Universal Inventory Formula

One formula for all inventory stages:

$\text{Out}=\text{Beginning}+\text{In}-\text{Ending}$

Or equivalently (balance form):

$\text{Beginning}+\text{In}=\text{Ending}+\text{Out}$

Application at Each Stage

Same structure, different labels for “In” and “Out”:

Stage	Beginning	+ In	− Ending	= Out
Raw Materials	Beg RM	Purchases	End RM	Materials Used
Work in Process	Beg WIP	Total Mfg Costs	End WIP	COGM
Finished Goods	Beg FG	COGM	End FG	COGS

Expanded Formulas

Direct Materials Used: $\text{DM Used}=\text{Beg RM}+\text{Purchases}-\text{End RM}$

Cost of Goods Manufactured: $\text{COGM}=\text{Beg WIP}+\text{Total Mfg Costs}-\text{End WIP}$

Where: Total Manufacturing Costs = DM Used + DL + MOH

Cost of Goods Sold: $\text{COGS}=\text{Beg FG}+\text{COGM}-\text{End FG}$

Example

Given	Amount
Beginning WIP	$90,000
Direct Materials Used	$50,000
Direct Labor	$60,000
Manufacturing Overhead	$40,000
Ending WIP	$60,000

Step 1: Total Manufacturing Costs = $50,000+$60,000 + $40,000=\ast \ast$150,000**

Step 2: COGM = $90,000+$150,000 − $60,000=\ast \ast$180,000**

The Recursive Structure

Each stage’s “Out” becomes the next stage’s “In”:

• Materials Used → feeds into Total Manufacturing Costs
• COGM → feeds into Finished Goods calculation
• COGS → goes to Income Statement

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North: Where this comes from

• Inventory Flow in Manufacturing (physical flow this formula tracks)
• Conservation Principle (what comes in must go out or stay)

East: What opposes this?

• Cash Basis Accounting (no inventory tracking)

South: Where this leads

• Schedule of Cost of Goods Manufactured (formal report using this formula)
• Income Statement - Manufacturing (COGS flows here)

West: What’s similar?

• Accounting Equation (Assets = Liabilities + Equity—same balance logic)
• Sources and Uses of Funds (cash flow: where it came from, where it went)