Accounting for Intangible, Non- Marketed and Sunk Capital Robert Cairns Department of Economics and Cireq McGill University

Capital 1.Irreversible (“sunk”) 2.A diverse composite in any project: MarketedNon-marketed TangibleMachinesSome mines IntangibleSoftwareOrganization

Accounting Prices for Capital? Financial accounting: market prices Green or extended accounting: 1.postulate SWF, W(K) 2.take partial derivatives ∂W/∂K i Shadow prices ∂W/∂K i very hard to obtain Dependent on choice of W(K); e.g., ρ

Fundamental Problem Accounting is trivial if prices can be written down for all goods at all times as in 1 & 2 Fundamental problem of accounting: to define accounting values when there aren’t prices Extend Cairns (2013), Cdn J Econ

Marketed Capital K Irreversible (sunk) for non-trivial periods: has prices only on sets of measure zero e.g. a forest: land and stand Some marketed intangible capital has no units, no ∂W/∂K i Financial accounting deals with it imperfectly Not economics

Non-Marketed Capital Important & increasingly so No units: e.g. “quality of management” Even if put V(K,N), no ∂V/∂N i Neither financial accounting nor economics deals with it Returns subsumed into aggregate K

No Price? We Want one, for Every t How much of p i K i to charge to current output? Cost recovery How much of NCF (variable profit) is profit? How much of “profit” in e.g. oil industry due to 1.Quality and scarcity of a reserve 2.Quality of management 3.Use of unpriced environmental sinks 4.Market power?

Can do. But… Only (expected) NPV of a project is unique No theoretic way to separate the four enumerated non-marketed items as NPVs They form a residual (cf. Hall, World Bank) Values of marketed & non-marketed capital sum to NPV

How? Axioms for User Cost For each marketed capital item and for the non-marketed residual, 1.User cost non-negative for all t ε (0,T) 2.For all t, sum of user costs is variable profit 3.Discounted user cost of each item is original cost (NPV for residual) (Shadow) prices not used

Methodology Allocation to assets constrained but not unique Can develop a theory of accounting based on NPV The math is easy Can understand accounting principles in terms of the axioms

Symmetry at Last The axioms imply symmetric treatment of all components of invested capital, marked and non-marketed (residual). ROR on each is r t. IRR too. Returns to non-marketed not attributed to marketed capital.

Propositions: Value Sunk 1. The value sunk in a project is the value of the option to continue with the project rather than to sell some or all of the marketed capital. 2. The user cost, the economic book or accounting value and the depreciation of any asset are not unique. Relative values of sunk capital goods are not uniquely defined.

Internalization Values are internal to the project. External prices are not used for sunk capital. External prices are the basis for determining when to exercise options to sell marketed capital. “Profit” (rent to residual) not unique

Propositions: Economic Accounting 3. Accounting value is not decomposed into accounting price and quantity. 4. The accounting rate of return, limited to marketed capital, is neither unique nor meaningful.

Propositions: Economic Valuation 5. Marginal values or marginal shadow prices apply only to tangible capital. They are inputs to stopping conditions in quantity space. They are not prices to be used in economic accounting for capital. 6. Cross-sectional depreciation is not defined. Depreciation is measured as a time series.

Shadow Prices For an optimally managed project, optimality conditions hold; values equated at the margin Still, the marginal value is not used. Non-priced capital, economies of scale, non- convexity

Conclusion Simplest project a composite of (K,N) Stylization: non-marketed capital has no natural measure, no marginal value, no price Confounded into a residual value Accounting and economics have neglected by subsuming into marketed capital and aggregating marketed capital Sunk, marketed capital in some ways similar: has values only on sets of measure zero

Methodology Can assign values (not prices) through time Based on three axioms Mathematically simple Some similarity to financial accounting Indicates the limitations of measurement