What is Inversion: Definition and 123 Discussions

A tax inversion or corporate tax inversion is a form of tax avoidance where a corporation restructures so that the current parent is replaced by a foreign parent, and the original parent company becomes a subsidiary of the foreign parent, thus moving its tax residence to the foreign country. Executives and operational headquarters can stay in the original country. The US definition requires that the original shareholders remain a majority control of the post-inverted company.

The overwhelming majority of the less than 100 material tax inversions recorded since 1993 have been of US corporations (85 inversions), seeking to pay less to the US corporate tax system. The only other jurisdiction to experience a material outflow of tax inversions was the United Kingdom from 2007 to 2010 (22 inversions); however, UK inversions largely ceased post the reform of the UK corporate tax code from 2009 to 2012.

The first inversion was McDermott International in 1983. Reforms by US Congress in 2004 halted "naked inversions", however, the size of individual "merger inversions" grew dramatically; in 2014 alone, they exceeded the cumulative value of all inversions since 1983. New US Treasury rules in 2014–16 blocked several major inversions (e.g. 2016 USD$160 billion Pfizer–Allergan plc inversion, and the 2015 USD$54 billion AbbVie–Shire plc inversion), and the Tax Cuts and Jobs Act of 2017 (TCJA) further reduced the taxation incentives of inversions. As of June 2019, there have been no material US inversions post-2017, and notably, two large Irish-based tax inversion targets were acquired in non-tax inversion transactions, where the acquirer remained in their higher-tax jurisdiction: Shire plc by Japanese pharma Takeda for US$63 billion (announced in 2018, closed in 2019), and Allergan plc by U.S. pharma AbbVie for US$64 billion (announced in 2019, expected to close in 2020); in addition, Broadcom Inc. redomesticated to the United States.
As of June 2019 the most popular destination in history for US corporate tax inversions is Ireland (with 22 inversions); Ireland was also the most popular destination for UK inversions. The largest completed corporate tax inversion in history was the US$48 billion merger of Medtronic with Covidien plc in Ireland in 2015 (the vast majority of their merged revenues are still from the US). The largest aborted tax inversion was the US$160 billion merger of Pfizer with Allergan plc in Ireland in 2016. The largest hybrid-intellectual property (IP) tax inversion was the US$300 billion acquisition of Apple Inc.'s IP by Apple Ireland in 2015.

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  1. T

    Mirror image inversion in the 4th dimension.

    I don't really know where this topic belongs. Let's say you're an ugly asymmetrical person, with your right hand much larger than the left. A 4th dimensional being removed you and "flipped" you in the 4th dimesion, then put you back. Would you come back with a large right hand...
  2. R

    Lateral inversion up-left and down-right confusion

    Hi :) So I'm learning about lateral inversion in plane mirrors and it's a bit confusing. I think of it like this:- Suppose you had a clone of your self who is standing next to you and facing the same direction. He walks a few steps forward and then turns to face you. When he turns to face...
  3. N

    Inversion Curve for a gas obeying Dieterici's equation of state

    Homework Statement For a gas obeying Dieterici's equation of state: P(V-b) = RTexp(-a/RTV) for one mole, prove that the equation of the inversion curve is P = ((2a/b^2) - (RT/b)) * exp((1/2) - (a/(RTb))) and hence find the maximum inversion temperature.Homework Equations N/A The Attempt...
  4. S

    General Relativity: Spatial Inversion Symmetry

    I am unable to find any source describing at any lengths transformations of the type x \rightarrow -x beyond the case of static spacetime (and even in the case of static spacetime, it is rarely the fundamental definition, which tends to be more along the lign of orthogonality with an...
  5. A

    Continuity of matrix multiplication and inversion in a normed vector space?

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  6. N

    Mellin's inversion integral, branch cut problem

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  7. V

    The error caused by the lagrange inversion

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  8. J

    Complex inversion formula (branch cut issue)

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  9. Q

    Need help with Weinberg's QFT-Space inversion and time-reversal

    Need help with Weinberg's QFT---Space inversion and time-reversal Weinberg's Quantum Theory of Fields VI. Page 78. He gave the last equation but he didn't prove it, although he qualitatively explained it. I tried to prove it quantitatively but I failed. Also, in page 80, he didn't prove...
  10. maistral

    What is wrong with my Laplace Transform inversion for y''+13y'-4y = 3exp(-t)?

