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Microlesson · 5-min read

Reverse Calculation Method

# Reverse Calculation of Joint Cost

This method is used when the problem gives all cost and revenue figures except the allocation method for joint cost. We work backwards from sales to isolate joint cost as a balancing figure.

## The Reverse Calculation Template

For each joint product, build a vertical reconciliation:

```

Joint Cost of A (balancing figure)

(+) Further Process Cost of A

(+) Selling Expenses of A

(+) Profit of A

────────────────────────

= Sales of A

```

Rearranging:

$$\text{Joint Cost of A} = \text{Sales}_A - \text{FPC}_A - \text{Selling Exp}_A - \text{Profit}_A$$

Do the same for Product B (and any other products).

## Adjustment When Balancing Figures Don't Sum to Total Joint Cost

Sometimes the sum of derived joint costs (A + B + ...) does not equal the total joint cost given in the problem. In such cases:

> Distribute the total joint cost in the ratio of the balancing figures of Joint Cost.

This preserves the relative allocation logic implied by profitability data while reconciling to the actual joint cost figure.

## When to Use

  • Sales, profits, further processing costs, and selling expenses are all given
  • The method of allocation is not specified
  • Need to determine implicit joint cost share per product

Worked example

### Example 1

Example: Total joint cost = ₹95,000. For Product A: Sales ₹1,20,000, FPC ₹15,000, Selling exp ₹5,000, Profit ₹40,000. For Product B: Sales ₹80,000, FPC ₹8,000, Selling exp ₹3,000, Profit ₹19,000.

Step 1 — Balancing figures:

  • Joint Cost A (bal.) = 1,20,000 − 15,000 − 5,000 − 40,000 = ₹60,000
  • Joint Cost B (bal.) = 80,000 − 8,000 − 3,000 − 19,000 = ₹50,000
  • Sum = ₹1,10,000 ≠ Total joint cost ₹95,000

Step 2 — Distribute total joint cost in balancing figure ratio (60:50 = 6:5):

  • Final Joint Cost A = 95,000 × 6/11 = ₹51,818
  • Final Joint Cost B = 95,000 × 5/11 = ₹43,182

⚠️ Common exam mistakes

  • Stopping after finding the balancing figures without checking whether they sum to the total joint cost.
  • Forgetting to subtract selling expenses or further processing costs in the reverse calc.
  • Distributing total joint cost in the ratio of sales instead of the ratio of balancing figures.
  • Including joint cost as a deduction inside the build-up (it is what we are solving for).
Reference:
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