amqata

LIFO Reserve represents profits not recognized and taxes that were not paid (because the higher costs were disguised).
1.) Add the LIFO reserve to the Inventory Balance
2.) (1-.4)(LIFO Reserve) = the profits made, but not recorded.
3.) (.4)(LIFO Reserve) = the tax liability

The numerator is as follow:
(Total Assets) + (LIFO Reserve) - (Tax Liability)

The denominator is as follows:

(Value of Common Stock) + (Retained Earnings) + (After-tax LIFO Reserve Profits)
$1,000,000 + $1,500,000 + $540,00= 3,040,000

They definitely gave too much information - Jan 31 LIFO Reserve and Inventory - to throw off the calculation, which never helps

"The change in equity equals to the after-tax rate of change COGS" is right and the same as the change in retained earnings. LIFO disguises COGS as to be higher, which results in a lower retained earnings. So a change in pre-tax COGS be the same as pre-tax retained earnings...

hopefully that helps some

AM