7.7 Choosing and Combining Models: Definitions of Value, Sum-of-the-Parts & Cross-Border Comparability

7.7 Choosing and Combining Models: Definitions of Value, Sum-of-the-Parts & Cross-Border Comparability

How this fits: sections 7.1 through 7.6 built each model. This section covers the learning outcomes about choosing among them — the definitions of value, sum-of-the-parts, conglomerate discounts, the criteria for selecting an approach, terminal value methods, and cross-border comparison. Item sets in this area present an analyst debating two models and ask which is most appropriate for the company described.

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1. Definitions of Value

The going-concern versus liquidation choice is the one Level II tests most directly: if the present value of continuing operations is below the net liquidation proceeds, the going-concern assumption is inappropriate and the liquidation value governs.

Perceived mispricing decomposes into two parts:

$V_E - P = (V - P) + (V_E - V)$

where $P$ is the market price, $V$ is the true intrinsic value, and $V_E$ is the analyst's estimate. The first bracket is true mispricing — the only part an investor can profit from. The second is estimation error. An analyst who finds a large apparent discount must ask which bracket it sits in, and the answer depends on how confident the model inputs are. This decomposition also explains why a valuation model with plausible inputs and enormous sensitivity to the growth assumption produces very little actionable signal.

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2. Absolute versus Relative Models, and How to Choose

Selection criteria

Dividend discount model is appropriate when the company pays dividends, the dividend policy bears a clear and stable relationship to profitability, and the investor takes a non-control perspective. It fails for non-payers and for companies whose payout is arbitrary relative to earnings.

Free cash flow models are appropriate when the company pays no dividend or pays one unrelated to capacity, when the investor takes a control perspective (a controlling owner can change the payout, so the relevant flow is the cash available rather than the cash distributed), and when free cash flow is positive and reasonably predictable. FCFF is preferred when leverage is high or changing, because discounting at WACC avoids modelling a changing cost of equity; FCFE is preferred when the capital structure is stable.

Residual income is appropriate when the company pays no dividend, when free cash flow is negative over the forecast horizon because of heavy investment, and when accounting quality is good enough that book value and clean surplus are meaningful. Its advantage is that a large fraction of value is recognized immediately in book value, so the terminal value carries far less of the total — the opposite of the dividend and free cash flow models.

Asset-based is appropriate for entities whose value is the sum of separable assets, and inappropriate for companies whose value rests on intangibles that do not appear on the balance sheet.

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3. Sum-of-the-Parts and the Conglomerate Discount

A diversified company's segments may deserve very different multiples. Sum-of-the-parts (SOTP) values each segment separately, then reconciles to equity value:

1. Value each segment using the model and peer multiple appropriate to that segment's economics.
2. Sum the segment enterprise values.
3. Deduct the capitalized value of unallocated corporate overhead, valued as a perpetuity at the corporate discount rate.
4. Add non-operating assets and deduct net debt, pension deficits, and minority interests.

Worked example. A diversified group reports three segments:

Unallocated corporate costs are 40 per year, capitalized at a 9% discount rate: $40/0.09 = 444$. Net debt is 900 and there is a pension deficit of 160.

• Enterprise value: $4{,}220 - 444 = 3{,}776$
• Equity value: $3{,}776 - 900 - 160 = \textbf{2{,}716}$

If the market capitalisation is 2,250, the conglomerate discount is $(2{,}716 - 2{,}250)/2{,}716 = 17.2%$.

Explanations for the conglomerate discount that vignettes offer, and which are supported:

• Internal capital market inefficiency — cash generated by a strong segment is reinvested in a weak one rather than returned to shareholders. Well supported.
• Endogenous factors — companies diversify because their core business is struggling, so the discount reflects the underlying problem rather than the structure. Well supported.
• Research measurement error — segment reporting is imperfect and comparable multiples are imprecise, so part of the measured discount is artefact. Partly supported.

The practical use is in restructuring analysis: a spin-off is value-creating when the discount exceeds the loss of genuine operating synergies and the incremental cost of running separate public companies.

