Analysis of Inventories: formula sheet

Key formulas

Cost of inventory (IAS 2)

Cost = purchase costs + conversion costs + other costs to bring to present location and condition

Purchase costs are net of trade discounts and rebates. Exclude abnormal waste, selling costs, general administration and most storage costs.

Purchase cost

Purchase cost = invoice price − trade discounts and rebates + import duties and non-recoverable taxes + freight-in and handling

Recoverable taxes, such as recoverable VAT, are not included in cost.

Net realisable value

NRV = estimated selling price − estimated costs of completion − estimated costs to make the sale

For finished goods there are no completion costs, so only selling costs are deducted.

Carrying amount

Carrying amount = lower of cost and NRV

Write-down = cost − NRV when NRV is lower. It is recognised in profit or loss.

Reversal rule

IFRS: reverse up to the original write-down (carrying amount cannot exceed cost). US GAAP: no reversal.

The reversal reduces COGS under IFRS. Under US GAAP, the written-down amount becomes the new cost basis.

US GAAP market (LIFO and retail method)

Market = replacement cost, limited to a ceiling of NRV and a floor of NRV − normal profit margin

Carry at the lower of cost and market. FIFO and average cost use the lower of cost and NRV.

Inventory identity

Beginning inventory + Purchases = COGS + Ending inventory

Cost of goods available for sale = Beginning inventory + Purchases. Rearrange to find any missing item.

Weighted average cost per unit (periodic)

Cost of goods available ÷ Units available

Apply this one cost to units sold and units left. In a perpetual system, a new average is recomputed after each purchase.

FIFO

COGS uses oldest costs; ending inventory uses latest costs

Gives the same result under periodic and perpetual systems.

LIFO

COGS uses latest costs; ending inventory uses oldest costs

Allowed under US GAAP, not under IFRS. Periodic and perpetual LIFO can differ.

Rising-price ranking

COGS: LIFO > Average > FIFO; Net income and inventory: FIFO > Average > LIFO

Holds when unit costs rise and inventory levels are stable or growing. Reverses when costs fall.

FIFO inventory

Inventory (FIFO) = Inventory (LIFO) + LIFO reserve

Use the reserve at the same date as the inventory. Apply it to both beginning and ending inventory when you need an average.

FIFO COGS

COGS (FIFO) = COGS (LIFO) − (Ending LIFO reserve − Beginning LIFO reserve)

Rising reserve means FIFO COGS is lower. Falling reserve (liquidation) means FIFO COGS is higher than LIFO COGS.

Pretax income effect

Pretax income (FIFO) = Pretax income (LIFO) + Change in LIFO reserve

Same amount as the COGS difference, with the opposite sign.

After-tax income effect

Net income (FIFO) = Net income (LIFO) + Change in LIFO reserve × (1 − t)

t is the tax rate. The tax payable rises when income rises.

Equity adjustment

Equity (FIFO) = Equity (LIFO) + Ending LIFO reserve × (1 − t)

Uses the cumulative reserve, not the annual change.

Deferred tax effect

Additional liability (deferred tax, analyst's adjustment) = Ending LIFO reserve × t

The reserve increases assets. The after-tax part, reserve × (1 − t), increases equity. The tax part, reserve × t, is treated as an additional liability in the analyst's adjustment, not necessarily one the company recognises. This assumes a constant tax rate.

Inventory turnover on FIFO basis

Inventory turnover (FIFO) = COGS (FIFO) ÷ Average FIFO inventory

Adjust both numerator and denominator. Turnover falls after conversion when the reserve rises, because COGS falls while inventory rises. If the reserve falls, FIFO COGS is higher and FIFO inventory is also higher, so calculate the result rather than assume the direction.

Net realisable value

NRV = estimated selling price − estimated costs of completion − estimated costs to sell

Used under IFRS, and under US GAAP for FIFO and average cost.

Write-down amount

Write-down = carrying amount (cost) − NRV, if cost > NRV

Zero if NRV is at or above cost. Recognised as an expense.

Journal entry for write-down

Dr COGS (or loss on write-down); Cr Inventory

Reduces assets and net income by the same pre-tax amount.

IFRS reversal limit

Reversal = min(NRV − current carrying amount, original cost − current carrying amount)

Carrying amount can never exceed original cost. Credit to COGS.

US GAAP market (LIFO or retail)

Market = middle value of (replacement cost, NRV ceiling, NRV − normal profit margin floor)

Carry at lower of cost and market. No reversals allowed.

Inventory turnover and days

Turnover = COGS ÷ average inventory; DOH = 365 ÷ turnover

If the write-down is recorded in COGS, it raises turnover and lowers DOH.

Inventory turnover

Inventory turnover = COGS ÷ Average inventory

Average inventory = (beginning + ending) ÷ 2, unless the question says to use another figure. Use COGS, not sales.

