid market for the shares. It is applied frequently in valuing non-controlling interests in private companies. A DLOM is conceptually distinct from a DLOC, but the two are usually linked in practice: if a valuation is being conducted on a non-controlling interest basis, a marketability discount is typically appropriate as well.

The key variables are the prospects for liquidity, which depend on market conditions, contractual restrictions on transfer, the size of the pool of potential buyers, and the concentration of ownership. Even in the most benign case, an illiquid investment carries an opportunity cost, because the funds committed to it cannot be redeployed.

Three families of data are used to quantify a DLOM.

Restricted stock transactions. Restricted stock is otherwise identical to freely traded stock of a listed company; only the trading restriction differs. The comparison is imperfect, because restricted stock usually becomes freely tradable quite soon whereas a private company interest may never do so. The most useful observations come from private sales of restricted blocks large enough to exceed normal public trading activity in the stock, where the discount reflects the price risk of holding a position that cannot be moved quickly.
Pre-IPO transactions. Comparing the price of stock sold shortly before an IPO with the IPO price gives another read. For early-stage or high-growth companies the gap partly reflects a genuine increase in value as risk and uncertainty fall with the progress of the business. As the range of possible future cash flows narrows, the implied marketability discount tends to fall too.
Option pricing models. The right to sell at a fixed price is what a put option provides, so the premium on an at-the-money put can stand in for the value of marketability. The put is priced at the money, and the premium expressed as a percentage of the share value gives the DLOM estimate.

Example 8 · Worked

To estimate a DLOM for Everfloat Ltd., Andrea Miceli identifies Shipline PLC, a non-dividend-paying stock, as the closest listed comparable. Shipline trades at GBP 50 and Miceli assumes a six-month horizon. The risk-free rate is 5.0 percent and observed implied volatility for Shipline is 60 percent.

Calculate the DLOM implied by an at-the-money put option.

Solution. The option is struck at the money against the six-month forward price, not the spot price:
GBP 50 × e^{(0.5 × 0.05)} = GBP 50 × 1.02532 = GBP 51.27.

Pricing a six-month put at that strike in a Black–Scholes model with 60 percent volatility gives a premium of GBP 8.40.

Express the premium as a percentage of the share value:
GBP 8.40 ÷ GBP 50 = 16.8 percent.

That is the estimated DLOM for Everfloat.

The option approach has one clear advantage: the volatility input lets the analyst address the perceived risk of the specific private company directly. In restricted stock and pre-IPO studies, volatility is only one of many influences on the observed discount and cannot be isolated. Volatility can be estimated from the historical or implied volatility of listed companies, or read out of the prices of traded options.

Two objections nonetheless stand against it. A put option provides price protection for the life of the option, but it does not provide liquidity: the holder still owns an asset that cannot be sold, and has merely insured its price. And a put leaves the holder free to enjoy any increase in the share price, whereas genuine illiquidity does not, so the option is not an exact model of what is being measured.

Beyond control and marketability, other discounts occasionally require consideration: key person discounts, portfolio discounts where the assets held are not homogeneous, and discounts for non-voting shares.

Combining the two discounts

When both a DLOC and a DLOM apply, they are applied in sequence and the total is multiplicative, not additive. The order matters conceptually even though multiplication commutes: first move from a controlling to a non-controlling basis, then from a marketable to a non-marketable basis.

Example 9 · Worked

Miceli has established a DLOC of 13 percent for Everfloat and a DLOM of 16.8 percent from the option analysis.

1. Calculate the total valuation discount for Everfloat.

Solution. Total discount = 1 − (1 − 0.13) × (1 − 0.168) = 1 − 0.87 × 0.832 = 1 − 0.72384 = 0.276, or 27.6 percent.

Adding the two discounts would give 29.8 percent, overstating the reduction by more than two percentage points, because the marketability discount applies to a value that has already been reduced for lack of control.

2. Starbeam LLC is a private company owned entirely by its managers. It wants to raise funds by selling an equity stake while keeping control. A valuation expert recently valued Starbeam on the basis of its current status as a 100 percent management-owned company. Which premium or discount should be applied to that recent valuation in order to value the proposed stake?

Solution. A DLOC only. The recent valuation already sits at the controlling, non-marketable level: it reflects the controlling position of management and it already reflects a DLOM, because Starbeam is a private company. Applying a DLOM again would double count it. Moving from that existing figure to the value of a non-controlling stake requires exactly one further step down the ladder, the discount for lack of control.

3. While looking for a buyer for the minority stake, Starbeam management is approached by a well-known public markets investor who habitually buys controlling stakes in well-managed private companies and leaves management in place. If this investor bids for control, should the offer include a premium over the recent valuation, and of what kind?

Solution. Yes, a financial control premium. It is tempting to answer that no premium is needed, since the recent valuation already reflected management’s controlling position. But management currently holds control and would have to be persuaded to give it up, and that requires a premium over the recent figure. Because this investor is a financial buyer who leaves management in place, there are unlikely to be synergies on which a larger, synergistic control premium could be based.

4. Starbeam eventually sells a non-controlling stake. If a typical control premium is 30 percent and a typical DLOM is 20 percent, what is the total discount for that stake relative to listed comparables?

Solution. First convert the control premium into a discount. DLOC = 1 − (1 ÷ 1.30) = 23.1 percent, not 30 percent. Then combine:
Total discount = 1 − (1 − 0.231) × (1 − 0.20) = 1 − 0.769 × 0.80 = 1 − 0.6154 = 38.5 percent.

