Case 1:20-cv-00393-LO-TCB Document 593-7 Filed 05/05/21 Page 1 of 4 PageID# 13647
`Case 1:20-cv-00393-LO-TCB Document 593-7 Filed 05/05/21 Page 1 of 4 Page|D# 13647
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`EXHIBIT Q
`EXHIBIT Q
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`Case 1:20-cv-00393-LO-TCB Document 593-7 Filed 05/05/21 Page 2 of 4 PageID# 13648
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`Converting Royalty Payment
`Structures for Patent Licenses
`J. Gregory Sidak*
`The parties to a patent-licensing agreement may choose from a variety of
`royalty structures to determine the royalty payment that the licensee owes
`the patent holder for using its patents. Three common structures of a royalty
`payment are (1) an ad valorem royalty rate, (2) a per-unit royalty, and (3) a
`lump-sum royalty. A royalty payment for a license might use a single royalty
`structure or a combination of these three structures.
`Converting a royalty payment with one structure into an equivalent
`payment with another structure enables one to compare royalty payments
`across different licensing agreements. For example, in patent-infringement
`litigation, an economic expert can estimate damages for the patent in suit
`by examining royalties of comparable licenses—that is, licenses that cover a
`similar technology and are executed under circumstances that are sufficiently
`comparable to those of the hypothetical license in question.1 However,
`licenses for a single patented technology might specify the royalty payment
`using different structures. One license might specify a per-unit royalty,
`a second might specify a lump-sum royalty, and a third might combine a
`lump-sum payment with a royalty rate. To analyze and compare the differ-
`ent royalty payments of those licenses, an economic expert or court must
`convert the royalties to a common structure. For example, a question related
`to the conversion of the royalty structure arose in August 2016 in Trustees of
`Boston University v. Everlight Electronics Co., where, in granting an interlocu-
`tory appeal, the court asked “whether a district court can correct a damages
`figure on a motion for remittitur by extrapolating a royalty rate and base
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`* Chairman, Criterion Economics, Washington, D.C. I thank Jeremy Skog and Jenny Jihyuon Park for
`
`helpful comments. The views expressed here are solely my own. Email: jgsidak@criterioneconomics.com.
`Copyright 2016 by J. Gregory Sidak. All rights reserved.
`1 See, e.g., LaserDynamics, Inc. v. Quanta Comput., Inc., 694 F.3d 51, 79 (Fed. Cir. 2012).
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` Electronic copy available at: https://ssrn.com/abstract=3178356
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`C r i t e r i o n
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`J o u r n a l
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`I n n o v a t I o n
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`Case 1:20-cv-00393-LO-TCB Document 593-7 Filed 05/05/21 Page 3 of 4 PageID# 13649
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`904
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`The Criterion Journal on Innovation
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`[Vol. 1:901
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`Thus, a lump-sum royalty might not reflect accurately the licensee’s ex post
`use of the patented technology.8
`
`II. Converting Royalty Payments
`of a One-Way License
`
`Using economic methodologies, one can convert a royalty with any given
`structure into an equivalent royalty that uses a different structure. For
`example, one can convert a royalty payment that is specified as a per-unit
`royalty into an equivalent royalty payment under a different structure, such
`as an ad valorem royalty rate. I will use the term derived royalty to indicate
`a royalty that one obtains from the deconstruction or transformation of a
`royalty payment. Because the derived royalty and the original royalty payment
`of a license imply the same expected payment at the time of a license’s issu-
`ance, the parties to a patent-licensing agreement will be indifferent between
`the two royalty payments.
`I begin my analysis by examining a one-way license—that is, a license in
`which the parties determine the royalty that the licensee will pay the patent
`holder to use its licensed patents. The parties might determine the royalty
`payment using a single royalty structure or by using a complex structure that
`combines multiple royalty structures.
`A. Licenses That Use a Single Royalty Structure
`Simple economic methodologies enable the conversion of royalties in one-way
`licenses that use a single royalty structure. Suppose that a license specifies
`a per-unit royalty and that one must convert that royalty into an equivalent
`ad valorem royalty rate. To do so, one should compare the expected royalty
`payments under the two royalty structures and find the royalty rate that
`makes the two payments equal under appropriate assumptions. For example,
`when the license specifies a per-unit royalty, the expected royalty payment
`that the patent holder will receive equals the per-unit royalty multiplied by
`the projected number of the patent-practicing product’s sold units, which
`the parties estimate at the time of the license’s issuance. Equation (1) states
`this relationship:
`
`(1)
`= Expected Royalty Payment.
`Per-Unit Royalty Fee × Projected Number of Units
`Conversely, when the license specifies an ad valorem royalty rate, the expected
`royalty payment equals the projected price of the licensed product multiplied
`
`8 See J. Gregory Sidak, How Relevant Is Justice Cardozo’s “Book of Wisdom” to Patent Damages?, 16 Columbia
`SCi. & TeCh. l. Rev. 246 (2016).
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`Case 1:20-cv-00393-LO-TCB Document 593-7 Filed 05/05/21 Page 4 of 4 PageID# 13650
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`2016]
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`Royalty Conversion for Patent Licenses
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`905
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`by the projected number of sold units (for simplicity, I will call this algebraic
`product the licensee’s projected sales revenue) and by the royalty rate, as
`Equation (2) shows:
`
`(2)
`= Expected Royalty Payment.
`Projected Revenue × Royalty Rate
`Setting Equations (1) and (2) equal, one can derive the following relationship:
`
`Per-Unit Royalty Fee ×
`= Projected Revenue ×
`Projected Number of Units
`Royalty Rate.
`Therefore, one can derive an ad valorem royalty rate simply by dividing the
`total projected royalty payment by the projected revenue. Equation (4)
`expresses that relationship:
`
`(3)
`
`Per-Unit Royalty Fee × Projected Number of Units
`Projected Revenue
`Because the licensee’s projected revenue equals the projected number of sold
`units of the patent-practicing product multiplied by the projected price per
`unit, one can state the relationship of Equation (4) more simply as:9
`
`= Derived Royalty Rate.
`
`(4)
`
`=
`
`Derived Royalty Rate.
`
`(5)
`
`Per-Unit Royalty Fee
`Projected Price Per Unit
`Thus, simply using the projected unit price of the licensed product enables
`one to convert a per-unit royalty fee into a derived royalty rate.
`Similarly, one can deconstruct a lump-sum royalty payment into a
`derived royalty rate. A licensee might make a lump-sum payment either
`collectively at the beginning of the license’s term or progressively following
`a schedule over that term. In either case, one can calculate the present value
`of projected revenues over the license’s term using the discounted cash flow
`(DCF) method by applying an appropriate discount rate,10 as Equation (6)
`shows:
`
`
`
`9 The following equation illustrates the substitution and reduction process:
`(Per-Unit Royalty Fee) (Projected Number of Units)
`Per-Unit Royalty Fee
`(Projected Price Per Unit) (Projected Number of Units)
`Projected Price Per Unit
`10 See William Choi & Roy Weinstein, An Analytical Solution to Reasonable Royalty Rate Calculations, 41
`
`J.L. & Tech. 49, 56 (2001) (emphasizing that a DCF method is used to “discount, into present value, the
`expected cash flow from a licensing agreement”); see also Heberden, supra note 6, at 21 (“[The discount rate]
`is a function of three factors: the risk free rate (yield on government bonds), the market risk premium (extra
`risk applying to the share market), and specific risks attached to the company and [(intellectual property)]
`IP.”).
`
`=
`
`