Goodwill Accounting II

Property rights versus going-concern contractual roles

David Ellerman A basic characteristic of a property right is that it may not rightfully be taken away from a person without the person’s consent. A going-concern business is typically at the center of a nexus of market contracts which have a rather limited duration. When a current contract expires, then a customer or supplier may decide for whatever reason to terminate the contract and take their business elsewhere. This does not require the consent of the business operator. The business operator has no property right to force customers and suppliers to continually renew past contracts. Future profits may have been anticipated from the continuation of the old contracts, but no rights were violated if the customers or suppliers decided not to renew the contracts. The anticipated future property rights that would result from the continued contracts, e.g., future profits, might not materialize but that is quite different from some present property right of the business operator being violated. The root of the controversy about “goodwill” is this basic distinction between:

  • presently owned property rights, and
  • possible future rights (presently not owned) resulting from a contractual position.

Unfortunately the confusion has been “canonized” into the basic capitalization formulas of finance theory. The standard formulas for the capitalized value of a capital asset routinely capitalize into the value of the asset the possible future profits that depend on a “non-owned” contractual position of the residual claimant in some productive opportunity. Hence our task to tease apart the two parts of the so-called “capitalized value” into:

  • the part that does represent present property rights, and
  • the part representing anticipated but not presently owned future profits.

It is this latter part, the capitalized value of anticipated future profits, that is called goodwill.

The capitalized value of an asset

Consider a simple example of a capital asset, e.g., a widget-maker machine, providing capital services K per period with which the labor services L will produce Q units of the product per period. Assume the asset provides these services for n periods with no maintenance required and then is finished with no salvage value. Let r be the competitive rental rate per unit of capital service so rK would be the competitive rental for the asset’s services per period. Anyone desiring to use the asset’s stream of capital services, K, K,…, K, for n periods would have the market choice to rent or buy. Competitive arbitrage would equate the present value of the rentals and the market cost C of the asset. If \rho is the interest or discount rate per period, then the equation of the market cost and the discount present value of the rentals is:

C = \frac{rK}{1+\rho}+\frac{rK}{(1+\rho)^{2}}+\ldots +\frac{rK}{(1+\rho)^{n}}

Market cost of the asset = Present value of rentals (no salvage value)

What is the “value” of such a machine to the its owner? If no other contracts were available, then the owner might have to rent out the machine at its rental rate and then the value C  would accrue to the owner. But suppose the machine owner, for whatever reason, is able to make another set of market contracts, namely to hire in the labor L per period at the wage rate w, and to sell the outputs of Q per period at the unit price p. Then the net revenue accruing to the business operator per period is pQ – wL. Assuming the continuation of these supplier and customer contracts for n periods, the net present value accruing to the business operator is:

V = \frac{pQ-wL}{1+\rho}+\frac{ pQ-wL }{(1+\rho)^{2}}+\ldots +\frac{ pQ-wL}{(1+\rho)^{n}}

Present value of anticipated business operation to asset owner

So far the analysis is straightforward and unproblematic. But now a subtle error creeps into the standard treatment in capital theory and finance theory. The present value V is characterized as the “capitalized value of the asset” as if the combined results of using the asset’s services K per period and the assumed supplier and customer contracts were all part of the property rights of the asset owner. The standard formulas for capitalized asset values and business valuation are all more complex versions of this simple formula. To make the point explicit, one has to parse the formula into the two parts: the present value representing (the future recovery of the value of) present property rights plus the present value of future profits resulting from the assumed “going concern” continuation of beneficial supplier and customer contracts, i.e., the goodwill. In our simple example, the profit each period is:

\pi = pQ-rK-wL

Anticipated profit per period

so the discounted present value of the profit, namely the goodwill, is:

GW = \frac{\pi}{1+\rho}+\frac{\pi }{(1+\rho)^{2}}+\ldots +\frac{\pi }{(1+\rho)^{n}}

Goodwill = Present value of future anticipated profits

Then since pQ – wL = rK + \pi, the capitalized value V is easily parsed into the sum of the asset’s market value C plus the goodwill GW:

V = \frac{pQ-wL}{1+\rho}+\frac{ pQ-wL }{(1+\rho)^{2}}+\ldots +\frac{ pQ-wL}{(1+\rho)^{n}}

= \frac{rK+\pi}{1+\rho}+\frac{rK+\pi }{(1+\rho)^{2}}+\ldots +\frac{rK+\pi }{(1+\rho)^{n}}=C+GW

“Capitalized value of asset” = market value of asset + goodwill. Thus the standard capitalized value formulas for business assets or businesses are not just the value of present property rights but include the value of certain anticipated but presently not owned future profits.

