TheHatlessScarf wrote:

I need help understanding the derivation of this formula:

Net Income_FIFO = Net Income_LIFO + LIFO Reserve_End - LIFO Reserve_Beginning

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

Your formula’s off just a bit:

Net Income_FIFO = Net Income_LIFO + (LIFO Reserve_End − LIFO Reserve_Beginning) × Marginal tax rate

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

Δ LIFO reserve = COGS_LIFO − COGS_FIFO

– or –

COGS_FIFO = COGS_LIFO − Δ LIFO reserve

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

Gross Margin_FIFO = Gross Margin_LIFO + Δ LIFO reserve    (because COGS is subtracted)

EBITDA_FIFO = EBITDA_LIFO + Δ LIFO reserve

EBIT_FIFO = EBIT_LIFO + Δ LIFO reserve

EBT_FIFO = EBT_LIFO + Δ LIFO reserve

EBT_FIFO × Marginal tax rate = (EBT_LIFO + Δ LIFO reserve) × Marginal tax rate

EBT_FIFO × Marginal tax rate = (EBT_LIFO × Marginal tax rate) + (Δ LIFO reserve × Marginal tax rate)

Net Income_FIFO = Net Income_LIFO + (Δ LIFO reserve × Marginal tax rate)

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

I’ve fixed it.

Good eye!