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`EXHIBIT 1
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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
`
`* 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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`[Vol. 1:901
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`from the jury’s lump-sum award without express expert testimony explain-
`ing how to do so.” 2
`Some courts have been skeptical that one can convert royalties across
`different structures. For example, also in August 2016 in Baltimore Aircoil Co.
`v. SPX Cooling Technologies Inc., Judge Catherine Blake of the U.S. District
`Court for the District of Maryland excluded, in an order ruling on the patent
`holder’s Daubert motion,3 the opinion of the alleged infringer’s economic
`expert, Kimberly Schenk of Charles River Associates, for using “lump sum
`agreements in calculating running royalty rates.”4 Judge Blake faulted Ms.
`Schenk for providing no justification for using the alleged infringer’s sales
`projections in converting between the two royalty structures and concluded
`that her opinion “offer[ed] mere speculation masquerading as quantitative
`analysis.”5
`In this article, I explain how economic methodologies can enable an
`expert or a court to convert royalty payments reliably across different royalty
`structures. I show that such conversion of royalty payments requires not an
`accounting framework, but rather an economic framework. Projecting future
`sales, product prices, and market conditions are vital not only to produc-
`ing accurate estimates of expected royalty payments, but also to converting
`those royalty payments across licenses that might specify different royalty
`payment schedules. Although those projection methods require addi-
`tional judgment beyond a simple and straightforward calculation, convert-
`ing royalty payments across different structures is a standard exercise that
`involves processes similar to those used to value patents outside adversarial
`proceedings.6 The conversion of royalty payments across different structures
`need not be unreliable or inherently speculative.
`In Part I, I describe three common structures of royalty payments for
`patents and analyze their main differences. In Part II, I explain how one can
`deconstruct a royalty payment into an equivalent payment with a different
`royalty structure in both simple and complex one-way licenses. In Part III,
`I show how to extend this framework to include the value of a cross license
`flowing back to the net licensor. I show that such methods enable courts to
`convert and reliably compare the royalty payments of different structures.
`
`2 Nos. 12-11935, 12-12326, 2016 WL 4238554, at *2 (D. Mass. Aug. 9, 2016).
`
`3 Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 589–97 (1993) (establishing the district court as
`
`“gatekeeper” for admitting scientific expert testimony); see also J. Gregory Sidak, Court-Appointed Neutral
`Economic Experts, 9 J. Competition L. & Econ. 359, 384–86 (2013) (analyzing Daubert and its progeny).
`
`4 No. CCB-13-2053, 2016 WL 4426681, at *25 (D. Md. Aug. 22, 2016).
`5 Id.
`
`6 See, e.g., Tim Heberden, Intellectual Property Valuation and Royalty Determination, in International
`
`Licensing and Technology Transfer: Practice and the Law ch. 4 (Adam Liberman, Peter Chrocziel
`& Russell Levine eds., Wolters Kluwer 2011).
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`Royalty Conversion for Patent Licenses
`
`903
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`I. Three Primary Structures
`of Royalty Payments
`
`A patent license typically contains one or more of the following three royalty
`structures: (1) an ad valorem royalty rate, (2) a per-unit royalty, or (3) a lump-
`sum royalty. If the license specifies a royalty rate, the parties calculate the
`royalty payment as a percentage of a royalty base, which is typically the
`sales price of each sold product that practices the licensed technology. The
`patent holder charges the licensee that royalty payment in increments at a
`predetermined frequency, often on a yearly or quarterly basis. Under a royal-
`ty-rate structure, the royalty payment is positively correlated with both the
`price and the number of sold units of the product that practices the licensed
`patent. An increase in the quantity of units sold, an increase in the per-unit
`price of the patent-practicing product, or some combination the two will
`increase the total royalty payment. However, the licensee will not pay the
`patent holder any royalty if it does not sell any patent-practicing products.