The two common errors both produce plausible-looking wrong answers. Using 30 percent as the DLOC and combining multiplicatively gives 44.0 percent. Adding 23.1 percent and 20 percent gives 43.1 percent. Only the correct conversion followed by the correct combination gives 38.5 percent.

Why the premium and the discount are different numbers

A control premium is quoted as a percentage uplift applied to the minority value, so a 30 percent premium takes 100 to 130. The corresponding discount is quoted as a percentage reduction applied to the control value, so it must take 130 back to 100, which is a fall of 30 divided by 130, or 23.1 percent. The two describe the identical gap measured from opposite ends. Whenever a question gives you a control premium and asks for a discount, or the reverse, the conversion is compulsory, and the answer choices will always include the unconverted figure.

The approaches available for a private company are conceptually the same as those used for a listed one. The labels differ, and so do the details of application, because the availability and reliability of information differ, as do the confidence an analyst can place in the data, the stage of the company in its life cycle, and the industry it operates in. Three approaches exist.

The income approach is the discounted cash flow approach under another name. Within it sit two variants that are specific to private company practice: the capitalised cash flow method, which treats the business as a growing perpetuity, and the excess earnings method, which is conceptually the residual income approach applied to intangible assets.
The market approach values the company on a ratio of a market-based price to a monetary variable, compared against companies with similar features. It is the method of comparables, with multiples built either on share price or on enterprise value.
The asset-based approach values the company as the value of its underlying assets less the value of the related liabilities.

The classification is worth holding on to. Discounted cash flow models and asset-based models are both absolute valuation models: each produces a value from the characteristics of the subject company alone. The market approach is a relative valuation model, because it prices the subject company against enterprise or price multiples observed on a comparable company.

Which approach fits which situation

The market approach relies on data generated in real transactions, which is why it is the most frequently used of the three and why many practitioners regard it as conceptually preferable to the income and asset-based approaches for private companies. It dominates compliance and litigation work, and it is routinely used alongside the other approaches when an analyst triangulates towards a transaction value. Its primary assumption is a demanding one: that the transactions supplying the pricing evidence really are reasonably comparable to the private company being valued.

The income approach comes into its own where the analyst has enough information to forecast cash flows over several periods, or where cash flow is expected to grow at different rates in different phases. Where projections are unavailable and market pricing evidence from similar listed companies or transactions is thin, the capitalised cash flow method offers a defensible alternative that needs only a normalised cash flow, a discount rate and a growth rate.

The asset-based approach is the natural choice for a company whose value is essentially the sum of its assets: an investment holding entity, a business in liquidation, or a firm whose operations generate returns below the cost of capital so that the going concern is worth less than the pieces. It is least appropriate for a going concern whose value rests on intangibles and future growth, because a balance sheet cannot capture them.

Terminal value inside the income approach

An FCFF model discounts a finite series of forecast cash flows at the WACC and adds a discounted terminal value.

The terminal value term represents firm value at the end of the explicit forecast period of n years.

FCFF is the flexible measure. It can be applied across different capital structures and it suits a controlling investor, because such an investor has influence over earnings distribution and debt policy. As with a listed company, the terminal value can be read either as the expected sale price at the end of a finite holding period, or as the point beyond which individual cash flow estimates become too uncertain to forecast and a perpetuity with constant growth takes over. Three routes to a terminal value are used in private company work: a capitalised cash flow, a market-based multiple, and an excess earnings calculation. Private companies frequently have limited financial data, significant intangible assets, or an uncertain growth path because they are early in the life cycle, and the choice among the three routes usually turns on which of those constraints binds hardest.

The capitalised cash flow method

The capitalised cash flow method (CCM) values a company as a growing perpetuity under an assumption of stable growth. It is used less often for listed companies, for larger private companies, and in acquisition or financial reporting contexts. Where it earns its place is in valuing a private company for which no projections exist and for which market pricing evidence from similar listed companies or transactions is limited. In its basic form, using expected FCFF as the cash flow measure, the capitalised cash flow is a perpetuity discounted at the WACC less the constant growth rate.

Expected FCFF can be built from expected after-tax EBIT and the firm’s reinvestment rate, the rate of investment in working capital and long-term assets that is needed to maintain operations and support the assumed growth. The reinvestment rate is analogous to the retention ratio.

This last relationship is worth pausing on, because it exposes an assumption that is otherwise invisible. Choosing a growth rate and a WACC in a capitalised cash flow model implicitly fixes the reinvestment rate. A model that capitalises FCFF at 5 percent growth with a 15 percent WACC has assumed, whether the analyst noticed or not, that the company reinvests one third of its after-tax operating income every year forever.

Firm value has to be converted into equity value by subtracting the market value of debt, and a constant WACC assumes the capital structure does not change. Estimating the market value of private debt is its own problem. Where debt is a small fraction of total financing and operations are stable, face value is an acceptable estimate. Where a private company is significantly leveraged, or its financial condition is changing, or its performance is expected to be volatile, the debt may be worth materially more or less than face value. Maturities and terms matter too, particularly if significant maturities fall inside the life of the investment. In those cases, market value can be estimated from public debt with similar characteristics: type, tenor, credit quality and industry.

The same logic applied to equity cash flows gives the FCFE version, which excludes payments to debt holders and discounts at the cost of equity rather than the WACC.

The denominator is called the capitalisation rate.

Example 10 · Worked

Alicia Carrenza is a private equity general partner assessing a purchase of Vinuvia Limitada, a successful privately held Brazilian wine distributor. Working from limited company disclosure and market information, she arrives at the following estimates.

