Valuation cross-checks

WACC

The weighted average cost of capital: the blended after-tax required return on the capital funding the enterprise, and the correct discount rate for unlevered free cash flow.

Field	Value
Formula	WACC = (E/V)*r_e + (D/V)*r_d*(1 - tau), where V = E + D
Worked	(2,400/3,000)*0.10 + (600/3,000)*0.06*0.75 = 0.080 + 0.009 = 0.089 = 8.900%
Cost of equity, CAPM	r_e = r_f + beta_L * ERP (+ any size or specific premium)
Relevering beta	beta_L = beta_U * (1 + (1 - tau)*D/E)

• Weights must be market values, and they must be the target capital structure rather than the current one if the current one is temporary. Using book equity weights in a company trading well above book systematically overweights debt and understates WACC.
• The tax shield belongs in exactly one place. Putting it in the discount rate through the (1 - tau) term and also in the cash flows by forecasting levered free cash flow double-counts it. Unlevered cash flow with WACC, or levered cash flow with cost of equity - never a mixture.
• WACC is not constant when leverage changes over the forecast, which is precisely the case in any LBO. A constant WACC applied to a deleveraging capital structure is internally inconsistent; the adjusted present value approach, valuing the unlevered business and the tax shield separately, is the consistent alternative.
• In practice the discount rate is where a valuation is quietly tuned to its answer, because a 100 basis point move in WACC moves a terminal-value-heavy DCF by more than most operating assumptions. Sensitivity to r should be shown, not buried.

Terminal value, Gordon growth

The value at the end of the forecast horizon of a perpetually growing cash flow stream. The largest single number in most DCF valuations and the one supported by the least analysis.

Field	Value
Formula	TV_n = FCF_(n+1) / (r - g) = FCF_n * (1 + g) / (r - g); PV = TV_n / (1 + r)^n
Worked	FCF_6 = 120.0, r = 0.089, g = 0.025: TV_5 = 120.0 / 0.064 = 1,875.0
Discounted	1.089^5 = 1.531579, so PV = 1,875.0 / 1.531579 = 1,224.23
Sensitivity	g from 2.0% to 3.0% moves TV_5 from 1,739.1 to 2,033.9, a 17% swing on a 100bp input

• The denominator r - g is small, so the terminal value is hypersensitive to both inputs. At r = 8.9 percent, moving g by 100 basis points moves the terminal value by roughly 17 percent. Any DCF where terminal value is most of the total is primarily a statement about two numbers.
• The perpetuity growth rate cannot exceed the long-run nominal growth rate of the economy for any sustained period, because a company growing faster forever eventually becomes the economy. That is a hard ceiling, not a convention.
• The terminal cash flow must be a steady state. If terminal capital expenditure is below terminal depreciation, the model has a company growing forever while shrinking its asset base. Set terminal reinvestment consistent with g: reinvestment rate = g / return on invested capital.
• The formula requires the cash flow of the period after the forecast, not the last forecast period. Using FCF_n rather than FCF_n*(1+g) understates terminal value by a factor of (1+g) and is a common error.

Terminal value, exit multiple

Terminal value estimated by applying a market multiple to the final forecast year's earnings measure. Intuitive, easy to communicate, and circular in a way the Gordon method is not.

Field	Value
Formula	TV_n = x_exit * EBITDA_n; PV = TV_n / (1 + r)^n
Worked	9.0x on EBITDA_5 of 150.0 gives TV_5 = 1,350.0; PV = 1,350.0 / 1.531579 = 881.42
At 10.0x	TV_5 = 1,500.0; PV = 979.36
Which EBITDA	The multiple must be applied to the same EBITDA definition the comparable multiples were computed on

• The exit multiple method imports today's market multiple as a forecast of the multiple five years from now. That is an assumption about market conditions, presented as an observation. The Gordon method at least states its assumption as a growth rate about the company.
• It is also circular when the multiple comes from comparables that are themselves being valued in the same exercise. A DCF whose terminal value is set by a trading multiple is a partially relative valuation wearing an absolute valuation's clothes.
• The two methods are only genuinely independent cross-checks if their implied assumptions are compared. Compute the implied perpetuity growth of the exit multiple and the implied exit multiple of the Gordon growth rate, and reconcile them.
• Using an EBITDA multiple to value a cash flow stream skips over the reinvestment question entirely: two companies with identical terminal EBITDA and different capital intensity are not worth the same multiple, and the method cannot see the difference.

