Tutorial 9: Cost Allocations: Theory and ApplicationsIn this tutorial, we are going to discuss three problems form the topic of cost allocations. In problem 1, a firm makes two products – standard and custom. Profit margin for the custom products is higher than the standard products – both in terms of higher CMR and higher unit profit ($65 versus $25 per unit). The management is considering emphasizing custom products because it is more profitable! The problem has four parts.In part a, you are asked to comment on the validity of the cost allocation scheme. We are also required to find the variable cost of manufacturing. Recall from module 5 that VCR = 1-CMR. Given the CMR, we can find VCR by subtracting CMR from 1. Also recall the definition of VCR. It equals Variable cost divided by revenue. So, we can estimate the variable cost for standard as (1-0.5) x $130 = $65. Similarly, the variable cost for Custom = (1-0.6) x 175 = $70. We know that the unit profit for Standard is given as $25. Therefore, the total cost of standard must equal $130 – 25 = $105. Given that the total variable cost for standard equals $65, this implies that the fixed cost allocated to one unit of standard = $105 - $65 = $ 40. Realize that this is the same as the difference between UCM and Unit profit margin. Similarly the allocated fixed cost per unit of custom = $ 40. Since both the products received the same allocated cost, it appears that the fixed costs are being allocated based on number of units as allocation basis. Given that custom consumes twice the machine hours, if the allocations were done based on machine hours, then that would result in twice the allocated cost for custom as standard. Let us also compute the total profits for the firm as the number of units of standard x unit profit for standard + the number of units of custom x unit profit for custom = $3.5 million.In part b, the allocation scheme changes to one based on machine hours. We are required to estimate the fixed costs allocation rate. We know that the first step in any allocation is to figure out how much costs need to be allocated. This can easily be computed from the given data. We know that the firm produced 75,000 units of standard and 25,000 units of custom giving a total volume of 100,000 units. Given the cost allocation scheme of $40 per unit produced in part a, we can infer that the total costs that need to be allocated = 100,000 x $40 = $4 million. The second step is to figure out the volume of allocation base or the denominator volume. Problem gives you that standard needs 2 hours and customer needs 4 hours of machine time. Therefore, the total number of machine hours to be used = 75,000 x 2 + 25,000 x 4 = 250,000 hours. The third step is to figure out the allocation rate by dividing thecost pool by the denominator volume. Cost allocation rate = $4,000,000 / 250,000 = $16 per machine hour.