Vinuvia Limitada valuation inputs

Item	Value
Most recent FCFF	BRL 15,000,000
Most recent FCFE	BRL 14,500,000
Required return on equity	15%
Cost of debt	10%
Total assets	BRL 50,000,000
Equity financing	90%
Debt financing	10%
Tax rate	34%
Expected constant FCFF growth	5%

1. Calculate Vinuvia’s equity value using the capitalised cash flow method on an FCFF basis.

Solution. Three steps.

Step 1. Grow the cash flow one period. FCFF_t+1 = BRL 15,000,000 × 1.05 = BRL 15,750,000.

Step 2. Build the WACC. r_WACC = w_dr_d + w_er_e = 0.1 × (1 − 0.34) × 10% + 0.9 × 15% = 0.66% + 13.5% = 14.16%, which rounds to 14.2%.

Step 3. Capitalise and deduct debt. Firm value = BRL 15,750,000 ÷ (0.1416 − 0.05) = BRL 15,750,000 ÷ 0.0916 = BRL 171,943,231. Vinuvia’s debt is 0.1 × BRL 50,000,000 = BRL 5,000,000, taken at book value given its small size and the stability of operations. Equity value = 171,943,231 − 5,000,000 = BRL 166,943,231.

2. How does the estimate change if expected growth is 2 percent instead of 5 percent?

Solution. Both the numerator and the denominator move. FCFF_t+1 = BRL 15,000,000 × 1.02 = BRL 15,300,000, and the capitalisation rate widens to 0.1416 − 0.02 = 0.1216.

Firm value = BRL 15,300,000 ÷ 0.1216 = BRL 125,822,368.
Equity value = 125,822,368 − 5,000,000 = BRL 120,822,368.

A 3 percentage point reduction in assumed perpetual growth cuts the estimated equity value by over 25 percent, from BRL 166,943,231 to BRL 120,822,368, a fall of 27.6 percent. Capitalised cash flow values are extremely sensitive to the growth assumption precisely because g appears in the denominator, where its effect is amplified as WACC and g converge.

3. What reinvestment rate is Vinuvia implicitly assumed to have if the model is run with a WACC of 15 percent and perpetual growth of 5 percent?

Solution. RIR = g ÷ WACC = 5% ÷ 15% = 33.33 percent. The reinvestment rate is not a free assumption in a capitalised cash flow model; it is pinned down the moment the growth rate and the discount rate are chosen.

Figure 5: Sensitivity of a capitalised cash flow value to the growth assumption

Equity value is FCFF of BRL 15 million grown one period and capitalised at 14.16 percent less g, then reduced by BRL 5 million of debt. The curve steepens sharply as g approaches the WACC, which is why a small revision to a growth assumption produces a large revision to value.

Where an analyst has enough information to forecast several periods of cash flow, or expects growth to run at different rates in different phases, a discrete forecast with multistage growth is theoretically preferable to the capitalised cash flow method. The CCM still earns its keep as a cross-check: running it backwards against a value produced by another approach reveals what discount rate or growth rate that value has implicitly assumed.

The excess earnings method

The excess earnings method (EEM) estimates the earnings that remain after deducting the returns required on working capital and fixed assets, that is, on the tangible assets, and treats what is left as the return generated by intangible assets. The steps are as follows.

Estimate normalised earnings using the adjustments covered earlier.
Determine the fair market value of the tangible assets, split between working capital and fixed assets, and set a required return for each. Working capital is the most liquid and lowest risk asset and therefore carries the lowest required return. Fixed assets typically require a higher return. Intangible assets, being illiquid, potentially valuable only to one specific owner and high risk, require the highest return of the three.
Deduct the required returns on tangible assets from normalised earnings. What remains is excess earnings, otherwise called residual income.
Capitalise the residual income as a growing perpetuity to obtain the value of the intangible assets, called the residual value.
Add the residual value to the fair market value of the tangible assets to reach firm value.

g is the residual income growth rate and r subscript RI is the required return on intangible assets.

Example 11 · Worked

Digigraf GmbH is a small privately held digital media firm holding several patents and seeking a new round of early-stage financing. It intends to use the excess earnings method. Its most recent financial statements show EUR 1,000,000 of total assets, made up of EUR 200,000 of working capital and EUR 800,000 of fixed assets, both close to fair market value. After several adjustments, normalised earnings for the most recent year were EUR 120,000. The required returns on working capital and fixed assets are estimated at 5 percent and 11 percent respectively, based on an assessment of the opportunity cost of each. The residual income discount rate is 12 percent and the residual income growth rate is 3 percent.

1. Calculate residual income and the value of the intangible assets.

Solution. Deduct the required returns on the tangible assets from normalised income:
RI = EUR 120,000 − (EUR 200,000 × 5%) − (EUR 800,000 × 11%)
RI = EUR 120,000 − EUR 10,000 − EUR 88,000 = EUR 22,000.

This residual income must be attributable to the intangible assets, which here represent customer relationships, technology, trade names and the assembled workforce taken together. Capitalise it as a growing perpetuity:
RV = EUR 22,000 × 1.03 ÷ (0.12 − 0.03) = EUR 22,660 ÷ 0.09 = EUR 251,778.

The EUR 22,000 is the residual income for the most recent year, so it is grown by the 3 percent rate to forecast next year’s figure before capitalising.

2. Calculate Digigraf’s firm value.

Solution. Firm value is the sum of working capital, fixed assets and intangible assets:
EUR 200,000 + EUR 800,000 + EUR 251,778 = EUR 1,251,778.