Implied growth cross-check

The perpetuity growth rate that a chosen exit multiple is equivalent to, given the discount rate and the terminal cash flow. The single most efficient sanity check available on a DCF.

Field	Value
Formula	g_implied = r - FCF_(n+1) / TV_n = r - FCF_(n+1) / (x_exit * EBITDA_n)
Worked, 10.0x	0.089 - 120.0/1,500.0 = 0.089 - 0.080 = 0.009 = 0.90%
Worked, 9.0x	0.089 - 120.0/1,350.0 = 0.089 - 0.088889 = 0.0001 = 0.01%
Worked, 8.0x	0.089 - 120.0/1,200.0 = -0.011 = -1.10%
Reverse direction	x_implied = FCF_(n+1) / [(r - g) * EBITDA_n] = 120.0 / (0.064 * 150.0) = 12.50x for g = 2.5%

• In the worked case a 9.0x exit multiple implies essentially zero perpetuity growth, while the Gordon method with a 2.5 percent growth rate implies a 12.50x exit multiple. Those are not two views of the same company - they are two incompatible views presented as a range.
• That gap is the normal outcome of running both methods without reconciling them, and it is why a football field chart with a DCF bar and a comparables bar can look like agreement while hiding a disagreement of 40 percent.
• The direction of the gap is diagnostic. An exit multiple implying negative growth means the multiple is low relative to the cash flow the model forecasts, which usually means the forecast cash conversion is too optimistic rather than that the multiple is wrong.
• Run the check both ways and state both numbers. It costs one line of arithmetic and it is the fastest way to find an inconsistent model.

Trading comparables

Valuation by applying multiples observed in the current trading prices of similar public companies. Measures what the market pays for a minority position in the business type today.

Field	Value
Formula	EV_target = median(EV/EBITDA of peers) * EBITDA_target; then bridge to equity value
Worked	Peer median EV/EBITDA 9.5x, target EBITDA 250.0: EV = 2,375.0; less net debt 450.0, preferred 50.0, NCI 25.0 gives equity 1,850.0
Per share	1,850.0 / 100.0 = 18.50
Consistency rule	Enterprise multiples pair with pre-interest measures (EBITDA, EBIT, revenue); equity multiples pair with post-interest measures (net income, book equity)

• The numerator and denominator must belong to the same claimants. EV/net income and price/EBITDA are both meaningless, and both appear in practice.
• Calendarisation and adjustment do more work than peer selection. Peers with different fiscal year ends, different treatment of stock compensation, and different lease accounting produce a spurious dispersion that is then reported as a valuation range.
• Trading multiples exclude a control premium by construction, so a trading comps range is a floor for a controlling acquisition, not an estimate of one. Adding an assumed control premium to a trading range re-derives transaction comps by a less reliable route.
• A small peer set is usually worse than a wider one with explicit adjustments, because the median of four companies is dominated by idiosyncratic facts about those four.

Transaction comparables and precedent premiums

Valuation by reference to multiples and premiums paid in completed acquisitions of similar businesses. Measures what control of the business type has cost, including whatever synergies those acquirers believed in.

Field	Value
Formula	EV_target = median(EV/EBITDA at announcement of precedents) * EBITDA_target; premium = P_offer / P_unaffected - 1
Premium, worked	Offer 24.00 against an unaffected 18.00: 24.00/18.00 - 1 = 0.3333 = 33.33%
Against a 30-day VWAP of 20.00	24.00/20.00 - 1 = 20.00%
Against a 52-week high of 26.00	24.00/26.00 - 1 = -7.69%
Aggregate premium paid	(24.00 - 18.00) * 100.0 shares = 600.0 transferred to target shareholders