`When a license specifies a per-unit royalty, the royalty payment is depen-
`dent on and positively correlated with the number of shipped units—that is,
`the volume of patent-practicing products that the licensee sells during the
`term of the license agreement. Thus, the royalty payment that a licensee pays
`under the terms of a per-unit royalty, like that of a royalty rate, varies directly
`with the licensee’s use of the patented technology. When the licensee’s ship-
`ment volume increases or decreases, the total royalty that the licensee pays
`changes accordingly. However, unlike a royalty rate, a per-unit royalty is
`independent of changes in the sales price of the patent-practicing product.
`In contrast to a royalty rate or per-unit royalty, a lump-sum royalty
`specifies a fixed, aggregate amount that the licensee must pay to obtain the
`right to use the patented technology during the term of the license. A lump-
`sum royalty removes the administrative burden and costs of monitoring the
`actual use of the licensed technology because the royalty payment is inde-
`pendent of the licensee’s actual sales. The licensing parties typically agree
`upon the amount of the lump-sum royalty before the royalty-bearing sales
`occur—that is, they typically calculate a lump-sum payment in advance by
`using the licensee’s projected sales revenue or unit shipments for the duration
`of the license.7 The licensee typically makes that payment at the beginning
`of the license term or according to a predetermined payment schedule. The
`licensee will pay the full amount of the predetermined lump-sum royalty
`regardless of the extent to which it actually uses the licensed technology.
`
`7 See, e.g., Linkco, Inc. v. Fujitsu Ltd., 232 F. Supp. 2d 182, 188 (S.D.N.Y. 2002) (“[A] reasonable royalty
`
`may be computed in various ways, including a lump-sum royalty based on expected sales.”).
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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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`Royalty Conversion for Patent Licenses
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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.”).
`
`=
`
`
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`Last Payment
`
`Total Projected Revenue
`Present Value of
`∑
`Projected Revenue.
`(1 + Discount Rate)Time
`First Payment
`Dividing the lump-sum royalty payment by the present value of the licensee’s
`projected sales revenue following Equation (7), one can calculate the derived
`royalty rate of a lump-sum royalty payment:
`
`=
`
`(6)
`
`(7)
`
`= Derived Royalty Rate.
`
`Lump-Sum Royalty Payment
`Present Value of Projected Revenue
`Note that Equations (5) and (7)—which one can use to convert a per-unit
`royalty and a lump-sum royalty into a derived royalty rate—are easily invert-
`ible. For example, multiplying a royalty rate by the projected per-unit price
`gives a derived per-unit royalty of equivalent value at the time of the license’s
`issuance. Similarly, multiplying a royalty rate by the present value of the
`licensee’s projected revenues gives a derived lump-sum royalty of equivalent
`value. Finally, it is possible to convert a lump-sum royalty into an equivalent
`per-unit royalty—and vice versa—by using either Equation (5) or Equation (7)
`to convert that royalty payment into a derived royalty rate as an intermediate
`step.
`In sum, economic projections enable one to convert seamlessly an
`observed royalty from any of the three main royalty structures into one
`under another structure.
`B. Licenses That Use a Complex Royalty Structure
`By employing similar techniques, an economic expert can likewise decon-
`struct a royalty payment for a complex license—that is, a license that
`combines multiple royalty structures to determine a royalty payment. For
`example, suppose that a license specifies both a lump-sum payment of
`$500,000 and an additional per-unit royalty of $1. One can deconstruct that
`license in two steps to calculate a derived royalty rate. First, one must convert
`each component of the complex royalty that corresponds to each structure
`that the complex royalty uses into an equivalent royalty rate using the tech-
`niques outlined above in Part I.A. One can then calculate a derived royalty
`rate by simply summing the calculated royalty rates of each component.
`For example, if an economic expert finds that the lump-sum payment of
`$500,000 is equivalent to a royalty rate of 3 percent, and the per-unit royalty
`of $1 is equivalent to a royalty rate of 2 percent, then the derived royalty rate
`would be 5 percent for the license agreement.
