Chapter 11, Problem 25P

1 a.

To determine

Identify whether the cost of instruction is fixed or variable cost.

Explanation of Solution

Fixed costs are the cost which remains constant when volume of activity changes but per unit value will change inversely with change in volume of the activity.

The cost of instruction is fixed cost as the total cost remains constant irrespectively of number of students attends the courses

1 b.

To determine

Compute the profit, assuming that 20 students take the course.

Explanation of Solution

Given information:

Number of students are 20. The salary of instructor is $4,000 per course taught. The F services offer course of instruction $600 per student to the employees of B incorporation

Number of Students	20
Revenue ($600 per student)	$ 12,000
Cost of instruction (fixed)	$4,000
Profit	$ 8,000

Table (1)

1 c.

To determine

Compute the profit with 10% of increase in enrolment and percentage of profitability.

Explanation of Solution

Given information:

Number of students are 22. The salary of instructor is $4,000 per course taught. The R services offer course of instruction $600 per student to the employees of B incorporation

Compute the profit with 10% of increase in enrolment:

Number of Students	22
Revenue ($600 per student)	$ 13,200
Cost of instruction (fixed)	$4,000
Profit	$ 9,200

Table (2)

Percentage change in profits:

$\begin{array}{c}\text{Percentage change in profitability}=\frac{\text{G}\text{.P}\text{. }\left(22\text{students}\right)-\text{G}\text{.P}\text{. }\left(\text{20students}\right)}{\text{G}\text{.P}\text{. in }\left(20\text{students}\right)}\\ =\frac{\$9,200-\$8,000}{\$8,000}\\ =15\%\end{array}$

Hence, the percentage change in profitability is 15%.

Percentage change in revenue:

$\begin{array}{c}\text{Percentage change in revenue}=\frac{\text{Revenue }\left(22\text{students}\right)-\text{Revenue }\left(20\text{students}\right)}{\text{Revenue }\left(20\text{students}\right)}\\ =\frac{\$13,200-\$12,000}{\$12,000}\\ =\frac{\$1,200}{\$12,000}\\ =10\%\end{array}$

Hence, the percentage change in revenue is 10%.

1 d.

To determine

Determine the profit with 10% of decrease in enrolment and percentage of profitability.

Explanation of Solution

Given information:

Number of students are 18. The salary of instructor is $4,000 per course taught. The R services offer course of instruction at $600 per student to the employees of B incorporation

Determine the profit with 10% of decrease in enrolment:

Number of Students	18
Revenue ($600 per student)	$ 10,800
Cost of instruction (fixed)	$4,000
Profit	$ 6,800

Table (3)

Percentage change in revenue and profitability:

$\begin{array}{c}\text{Percentage change in profitability}=\frac{\text{G}\text{.P}\text{. }\left(20\text{students}\right)-\text{G}\text{.P}\text{. }\left(\text{18students}\right)}{\text{G}\text{.P}\text{. in }\left(20\text{students}\right)}\\ =\frac{\$8,000-\$6,800}{\$8,000}\\ =-15\%\end{array}$

Hence, the percentage change in profitability is (15%).

Percentage change in revenue:

$\begin{array}{c}\text{Percentage change in revenue}=\frac{\text{Revenue }\left(18\text{students}\right)-\text{Revenue }\left(20\text{students}\right)}{\text{Revenue }\left(20\text{students}\right)}\\ =\frac{\$10,800-\$12,000}{\$12,000}\\ =\frac{\left(\$1,200\right)}{\$12,000}\\ =-10\%\end{array}$

Hence, the percentage change in profitability is (10%).

1 e.

To determine

Explain the reason for 10% shift in enrolment produces more than 10% shift in profitability, use the term identifies this phenomenon.

Explanation of Solution

Operating leverage: It is a ratio that measures the proportion of fixed cost on the total costs and the extent to which the changes in the sales volume affects the income from operations. It shows the relationship between the contribution margin and income from operations.

The term which identifies these phenomena is operating leverage. This causes the percentage change in profitability to higher than the percentage change in revenue.

This is because that the fixed cost remains same and covered and there is no variable cost. So each additional dollar of revenue pays directly to the profitability.

2 f.

To determine

Identifies whether the cost of instruction is fixed or variable cost.

Explanation of Solution

Variable cost will change proportionately or directly with the change in the volume of the activity on the other hand per unit value will remain constant irrespective of the change in volume of activity.

Given information:

The instructor needs $360 per person attending the class. The F services offer course of instruction at $600 per student to the employees of B incorporation

The cost of instruction is variable cost as the total cost varies respectively of number of students attends the courses

2 g.

To determine

Determine the profit, assuming that 20 students take the course.

