We can determine the value of any asset, including intangible assets, from knowledge about its initial investment, comparable rate of return, and estimated life of the identifiable asset. For this purpose, CAPM (capital asset pricing model) is inapplicable to determine a comparable rate of return for intangible assets because CAPM is designed to estimate rates of return of traded equity shares, which reflect a stream of prospective dividends plus share price variation (capital gains or loss), and not a stream of operating profits. For a selected enterprise, the streams of income (operating profits versus dividends and capital gains) and measures of risks are not the same for the return of intangible assets compared to that of equity shares.
If we denote the value of the stock of assets (means of production; hereafter assets, including intangible assets) by Kt, which is a function of time, and the value of the identifiable assets at the initial period by K0, then we obtain in period t :
(1) Kt = K0 + K0 (1 + r) + K0 (1 + r)2 + ... + K0 (1 + r)t − 1
Formula (1) shows that the value of an asset (e.g., intangible assets transferred between two associated enterprises) starts from the amount of initial investment in the first period, K0, second period it’s K0 + K0 (1 + r), third period it’s K0 + K0 (1 + r) + K0 (1 + r)2, and this sequence follows until T (life span of the identifiable asset or average life span of a portfolio of identifiable assets). Abiding by transfer pricing rules, we must determine r from comparable enterprises because we obtain K0 and t = 0, 1, 2 , ..., T from internal data of the “tested party” (audited affiliate that self-developed the intangible assets being transferred).
We postmultiply equation (1) by the operating profit markup factor (1 + r) to obtain (2):
(2) Kt (1 + r) = K0 (1 + r) + K0 (1 + r)2 + K0 (1 + r)3 + ... + K0 (1 + r)t
Next, we subtract (2) from (1) to obtain (3):
(3) Kt − Kt (1 + r) = K0 − K0 (1 + r)t
which we simplify to obtain our computational equation (4):
(4) Kt = K0 [(1 + r)t − 1] / r, or
(5) Kt = β K0, where the multiplier is β = [(1 + r)t − 1] / r
We can use formula (5) to calculate the value of any asset, including the value of identifiable intangible assets of a selected enterprise to satisfy tax compliance rules in the event of an associated enterprise asset purchase.
From knowledge about the intitial investment (K0) employed to create an identifiable asset subject to related party transfer, plus estimated expected life of the asset (T), we can perform sensitive analyses by varying the rate of return within narrow limits (0 < r ≤ rmax) and compute a defensible range of values of the target asset(s) purchase.
OECD is misguided about “hard-to-value intangibles” because it ignores known economic principles expressed in canonical equation (1) or its simplified form (5). Only comparables that we need to establish intangible value are those used to determine r because the amount of the intital investment to create the identifiable intangibles is obtained from internal enterprise data.