`A complex license might also combine an ad valorem royalty rate with
`a royalty cap—that is, an upper limit on the royalty fee that the licensee
`
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`Royalty Conversion for Patent Licenses
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`907
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`would pay for each licensed product. Under that structure, the royalty rate
`determines the per-unit royalty payment unless that payment exceeds the
`specified cap, in which case the royalty payment becomes a fixed, per-unit
`fee equivalent to the (binding) cap. One can estimate the value of a royalty
`defined under this structure by calculating a probability-weighted expected
`royalty fee—that is, by multiplying the royalty fee associated with each possi-
`ble unit price by the respective probability that the product will sell at that
`price and then taking the sum of the resulting products.
`For example, consider a technology that is licensed at a 1-percent
`royalty rate with a $2 cap on the per-unit royalty fee. Suppose that there is a
`60-percent probability that the product incorporating this technology will
`sell at $180 per unit and a 40-percent chance that it will sell at $220 per unit.
`If the product sells at $180 per unit, then the licensee pays a $1.80 per-unit
`royalty fee ($180 × 1% = $1.80). Alternatively, if the product sells at $220 per
`unit, the royalty rate would yield a $2.20 per-unit royalty fee ($220 × 1% =
`$2.20), which exceeds the $2 cap. In that case, the royalty cap takes effect,
`and the licensee pays a flat $2.00 royalty fee, which is equivalent to the
`binding cap. Taking a probability-weighted average of those results, one can
`calculate an overall per-unit royalty fee of $1.88.11
`Although deconstructing the royalty payment for a complex license can
`be burdensome, as it requires more data and estimation of the probabilistic
`price distribution, the theoretical basis is straightforward. If sufficient data
`are available, this methodology produces an economically sound value for
`the derived royalty rate.
`
`III. Converting Royalty Payments
`of a Cross License
`
`Unlike a one-way license, a cross license assigns to each party the right to use
`the counterparty’s patents. Implicit in a cross license is the idea that each
`party pays to use the counterparty’s licensed patents. However, the one-way
`royalties that the two parties pay each other are not determined separately
`in the license. Rather, the license specifies only a single balancing royalty—
`that is, the ultimate royalty that one party (the net payor) must pay to the
`counterparty (the net payee). Specifying only the balancing royalty payment
`reduces the license agreement’s transaction costs and accounting costs by
`simultaneously accounting for both parties’ royalty payments.
`
`
`
`11 That is, ($1.80 60%) + ($2.00 40%) = $1.88.
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`A. A Framework for Understanding the Balancing Royalty
`The following analogy illustrates the concept of a balancing royalty.12 Consider
`a driver who wants to replace his old BMW 328i with a new Toyota Camry. At
`the dealership, he decides to accept the dealer’s offer to trade in his used car
`and receive a credit (a trade-in allowance) toward the price of the Camry. The
`dealer and the driver are each, in effect, buying and selling simultaneously
`in this transaction. The dealer offers to buy the used BMW at a price equal
`to the trade-in allowance. The better the condition of the used BMW, the
`higher the credit the dealer will grant the driver toward the net price—that
`is, the total amount of cash that the driver will pay for the new Camry. If the
`BMW’s fenders were rusted, the dealer would offer less than if the car were
`in a pristine condition.
`An analogous transaction occurs when two patent holders cross license
`their respective portfolios. Each patent portfolio commands a particular
`one-way royalty payment from the counterparty. Typically, the royalty that
`a cross license specifies is a balancing royalty that one party must pay to the
`other—that is, the difference between the two opposing one-way royalties
`that each party owes the other for the use of its respective patent portfo-
`lio. The value that each party’s patent portfolio generates for the other party
`determines the net-paying and net-receiving parties, as well as the amount of
`the balancing royalty. As Figure 1 illustrates, the balancing royalty is analo-
`gous to the net price that the driver pays the dealer for the new Camry.
`
`12 See J. Gregory Sidak, How Licensing a Portfolio of Standard-Essential Patents Is Like Buying a Car, WIPO,
`
`June 2015, at 11.
