# How do you allocate joint costs?

When I discussed the notion of cost traceability and the distinction between direct and indirect costs, I also mentioned that costs could be indirect for two reasons: it is too expensive to trace them (common costs) or it is impossible to trace them (joint costs). The methods I described previously are used to allocate common costs. A slightly different method must be used for joint costs.

Let’s assume that when our bakery makes bread, a certain proportion of the units produced does not meet the standards of quality to be sold as bread because it is not the right size, badly cooked or ugly. This can happen because no production process is perfectly reliable, even when it is automated.

Bread which can be sold as such and bread which will end up as breading are joint products because (1) they are not separately identifiable before the end of the baking time, after which they are sorted out, and (2) both have a market value (if one had no market value, it would be a by-product). So how should you split the joint costs, i.e. the costs incurred for both together until they are separated?

Two main approaches have been suggested to allocate joint costs. The first approach, the physical measure method, relies on physical measures used as allocation bases, like weight or volume.

The physical measure method is a joint cost allocation method which allocates joint costs on the basis of their relative proportions at the split-off point, using a common physical measure such as weight or volume.

The second approach uses market data instead as allocation base. It can rely either on the sales value at split-off point or on the estimated net realizable value (NRV). These approaches have the advantage of maintaining a constant gross margin percentage of the products. Sales value at split-off point is the amount for which you could sell the joint product as it is, without additional processing. The net realizable value is the market value of the joint product after it has been processed further to be marketable, minus the additional (separable) processing costs dedicated to that joint product.

The sales value at split-off point method is a joint cost allocation method which allocates joint costs on the basis of the sales value of each joint product just after the split-off point.

The estimated net realizable value (NRV) method is a joint cost allocation method which allocates joint costs on the basis of the relative estimated net realizable value of each joint product. This method preserves the relative gross margin of each joint product.

Physical measures are neither the cost driver nor the purpose of incurring the joint costs, have little relationship with the value of the joint products, serve no purpose beyond allocating joint costs and can be highly misleading. Physical measures are arbitrary allocation bases which should be avoided. Moreover, the physical method assumes that the joint products can be expressed in the same physical units. In some processes, joint product can be a gas while the other is a liquid or even a solid. Market value is not the underlying cost driver either, but it can be argued that it is the purpose of incurring the joint costs. Moreover, money is a common unit for all joint products. Therefore, NRV is a far better allocation base for joint costs.

Solution.

Out of 500 loaves of 200 grams each, 400 (80,000 grams) are sold as bread for 1 euro a piece without additional processing costs. Therefore, the NRV of one batch of bread is 400 euros for 400 loaves resulting from 1 batch processed.

Out of 500 loaves of 200 grams each, 100 (20,000 grams) are dried and crushed into 20,000 / 500 = 40 bags of breading sold 1.5 euro the bag. Additional processing costs incurred after the split-off point (i.e. separable costs) are 10 euros to crush 20,000 grams of breading and 40 x 0.5 = 20 euros to package them. The net realizable value of one batch of breading is therefore 40 x 1.5 - 10 - 20 = 30 euros for 40 bags resulting from 1 batch processed.

Case 1: physical measure method

If we use the number of units or the number of grams as allocation base, the joint costs of 200 euros (125 euros of raw materials plus 75 euros of processing before the split-off point) are divided by 500 units to give an allocation rate of 0.4 euro per unit. 400 x 0.4 = 160 euros are allocated to bread and 100 x 0.4 = 40 are allocated to breading.

The profit made on 1 batch of bread is therefore 400 - 160 = 240 euros. The profit made on 1 batch of breading is 30 - 40 = -10 euros.

Case 2: estimated net realizable value (NRV) method

If we use the NRV allocation base, the joint costs of 200 euros are divided by 400 + 30 = 430 euros to give an allocation rate of 0.465 euro per euro of NRV. 400 x 0.465 = 186 euros are allocated to bread and 30 x 0.465 = 14 are allocated to breading.

The profit made on 1 batch of bread is therefore 400 - 186 = 214 euros. The profit made on 1 batch of breading is 30 - 14 = 16 euros.