Cost of capital

From operating risk to equity risk

The starting beta is unlevered: it represents operating risk before financing. TANGE relevers it with the selected target debt-to-equity ratio and the tax rate. The debt weight is constrained between zero and 90%; a company with net cash therefore has zero leverage rather than a negative debt weight.

D/E = wd / (1 − wd)

β relevered = βu × [1 + (1 − t) × D/E]

Equity and debt costs

The cost of equity is the risk-free rate plus relevered beta multiplied by the sum of the mature-market equity risk premium and the country risk premium. The country premium is therefore multiplied by beta in the implemented model; it is not added afterward as an unscaled surcharge.

Cost of equity = rf + β relevered × (ERP + CRP)

The pre-tax cost of debt is the risk-free rate plus the debt spread. WACC uses that debt cost after tax.

Cost of debt = rf + spread

WACC = we × cost of equity + wd × cost of debt × (1 − t)

Sector weighting

In Sector mode, wd is the sector target leverage or the declared model fallback when sector data are absent. The same fixed weight is used throughout the valuation. The estimate does not infer a new capital structure from the resulting equity value.

Company weighting and the single pass

In Company mode, the target starts from current leverage. If book equity is supplied, current leverage uses net debt and book equity. Otherwise TANGE first values the company with sector WACC, uses that first-pass equity value to estimate current leverage, and then performs the valuation once with the resulting company weight.

There is no iteration back from the second valuation to a new leverage ratio. This is deliberate: Company mode is a single adjustment, not a circular convergence procedure.

What the two criteria change

The operating plan is identical under Sector and Company weighting. Only target leverage, relevered beta, cost of equity and WACC can change. Book equity consequently affects the estimate in Company mode, but not in Sector mode.

The specific risk premium

Beta and leverage come from listed companies. Applied unchanged to an unlisted business they price it as though its shares traded daily, so a premium is added to the cost of equity, interpolated linearly in log₁₀ of revenue between three anchors placed at the geometric centre of each band — 4.0% at √500/5, 2.5% at √500, 1.5% at √500×5 million of revenue — flat outside that range. The construction makes the band boundaries exact: at €10m the premium is 3.25%, the mean of 4.0% and 2.5%, and at €50m it is 2.00%, the mean of 2.5% and 1.5%. There are no bands and no step: two businesses a hundred thousand euro apart in turnover receive premiums a fraction of a basis point apart. It is additive and is not scaled by beta, because it is not market risk. Zero is the listed company, not the middle band: setting the middle band to zero would give large companies a cost of capital below a comparable listed peer.

Ke = rf + β relevered × (ERP + CRP) + SP

There is no free public measurement of this premium for unlisted Italian companies: it is a signed methodological choice, not a datum. It must not be combined with a marketability or minority discount on the result, which would count the same thing twice.

Growth, the cost of capital and the threshold that is not the WACC

The textbook rule says perpetual growth creates value when the return on capital exceeds the cost of capital. For the terminal form this model uses — NOPAT₅(1+g)(1−g/R) / (WACC−g) — that is not exact. Setting the derivative with respect to g to zero and solving for R gives:

R* = [ (1+2g)(WACC−g) + g(1+g) ] / [ (WACC−g) + (1+g) ]

R* lies below the WACC, always, and it stays below it even at zero growth. As g tends to zero the expression tends to WACC / (1 + WACC): with a WACC of 10% the threshold is 9.0909%, nine tenths of a point under the cost of capital, and with a WACC of 12% it is 10.7143%. At g of 2% and a WACC of 10% it is 9.4182%. Between R* and the WACC, raising perpetual growth still raises the value, and a warning built on the textbook rule would say the opposite in exactly the cases where someone stops to read it.

The tool computes the direction from this threshold, not from a comparison with the WACC, and warns on screen when raising growth lowers the value — which is correct, and will be read as a fault unless it is explained.

The specific risk premium under III.1.45 c and III.2.4

References are to the Exposure Draft — Principi Italiani di Valutazione 2026 and to the accompanying Razionale dei PIV 2026, Fondazione OIV, December 2025. They are drafts in consultation, not standards in force. The Razionale is by its own statement an illustrative guide to the logic of the principles, not a prescriptive text.

The premium has a place in the ED. III.1.45 lists among the criteria for obtaining discount rates, at letter c, “mixed methods which consider, in addition to the preceding criteria, specific risk premiums (size, industry, and so on)”. What this tool applies is one of those.