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`Royalty Conversion for Patent Licenses
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`909
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`Figure 1. The Balancing Royalty Payment in a Cross License
`= Net Amount
`Due
`
`–
`
`Value of Trade-In
`
`Price of New Car
`
`–
`
`=
`
`Payment
`
`=
`
`Balancing
`Royalty
`Payment
`
`–
`
`Value that Party B’s
`Value that Party A’s
`Patented Technology
`Patented Technology
`Generates for
`Generates for
`Party A’s Products
`Party B’s Products
`Sources: BMW Pre-Owned Inventory, BMW of Visalia, http://bmwofvisalia.com/Used-
`Cars/2014-BMW-328i-Visalia-MtnSLvfCnk_h4ZcN_gg4uA; New 2016 Toyota Camry LE Sedan
`Front-Wheel Drive in Klamath Falls, Lithia Toyota of Klamath Falls, https://www.lithiatoy-
`otaklamathfalls.com/new/Toyota/2016-Toyota-Camry-klamath-falls-OR-7992e7a90a0e0adf-
`001605dee09e18b0.htm.
`The following equation captures the relationship between the balancing
`royalty, royalty rates, and sales revenues of the two parties to the license:
`
`(8)
`
`=
`
`Balancing Royalty.
`
`(Royalty Rate of B × Sales Revenue of A) –
`(Royalty Rate of A × Sales Revenue of B)
`Figure 2 illustrates this relationship. Party A’s one-way royalty payment for
`the use of Party B’s patent portfolio is the area of the entire box in Figure 2.
`That is, the royalty equals Party A’s sales revenue from its licensed products
`multiplied by Party B’s royalty rate. Party B’s one-way royalty payment for the
`use of Party A’s portfolio is the area of the dotted box. Similarly, that amount
`is Party B’s sales revenue from its licensed products multiplied by Party A’s
`royalty rate. The difference in the areas of the two boxes, shaded in solid,
`equals the balancing royalty that Party A (the net payer) pays Party B (the net
`payee) under the cross license.
`
`
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`Figure 2. The Balancing Royalty in a Cross License
`
`The magnitude and direction of the balancing royalty depend on the differ-
`ence between the royalty payment that Party A owes Party B and the royalty
`payment that Party B owes Party A. Suppose that Party B’s patent portfolio
`has a higher royalty rate, and that Party A has higher sales revenues from its
`licensed product. Given those conditions, Party A gains higher value from
`the licensed patents and must therefore pay the balancing royalty to Party B,
`as Figure 2 shows.
`The balancing royalty in the cross license is necessarily less than the
`one-way royalty that the net-receiving party would charge the net-paying
`party for using its licensed patents. It bears emphasis that the net-receiv-
`ing party is determined on the basis of both (1) the relative strength of each
`party’s patent portfolio and (2) the amount of each party’s sales. Assume,
`for example, that Party A charges a royalty rate of 10 percent, while Party B
`charges a rate of 1 percent. Assume further that Party A generates sales reve-
`nues of $1,000 from its patent-practicing product and that Party B generates
`only $100. Applying Equation (8) shows that, although Party A possesses a
`stronger patent portfolio, the balancing royalty in this situation would be
`zero percent. Therefore, the net recipient is not necessarily the party with
`the strongest patent portfolio. In a cross license where the parties’ sales are
`assumed to be equal, the closer the value of the weaker patent portfolio is
`to the value of the stronger patent portfolio, the lower the balancing royalty
`rate because the value of the exchanged technology accounts for a larger
`portion of the implicit royalty payment.
