Deriving CM per Garment & CM per Dozen Formulas

This lesson completes the chain that Module 1 has been building. Lesson 1 priced a minute of factory time through Cost Per Minute. Lesson 2 explained how operators are paid for those minutes. Lesson 3 split the factory's costs into fixed and variable heads so the minute price could be understood. Now the chain closes: a garment's SMV counts its minutes, CPM prices each minute, and their product is CM, the Cost of Making per garment. Multiply by 12 and you have CM per dozen, the figure many buyers order and price by.

The formula is short enough to write on a whiteboard: CM per garment equals SMV times CPM. Everything that makes it go wrong lives in the definitions of its two inputs. SMV must be the engineered SMV from the operation bulletin, not a buyer's estimate and not last season's figure for a similar style. CPM must be the current monthly figure, and its efficiency basis must be stated and handled exactly once. Get those two inputs right and the formula cannot fail. Get either wrong and no amount of careful multiplication will save the quotation.

There are two standard ways to write the formula, and they look different but always agree. Convention A uses CPM at target efficiency: CM per garment equals SMV times CPM at target efficiency. Convention B uses CPM at 100 percent attendance: CM per garment equals SMV times CPM at 100 percent divided by efficiency. The two agree because CPM at target efficiency is defined as CPM at 100 percent divided by efficiency, so Convention A already contains the division that Convention B writes out.

Take the worked base from the CPM lesson: CPM is BDT 2.00 per minute at 100 percent attendance, and the line runs at 80 percent efficiency. By Convention B, a T-shirt at 4.50 SMV costs 4.50 times 2.00 divided by 0.80, which is BDT 11.25. By Convention A, CPM at target efficiency is 2.00 divided by 0.80, which is BDT 2.50, and 4.50 times 2.50 is also BDT 11.25. Same answer, two routes, and the agreement between them is the cheapest audit a costing department owns.

That audit deserves a formal place in the quotation routine. Every quotation sheet should carry both conventions side by side, or the costing officer should recompute by the other convention before issue. If the two results differ, something is wrong: a stale SMV, a stale CPM, a mistyped efficiency, or the classic error this lesson exists to prevent, which is dividing by efficiency twice.

The double-division trap is the most expensive single formula error in garment costing, and it is easy to commit because each step looks careful on its own. The costing officer takes CPM at target efficiency, BDT 2.50, and then, remembering that efficiency must be accounted for, divides by 0.80 again. The T-shirt becomes 4.50 times 2.50 divided by 0.80, which is BDT 14.06 instead of BDT 11.25. The overquotation is BDT 2.81 per piece, which is 25 percent above the correct figure, because dividing by 0.80 a second time multiplies by 1.25.

The factory example in this lesson shows the commercial consequence. A Chattogram factory requoted a woven shirt at BDT 56.25 after double division, against its own earlier correct quotation of BDT 45.00, and the buyer, holding both sheets, asked why the same shirt had become 25 percent more expensive in a week. The factory lost the order before the error was found. The fix was a guard on the quotation sheet: both conventions printed side by side, with any disagreement blocking issue. No double-division error has reached a buyer since, and the incident is now the factory's standard training example.

The mirror error is equally real: forgetting efficiency entirely. Quoting the T-shirt at 4.50 times 2.00, which is BDT 9.00, understates CM by BDT 2.25 per piece and guarantees a loss of BDT 225,000 on a 100,000-piece order. Underquoting loses money quietly; overquoting loses orders loudly. Both come from mishandling the same single number.

Using the same CPM base throughout, BDT 2.00 at 100 percent and 80 percent efficiency, the four-style table in this lesson gives the complete quotation picture. The basic T-shirt at 4.50 SMV costs BDT 11.25 per piece and BDT 135.00 per dozen. The polo shirt at 9.00 SMV costs BDT 22.50 per piece and BDT 270.00 per dozen. The woven shirt at 18.00 SMV costs BDT 45.00 per piece and BDT 540.00 per dozen. The denim jeans at 22.50 SMV costs BDT 56.25 per piece and BDT 675.00 per dozen. Each figure is SMV times 2.50, and each dozen figure is the per-piece figure times 12, computed before rounding.

Currency conversion comes last and must carry its rate on the sheet. At an illustrative exchange rate of BDT 110 per USD, the per-piece USD figures are BDT 11.25 divided by 110, which is USD 0.10 for the T-shirt; BDT 22.50 divided by 110, which is USD 0.20 for the polo; BDT 45.00 divided by 110, which is USD 0.41 for the woven shirt; and BDT 56.25 divided by 110, which is USD 0.51 for the jeans. If the rate moves to BDT 120, the T-shirt figure becomes USD 0.09 without any change in factory cost, which is why the rate must be printed: otherwise a currency movement looks like a price change to the buyer, and the factory ends up defending a price it never changed.

CM moves inversely with efficiency, and the sensitivity table in this lesson makes the relationship concrete for the T-shirt. At 70 percent efficiency CM is BDT 12.86 per piece and BDT 154.29 per dozen. At 75 percent it is BDT 12.00 and BDT 144.00. At 80 percent it is BDT 11.25 and BDT 135.00. At 85 percent it is BDT 10.59 and BDT 127.06. At 90 percent it is BDT 10.00 and BDT 120.00. The arithmetic is the same in every row: 4.50 times 2.00 divided by the efficiency figure. A ten-point efficiency swing from 80 to 70 percent raises CM by BDT 1.61 per piece, which on a 100,000-piece order is BDT 161,000 of cost that appears from nowhere unless the quotation anticipated it.

This sensitivity is why efficiency is a commercial variable, not just a production one. A factory quoting a difficult new style at its normal efficiency is quoting on hope, and the cost of hope arrives at month end. The honest approach is to quote difficult styles at the efficiency they have actually achieved on comparable styles, and to state the efficiency on the quotation sheet so the buyer understands that the price assumes a stated performance level.

The routine that prevents every error in this lesson has six steps. Confirm SMV and CPM, checking both dates. Choose one convention and state it on the sheet. Compute CM per garment at full precision. Convert to CM per dozen from the unrounded figure. Convert currency at a printed rate if needed. Run the two-convention check and stop if the two results disagree. A sheet that follows these steps can be defended in front of any buyer or auditor, because every number on it shows its derivation.

Five habits keep the routine honest over time. Never round before multiplying by 12. Never use a buyer's SMV without labelling it as buyer-supplied and showing the engineered figure beside it. Never quote from a stale CPM after a wage revision or an efficiency swing. Never omit the exchange rate from a USD quotation. And never issue a quotation where the two conventions disagree. Factories that keep these habits quote prices they can defend; factories that do not spend their time explaining prices they cannot.