Chapter 15, Problem 22P

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.

Required:

1. 1. Determine the total number of pizzas, pitchers of root beer, and salads that must be ordered for the 60 employees.
2. 2. One of the CPAs offered to determine the amount that each should pay. He suggested that the easiest way is to assign the average cost to each person eating in the group. Based on this suggestion, how much would each CPA pay for lunch?
3. 3. One CPA objected to using average cost, noting that half of the CPAs are much lighter eaters than the other half. Based on the large differences in consumption behaviors, he suggested forming two groups: one for the light eaters and one for the heavier eaters. Calculate the lunch cost for each CPA for each group. Discuss the analogy to formation of focused value streams in a manufacturing environment. Calculate the cost that would be assigned using ABC. What does this tell you?

To determine

Compute the total number of each item to be ordered.

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.

Compute the number of pizzas to be ordered:

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{ Pizzas}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)+\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)}{10}\\ =\frac{\left(3\times 30\right)+\left(7\times 30\right)}{10}\\ =\frac{90+210}{10}\\ \text{= 3}0\text{ pizzas}\end{array}$

Compute the number of pitchers of root beer to be ordered:

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{Pitchers of}\\ \text{Root Beer}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)+\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)}{5}\\ =\frac{\left(3\times 30\right)+\left(2\times 30\right)}{5}\\ =\frac{90+60}{5}\\ \text{= 3}0\text{ pitchers}\end{array}$

Compute the number of bowls of salad to be ordered:

$\begin{array}{c}\text{Salad Bowls = Number of Bowls}\times \text{Number of Persons}\\ =1\times 60\\ =60\text{ bowls}\end{array}$

To determine

Compute the average cost of lunch to be paid by each CPA.

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.

In the single product value stream all the products being produced are assumed to belong to one value stream.

Compute the total cost of lunch:

Particulars	Number of Units (A)	Cost per Unit (B)	Amount $\left(\text{C=B×A}\right)$
Pizza	30	$10	$300
Root Beer	30	$3	$90
Salad	60	$2	$120
Total Cost			$510

Table (1)

Compute the average cost of lunch:

$\begin{array}{c}\text{Average cost of lunch = }\frac{\text{Total cost of lunch}}{\text{Number of employees}}\\ =\frac{\$510}{60}\\ =\$8.50\end{array}$

To determine

Compute the average cost of lunch to be paid by each CPA, if the employees were grouped on the basis of their eating pattern and compare the result with the ABC costing.

Explanation of Solution

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	9	$10	$90
Root Beer	18	$3	$54
Salad	30	$2	$60
Total Cost			$204

Table (2)

Working Notes:

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

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{ Pizzas}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)}{10}\\ =\frac{\left(3\times 30\right)}{10}\\ =\frac{90}{10}\\ \text{= 9 pizzas}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{Pitchers of}\\ \text{Root Beer}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)}{5}\\ =\frac{\left(3\times 30\right)}{5}\\ =\frac{90}{5}\\ \text{= }18\text{ pitchers}\end{array}$

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:

$\begin{array}{c}\text{Average cost of lunch = }\frac{\text{Total cost of lunch}}{\text{Number of employees}}\\ =\frac{\$204}{30}\\ =\$6.80\end{array}$

The average cost of lunch for Group A 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	21	$10	$210
Root Beer	12	$3	$36
Salad	30	$2	$60
Total Cost			$306

Table (3)

Working Notes:

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

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{ Pizzas}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Slices}\times \\ \text{Number of Persons}\end{array}\right)}{10}\\ =\frac{\left(7\times 30\right)}{10}\\ =\frac{210}{10}\\ \text{= 21 pizzas}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Number of}\\ \text{Pitchers of}\\ \text{Root Beer}\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Number of Glasses}\times \\ \text{Number of Persons}\end{array}\right)}{5}\\ =\frac{\left(2\times 30\right)}{5}\\ =\frac{60}{5}\\ \text{= }12\text{ pitchers}\end{array}$

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

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

The unit material cost for Model A is $80 and for Model B is $30.

Compute the average unit conversion cost:

$\begin{array}{c}\begin{array}{l}\text{Average unit }\\ \text{Conversion cost}\end{array}\}\text{= }\frac{\text{Conversion Cost}}{\text{Number of Units}}\\ =\frac{\$192,000+\$78,000+\$30,000}{15,000\text{ units}}\\ =\frac{\$300,000}{15,000\text{ units}}\\ \text{= \$2}0\text{ per unit}\end{array}$

Compute the average cost of lunch for Group B:

$\begin{array}{c}\text{Average cost of lunch = }\frac{\text{Total cost of lunch}}{\text{Number of employees}}\\ =\frac{\$306}{30}\\ =\$10.20\end{array}$

The average cost of lunch for Group B is $10.20.

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 (4)

The unit cost as per ABC costing is $3.60.

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

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 (5)

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

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

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 (6)

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

Thus, under both focused value stream approach and ABC costing the costs are similar and very accurate.