Chapter 15, Problem 23P

Sixty employees (all CPAs) of a local public accounting firm eat lunch at least twice weekly at a very popular pizza restaurant. The pizza restaurant recently began offering discounts for groups of 15 or more. Groups would be seated in a separate room, served individual bowls of salad costing $2 each, pitchers of root beer costing $3 each (each pitcher has a five-glass capacity), and medium, two-topping pizzas for $10 (10 slices each). The food would have to be ordered in advance.

Thirty of the CPAs commit to eating three slices of pizza, three glasses of root beer, and one bowl of salad [a consumption pattern of (3,3,1)]. The other 30 are more hearty eaters and commit to seven slices of pizza, two glasses of root beer, and one bowl of salad [a consumption pattern of (7,2,1)]. Each member of the group must pay an assessed amount for the lunch.

After some detailed polling among the 60, four types of eaters were identified: two types of light eaters and two types of heavy eaters. The consumption patterns for each group are given (slices of pizza, glasses of root beer, and bowls of salad): Light Eaters (Group A): A1 = (2,2,1) and A2 = (3,3,1); Heavy Eaters (Group B): B1 = (6,3,1) and B2 = (7,2,1). There are an equal number of CPAs in each of the four groups.

Required:

1. 1. Calculate the average lunch cost for each CPA in each of the two groups, A and B. Compare this to the ABC cost assignments. Discuss the merits of grouping based on similarity. Discuss the analogy to multiple-product value streams.
2. 2. Suppose that members of the heavy-eating group (Group B) decided that they were eating more than necessary for their health and well-being and decided to reduce their total calories. They therefore agreed to reduce consumption of pizza by one slice and consumption of root beer by one glass for each member of the group. Relative to the original order, how much extra capacity exists? If the excess capacity is eliminated by reducing the order, what is the new average cost? Suppose that the decision is to use the extra capacity to invite four guests (two of Type B1 and two of Type B2) to lunch (at the cost of the CPAs). If the original order is used as the benchmark cost, what is the extra cost of the guest program? Comment on the conceptual significance of this for manufacturing firms.

To determine

Compute the average cost of lunch to be paid by each CPA for both the groups and compare the result with the ABC cost.

Explanation of Solution

Value stream: The value stream refers to all the processes involved in the production of a product from the starting point to the finished product, till it reaches the hands of the customer.

Focused value stream: The focused value stream refers to all the processes involved in the production of one particular product from the starting point to the finished product, till it reaches the hands of the customer.

Activity-based costing: It is a method that helps in finding the activities performed by a company and it tracks the indirect costs to the activities of the company that consumes resources.

Compute the total lunch cost for Group A:

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	8	$10	$80
Root Beer	15	$3	$45
Salad	30	$2	$60
Total Cost			$185

Table (1)

Working Notes:

Compute the number of pizzas to be ordered by Group A:

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{ Pizzas}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)+\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)}{10}\\ =\frac{\left(2\times 15\right)+\left(3\times 15\right)}{10}\\ =\frac{30+45}{10}\\ \text{= 8 pizzas}\end{array}$

Compute the number of pitchers of root beer to be ordered by Group A:

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{Pitchers of}\\ \text{Root Beer}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)+\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)}{5}\\ =\frac{\left(3\times 15\right)+\left(2\times 15\right)}{5}\\ =\frac{45+30}{5}\\ \text{= }15\text{ pitchers}\end{array}$

Compute the number of bowls of salad to be ordered by Group A:

$\begin{array}{c}\text{Salad Bowls = Number of Bowls}\times \text{Number of Persons}\\ =1\times 30\\ =30\text{ bowls}\end{array}$

Compute the average cost of lunch for Group A:

$\begin{array}{c}\text{Average cost of lunch = }\frac{\text{Total cost of lunch}}{\text{Number of employees}}\\ =\frac{\$185}{30}\\ =\$6.17\end{array}$

The average cost of lunch for Group A is $6.17.

