How does FIFO represent current costs for inventory?

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It will be a closer approximation than LIFO as the inventory that has more recently been obtained will be closer to market value. Under LIFO the more recent inventory purchases are used in the calculation of COGS meaning that the older stock is used to value the inventory at historical prices, which over time may have begun to deviate further and further from market. The reverse is true for FIFO

FIFO gives a more economically accurate value to ending inventory than does LIFO, and LIFO (assuming no LIFO liquidation) gives a more economically accurate value to COGS than does FIFO.