Roughly EUR 252,000 of the total, one fifth of the value of the business, rests on a residual income figure of EUR 22,000 that is itself the small difference between two much larger numbers.

3. An analyst reviewing the work discovers that all three discount rates were entered incorrectly. The correct rates are 4 percent for working capital, 10 percent for fixed assets and 11 percent for intangible assets. Recalculate the EEM value.

Solution. Recompute residual income first:
RI = EUR 120,000 − (EUR 200,000 × 4%) − (EUR 800,000 × 10%) = EUR 120,000 − EUR 8,000 − EUR 80,000 = EUR 32,000.

Then the residual value at the corrected intangible discount rate:
RV = EUR 32,000 × 1.03 ÷ (0.11 − 0.03) = EUR 32,960 ÷ 0.08 = EUR 412,000.

Firm value = EUR 200,000 + EUR 800,000 + EUR 412,000 = EUR 1,412,000.

Modest changes to three discount rates, none larger than one percentage point, moved the valuation by EUR 160,222, or nearly 13 percent. That leverage is exactly the objection practitioners raise against the method.

The excess earnings method is used only rarely to price an entire private business, and then only a very small one. The criticism is that the specific return requirements for working capital, fixed assets and the residual income attributable to intangibles are not readily measurable and are relatively subjective. Against that, the residual income concept behind it is an important and widely accepted element of intangible asset valuation for financial reporting purposes, which is where the method is most at home. When the choice lies between the CCM and the EEM for valuing a whole business, the CCM has one decisive practical advantage: it requires a single discount rate, the WACC, where the EEM requires three separate ones.

The market approach uses direct comparisons with listed companies and with acquired businesses to estimate the fair value of an equity interest in a private company. It comes in three variations.

The guideline public company method (GPCM) builds a value from multiples observed in trading in the shares of listed companies judged comparable to the subject private company.
The guideline transactions method (GTM) builds a value from pricing multiples derived from acquisitions of control of entire companies, public or private.
The prior transaction method looks at actual transactions in the stock of the subject private company itself.

The guideline public company method

Comparable companies should match the subject company on relative risk and growth prospects as closely as possible. Industry alone is not enough. Size, leverage and stage in the company life cycle all matter when the set is being assembled.

The choice of multiple differs between public and private practice. Price-based multiples such as the price to earnings ratio dominate listed company work. Enterprise value multiples are more common in private company valuation, because they take the value of the whole firm into account and therefore accommodate changes to the capital structure over the valuation period more comfortably.

Leverage is the adjustment that must not be skipped. An observed beta for a listed company is a levered beta, reflecting that company’s own debt. To use it for a private company with different leverage, the beta must first be stripped of the effect of the comparable company’s debt, then re-levered at the private company’s own tax rate and debt to equity ratio.

The tax rate and debt to equity ratio here are those of the listed company.

The starred inputs are those of the private company being valued.

Example 12 · Worked

Quik Chip S.A. runs a chain of 50 quick-service restaurants across Europe. The valuation begins by assembling multiples and fundamentals for a set of guideline public companies operating in the quick-service restaurant industry globally, limited to those expected to be similar in enterprise value to Quik Chip.

Quik Chip guideline public company data

Guideline company	P/E	EV/EBITDA	EV/EBIT	EV/Sales	Beta	Debt/Equity	Tax rate
Peer A	21.6	13.6	18.5	3.7	1.3	61%	25%
Peer B	21.6	12.5	17.5	1.7	1.2	47%	19%
Peer C	24.3	8.8	15.0	1.5	1.2	56%	20%
Peer D	17.7	11.8	15.7	2.2	1.1	33%	24%
Peer E	18.4	10.8	16.1	1.0	1.0	22%	25%
Peer F	29.1	11.8	16.5	1.8	1.3	54%	18%
Peer G	29.9	11.2	21.5	1.5	1.5	67%	20%
Peer H	16.6	9.6	14.0	0.8	0.9	28%	21%
Peer I	24.2	18.8	20.7	3.6	1.4	82%	22%
Mean	22.6	12.1	17.3	2.0	1.21	50.0%	21.6%
Median	21.6	11.8	16.5	1.7	1.2	53.8%	21.0%
Low	16.6	8.8	14.0	0.8	0.9	22.0%	18.0%
High	29.9	18.8	21.5	3.7	1.5	81.8%	25.0%

Nine comparable companies. The summary rows give the mean, median, low and high of each column.

1. Quik Chip has a debt to equity ratio of 25 percent and a tax rate of 18 percent. What is a reasonable beta estimate for Quik Chip?

Solution. Start from the mean beta of the comparables, 1.21, and unlever it using the mean debt to equity ratio of 50.0 percent and the mean tax rate of 21.6 percent:

β_unlevered = 1.21 ÷ [1 + (1 − 0.216) × 0.50] = 1.21 ÷ 1.392 = 0.8693.

Then re-lever at Quik Chip’s own tax rate and debt ratio:
β* = 0.8693 × [1 + (1 − 0.18) × 0.25] = 0.8693 × 1.205 = 1.0474.

Note the direction of travel. Quik Chip carries half the leverage of the average comparable, so its re-levered beta of 1.0474 is below the observed average of 1.21, but it is above the unlevered figure of 0.8693 because Quik Chip does carry some debt. The published solution to this case prints 0.8693 a second time at the re-levering step; carrying the multiplication through gives 1.0474.