`
`
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`Royalty Conversion for Patent Licenses
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`911
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`B. Relative Patent-Portfolio Strength Between the Two Parties to a Cross License as
`the Second Dimension of a Lump-Sum Royalty
`Deconstructing a lump-sum royalty in a cross license into a derived one-way
`royalty rate requires an economic expert to consider a second factor that is
`absent in the case of one-way licenses—the relative patent-portfolio strength
`of the two parties to the cross license. Two variables remain unknown in the
`calculation of the balancing payment: (1) the implicit royalty rate that Party
`A sets and (2) the implicit royalty rate that Party B sets. Because the royalty
`rate at which a patent holder licenses its patent portfolio reflects the strength
`of that patent portfolio, the ratio of those two implicit rates is equal to the
`strength of Party A’s patent portfolio relative to Party B’s patent portfolio, as
`Equation (9) shows:
`
`=
`
`Relative Portfolio Strength.
`
`(9)
`
`Royalty Rate of Party A
`Royalty Rate of Party B
`Assuming that the royalty a firm charges for licensing its portfolio is posi-
`tively related to the strength of that portfolio, an economic expert can
`deconstruct the implicit royalty rates using a separate exogenous measure of
`the portfolios’ relative strengths. Although the relative portfolio strength of
`two parties can change over time, those changes are likely to occur slowly
`due to the pace of patent filings and patent issuances.13
`It also bears emphasis that, although the relative portfolio strength
`serves as a practical proxy for the ratio of the royalty rates, the correspon-
`dence is unlikely to be perfect. That is, the relative strength of a patent
`portfolio and the actual royalty rates might depend on other factors, such
`as the relative demand for the patented technology. For example, suppose
`that the two parties are smartphone manufacturers. One produces basic,
`low-end smartphones, whereas the other produces high-end smartphones.
`Suppose further that the patented technology in question is part of the 4G
`standard. Assuming that 4G readability forms a greater percentage of the
`value of low-end smartphones, a greater royalty rate might be justified for
`the low-end smartphone manufacturer.
`For the purposes of my analysis, I treat relative portfolio strength as
`an exogenous parameter that the expert must estimate. One can rearrange
`Equation (9) such that the royalty rate that Party A sets is some multiple of
`the royalty rate of Party B:
`13 For ease of exposition, I assume here that the relative portfolio strength has a direct and linear re-
`lationship with respect to the ratio of the parties’ one-way royalty rates. Intuitively, a firm with a stronger
`patent portfolio will be able to charge a higher royalty for a license to its patents. One could replace this
`direct and linear measure of relative portfolio strength with a nonlinear functional form if the necessary
`data were available to estimate that nonlinear functional form.
`
`
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`(10)
`Royalty Rate of A = Relative Portfolio Strength × Royalty Rate of B.
`Using Equation (10), one can solve for the derived one-way royalty rates. For
`example, to solve for Royalty Rate of B, one can first substitute the term for
`Royalty Rate of A in Equation (8) into Equation (10), so that:
`
`(11)
`Balancing Royalty = (rB × SA) – (Relative Portfolio Strength × rB × SB),
`where rB denotes the royalty rate of Party B’s patent portfolio, and SA and SB
`denote the sales revenue of Party A and Party B, respectively. Assuming that
`relative portfolio strength is known, there is only one unknown variable in
`this equation: the royalty rate of Party B’s patent portfolio (rB). One can thus
`solve for that royalty rate in terms of the other known variables. Rearranging
`to isolate the variable rB, Equation (11) becomes:
`Balancing Royalty
`SA – (Relative Portfolio Strength × SB)
`Therefore, by making certain assumptions about the relationship between
`the portfolio strength of any two counterparties, one can transform a balanc-
`ing royalty payment in a cross license into a derived one-way royalty rate.
`
`(12)
`
`=
`
`rB.