    I'm inverting this: Y = s2 + 15s + 17 / [(s+1)(s2 + 13s - 4)] I'm using PF expansion, A/(s+1) + Bs + C/(s2 + 13s - 4), I however keep on getting wrong answers, seeing how Runge-Kutta and Taylor approximation disagrees with my final equation. My final equation is...
  11. G

    Topological Insulators and Inversion Symmetry

    Hi, I was curious if specific symmetries (or lack thereof) in crystal structure are necessary for the formation of topological insulators. Specifically, do we require that inversion symmetry (or inversion asymmetry) be present in the lattice in order to form the TI state? Thanks, Goalie33
  12. C

    Lateral Inversion of Images Formed by Convex & Concave Lenses

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  13. S

    Dynamic light scattering laplace inversion

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  14. C

    Can the Diagonal Property of a Matrix be Used to Speed Up Inversion?

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  15. N

    Inversion w.r.t. a sphere: Operator

    Hello everyone, I have enquired about inversion in a sphere here in past: https://www.physicsforums.com/showthread.php?t=440759 Although that time I could not come back to the discussion (apologies to Jason), later I went through some of the properties mentioned by him...
  16. M

    Inversion Temp: Critical Temperature Explained

    Invesion temp Critical temperature depends on increase or decrease of inversion temp?
  17. K

    Derivative of the inversion operator and group identity

    Homework Statement Let G be a Lie group, e be its identity, and \mathfrak g its Lie algebra. Let i be group inversion map. Show that d i_e = -\operatorname{id} . The Attempt at a Solution So this isn't terribly difficult if we have the exponentiation functor, since in that case e^{-\xi}...
  18. J

    Chromosphere population inversion?

    Assuming you could put two mirrors (one half-silvered) into the chromosphere, stationary, without them vaporizing/warping..., could they form a resonant chamber and produce laser radiation?
  19. B

    Laplace Inversion: Why Contour Must Exceed Singularities

    Maybe I am just being stupid, but I don't understand why in the Laplace inversion formula (\mathcal{L}^{-1} F)(t) = \frac{1}{2\pi i} \int_{\sigma-i\infty}^{\sigma+i\infty} e^{st} F(s) ds the contour of integration must be chosen so that \sigma is greater than the real part of all...
  20. Z

    Prove Analytically: Inversion of a Circle is Also a Circle

    Homework Statement Given the unit circle (in the Euclidean plane) centered at the origin x^2+y^2=1, and a general circle D with equation (x-a)^2+(y-b)^2=c^2 that does not pass through the origin (ie the center of inversion, ie a^2+b^2≠c^2, prove analytically that the inversion of D in the...
  21. R

    Compute Inversion of (143) Cycle

    Homework Statement Find an inversion of the following cycle (143) Homework Equations (143)^{-1} The Attempt at a Solution Could someone show me how do we compute this?
  22. H

    Circle Inversion Mapping: Proof of w = 1/z Transforming |z-1| = 1 to x = 1/2

    Homework Statement Show that the inversion mapping w = f(z) = 1/z maps the circle |z - 1| = 1 onto the vertical line x = 1/2. Homework Equations The Attempt at a Solution z = a + ib w = x + yi = a^2/(a^2 + b^2) + ib^2/(a^2 + b^2) |z - 1| = |(a -1) + ib | = 1 (a - 1)^2 + b^2 = 1...
  23. C

    Inversion of curl of A formula

    Hello! I'm reading up on Hamiltonian mechanics and i stumbled on the fact that the curl of the vector potential can be expressed as B_k = \sum_k \epsilon_{kij}\frac{\partial A_i}{\partial x_j} Now the text that I'm reading says that this formula can be inverted as \sum_k \epsilon_{kij}...
  24. S

    Help with Mobius Inversion in Riemann's Zeta Function by Edwards (J to Prime Pi)

    Help with Mobius Inversion in "Riemann's Zeta Function" by Edwards (J to Prime Pi) Can someone please add more detail or give references to help explain the lines of math in "Riemann's Zeta Function" by Edwards. At the bottom of page 34 where it says "Very simply this inversion is effected...
  25. A

    Lagrange inversion theorem

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  26. T

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  27. blindconsole

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  28. E

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  29. H

    Find the loss for the power inversion that would take place in the UPS

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  30. H

    Algebraic Inversion of Stress-Strain Relations?

    How is this accomplished? How can one derive equations for stress in terms of strain from equations of strain in terms of stress or vice versa?
  31. M

    Prove Summation of Mobius Inversion w/ Sigma Function

    Would like to show \sum_{d \mid n} \mu (d) \sigma_0 (d) = (-1)^{\omega (d)}. This proof is just left out of text I'm looking at and I can't seem to piece how F(n/d) = \sigma_0 (d), where F(x) = \sum_{s \mid x} f(x).
  32. H

    Question on MOS strong inversion

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  33. D

    Inversion of infinite continued fractions

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  34. N

    Are there methods for inverting non-square matrices under constraints?