2. Quik Chip has sales of EUR 250,000,000 and EBIT of EUR 35,000,000. Establish a range for its enterprise value using peer multiples.

Solution. Apply the mean EV/EBIT and EV/Sales multiples:

EV from EV/EBIT = 17.3 × EUR 35,000,000 = EUR 605,500,000.
EV from EV/Sales = 2.0 × EUR 250,000,000 = EUR 500,000,000.

The EBIT-based figure is the higher of the two because Quik Chip is more profitable than its peers on an EBIT to sales basis. Quik Chip earns EUR 35,000,000 on EUR 250,000,000 of sales, a margin of 14 percent. The peer group implies a margin of 2.0 ÷ 17.3 = 11.6 percent, obtained by dividing the EV/Sales multiple by the EV/EBIT multiple so that enterprise value cancels. A sales multiple prices Quik Chip as though it converted revenue into operating profit at the peer rate, which understates it.

Composite multiples for a multi-segment business

Where a private company operates in more than one sector or industry, a single comparable set will not describe it, and a composite profile has to be built from more than one group. Composites are usually derived by weighting the multiples by a percentage of sales or of net income, which brings in the effects of sales margin, leverage and tax. The technique matters most when risk or growth levels vary significantly between the segments of the private company.

Example 13 · Worked

Everfloat Ltd. is well known as a traditional marine navigation equipment provider, but a decade of diversification has left that business at just 70 percent of revenue. The company now has a growing logistics equipment business serving ground transportation, and an alternative energy technology business for marine applications. Everfloat is pursuing electrification solutions as the shipping industry moves away from fossil fuels, an effort that produces revenue but is not yet profitable.

Everfloat Limited financial data (GBP millions)

Line of business	Revenue	Assets	EBITDA
Marine Navigation	700	1,560	187.5
Logistics Services	250	400	75
Energy Solutions	50	40	−12.5
Total	1,000	2,000	250

Andrea Miceli identifies a group of listed comparables for each of the three business lines, of similar size and stage of development, and calculates the average multiple for each segment. Public peers in Logistics Services and Marine Navigation show similar EV/EBITDA multiples, while listed firms in Energy Solutions businesses like Everfloat’s trade at significantly higher EV/EBITDA multiples. The EV/Sales pattern is similar, except that EV/Sales multiples are significantly higher for Marine Navigation than for Logistics Services.

Everfloat Limited comparable multiples

Line of business	EV/Sales	EV/EBITDA
Marine Navigation	2.8	8.2
Logistics Services	1.1	8.1
Energy Solutions	8.0	20.0

1. Calculate a single EV/Sales multiple with which to value Everfloat.

Solution. Weight the peer multiples by Everfloat’s own sales mix:
(700 ÷ 1,000) × 2.8 + (250 ÷ 1,000) × 1.1 + (50 ÷ 1,000) × 8.0
= 1.96 + 0.275 + 0.40 = 2.635, which rounds to 2.6.

2. Calculate a single EV/EBITDA multiple with which to value Everfloat.

Solution. Here the weights must be EBITDA proportions, and Energy Solutions contributes negative EBITDA:
(187.5 ÷ 250) × 8.2 + (75 ÷ 250) × 8.1 + (−12.5 ÷ 250) × 20.0
= 6.15 + 2.43 − 1.00 = 7.58, which rounds to 7.6.

The negative weight is the awkward part. An alternative that avoids it is to value Energy Solutions on a sales multiple and the other two divisions on EBITDA multiples.

The main advantage of the guideline public company method is the size of the pool of candidate companies and the volume of descriptive, financial and trading information available on each. The disadvantages are the perennial question of whether the comparables really are comparable, and the subjectivity of the risk and growth adjustments made to the multiple.

Control premiums applied to public company multiples

Trading in listed shares typically involves small blocks that convey no control of the entity, so many, though not all, practitioners hold that multiples derived from that trading do not reflect control. Where a controlling interest is being valued, a control premium adjustment may therefore be appropriate. Control premiums have historically been estimated from transactions in which listed companies were acquired, and three factors require care.

Type of transaction. Databases often classify acquisitions as financial or strategic. Control premiums in strategic acquisitions are typically larger, because they include payment for expected synergies.
Industry factors. A sector with visible acquisition activity is considered to be in play at the valuation date, meaning that the share prices of listed companies in it may already embed part of a control premium. A premium measured at a different time may reflect an entirely different industry environment.
Form of consideration. Transactions settled largely in stock rather than cash are less reliable as evidence, because management of the acquirer may choose to issue shares precisely when it believes those shares are overvalued in the public market.

Whatever premium is selected, the resulting multiple should be tested for reasonableness rather than accepted mechanically.

Guideline transactions and prior transactions

The guideline transactions method is conceptually the same as the guideline public company method, but the multiples come from acquisitions of whole companies, public or private, rather than from share trading. Data on publicly reported acquisitions are compiled from the filings that the parties to a deal make with their regulator, examples being the Securities and Exchange Commission in the United States and, in the United Kingdom, the Financial Conduct Authority. Transactions not subject to public disclosure may appear in commercial databases, but because the information is limited and generally cannot be verified, many appraisers question its reliability. All else equal, transaction multiples are the most relevant evidence for valuing a controlling interest in a private company, since they are drawn from actual purchases of control. Several factors qualify them.

