A listed company's cost of equity comes from a beta regression against an index in which the company itself trades. A private company has no price series, so beta cannot be regressed, and the discount rate has to be built.
The build-up method assembles it additively, and each layer is a separately sourced number:
k = risk-free + equity risk premium + size premium + industry risk premium + company-specific risk premium
Worked example: Cardinal Fluid Systems
Cardinal Fluid Systems, Inc. (synthetic) is a US industrial distributor with $42 million of revenue. Its layers are a risk-free rate of 4.30%, being the 20-year Treasury yield on the valuation date, which moves daily and must be date-stamped and re-pulled; an equity risk premium of 5.00%; a size premium of 3.40% from the smallest decile of a published size study; and an industry risk premium of 0.60%. On top of those sits a company-specific premium of 3.00%, charged for a top customer at 28% of revenue, dependence on a founder who is also the head of sales, and no audited statements before the third-most-recent year.
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The build-up gives 16.30%.
The first four layers are sourced. The fifth is judgment, and it is where every argument about a private valuation eventually lands. A company-specific premium is defensible only if the risks that justify it are written down and are not already priced somewhere else in the model. Charging 3% for customer concentration and modelling the loss of that customer in the cash flow is double-counting, and it is the commonest way a defensible-looking rate becomes indefensible.
The expanded capital asset pricing model does the same job with a beta in the middle:
k = risk-free + beta × equity risk premium + size premium + company-specific premium
Using the peer group's average levered beta of 1.15, Cardinal comes out at 16.45%, fifteen basis points from the build-up. Two independent constructions landing within a quarter-point of each other is worth reporting, because it is genuine evidence rather than an assertion, and the corpus's cross-check discipline applies here exactly as it does to a tree that must reprice its own curve.
What is total beta?
Total beta asks a different question, and the answer is uncomfortable. A market beta prices only the risk a diversified investor cannot escape, because the diversified investor is the one setting listed prices. The buyer of a private industrial distributor is frequently not diversified at all: the business will be most of their net worth. Total beta strips out the diversification discount by dividing by the correlation with the market:
total beta = market beta ÷ ρ = σ(firm) ÷ σ(market)
Cardinal's peer group regresses with an average R-squared of 0.16, so ρ = 0.40 and total beta = 1.15 ÷ 0.40 = 2.875. The cost of equity for an undiversified buyer becomes 4.30 + 2.875 × 5.00 = 18.68%, which is 2.38 percentage points above the build-up. Put another way, the total-beta route says that the appropriate premium beyond the risk-free rate, the market premium, the size premium and the industry premium is 5.38 points, not the 3.00 the build-up charged.
The valuation consequence is large and one-directional. On a normalised cash flow of $3.10 million growing at 3.0%, the build-up rate gives $24.01 million and the total-beta rate gives $20.37 million, a 15.15% gap on the same cash flow with no disagreement about the business at all.
The disagreement is entirely about the buyer. The business is the same business either way.
Which discount rate is right for which buyer?
Which rate is right depends entirely on who the buyer is, and that is a fact about the transaction rather than about the company. A diversified strategic acquirer or a private-equity fund holding twenty positions is correctly priced with a market beta, and can therefore rationally outbid the founder's own reservation price for the identical asset. An individual buying their first and only business is correctly priced with total beta. Using total beta to value a listed minority stake is simply wrong, because the marginal price-setter in that market is diversified.
{
"skill": "Building and stress-testing a cap table and a preference waterfall across exit values",
"use": "Have a code-writing assistant generate a cap-table and liquidation-preference model from your stated terms, then run it across a grid of exit values and report the crossover points, while you supply every term and check the identities by hand first.",
"tools": ["Code-writing assistants (Claude, ChatGPT) producing Python or a spreadsheet", "A notebook environment you can inspect line by line"],
"prompt": "Write Python that takes a cap table (holder, share count, class), a list of preferred rounds (investment, price per share, preference multiple, participating or not, participation cap, seniority rank), and an exit value, and returns each holder's proceeds. Then sweep exit values from 0 to 5x the last post-money in 100 steps and report: the exit at which each preferred holder becomes indifferent between converting and taking its preference, the exit at which each cap first binds, and the exit at which common first receives anything. Do not assume any term I have not given you; list every assumption you had to make.",
"verify": "Three identities must hold at every exit value before the output is admissible: the sum of all holders' proceeds equals the exit value exactly; each holder's proceeds are weakly increasing in the exit value; and the as-converted share counts sum to the fully diluted total. Recompute at least two exit values by hand, one below and one above each crossover, because the failure mode here is a model that runs cleanly and mis-ranks seniority or applies participation after the cap. Trace every term back to the term sheet's own words rather than to the assistant's summary of them, since 'broad-based' and 'narrow-based' differ by one adjective and by more than a factor of two in the extra shares issued, and a full ratchet differs from either by more again.",
"diy": "The gate is unaided: you build the cap table from share counts, compute the price per share from the pre-money and the pre-money fully diluted count, run the pool shuffle both ways, and derive both preference crossover points algebraically. A model you cannot reproduce on paper for one exit value is a model you cannot defend in a negotiation.",
"market": "US"
}