We can determine a present value of identifiable assets, including a present value of specific intangible assets, from knowledge about their (a) initial investment, (b) comparable operating rate of return, and (c) estimated useful lives. For this purpose, CAPM (capital asset pricing model) is inapplicable to determine comparable operating rates 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) during a certain period, and not a prospective stream of operating profits attributed to specific intangibles. For a given enterprise, streams of dividends and capital gains and their calculated risks (measured during a specified useful period) are unlikely to be discounted or capitalized by an operating rate of return attributed to intangible assets. Inter alia, intangible assets are not frequently traded in ask-bid exchange markets and subject to speculative capital gains.
If we denote the present value of a stock of identifiable assets (hereafter assets, including intangible assets) at the end of the measured period by Kt, and the value of those assets at the initial period by K0, we obtain in period t :
(1) Kt = K0 + K0 (1 + r) + K0 (1 + r)2 + ... + K0 (1 + r)t − 1
This formula (1) shows that a present value of identifiable assets (e.g., intangible assets transferred between two associated enterprises in period t) starts from the amount of the 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 asset or average life span of a portfolio of identifiable assets).
Abiding by OECD transfer pricing rules, we must determine a discount rate (r ) from comparable enterprises and obtain K0 and t = 0, 1, 2 , ..., T from internal data of the “tested party” (audited entity that has self-developed the intangible assets being transferred to an offshore affiliate).
We postmultiply equation (1) by a comparable 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
r Kt = K0 [(1 + r)t − 1]
which we simplify further to obtain a present value equation (4) of the selected identifiable assets:
(4) Kt = K0 [(1 + r)t − 1] / r, or stated in more parsimonious fashion:
(5) Kt = β K0, where the assets value multiplier is β = [(1 + r)t − 1] / r
Example: If an average investment (including CAPX, Research & Development, Advertising) of 850 thousand USD is made at the end of each 12 years to create valuable assets expected to generate an operating profit return r = 7.5% per year, their present value can be determined by using (4):
(4) K12 = 850 [(1 + 0.075)12 − 1] / 0.075 = 15,660 thousand USD,
This example (4) is based on a case specific (given facts and circumstances determined by r = 0.075 and T = 12 years) multiplier of β = [(1 + r)t − 1] / r = [(1 + 0.075)12 − 1] / 0.075 = 18.424.
We can use formula (4) to calculate a present value of any indentifiable asset (including the value of identifiable intangible assets) to satisfy tax compliance rules in the event of an associated enterprise asset purchase.
In conclusion, from knowledge about an intitial investment (K0) to create identifiable assets subject to related party transfers, plus estimated average expected life of the created assets (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 assets purchase agreement.
