Unlike the debutant affection of the OECD, we discourage using projected profits or cash flows to measure hard-to-value-intangibles (HTVI) for transfer pricing purposes because this method is speculative and based on several impeachable assumptions.

On May 23, 2017, the OECD released a draft of Action 8 of the Base Erosion and Profit Shifting (BEPS) plan, providing taxpayers and tax administrations with a new transfer pricing approach to measure hard-to-value-intangibles: https://www.oecd.org/tax/transfer-pricing/BEPS-implementation-guidance-on-hard-to-value-intangibles-discussion-draft.pdfDeviating from the past__,__ the new OECD guidance states that “a tax administration is entitled to use, in evaluating the *ex-ante* pricing arrangements, the *ex-post* evidence about financial outcomes to inform the determination of the arm’s length pricing arrangements that would have been made between independent enterprises at the time of the transaction.” This provision is near the US “commensurate with income” rules applied to controlled intangibles.

Unlike the debutant affection of the OECD, we discourage using discounted projected profits or cash flows to measure hard-to-value-intangibles for transfer pricing purposes because this method is speculative and based on many impeachable assumptions.

Instead, we recommend use of objective, tractable data from separate and identifiable past enterprise investments to measure capital stock, including intangibles.

In practice, capital expenditures (CAPX) recorded on the cash flow statement of an enterprise measures investment in property, plant, and equipment (PPENT), excluding intangibles. Thus, we must find intangible producing investments, such as detailed historical advertising, R&D, and software incurred expenses obtained from the tested party’s general ledger or from comparable aggregate disclosed filings.

According to current accounting practices, research and development (XRD), advertising (XAD), and software expenses are deducted in the fiscal year incurred and are not accumulated on the tested party’s balance sheet or its comparables. The relevant variables of the selected enterprise are: K* _{t}* is a calculated value of the capital stock in period

*t*, D

*is depreciation (or amortization) of the capital stock employed in the previous period, and X*

_{t}*are the separate and distinct deductible expenses attributed to the property being valued.*

_{t}To start, we collect separate annual expense streams X* _{t}* to construct an identifiable asset, ditto net capital stock:

(1) ∆K* _{t}* = X

*− D*

_{t}

_{t}counting each fiscal period backwards, starting with the current *t*, *t* – 1, *t* – 2, etc. The symbol ∆ represents one-period change, such as ∆K* _{t}* = K

*− K*

_{t}

_{t}_{ – 1}.

Although cumulative XRD, software, and XAD expenses add to an enterprise capital stock, they may do so with a different time-lag than PPENT, and we can accommodate these differences. In general, we assume a fixed depreciation (or amortization) rate calculated on the value of the capital stock (or discernible assets) at the end of a measured period:

(2) D* _{t}* = δ K

_{t}_{ − 1}

where the parameter 0 < δ < 1 is the depreciation (or amortization) rate specific to each identifiable asset we need to measure.

In economics, tangible assets represent the accumulation of CAPX. Likewise, intangible assets represent the accumulation of XRD, software, or XAD investments, which we measure in the combined or aggregate form of production (also called “trade”), software, and marketing intangibles, or by considering the separate accumulated flows of XRD, software, or XAD annual investments (treated as deductible expenses for tax purpose).

We combine (1) and (2), and obtain a recursive formula for the capital stock based on past annual expense flows:

(3) K* _{t}* = X

*+ β K*

_{t}

_{t}_{ − 1}

where 0 < (β = (1 – δ)) ≤ 1 is the rate of capital accumulation.

Next, we lag (3) repeatedly and substitute back to create a recursive formula__:__

(4) K* _{t}* = X

*+ β X*

_{t}

_{t}_{ – 1 }+β

^{2}X

_{t}_{ – 2 }+ … + β

*K*

^{k}

_{t}_{ − k}

where the index *k* counts the terminal year back.

Declining beta coefficients imply that we don’t need to backtrack to time immemorial because several years backward iterations can produce reliable results. For example, if δ = 0.2 (or 20% depreciation rate per year), β = 0.8, and we obtain from the recursive formula (4) going back three years:

(5) K* _{t}* = X

*+ 0.8 X*

_{t}

_{t}_{ – 1 }+0.64 X

_{t}_{ – 2 }+ 0.512 X

_{t}_{ – 3}+ 0.4096 K

_{t}_{ − 4 }

In this example, tracking back 12 years of identifiable expenses, we would obtain the vanishing residual 0.0687 K_{t}_{ – 13}. This means that only a diminished 6.87% of the capital stock back in the 13th year adds to the current accumulated sum (4), and eventually the beta coefficients become too negligible to count into (5).

The recursive economic formula (4) is general, and thus applies for CAPX, XRD, software, XAD or any separate and identifiable expense flow. Intangibles are not hard-to-value if we use an objective (known historical data; no speculative profit projections into an uncertain future) economic formula (4) and approach this HTVI problem *sans mystère*.

**Ednaldo Silva**(Ph.D.) is founder and managing director at RoyaltyStat. He helped draft the US transfer pricing regulations and developed the comparable profits method called TNNM by the OECD. He can be contacted at: esilva@royaltystat.com

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