Examples in the literature

The confusions about capitalized value are also expressed in the rather muddled idea that these anticipated future profits are somehow “attached” to the physical assets or the “business.”

When a man buys an investment or capital-asset, he purchases the right to the series of prospective returns, which he expects to obtain from selling its output, after deducting the running expenses of obtaining that output, during the life of the asset. [Keynes 1936, 135]

But the buyer of the asset buys no such right against the customers and suppliers who may freely decide not to continue the past contracts and thus to change the “series of prospective returns” which the asset owner “expects to obtain”. Unfortunately these confusions about the property rights involved in owning a capital asset are carried over in modern corporate finance theory to the valuation of an entire going-concern business as an “asset”.

There, in valuing any specific machine we discount at the market rate of interest the stream of cash receipts generated by the machine; plus any scrap or terminal value of the machine; and minus the stream of cash outlays for direct labor, materials, repairs, and capital additions.  The same approach, of course, can also be applied to the firm as a whole which may be thought of in this context as simply a large, composite machine. [Miller and Modigliani 1961, 415]

Miller and Modigliani [1961] give four equivalent formulas for corporate valuation. The formulas can be shown equivalent [Ellerman 1982, 154-5] to a fifth formula that gives the parsing of the capitalized value into the value of the property rights in the underlying assets plus the goodwill (present value of assumed future profits). The essentials of the proof are captured in the simple example used here.

Accounting for goodwill

Accounting rules typically do not allow “unpurchased” goodwill to be listed on the balance sheet as an asset, and our analysis indicates this is correct if the balance sheet is to give the value of present property rights. But some accounting rules rather mysteriously allow “purchased goodwill” to be recorded as an asset. This is reminiscent of the old joke about a country bumpkin who comes to New York where a con man sells him the Brooklyn Bridge. Can the buyer then put the Brooklyn Bridge on his balance sheet since he “purchased those rights”? Surely the point is that the buyer cannot purchase a right which the seller does not own in the first place. Hence “purchased goodwill” is no more a present property right than unpurchased goodwill since the seller had no such property right to sell. Capital expended to “purchase” such a non-right should not be recorded as an owned asset but as a debit to equity. Some accountants have courageously argued for this correct procedure, e.g., George Catlett and Norman Olson in Accounting for Goodwill.

The amount assigned to purchased goodwill represents a disbursement of existing resources, or of proceeds of stock issued to effect the business combination, in anticipation of future earnings.  The expenditure should be accounted for as a reduction of stockholders’ equity. [Catlett and Olson 1968, 106]

The debit to equity would then be replenished if and when the anticipated future profits were earned, i.e., were realized as present property rights. However, one should not expect conceptual clarity in the standard literature on this issue anytime soon. It is not just an issue about accounting for goodwill. As we have noted, the issue involves very basic ideas about just what is owned in the ownership of an asset or a corporation, and the confusion is embedded in the standard asset capitalization formulas of finance theory.

References

Catlett, G. and N. Olson 1968. ARS No.10: Accounting for Goodwill. New York: American Institute of Certified Public Accountants. Ellerman, David 1982.  Economics, Accounting, and Property Theory. Lexington MA: D.C. Heath. Keynes, J.M. 1936. The General Theory of Employment, Interest, and Money. New York: Harcourt, Brace & World. Miller, M. H. and F. Modigliani 1961. Dividend Policy, Growth, and the Valuation of Shares. The Journal of Business. 34 (October 1961): 411-433.

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