Synergies. The price paid in a strategic acquisition may include payment for anticipated synergies, such as cost savings from consolidating corporate functions or revenue growth from cross-selling, and includes a control premium. Whether payments for synergies are relevant to the case in hand has to be considered explicitly.
Contingent consideration. This is a potential future payment to the seller conditional on achieving defined milestones, such as obtaining a regulatory approval or reaching a target level of EBITDA. Its inclusion in a purchase price usually signals uncertainty about the future financial performance of the target. An acquirer of a company like Nano Beta, whose value hinges on a regulatory decision, would be a natural candidate to structure the price this way.
Non-cash consideration. Where stock forms part of the consideration, the cash equivalent value of a large block creates uncertainty about the true transaction price.
Availability of transactions. Meaningful transactions for a specific private company may simply not exist, and the relevance of a historical transaction can be challenged if the company, the industry or the economy has changed since.
Changes between transaction date and valuation date. The guideline public company method develops multiples from share prices at or near the valuation date. The guideline transactions method relies on past acquisitions, and in many industries transactions are so infrequent that evidence several months old or more is all there is. Shifts in market conditions change risk and growth expectations, and the multiple must be adjusted for them.
Other differences. Company size, country, tax status and leverage may all be relevant.

The prior transaction method uses actual transactions in the stock of the subject company itself. When such transactions exist and were struck at arm’s length reasonably recently, they are compelling evidence. In practice they are often stale, few, or between related parties, which is precisely why the other two variations exist.

Everything covered so far now assembles into a single sequence. Estimate the WACC from listed comparables. Build a base-year FCFF from normalised earnings. Forecast, discount and add a terminal value to reach enterprise value. Deduct debt to reach equity value. Then adjust for control and marketability according to the interest being appraised. The order is not arbitrary: each step consumes the output of the one before it, and the discounts come last because they apply to a value, not to a cash flow.

The top-down construction of free cash flow to the firm used in this valuation.

Example 14 · Worked

Dev Khan is asked to value FLI from the perspective of a non-controlling shareholder, using the income approach and the normalisation work of Example 3 and the discount rate work of Example 6.

Step 1. Estimate the WACC.

Solution. The discount rate work produced the following.

FLI discount rate summary

Estimate	Basis	Result
Cost of equity	CAPM	9.3%
Cost of equity	Expanded CAPM	13.3%
Cost of equity	Build-up approach	12.8%
WACC	At the FLI actual debt ratio	12.8%
WACC	At the FLI optimal debt ratio	12.3%

The expanded CAPM gave 13.3 percent and the build-up approach gave 12.8 percent, and Khan combines them into a 13.0 percent required return on equity for the WACC calculation. He then averages across differing assumptions about FLI’s future debt ratio and settles on a WACC of 12.55 percent, the midpoint of the 12.8 percent and 12.3 percent figures in the table above. Note that the same inputs, worked without intermediate rounding in Example 6, produce 12.9 percent rather than 12.8 percent for the actual debt ratio; the summary table carries 12.8 percent and the 12.55 percent WACC follows from it.

Step 2. Develop a base-year estimate of FCFF.

Solution. Normalisation raised FLI’s EBIT from a reported SGD 14 million to SGD 15.4 million, with EBITDA of SGD 16,300,000 and depreciation and amortisation of SGD 900,000.

FLI normalised operating income

Line item, year to 31 December (SGD)	As adjusted
Revenue	50,000,000
Cost of sales	30,000,000
Gross profit	20,000,000
Selling, general and administrative	3,700,000
EBITDA	16,300,000
Depreciation and amortisation	900,000
EBIT	15,400,000

FLI had capital expenditures of SGD 1,200,000 and increased working capital by SGD 500,000 over the period, and the tax rate is 17 percent. The formula is written in terms of EBIT, but the operating earnings figure substituted here is the normalised SGD 16,300,000, which is the pre-depreciation measure shown as EBITDA in Example 3:

FCFF = 16,300,000 × (1 − 0.17) + 900,000 × 0.17 − 1,200,000 − 500,000
FCFF = 13,529,000 + 153,000 − 1,200,000 − 500,000 = SGD 11,982,000.

Step 3. Estimate enterprise value from forecast FCFF and a terminal value.

Solution. Khan forecasts five years, with an optimistic case of 8 percent FCFF growth, a base case of 5 percent and a downside case of 2 percent. The terminal value uses a perpetual growth rate of 3 percent.

Take the downside case as the worked illustration. Year 5 FCFF is the base-year figure grown five times:
FCFF₅ = SGD 11,982,000 × (1.02)⁵ = SGD 13,229,096.

The terminal value capitalises the following year’s cash flow at the WACC less the perpetual growth rate:
Terminal value = SGD 13,229,096 × 1.03 ÷ (0.1255 − 0.03) = SGD 13,625,969 ÷ 0.0955 = SGD 142,680,302.

FLI FCFF and terminal value forecasts (SGD millions)

Year	Downside	Base	Optimistic
Base year	11.982	11.982	11.982
Year 1	12.222	12.581	12.941
Year 2	12.466	13.210	13.976
Year 3	12.715	13.871	15.094
Year 4	12.970	14.564	16.301
Year 5	13.229	15.292	17.605
Terminal value	142.680	164.934	189.881

Discounting the five annual cash flows plus the terminal value at the 12.55 percent WACC gives the enterprise value in each case. FLI has debt outstanding with a market value of SGD 2.5 million, which is deducted from enterprise value to give equity value.

FLI enterprise and equity value estimates (SGD millions)

Case	Downside	Base	Optimistic
Enterprise value	124.027	140.202	158.161
Equity value	121.527	137.702	155.661

The terminal value dominates. In the downside case, SGD 142.680 million of terminal value discounted five years at 12.55 percent contributes roughly SGD 79 million of the SGD 124.027 million enterprise value, close to two thirds of the total.