III.2.4 sets out what the size factor is supposed to capture. It states that size is generally a relevant factor in estimating the value of a business, listed or unlisted, because it can influence the risk profile through: (a) exposure to systematic risk; (b) exposure to specific risk — with reference, for example, to the quality of the organisational structure, to customer concentration, or to the concentration of the firm’s success factors in one or few people; (c) the availability of formalised plans and of adequate managerial or organisational structures. The valuer must take these aspects into account and give reasons for the choices made.

Read against that list, a premium keyed only to revenue is a crude proxy. Customer concentration, dependence on key people and the quality of the organisational structure are properties of a specific business, and this tool asks for none of them. Turnover is a stand-in for all three, chosen because it is a number the user already has. Whoever uses the figure should move it on the evidence of the actual business, which is why the parameter remains adjustable.

The three cautions. The Razionale at III.2.4 notes that professional literature often treats size by adjusting the discount rate, drawing on statistics of the return differentials of small caps against larger listed companies, and that those statistics must be used with caution for three main reasons: (a) the breakdown into size classes may take as its reference parameters — market capitalisation, for example — that are not known for the business being valued; (b) small-cap returns may also be influenced by the lower liquidity of smaller companies, hence by a factor conceptually separate from size alone, which does not necessarily belong in the configuration of value being estimated; (c) the small size effect on financial markets has progressively diminished over time. In any case the valuer must state how the size factor was treated and the sources used.

All three bite here, and together they settle what the series can be used for. (a) The US decile series are cut by market capitalisation, which an unlisted company does not have; this tool substitutes revenue, and the substitution is an assumption, not a mapping. (b) Liquidity is not separated out: here the premium deliberately carries the non-listing component too, which is why it must not be combined with a marketability discount on the result — but it also means the figure is not comparable, term for term, with a pure size premium. (c) The small size effect has been contracting, and the figures available are as of 31 December 2016.

The conclusion is not that the calibration is waiting for a better series. Taken together the three cautions say that no edition of those statistics, however current, could calibrate this premium: wrong size measure, wrong market, and a liquidity component that is separated there and included here on purpose. The series indicate an order of magnitude and no more. The three values are a declared professional judgement about the Italian unlisted business, of the same kind as the cap on perpetual growth, and they are complete as they stand. They are not provisional, and they are not waiting on a measurement that does not exist: there is no published series of the non-listing premium for the Italian market, and it is unlikely there will be one. Whoever uses the tool can and should replace them with their own judgement about the business in front of them.

Using the drivers: how to move the premium off the interpolated value

The curve gives a starting point read off turnover alone. III.2.4 names the drivers that should move it. Four of them are assessable properties of a specific business, and they are the ones to work with; the fifth item on that list, exposure to systematic risk, is not among them, because systematic risk belongs to beta and adding it again here would count it twice.

Two worked examples, in both directions. A manufacturer with €18m of revenue reads 2.70% off the curve. It sells to four customers, the largest is 40% of turnover, the founder holds every commercial relationship and there is no successor: three of the four drivers point the same way, and a premium at or near the maximum the curve reaches — 4%, what it gives a business under €4.5m — is easier to defend than the interpolated value. The same €18m of revenue in a business with two hundred customers, none above 5%, a general manager who is not the owner, an approved plan met for three years running and monthly reporting to a board: the drivers point the other way, and 2% or below is the defensible figure — 2.00% is what the curve gives a business of €50m, nearly three times its size.

The parameter is adjustable for exactly this reason, and III.2.4 requires that the choice be reasoned: whoever moves it should record which drivers they moved it on. Moving it is the normal case, not an exception — the curve knows the turnover and nothing else about the business.

Why the tool refuses under financial distress: III.1.50 and III.1.52

III.1.52 states that when the Modigliani-Miller model is used to compute the weighted average cost of capital, the model is valid only in the absence of distress costs, since it assumes the risk of debt is nil. This tool computes the WACC in exactly that framework: a cost of debt built as risk-free plus a sector spread, weighted by a target leverage, with no term for the probability of default.

It follows that the model has no validity precisely where a distressed company would need it. Extending it there would not give a conservative answer, it would give a meaningless one: as leverage rises the debt weight dominates and the computed cost of capital falls, so the more compromised the business, the cheaper its capital appears. The tool therefore refuses rather than returning a number, and the refusal is a property of the model, not a limitation of the software.

III.1.50 supports the same conclusion from the other side. It requires that the financial structure used be the prospectively sustainable one, expressed at market and not book values, and adds that where that structure is destined to change materially as a result of planned choices, or of change-of-control clauses on financial debt, appropriate technical solutions are needed. A business in distress has, by definition, a current structure that is not prospectively sustainable, and choosing a sustainable target for it is a judgement about a restructuring — not a number a form can read.