• The reference price is the whole argument. On identical facts the same offer is a 50 percent premium, a 33 percent premium, a 20 percent premium, or a discount, depending on whether the reference is the pre-leak price, the last close, a volume-weighted average, or the 52-week high. Every proxy statement chooses, and the choice is advocacy.
• Where a leak or rumour has already moved the price, the last unaffected trading day is the only economically meaningful reference, and identifying it is a judgement rather than a lookup.
• Transaction multiples embed the acquirer's synergy assumptions. Paying a precedent multiple without the same synergy opportunity means paying for someone else's synergies.
• Precedent samples are small and selected: completed deals at announced prices, with abandoned processes and lower bids invisible. The distribution is truncated from below, which biases the apparent range upward.
• Where a board relies on a financial advisor's analysis, the underlying reports and opinions are disclosure items under Item 1015 of Regulation M-A, which is why the premium reference and comparable set used in an opinion are visible in the filed documents.

Source: Item 1015 of Regulation M-A (17 CFR 229.1015)

LBO as a valuation floor

The highest price a financial buyer requiring a target return can pay, computed by inverting the LBO. Because a financial buyer without synergies is the least aggressive credible bidder, that price behaves as a floor under a competitive process.

Field	Value
Formula	EV_max = [E_required + D_0] / (1 + fee%), where E_required = (x_exit*EBITDA_t - D_t) / (1 + IRR_target)^t
Worked inputs	EBITDA_0 = 250.0, g = 4.0%, uFCF = 55% of EBITDA, D_0 = 1,250.0 at 6.5%, x_exit = 9.0x, t = 5, IRR target 20%, fees 2% of EV
Worked	EBITDA_5 = 304.1632; EV_exit = 2,737.47; D_5 = 834.97; E_5 = 1,902.50; E_required = 1,902.50/2.48832 = 764.57
Affordable EV	(764.57 + 1,250.0)/1.02 = 1,975.07, or 7.90x EBITDA_0
Check	Uses 1,975.07*1.02 = 2,014.57 = sources 1,250.0 + 764.57. MOIC = 1,902.50/764.57 = 2.4883x, IRR = 20.00%

• The floor is a floor on the sponsor's willingness to pay, and it is driven entirely by the debt markets. A one-turn change in available leverage moves the affordable entry multiple by roughly the same amount times the equity discount factor - which is why sponsor bids are more sensitive to credit conditions than to the target's operating outlook.
• This is also the practical explanation for why financial buyers win auctions in loose credit conditions and lose them to strategics in tight ones. The floor rises with leverage availability; the strategic ceiling, driven by synergies, does not.
• The floor is not a valuation. It states what a buyer with a required return can afford, not what the business is worth, and a sponsor's required return is a fund-level constraint rather than a market discount rate.
• Running the calculation with the exit multiple set equal to the entry multiple removes the multiple-expansion assumption and produces the honest version of the number - the price at which the deal works on operations and deleveraging alone.

Triangulating the methods

The discipline of running several valuation approaches with genuinely independent inputs and treating the disagreements as information rather than noise to be averaged away.

Field	Value
Worked spread	Trading comps 18.50 per share; LBO floor 7.90x on 250.0 EBITDA implies 1,975.07 EV or 14.50 per share; offer 24.00 at a 33.33% premium to an 18.00 unaffected price
What the spread says	The offer sits above both the minority-stake reference and the financial-buyer floor, so it is being justified by control and synergies - which should be quantified

• Averaging methods destroys the information. The useful output of a valuation exercise is not a midpoint but a statement of which assumption each method is most sensitive to and which of those assumptions the deal actually depends on.
• Methods are only independent if their inputs are. A DCF with a terminal exit multiple taken from trading comps and a trading comps analysis on the same peer set are one method presented twice, and their agreement means nothing.
• The single most informative comparison is the strategic ceiling against the financial floor. The gap between them is the value of control plus synergies, and if the offer exceeds that gap the acquirer is paying the target for value it has not identified.
• The offer price ultimately reflects process and alternatives, not method. A method is a way of testing whether a price is defensible, not of generating one, and treating it as the latter is how a fairness analysis becomes a rationalisation.