    Hello, I need to invert a non-square matrix A under the constraint that the absolute value of each component of the solution is less than some maximum. In other words, I want \vec{b} such that A . \vec b = \vec c and |b_i| < \alpha. Are there any established methods for doing this? My...
  35. ApexOfDE

    [Laser] Inversion number above and below threshold

    Homework Statement Consider a 3-level laser. Give the occupation numbers N1(R), N2(R), the inversion \DeltaN(R)/N = [N2(R) - N1(R)]/N and the flux below and above the threshold as a function of pump rate R. F - the photon flux Homework Equations The Attempt at a Solution I have...
  36. Z

    A question about perturbation series inversion

    let be m a measures (by expermients) physical quantity and m0 a 'bare' value of these physical quantity , let us suppose that we can expand m= m_{0}+f(k,m_{0})+ \sum_{n} u^{n}c_{n} for some finite quantities c_n and u=log(\Lambda) with lambda a regulator can we then invert the...
  37. P

    Laser rate equation (population inversion)

    Homework Statement Problems and information is as attached. Homework Equations As attached. The Attempt at a Solution As attached, I can solve part b (although I do not know whether it is correct or not). For part c, I cannot simplify reach the given equation. For part d, I not...
  38. S

    Trouble With The Inversion Transformation

    Homework Statement 1) Given a circle, construct another circle which is orthogonal to it. List the steps taken in this construction. 2) For a fixed circle and a point P not on the circle nor equal to the center of the circle, construct the image of P under inversion with respect to the...
  39. J

    Using inversion formula for the fourier transform

    I need to deduce that \hat{\hat{f}}(x)=2\pif(-x) using the inversion formula for the Fourier transform, I was wondering if someone could explain why there's f(-x) because i just can't get started on this problem!
  40. M

    Is there a theorem that guarantees this?

    Homework Statement Let A be a 2x3 matrix with real coefficients, and suppose that neither of the two rows of A is a scalar multiple of the other. By quoting an appropriate theorem from linear algebra, show that for some j \in {1,2,3}, the 2x2 matrix obtained by omitting the jth column of A is...
  41. S

    Inversion of permutations (Algorithms problem)

    Homework Statement An inversion of a permutation is a pair of elements that are out of order. (a) Show that a permutation of n items has at most n(n−1)/2 inversions. Which permutation(s) have exactly n(n − 1)/2 inversions? (b) Let P be a permutation and Pr be the reversal of this...
  42. E

    How can I use inversion in a circle to simplify a problem?

    Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period. Thank you
  43. J

    Vector division or inversion

    How do you get a vector to the power of negative one? I.E. : V ^ (-1)? Or inversion if that's what it's called? Thank you.
  44. L

    Understanding Matrix Inversion in SL(2,C)

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  45. J

    2d temperature in a plate using Matrix Inversion and MATLAB

    Hi, I think i should have posted here instead of where I posted before. I don't know how I missed the homework help section... anyway Well, I'm required to solve this heat transfer problem. T1 is 25c and q'' is 100w/m2 Ok, so I can get it to do it in 1 dimension and my numbers...
  46. M

    Solving Laplace Inversion with Erfc

    When trying to solve a pde using Laplace transform, I need to invert an expression of the form \frac{\exp{(-as-b\sqrt{s})}}{s^2} A friend told me that Mathematica cannot invert such expression. I try using convolution but a bit loss when trying to evaluate the integral of Erfc(.)...
  47. G

    Inversion of this Vandermonde matrix

    I was trying to expand a three and more parameter functions similarly to the two-parameter case f(x,y)=(f(x,y)+f(y,x))/2+(f(x,y)-f(y,x))/2. Anyway, to do the same for more parameters I need to solve \begin{pmatrix} 1 & 1 & 1 & \dotsb & 1\\ 1 & \omega & \omega^2 & \dotsb & \omega^{n-1}\\ 1 &...
  48. Z

    What are efficient methods for solving A.x = b with a large sparse matrix?

    Hello everyone! I need to find the vector x in the problem A.x = b I have matrix A and vector b. Inverting the matrix would do it, but in my case, the matrix is quite big. Luckily, it is extremelly sparse (lots of 0), so I guess there could be some way to take advantage of it. The best...
  49. Z

    Solving equations by inversion formulae

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  50. S

    How to find the inverse of a Laplace Transform?

    Hi, I want to inverse this laplace transform, -(s^(1/2)), seems that the inverse is in complex plane. Where should i start to find this inverse... Thank you.
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