Step 4. Apply the appropriate discounts or premiums.

Solution. The equity values in Step 3 describe a marketable position. To reflect the privately held status of FLI they must be discounted for lack of marketability, for lack of control, or for both. Khan used an option-based approach and concluded that an 18 percent DLOM is appropriate. Xin holds a controlling stake, but Khan saw no reason to treat the current value of that controlling interest as including a control premium, so he applied no DLOC.

FLI equity value after the marketability discount (SGD millions)

Scenario	Downside	Base	Optimistic
Equity value net of DLOM	99.653	112.916	127.642

Each figure is the corresponding equity value multiplied by (1 − 0.18). For the base case, SGD 137.702 million × 0.82 = SGD 112.916 million. The final range runs from SGD 99.653 million to SGD 127.642 million. The downside sits 11.7 percent below the base case and the optimistic case 13.0 percent above it, a spread driven entirely by a growth assumption that varies between 2 percent and 8 percent.

Judgement points in the sequence

A worked case can make the process look mechanical. Four decisions in it were not.

Normalising compensation. Where an owner-manager has been overpaid, normalising lowers costs and raises EBIT, which raises the base-year FCFF. Where an owner-manager has been underpaid, the correction runs the other way. A candidate must be able to say which direction applies before reaching for a calculator.
Choosing the required return model. Where no credible listed comparable exists, no beta can be borrowed, and the build-up approach becomes the natural choice precisely because it needs no beta. Its implicit assumption of a beta of one is a cost, not a benefit, but it is a cost that can be stated openly.
Choosing the terminal value method. For a whole-business valuation, the capitalised cash flow method needs one discount rate, the WACC. The excess earnings method needs three, one each for working capital, fixed assets and residual income, and is better suited to valuing intangible assets than an entire operating company.
Choosing the discounts. Khan applied a DLOM and no DLOC. That combination follows from the perspective adopted and from the fact that the cash flows and discount rate were built on a controlling basis, so no further control adjustment was warranted.

The market approach follows a parallel sequence. Choose listed comparables and weight them to match the business mix of the private company. Gather and summarise the multiples. Apply them to the fundamentals of the private company to estimate enterprise value. Then discount that estimate for illiquidity or minority ownership. The critical point, and the one candidates most often miss, is that a value derived from listed company multiples is a value at the marketable minority level, so it needs adjusting in one direction or the other depending on the interest being appraised.

Example 15 · Worked

Andrea Miceli now values Everfloat Ltd. from the perspective of a non-controlling, non-marketable minority shareholder, using the market approach and the segment data of Example 13.

Step 1. Express the business mix as proportions of the total.

Solution. Each segment is measured against group revenue of GBP 1,000 million, assets of GBP 2,000 million and EBITDA of GBP 250 million.

Everfloat Limited financial data (percentage of total)

Line of business	Revenue	Assets	EBITDA
Marine Navigation	70%	78%	75%
Logistics Services	25%	20%	30%
Energy Solutions	5%	2%	−5%

Marine Navigation dominates on every measure, so its comparables carry the largest weight. Energy Solutions is small on revenue and assets and negative on EBITDA.

Step 2. Summarise the comparable multiples and compute the composites.

Solution. The segment multiples come from the listed peers identified for each business line, and the composites are the revenue-weighted and EBITDA-weighted averages calculated in Example 13.

Everfloat Limited public comparable multiples

Line of business	EV/Sales	EV/EBITDA
Marine Navigation	2.8	8.2
Logistics Services	1.1	8.1
Energy Solutions	8.0	20.0
Composite	2.635	7.58

Step 3. Derive an initial estimate of value.

Solution. Multiply the composite by the matching group fundamental.

EV from EV/Sales = 2.635 × GBP 1,000,000,000 = GBP 2,635,000,000.
EV from EV/EBITDA = 7.58 × GBP 250,000,000 = GBP 1,895,000,000.

An equivalent route for the sales multiple is to value each segment separately at its own multiple and add the results.

Everfloat valuation by segment based on EV/Sales

Line of business	Revenue (GBP million)	EV/Sales	Stand-alone value (GBP million)
Marine Navigation	700	2.8	1,960
Logistics Services	250	1.1	275
Energy Solutions	50	8.0	400

The three stand-alone values sum to GBP 2,635 million, identical to the composite result, but each term can now be read as an initial estimate for one division. Ignoring synergies between the segments and any adjustment for a controlling buyer, Energy Solutions would be worth GBP 400 million as a stand-alone entity despite losing money, because a sales multiple does not require positive earnings. Note also that Logistics Services is the least valuable division at GBP 275 million, even though its revenue is five times that of Energy Solutions, because its comparable multiple of 1.1 is the lowest of the three.

The same segment-by-segment approach using EV/EBITDA fails for Energy Solutions, because a positive multiple applied to negative EBITDA implies negative value. Rather than conclude that the division is a badly run business worth less than nothing, an analyst may reasonably take the view that it is simply early in its life cycle. These estimates are based on listed company comparables and still require adjustment.

Step 4. Apply the discounts to complete the valuation.

Solution. Miceli estimated a DLOC of 13 percent and a DLOM of 16.8 percent, giving a total discount of 27.6 percent in Example 9. Apply it to both value estimates.

