# Net Income under FIFO Vs. LIFO

I need help understanding the derivation of this formula:

Net IncomeFIFO = Net IncomeLIFO + (LIFO ReserveEnd - LIFO ReserveBeginning)*(1-TaxRate)

It works, but I do not understand why it works. EDIT: Updated for future readers to the corrected formula

Your formulaâ€™s off just a bit:

Net IncomeFIFO = Net IncomeLIFO + (LIFO ReserveEnd âˆ’ LIFO ReserveBeginning) Ã— Marginal tax rate

The change in LIFO reserve (Î” LIFO reserve = LIFO ReserveEnd âˆ’ LIFO ReserveBeginning) is, by definition, the difference between LIFO COGS and FIFO COGS for that period:

Î” LIFO reserve = COGSLIFO âˆ’ COGSFIFO

â€“ or â€“

COGSFIFO = COGSLIFO âˆ’ Î” LIFO reserve

As you work your way down the income statement, no other line item changes (until taxes), so,

Gross MarginFIFO = Gross MarginLIFO + Î” LIFO reserve (because COGS is subtracted)

EBITDAFIFO = EBITDALIFO + Î” LIFO reserve

EBITFIFO = EBITLIFO + Î” LIFO reserve

EBTFIFO = EBTLIFO + Î” LIFO reserve

EBTFIFO Ã— Marginal tax rate = (EBTLIFO + Î” LIFO reserve) Ã— Marginal tax rate

EBTFIFO Ã— Marginal tax rate = (EBTLIFO Ã— Marginal tax rate) + (Î” LIFO reserve Ã— Marginal tax rate)

Net IncomeFIFO = Net IncomeLIFO + (Î” LIFO reserve Ã— Marginal tax rate)

Thatâ€™s perfect! I see it now, thanks!

â€“

Sometimes I see that a definition of change in LIFO as Î” LIFO reserve = COGSLIFO - COGSFIFO

Is this just a preference on starting points of where we reconcile from?

My mistake: I got the Fs and the Ls backward. (I was thinking Ending Inventory and writing COGS.)

Iâ€™ve fixed it.

Good eye!