Throughput Accounting 1 · Lesson 2 of 6
The P&Q plant
Meet a small plant with two products, four workers and ₹6,000 a week of expenses. Work out its best possible week, discover it can’t make everything, and decide which product comes first.
An ideal world
To test cost accounting fairly, we need a plant where nothing else can go wrong. So imagine an ideal world:
- Demand is known and steady. You can’t sell more than the market wants, even if you make it.
- Prices are fixed. Raw material prices are agreed, and supply and quality are perfect.
- There are no breakdowns, no absences and no variation: every operation takes exactly its standard time.
The plant makes two products, P and Q, from three raw materials and one bought-in part. Four operations, A, B, C and D, each have one skilled worker who can’t do anyone else’s job. Each works 8 hours a day, 5 days a week: 2,400 minutes a week. All of the company’s expenses, wages, salaries and overheads, come to ₹6,000 a week.
Read the drawing from the bottom up. To make one P: RM1 goes through A (15 min) and C (10 min); RM2 goes through B (15 min) and C (5 min); D assembles both with a ₹5 bought-in part (15 min). To make one Q: the same middle part from RM2 (B 15, C 5); RM3 goes through A (10 min) and B (15 min); D assembles them (5 min).
| P | Q | |
|---|---|---|
| Demand a week | 100 | 50 |
| Price | ₹90 | ₹100 |
| Raw material and part | ₹20 + ₹20 + ₹5 = ₹45 | ₹20 + ₹20 = ₹40 |
| Total minutes per unit | 60 | 50 |
Question 1: what is the best possible week?
Before reading on, work it out: what is the maximum net profit this plant can make in a week? Take a few minutes with a pencil.
In a classroom, two kinds of answer come up.
The allocation answer. Spread the ₹6,000 over all the minutes available, 4 workers × 2,400 = 9,600 minutes, which is ₹0.625 a minute. Then:
| P | Q | |
|---|---|---|
| Material | ₹45 | ₹40 |
| Overhead (60 or 50 min × ₹0.625) | ₹37.50 | ₹31.25 |
| Product cost | ₹82.50 | ₹71.25 |
| Price | ₹90 | ₹100 |
| Margin | ₹7.50 | ₹28.75 |
Make everything: 100 × ₹7.50 + 50 × ₹28.75 = ₹2,187.50 a week.
The no-allocation answer. Sales are 100 × ₹90 + 50 × ₹100 = ₹14,000. Material is 100 × ₹45 + 50 × ₹40 = ₹6,500. Take off the ₹6,000 of expenses: ₹1,500 a week.
Pause and think: the same plant, two different answers. Why?
- Someone made an arithmetic mistake
- The allocation answer is right; the other forgot overhead
- The allocation answer only charges overhead for the minutes it uses; the unused minutes, and their cost, have vanished from the sum
- They should be the same; it’s rounding
Making everything would use 8,500 minutes of the 9,600 paid for. The allocation answer charges only 8,500 × ₹0.625 = ₹5,312.50 of overhead. The other ₹687.50 is still spent; it just doesn’t appear. Companies run on exactly this kind of budgeted product cost and margin, which is why actual results so often differ from the budget, and why so much effort goes into variance analysis.
And both answers assume something we haven’t checked yet.
Question 2: can we make everything?
Add up each worker’s minutes for 100 P and 50 Q:
| Worker | For 100 P | For 50 Q | Needed | Available |
|---|---|---|---|---|
| A | 1,500 | 500 | 2,000 | 2,400 |
| B | 1,500 | 1,500 | 3,000 | 2,400 |
| C | 1,500 | 250 | 1,750 | 2,400 |
| D | 1,500 | 250 | 1,750 | 2,400 |
Worker B is short by 600 minutes. The plant can’t make everything, so both answers above are impossible. Something has to give. Which product should be made first?
Three departments, one answer
Ask the three people who usually decide:
- Sales: Q sells for ₹100, P for ₹90. And Q’s customers are easier to sell to. Push Q.
- Production: Q takes 50 minutes, P takes 60. More units for the same effort. Make Q.
- Finance: Q’s margin is ₹28.75, P’s only ₹7.50. Q, obviously.
Everyone agrees. So make all 50 Q, and use the minutes that are left for P. Worker B has 2,400 − 1,500 = 900 minutes left, enough for 60 P.
Now play the week yourself. Pick a product, set a plan, and run it. Then try other plans.
Before you play
Your job. Plan one week: how many P and how many Q to make. The bars show each worker’s minutes; a plan that needs more than 2,400 from anyone can’t be run.
What you see. After each run, the profit the cost report predicted and the profit the week actually made. Material is the only cost that changes with the plan; the ₹6,000 is spent whatever you do.
Your goal. The highest weekly profit you can find. When you’ve tried a few plans, ask for the throughput view.
What just happened?
Following sales, production and finance, 50 Q and 60 P, the cost report promised ₹1,887.50. The week lost ₹300. Going against all three, 100 P and 30 Q, made a profit of ₹300.
We made more of the “least profitable” product and less of the “most profitable” one, and profit went up by ₹600. Either the plant is strange, or the cost report gave us the wrong information about which product earns the most. The next lesson finds out which.
Check your understanding
Answer all five. Get four right to complete the lesson.
1. Spreading ₹6,000 over 9,600 minutes gives an overhead rate of…
- ₹0.80 a minute
- ₹0.625 a minute
- ₹1.60 a minute
- ₹6 a minute
₹6,000 ÷ 9,600 = ₹0.625.
2. To make all 100 P and 50 Q, worker B would need…
- 1,500 minutes
- 2,000 minutes
- 2,400 minutes
- 3,000 minutes
P uses 15 B minutes, Q uses 30: 1,500 + 1,500 = 3,000, against 2,400 available.
3. Following the cost report (all Q first, then P), the plant makes…
- A loss of ₹300
- A profit of ₹1,887.50
- A profit of ₹300
- A profit of ₹2,187.50
50 Q and 60 P bring ₹3,000 + ₹2,700 = ₹5,700 of sales minus material, against ₹6,000 of expenses.
4. Which plan made the most money?
- All Q first, then P
- Half of each
- All P first, then Q: 100 P and 30 Q
- Only Q
₹4,500 + ₹1,800 = ₹6,300 of sales minus material, a ₹300 profit.
5. Why do the allocation and no-allocation answers to “the best week” differ?
- A rounding error
- Allocation charges overhead only for the minutes used, so the cost of unused minutes disappears from the sum
- The no-allocation answer forgot material
- Prices were different
The ₹6,000 is spent in full either way.