|                BCD-UK plc manufactures a product and sells that product to its parent
|                corporation, BCD. BCD-UK plc also sells the product to WXY Corp, that
|                it does not control, at a price of $100 per unit. Except for the
|                volume of each transaction, the sales to BCD and to WXY Corp take
|                place under substantially the same economic conditions and contractual
|                terms. In uncontrolled transactions, BCD-UK plc offers a 2% discount
|                for quantities of 20 per order, and a 5% discount for quantities of
|                100 per order. If BCD purchases the product in quantities of 60 per
|                order, in the absence of other reliable information, it may reasonably
|                be concluded that the arm's length price to BCD would be $100, less a
|                discount of 3.5%.
|
|                        http://www.intltaxlaw.com/shared/transfer/regs.htm



the scenario some-type uses some-method with controlled seller some-seller1 controlling buyer some-co1 and uncontrolled buyer some-co2
in the scenario that-type the controlling buyer that-co1 purchases items in a quantity some-ctrld-qty
the scenario that-type has a base price some-price and an uncontrolled volume discount some-lo-disc for a quantity some-lo-qty
the scenario that-type has a base price that-price and an uncontrolled volume discount some-hi-disc for a quantity some-hi-qty
that-lo-qty is less than that-hi-qty
interpolating between that-lo-qty that-lo-disc and that-hi-qty that-hi-disc yields that-ctrld-qty and some-ctrld-discount
that-price discounted by that-ctrld-discount % is some-transfer-price
---------------------------------------------------------------------------------------------------------------------------
in the scenario that-type the price for a controlled quantity that-ctrld-qty is that-transfer-price


the scenario this-type uses this-method with controlled seller this-co1 controlling buyer this-co2 and uncontrolled buyer this-co3
==================================================================================================================================
              d-3-ii      arms length method                  BCD-UK plc                 BCD Corp                         WXY Corp


in the scenario this-type the controlling buyer this-co purchases items in a quantity this-qty
====================================================================================
                 d-3-ii                        BCD Corp                     40
                 d-3-ii                        BCD Corp                     60


the scenario this-type has a base price this-price and an uncontrolled volume discount this-disc for a quantity this-qty
=======================================================================================================================
              d-3-ii                   100                                             2                          20
              d-3-ii                   100                                             5                         100


100 - some-discount = some-difference
that-difference / 100 = some-factor
some-price * that-factor = some-discounted-price
-----------------------------------------------------------------
that-price discounted by that-discount % is that-discounted-price


some-x1 is less than some-x
that-x is less than some-x2
that-x2 - that-x1 = some-xdifference
some-y1 is less than some-y2
that-y2 - that-y1 = some-ydifference
that-x - that-x1 = some-xinterp
that-xinterp / that-xdifference = some-xratio
that-ydifference * that-xratio = some-ybonus
that-y1 + that-ybonus = some-y
----------------------------------------------------------------------------------
interpolating between that-x1 that-y1 and that-x2 that-y2 yields that-x and that-y