# RoyaltyStat Blog

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The initial stock of identifiable assets ("capital stock"), including tangible and intangible assets, is based on the project's initial investment, rate of depreciation or amortization, and estimated growth rate of revenue. This initial capital stock can be estimated by a straight-line equation:

##### (1)     K0 = λ I1,

where the multiplier is λ = 1 / (g + δ) and Iis the gross investment (Capex, XRD, XAD) made in the first year of the project.

The index t = 0, 1, 2, …, T keeps track of time; δ is the depreciation or amortization rate, and g is the estimated growth rate of the capital stock, g = ∆Kt/Kt − 1.

The stock of identifiable assets, including intangibles, can be accumulated from this initial amount Kby using the perpetual inventory method (PIM):

##### (2)     Kt = β Kt – 1 + It

where β = (1 – δ) is the capital accumulation coefficient. Equation (2) represents the "law of motion" of capital.

This first-order dynamic equation (2) is a workhorse in Dan Usher (ed.), The Measurement of Capital (Chicago University Press, 1980). Among other references, see also Zvi Griliches, “Capital Stock in Investment Functions,” in Carl Christ, et. al., Measurement in Economics (Stanford University Press, 1963) and Charles Hulten, "The Measurement of Capital," in Ernst Berndt & Jack Triplett (eds.), Fifty Years of Economic Measurement (University of Chicago Pres, 1990). However, we can escape equation (1) by converting equation (2) into a geometric weighted sum of identifiable past investments.

In principle, specific investments tracked in a company's general ledger (GL) determine the stock of identifiable assets, as follows:

• Capex + ∆ Inventories → Tangible assets;
• Advertising expenses → Marketing intangibles;
• R&D expenses → Technology intangibles; and