We can determine a future *value* of any identifiable asset, including intangible assets, from knowledge about its initial investment, comparable *rate of return*, and estimated life of the asset. For this purpose, CAPM (capital asset pricing model) is inapplicable to determine comparable 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*. The streams of income (operating profits versus dividends and capital gains) and measures of risks of a selected enterprise are not the same as the return of intangible assets compared to that of equity shares.

If we denote the future *value* of the stock of identifiable assets (hereafter assets, including intangible assets) at the end of the measured period by K_{t}, and the value of the assets at the initial period by K_{0}, we obtain in period *t *:

(1) K_{t} = K_{0} + K_{0} (1 + *r*) + K_{0} (1 + *r*)^{2} + ... + K_{0} (1 + *r*)^{t − 1}

Formula (1) shows that the value of an asset (*e.g*., intangible assets transferred between two associated enterprises in period *t*) starts from the amount of initial investment in the first period, K_{0}, second period it’s K_{0} + K_{0} (1 + r), third period it’s K_{0} + K_{0} (1 + r) + K_{0} (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 transfer pricing rules, we must determine the discount rate (*r* ) from *comparable enterprises* because we obtain K_{0} 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 the operating profit markup factor (1 + *r*) to obtain (2):

(2) K_{t} (1 + *r*) = K_{0} (1 + *r*) + K_{0} (1 + *r*)^{2} + K_{0} (1 + *r*)^{3} + ... + K_{0} (1 + *r*)^{t }

Next, we subtract (2) from (1) to obtain (3):

(3) K_{t} − K_{t} (1 + *r*) = K_{0} − K_{0} (1 + *r*)^{t }

which we simplify to obtain our future value equation (4):

(4) K_{t} = K_{0} [(1 + r)^{t}* ** −* 1] / *r*, or

(5) K_{t} = β K_{0}, where the multiplier is β = [(1 + r)^{t}* ** −* 1] / *r*

*Example*: If an investment (CAPX, XRD, XDA) of 725 thousand USD is made at the end of each year for 12 years to create a valuable asset that is expected to generate an operating profit return *r* = 9% per year, the terminal value of the asset can be determined by using (4):

(4) K_{12} = 725 [(1 + 0.09)^{12}* ** −* 1] / 0.09 = 14,602 thousand USD,

which is based on a case specific (fact and circumstance) multiplier of β = [(1 + r)^{t}* ** −* 1] / *r *= 20.141.

We can use formula (4) to calculate the future *value* of any asset (including the value of identifiable intangible assets) to satisfy tax compliance rules in the event of an associated enterprise asset purchase.

From knowledge about an intitial investment (K_{0}) to create an identifiable asset subject to related party transfers, plus estimated expected life of the asset (*T*), we can perform *sensitive analyses* by varying the rate of return *within narrow limits* (0 < *r* ≤ *r*_{max}) and compute a defensible range of values of the target asset(s) purchase.