`
`IV. Conclusion
`
`Basic economic techniques equip a damages expert with a reliable means
`of converting a royalty payment with one structure to a royalty of equiva-
`lent value under a different structure. I have shown that one can use reliable
`methodologies to convert royalty payments across structures both (1) in cases
`where the parties have executed a one-way license—that is, a license in which
`the parties determine the conditions for the licensee’s use of the patent hold-
`er’s patents—and (2) in cases where the parties have executed a cross license,
`which grants each party the right to use the counterparty’s patents. When
`the license uses a simple royalty structure, converting the royalty payment
`across different structures is also relatively simple. For example, informa-
`tion about the patent-practicing product’s projected price might suffice to
`convert a per-unit royalty fee to a derived royalty rate. However, when the
`license in question is a cross license or complex license, converting royalty
`payments to a derived royalty rate might be more burdensome, as it might
`require the estimation of additional parameters, such as relative portfolio
`strength. Nevertheless, with sufficient data, existing economic methodolo-
`gies offer a reliable basis for estimating and comparing the derived royalty
`rates of different licenses. Courts can supplement the derived royalty rate
`
`
`
`Case 1:20-cv-00393-LO-TCB Document 1093-1 Filed 02/25/22 Page 14 of 16 PageID# 29967
`
`2016]
`
`Royalty Conversion for Patent Licenses
`
`913
`
`with adjustments to account for a company’s bargaining power or market risk
`implicit in the different royalty structures.
`
`V. Appendix
`
`Here, I present a concise set of equations to summarize each royalty-struc-
`ture-conversion process. This appendix can serve as a reference for economic
`experts and courts when converting royalty payments across different
`structures.
`
`Table A1. Variables Used in Calculations
`
`Variable
`Ru
`Rl
`rs
`rd
`Rc
`E[u]
`E[R]
`E[S]
`E[p]
`E[S0]
`d
`t
`wi
`rA
`rB
`SA
`SB
`Rb
`x
`
`Definition
`Per-Unit Royalty Fee
`Lump-Sum Royalty Payment
`Ad Valorem Royalty Rate
`Derived Royalty Rate
`Per-Unit Royalty Cap
`Projected Number of Units
`Expected Royalty Payment
`Projected Revenue
`Projected Price Per Unit
`Present Value of Projected Revenue
`Discount Rate
`Time
`Probability of Event i
`Royalty Rate of Party A
`Royalty Rate of Party B
`Sales Revenue of Party A
`Sales Revenue of Party B
`Balancing Royalty Payment
`Relative Portfolio Strength
`
`
`
`Case 1:20-cv-00393-LO-TCB Document 1093-1 Filed 02/25/22 Page 15 of 16 PageID# 29968
`
`914
`
`The Criterion Journal on Innovation
`
`[Vol. 1:901
`
`A. Converting Royalty Payments of One-Way Licenses
`
`1. Deriving a Royalty Rate from a Per-Unit Royalty
`
`Ru × E[u]
`
`Ru × E[u]
`E[S]
`
`Ru × E[u]
`E[p] × E[u]
`
`=
`
`=
`
`=
`
`E[R]
`
`E[R]
`E[S]
`
`Ru
`E[p]
`
`=
`
`=
`
`rd
`
`rd
`
`2. Deriving a Royalty Rate from a Lump-Sum Royalty
`
`∑T
`
`t=1
`
`E[S]
`(1 + d)t
`Rl
`E[S0]
`
`= E[S0]
`
`=
`
`rd
`
`3. Converting Across the Three Royalty Structures
`
`(A1)
`
`(A2)
`
`(A3)
`
`(A4)
`
`(A5)
`
`Rl
`Ru
`E[S0]
`E[p]
`4. Deriving a Royalty Rate of a Complex License with Multiple Structures
`
`~
`
`rs
`
`~
`
`(A6)
`
`Rtotal
`
`rd
`
`rd
`
`=
`
`=
`
`=
`
`RPer-Unit
`Ru
`E[p]
`rd,Per-Unit
`
`+
`
`+
`
`+
`
`RAd-Valorem
`
`rs
`
`rd,Ad-Valorem
`
`+
`
`+
`
`+
`
`RLump-Sum
`Rl
`E[S0]
`rd,Lump-Sum
`
`(A7)
`
`(A8)
`
`(A9)
`
`
`
`Case 1:20-cv-00393-LO-TCB Document 1093-1 Filed 02/25/22 Page 16 of 16 Pag