Explanation of Solution

Given information:

Number of students are 20. The instructor needs $360 per person attending the class. The R services offer course of instruction at $600 per student to the employees of B Incorporation

Number of Students	20
Revenue ($600 per student)	$ 12,000
Cost of instruction (Variable)	$7,200
Profit	$ 4,800

Table (4)

2 h.

To determine

Determine the profit with 10% of increase in enrolment and percentage of profitability.

Explanation of Solution

Given information:

Number of students are 22. The instructor needs $360 per person attending the class. The R services offer course of instruction at $600 per student to the employees of B Incorporation

Number of Students	22
Revenue ($600 per student)	$ 13,200
Cost of instruction (Variable)	$7,920
Profit	$ 5,280

Table (5)

Percentage change in profitability:

$\begin{array}{c}\text{Percentage change in profitability}=\frac{\text{G}\text{.P}\text{. }\left(22\text{students}\right)-\text{G}\text{.P}\text{. }\left(20\text{students}\right)}{\text{G}\text{.P}\text{. in }\left(20\text{students}\right)}\\ =\frac{\$5,280-\$4,800}{\$4,800}\\ =\frac{\$480}{\$4,800}\\ =10\%\end{array}$

Hence, the percentage change in profitability is 10%.

Percentage change in revenue:

$\begin{array}{c}\text{Percentage change in revenue}=\frac{\text{Revenue }\left(22\text{students}\right)-\text{Revenue }\left(20\text{students}\right)}{\text{Revenue }\left(20\text{students}\right)}\\ =\frac{\$13,200-\$12,000}{\$12,000}\\ =\frac{\$1,200}{\$12,000}\\ =10\%\end{array}$

Hence, the percentage change in revenue is 10%.

2 i.

To determine

Determine the profit with 10% of decrease in enrolment and percentage of profitability.

Explanation of Solution

Given information:

Number of students are 18. The instructor needs $360 per person attending the class. The R services offer course of instruction at $600 per student to the employees of B Incorporation

Determine the profit with 10% of decrease in enrolment:

Number of Students	18
Revenue ($600 per student)	$ 10,800
Cost of instruction (Variable)	$6,480
Profit	$ 4,320

Table (6)

Percentage change in profit:

$\begin{array}{c}\text{Percentage change in profitability}=\frac{\text{G}\text{.P}\text{. }\left(20\text{students}\right)-\text{G}\text{.P}\text{. }\left(\text{18students}\right)}{\text{G}\text{.P}\text{. in }\left(20\text{students}\right)}\\ =\frac{\$4,320-\$4,800}{\$4,800}\\ =\frac{\$480}{\$4,800}\\ =10\%\end{array}$

Hence, the percentage change in profitability is 10%.

Percentage change in revenue:

$\begin{array}{c}\text{Percentage change in revenue}=\frac{\text{Revenue }\left(18\text{students}\right)-\text{Revenue }\left(20\text{students}\right)}{\text{Revenue }\left(20\text{students}\right)}\\ =\frac{\$10,800-\$12,000}{\$12,000}\\ =\frac{\$1,200}{12,000}\\ =10\%\end{array}$

Hence, the percentage change in revenue is 10%.

2 j.

To determine

Explain the reason for 10% change in enrolment produces a proportional 10% shift in profitability.

Explanation of Solution

The change in profit is relative to change in revenue because the revenue as well as cost changes relatively to the change in number of students attending the course.

3 k.

To determine

Determine the total cost and the cost per student.

Explanation of Solution

Given information:

The cost of the work book is $30 and selling price is $50. The numbers of students are 18, 20, or 22. The company printed 20 copies of books.

The formula to calculate the cost per students:

$\text{Cost per students}=\frac{\text{Total cost}}{\text{Number of students}}$

Compute the total cost and cost per student:

Number of Students Attempting to Attend	18	20	22
Number of students accepted (a)	18	20	20
Total cost of workbooks $\left(\text{b=}\left[\text{20}\times \text{\$30}\right]\right)$	$600	$600	$600
Cost per student $\left(\text{b}\text{/}\text{a}\right)$	$33.33	$30	$30

Table (7)

3 l.

To determine

Identify whether the cost of work book is fixed or variable cost.

Explanation of Solution

The cost of work book is fixed cost as the cost incurred is before the sale of work book. Therefore, sales of number of work book will not affect the total cost.

Thus, it is fixed cost.

3 m.

To determine

Discuss the risk of holding inventory as it applies to workbooks.

Explanation of Solution

The risk faced by the company is that it produces very few or too many books. If the company produces too many books then the expenses will more due to wastage.

When the company produces less numbers then the will not get the opportunity to earn any additional profits.

It will also incur costs like maintenances, interest and storage.

3 n.

To determine

Explain whether just in time can reduce the cost and risk of holding inventory.

Explanation of Solution

JIT-Just in time produces only when there is any demand of goods. There will not be any risk on over or under production.

There will not be any stock piling of inventory as it will avoid the cost of storage, interest and maintenance.