Days of inventory on hand (DOH)

DOH = Number of days in period ÷ Inventory turnover = Average inventory ÷ COGS × Number of days

Use 365 unless the question gives another day count.

Gross profit margin

Gross margin = (Revenue − COGS) ÷ Revenue

A change in inventory method flows straight into this ratio through COGS.

LIFO to FIFO inventory

FIFO inventory = LIFO inventory + LIFO reserve

Do this for both beginning and ending balances if averaging.

LIFO to FIFO COGS

FIFO COGS = LIFO COGS − (Ending LIFO reserve − Beginning LIFO reserve)

When the reserve rises, FIFO COGS is lower than LIFO COGS. When prices fall or the reserve shrinks, the adjustment reverses.

Cash conversion cycle link

Cash conversion cycle = DSO + DOH − Days payable outstanding

DOH is one of three components, so rising DOH lengthens the cycle.

Write-down rules

IFRS: inventory is carried at the lower of cost and net realisable value (NRV). Reversals are allowed, limited to the amount of the original write-down, so the carrying amount never exceeds original cost. US GAAP: reversals are not allowed.

The lower-of-cost-or-market rule is a US GAAP rule only. Under US GAAP, FIFO and average cost use lower of cost and NRV, while LIFO and the retail method use lower of cost or market. IFRS has no LIFO and applies lower of cost and NRV to every permitted cost formula.

Quick revision

• Opening inventory + purchases = COGS + ending inventory.
• Inventory cost includes purchase cost, conversion costs and other costs to bring it to its present location and condition.
• Selling costs, abnormal waste and storage costs not needed in production are expensed, not capitalised.
• Under IFRS, all inventory is carried at the lower of cost and net realisable value.
• Under US GAAP, FIFO and weighted average inventory use the lower of cost and NRV; LIFO and the retail method use the lower of cost or market.
• FIFO: oldest costs go to COGS, newest stay in inventory.
• LIFO: newest costs go to COGS; it is not permitted under IFRS.
• In rising prices with stable or growing inventory, LIFO gives higher COGS, lower profit and lower tax than FIFO.
• FIFO inventory = LIFO inventory + LIFO reserve.
• FIFO COGS = LIFO COGS − change in LIFO reserve (ending reserve − beginning reserve).
• IFRS permits reversal of write-downs, limited to the original write-down; US GAAP does not permit reversals.
• Inventory turnover = COGS ÷ average inventory; days of inventory on hand = 365 ÷ inventory turnover.
• Adjust to a common method before comparing firms that use different cost flow methods.

Common mistakes

• Including selling costs or storage costs in inventory cost. Fix: Only costs of bringing inventory to its present location and condition are included. Selling costs are expensed. Storage is included only if needed in the production process.
• Forgetting to deduct selling costs when computing NRV. Fix: Always compute NRV = selling price − costs to complete − costs to sell before comparing.
• Mixing up which end of the layers FIFO and LIFO use for ending inventory. Fix: Remember FIFO ending inventory holds the newest costs and LIFO ending inventory holds the oldest costs.
• Using a simple average of unit costs instead of a weighted average. Fix: Divide total cost of goods available by total units. Unequal purchase sizes make the two answers differ.
• Using the ending reserve instead of the change in reserve to adjust COGS. Fix: Balance sheet items use the level of the reserve. Income statement items use the change in the reserve over the period.
• Adding the change in reserve to COGS instead of subtracting it. Fix: A rising reserve means FIFO profit is higher, so FIFO COGS is lower. Subtract the increase.
• Ignoring selling costs when computing NRV Fix: Always subtract costs of completion and costs to sell before comparing with cost.
• Allowing reversals under US GAAP Fix: Tie reversals to IFRS only. Under US GAAP the written-down value is the new cost.
• Using sales instead of COGS in turnover. Fix: Inventory is carried at cost, so match it with COGS. Use revenue only for gross margin.
• Using ending inventory instead of average inventory. Fix: Average the beginning and ending balances unless the question tells you otherwise. The wrong-input answers are usually among the options.

Exam tips

• Questions often hand you irrelevant costs. Scan for selling, administration, abnormal waste and storage first and ignore them.
• When asked about IFRS vs US GAAP, think reversal of write-downs and LIFO. Both are the usual testing points.
• For NRV, check whether goods are finished or still need completion. Subtract completion costs only for unfinished goods.
• With three options, a number that uses selling price or omits freight is usually a distractor. Compute the exact figure rather than estimating.
• Link write-downs to ratios: they lower inventory and profit, raise the COGS ratio and reduce current assets.
• Write the rising-price ranking on your scratch paper at the start: LIFO COGS highest, FIFO net income and inventory highest. Use it as a check.
• Look for the words periodic, perpetual, IFRS and US GAAP in the stem. They change which methods and results apply.
• Do the ending inventory calculation first. It usually involves fewer units and is quicker.