4. Terminal Value: The Choice That Dominates the Answer

In a multistage model the terminal value routinely accounts for 60% to 80% of total present value, so the method chosen matters more than the explicit forecast.

Method 1 — Gordon growth (perpetuity) formula

$TV_n = \frac{CF_{n+1}}{r - g} = \frac{CF_n (1+g)}{r - g}$

Discipline required:

• $g$ must be a sustainable long-run rate, no higher than long-run nominal GDP growth. A perpetual growth rate above the economy's implies the company eventually becomes the economy.
• $r$ must be the terminal-period discount rate, which may differ from the near-term rate if leverage or risk changes over the forecast.
• The result is a value at time $n$ and must be discounted back $n$ periods, not $n+1$.
• Sensitivity is extreme: with $r = 9%$, raising $g$ from 2.5% to 3.5% raises the terminal value by 18%.

Method 2 — Exit multiple

$TV_n = \text{Terminal-year metric} \times \text{Exit multiple}$

Discipline required:

• Use a mature-company multiple, not the subject company's current multiple. Applying today's high-growth multiple in perpetuity smuggles today's growth into the terminal value and double-counts it against the explicit forecast.
• Match the multiple to the flow: an EV/EBITDA exit multiple produces an enterprise value that requires a net debt deduction; a P/E exit multiple produces an equity value directly.
• Cross-check the implied growth rate. Setting the exit multiple and solving the Gordon formula backwards for $g$ reveals whether the multiple embeds a plausible assumption.

A well-constructed model reports both methods, and a large divergence between them is a signal that one of the assumptions is unsupportable.

Method 3 — Liquidation or net asset value

Appropriate where the business has a finite life: a mine, an oilfield, a single-asset property vehicle, or a patent-dependent pharmaceutical franchise.

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5. Cross-Border Comparability

Comparing multiples across countries introduces four distinct distortions:

EV-based multiples travel better than equity multiples across borders, because they are less sensitive to differences in capital structure and in the tax treatment of interest. EV/EBITDA is also less distorted by depreciation policy differences than P/E, which is one of the main reasons it is preferred for cross-border comparisons. It remains sensitive to differences in capital intensity, so it is not a complete solution.

Central tendency of a group of multiples

When summarising a peer group's multiples, the choice of average matters:

• The arithmetic mean is upward-biased by outliers, since a company with near-zero earnings produces an enormous P/E.
• The median is robust to outliers and is the common practical choice.
• The harmonic mean — the reciprocal of the mean of the reciprocals — corrects the upward bias in a mean of ratios and is equivalent to weighting each company by its earnings rather than its multiple.
• The weighted harmonic mean, weighting by market capitalisation, is what an index-level P/E actually represents.

Illustration. Three comparables trade at P/E ratios of 10, 15, and 60.

• Arithmetic mean: $(10 + 15 + 60)/3 = 28.3$
• Median: $15.0$
• Harmonic mean: $3 / (1/10 + 1/15 + 1/60) = 3/0.1833 = 16.4$

The arithmetic mean of 28.3 is dominated by the single outlier and would produce a valuation almost twice the median-based estimate.

Momentum indicators

Three momentum measures appear in the market-based valuation module and belong in the model-selection discussion because they are used to time an entry rather than to establish value:

• Earnings surprise — actual EPS less expected EPS; scaled by its standard deviation this becomes standardized unexpected earnings (SUE).
• Relative strength — the security's return divided by, or compared against, a benchmark's return over the same period.

These are empirically related to subsequent returns over intermediate horizons, but they are not valuation measures and should never substitute for an intrinsic estimate.

Level II traps in model selection

1. Applying a DDM from a control perspective, where the acquirer can change the payout, instead of a free cash flow model.
2. Using the company's current multiple as the exit multiple in the terminal value.
3. Comparing a high-inflation market's P/E directly against a low-inflation market's without adjustment.
4. Using an arithmetic mean of peer multiples when one comparable has near-zero earnings.
5. Forgetting to deduct capitalized unallocated corporate costs in a sum-of-the-parts calculation, which overstates equity value.