Compute the ABC cost of each item:

Particulars	Cost per Unit (A)	Number of Units (B)	Amount $\left(\text{C=}\frac{\text{B}}{\text{A}}\right)$
Pizza	$10	10	$1.00
Root Beer	$3	5	$0.60
Salad	$2	1	$2.00
ABC Cost			$3.60

Table (2)

The unit cost as per ABC costing is $3.60.

Using the ABC cost compute, the average lunch cost for Group A1:

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	2	$1.00	$2
Root Beer	2	$0.60	$1
Salad	1	$2.00	$2
Total Cost			$5.20

Table (3)

The average lunch cost for Group A1, using ABC costing is $S5.20.

Using the ABC cost compute, the average lunch cost for Group A2:

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	3	$1.00	$3
Root Beer	3	$0.60	$2
Salad	1	$2.00	$2
Total Cost			$6.80

Table (4)

The average lunch cost for Group A2, using ABC costing is $6.80.

Compute the total lunch cost for Group B:

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	20	$10	$200
Root Beer	15	$3	$45
Salad	30	$2	$60
Total Cost			$305

Table (5)

Working Notes:

Compute the number of pizzas to be ordered by Group B:

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{ Pizzas}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)+\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)}{10}\\ =\frac{\left(6\times 15\right)+\left(7\times 15\right)}{10}\\ =\frac{90+105}{10}\\ \text{= 20 pizzas}\end{array}$

Compute the number of pitchers of root beer to be ordered by Group B:

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{Pitchers of}\\ \text{Root Beer}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)+\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)}{5}\\ =\frac{\left(3\times 15\right)+\left(2\times 15\right)}{5}\\ =\frac{45+30}{5}\\ \text{= }15\text{ pitchers}\end{array}$

Compute the number of bowls of salad to be ordered by Group B:

$\begin{array}{c}\text{Salad Bowls = Number of Bowls}\times \text{Number of Persons}\\ =1\times 30\\ =30\text{ bowls}\end{array}$

Compute the average cost of lunch for Group B:

$\begin{array}{c}\text{Average cost of lunch = }\frac{\text{Total cost of lunch}}{\text{Number of employees}}\\ =\frac{\$305}{30}\\ =\$10.17\end{array}$

The average cost of lunch for Group B is $10.17.

Compute the ABC cost of each item:

Particulars	Cost per Unit (A)	Number of Units (B)	Amount $\left(\text{C=}\frac{\text{B}}{\text{A}}\right)$
Pizza	$10	10	$1.00
Root Beer	$3	5	$0.60
Salad	$2	1	$2.00
ABC Cost			$3.60

Table (6)

The unit cost as per ABC costing is $3.60.

Using the ABC cost compute, the average lunch cost for Group B1:

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	6	$1.00	$6
Root Beer	3	$0.60	$2
Salad	1	$2.00	$2
Total Cost			$9.80

Table (7)

The average lunch cost for Group B1, using ABC costing is $9.80.

Using the ABC cost compute, the average lunch cost for Group B2:

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	7	$1.00	$7
Root Beer	2	$0.60	$1
Salad	1	$2.00	$2
Total Cost			$10.20

Table (8)

The average lunch cost for Group B2, using ABC costing is $10.20.

The ABC cost of Group B are more alike to the average cost of Group B as the input costs are more alike and the assignment of these costs are analogous. Hence, the costing is more similar.

To determine

Identify the excess capacity on the basis of new proposal, and the decision to invite guests to fill the excess capacity. Describe the conceptual significance as well.

Explanation of Solution

The new proposal shall have an excess capacity of 30 slices of pizza, which makes 3 pizzas and 30 glasses of Root beer which shall sum up to 6 pitchers of Root beer. The guests can be invited and offered the now excess 3 pizzas and 6 pitchers of Root beer.

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	30	$1.00	$30
Root Beer	30	$0.60	$18
Excess amount			$48.00

The amount that could be saved is $257$\left(\$305-\$48\right)$.

In a manufacturing industry, reduction of wastes shall provide for greater productivity and optimize the profitability of the firm.