EV from EV/Sales = GBP 2,635,000,000 × (1 − 0.276) = GBP 1,907,740,000.
EV from EV/EBITDA = GBP 1,895,000,000 × (1 − 0.276) = GBP 1,371,980,000.

A single estimate can be obtained by averaging the two:
(GBP 1,907,740,000 + GBP 1,371,980,000) ÷ 2 = GBP 1,639,860,000.

Alternatively the analyst can widen the exercise by bringing in further multiples. The gap between the two estimates, GBP 740 million before the discount, is a reminder that a market-based valuation is only as good as the fundamental variable the multiple is applied to.

Step 5. Miceli discovers that most of the listed companies she identified in the marine equipment industry have divisional revenue and EBITDA proportions similar to Everfloat’s own. How should this change her choice of comparables?

Solution. She should use only the marine equipment comparables. If those companies already have the same business mix as Everfloat, they are appropriate comparables for the group as a whole, and there is no need to build a composite from three separate peer sets. Replacing them with a different set of marine navigation companies would not help either: any listed company with marine navigation as its only line of business would almost certainly have surfaced in the original search.

Weighing the market approach against the income approach

The two approaches answer the same question with different evidence, and their strengths are close to complementary.

Comparing the approaches for a private company

Consideration	Income approach	Market approach
Source of the value	The subject company’s own forecast cash flows	Prices observed on other companies or transactions
Classification	Absolute valuation model	Relative valuation model
Main input risk	Growth rate, discount rate, forecast quality	Comparability of the peer set
Level of value produced	Depends on whether control cash flows and an optimal capital structure were used	Marketable minority, when built from listed share prices
Handles negative earnings	Yes, through explicit forecasts	Not with an earnings multiple; a sales multiple is required
Typical use	Transactions where forecasts exist	Compliance, litigation and triangulation

In practice an analyst rarely relies on one alone. The market approach anchors the answer to observable prices, the income approach explains why the business is worth what it is worth, and the gap between the two is itself informative. Where a market-based value substantially exceeds an income-based value, the peer multiples are embedding growth or margin expectations that the cash flow forecast does not share, and one of the two needs revisiting.

Check yourself

1. A private company owner pays herself SGD 1.5 million where the market rate for the role is SGD 500,000, and separately occupies a building owned by her family for which the company records no rent. State the direction of each normalisation adjustment to EBIT.

They run in opposite directions. Reducing compensation to the market rate removes SGD 1,000,000 of expense and raises EBIT. Adding a market rental charge for the building introduces an expense that was previously absent and lowers EBIT. The test is always the same: what would an independent third party have charged, and is that amount currently in the income statement?

2. A build-up model and an expanded CAPM use the identical risk-free rate, equity risk premium, small stock premium and company-specific premium, and the industry risk premium is set to zero. Under what condition does the build-up model produce the higher required return?

When beta is below one. The only difference between the two models in that case is that the expanded CAPM multiplies the equity risk premium by beta while the build-up model applies it unscaled, which is equivalent to assuming a beta of one. A beta below one therefore shrinks the expanded CAPM premium and leaves the build-up result higher. With a beta above one, as in the FLI case where beta was 1.1, the ranking reverses.

3. An analyst values a private company by discounting control-basis cash flows at a WACC built on the optimal capital structure, then applies a discount for lack of control and a discount for lack of marketability. What is wrong with this?

Nothing, provided a non-controlling interest is genuinely what is being valued. The error to avoid is the reverse case: if the cash flows were not control cash flows, or the discount rate did not reflect an optimal capital structure, the resulting value already reflects a lack of control, and applying a DLOC on top of it counts the same disadvantage twice.

4. Comparable transactions in an industry imply a control premium of 25 percent, and restricted stock studies suggest a marketability discount of 15 percent. Calculate the total discount from a marketable controlling value to a non-marketable minority value.

Convert the premium first: DLOC = 1 − (1 ÷ 1.25) = 20.0 percent. Then combine multiplicatively: 1 − (1 − 0.20) × (1 − 0.15) = 1 − 0.80 × 0.85 = 1 − 0.68 = 32.0 percent. Using 25 percent directly as the discount would give 36.3 percent, and simply adding 20 and 15 would give 35 percent. Both are wrong.

5. A capitalised cash flow model uses a WACC of 12 percent and perpetual growth of 4 percent. What reinvestment rate has been assumed, and why does it matter?

RIR = g ÷ WACC = 4% ÷ 12% = 33.3 percent. It matters because the assumption is invisible in the model output. A company that in fact reinvests 10 percent of after-tax operating income cannot sustain 4 percent perpetual growth at a 12 percent WACC, so the value the model produces would rest on a growth path the business cannot fund.

6. A private company has three divisions, one of which reports negative EBITDA. Explain why a composite EV/EBITDA multiple is problematic here and what the alternative is.

Weighting by EBITDA proportion gives the loss-making division a negative weight, so applying a positive peer multiple to it subtracts value from the group. Read literally, that says an acquirer would have to be paid to take the division away, which is rarely what an analyst means. The usual alternative is to value the loss-making division on a sales multiple, which does not require positive earnings, and value the profitable divisions on EBITDA multiples.

7. Explain why the excess earnings method is rarely used to value an entire operating business, and where it is genuinely at home.

It requires three separate required returns, one each for working capital, fixed assets and residual income, and none of them is readily observable. Residual income is also the small difference between two much larger numbers, so modest errors in the asset returns swing the answer sharply. Where the method is accepted is in valuing intangible assets for financial reporting purposes, and in pricing very small businesses where no market approach method is feasible.

End of lesson.

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