Direct Costing (with Defects)

In the ideal world, every bit of material and labour allocated to a product is used, and no waste is generated. Unfortunately, materials can have defects and precious labour is spent on dealing with it. This means that more input than ideally required is actually used.

In developing standard costs for products, management accountants must take defects into account. To do so, they need to have a good grasp of division and multiplication.

If C is the theoretical amount of material or labour and r is its defect rate, the total amount of material/labour actually used (T) is:

T = ^C/_{1 - r}

The definition of the proportion
A proportion (p) is the size of a component (C) relative to the size of its total (T). That is:

p = ^C/_T

This definition is useful for standard costing of direct materials and direct labour. If C refers to the ideally required quantity of input and T refers to the actual amount of input used (being the sum of ideal and defective input), then p measures the success rate of the input. Also, given the success rate, the defect rate r must be the one's complement of the success rate (since something can only either succeed or fail):

p = 1 - r

So:

1 - r = ^C/_T

Rearranging for T:

T = ^C/_{1 - r}

Therefore, to calculate the total amount of input required for the purposes of standard costing, the theoretical amount of input must be divided by the one's complement of the defect rate.

A common pitfall
It is a common mistake to instead multiply theoretical input by one more than the defect rate. While it may seem intuitive, this technique actually involves either generating an area or factoring in change with respect to another variable, neither of which are relevant to standard costing.

Example: Aspire Pty Ltd
Aspire produces wooden ladders. One of its products, the E200, is made from 10m of eucalyptus planks costing $6/m. Due to knots and other defects in the wood, 15% of ladders produced are structurally weak and must be discarded. On average, how much eucalyptus is Aspire actually using for each E200, and how much is being spent in direct materials for each?

T = ^C/_{1 - r}
C = 10, r = 0.15
T = ¹⁰/_{1 - 0.15} = 11.76m
Cost = 11.76 × 6 = $70.56