# 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 :)

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TheHatlessScarf wrote:
I need help understanding the derivation of this formula:

Net IncomeFIFO = Net IncomeLIFO + LIFO ReserveEnd - LIFO ReserveBeginning

It works, but I do not understand why it works.

Your formula’s off just a bit:

Net IncomeFIFO = Net IncomeLIFO + (LIFO ReserveEnd − LIFO ReserveBeginning) × Marginal tax rate

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

Δ LIFO reserve = COGSLIFO − COGSFIFO

– or –

COGSFIFO = COGSLIFO − Δ LIFO reserve

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

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

EBITDAFIFO = EBITDALIFO + Δ LIFO reserve

EBITFIFO = EBITLIFO + Δ LIFO reserve

EBTFIFO = EBTLIFO + Δ LIFO reserve

EBTFIFO × Marginal tax rate = (EBTLIFO + Δ LIFO reserve) × Marginal tax rate

EBTFIFO × Marginal tax rate = (EBTLIFO × Marginal tax rate) + (Δ LIFO reserve × Marginal tax rate)

Net IncomeFIFO = Net IncomeLIFO + (Δ LIFO reserve × Marginal tax rate)

Simplify the complicated side; don't complify the simplicated side.

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That’s perfect! I see it now, thanks!

Sometimes I see that a definition of change in LIFO as Δ 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.)

I’ve fixed it.

Good eye!

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/