This analysis considers the cost behavior of the various cost items in order to determine the cost and profit at various levels of activity. Fixed costs are costs that do not vary with changes in output. Variable costs are costs that change with changes in output. Semi-variable costs are costs that are partly variable and partly fixed. Stepped fixed costs are costs that remain at a particular level of activity but step-up to a new level when activity level exceeds a particular point (Drury, 2012).
In this case, the cost items are classified into either fixed costs, variable costs, semi-variable costs and stepped fixed costs. Instructors salary are step fixed costs that increase at $1,600 per class. Salary of part time cook and Occupancy and other admin costs are fixed meaning that they will remain unchanged at various level of activity. Supplies expense is semi-variable with a fixed cost component of $520 and a variable cost component of $1 per child. Variable costs include food expense at $1.25 per child, staff benefits at 10% of the total wage in addition to a unit benefit of $200 per employee.
Middlehurst House day care is currently making $2,500 in operating profit. Reducing the class size would increase the number of teachers from six to eleven. According to Exhibit 2, this would increase instructor salaries by $8,000, and the staff benefits by $1,800. Fixed costs would increase by $8,000, while variable costs would increase by $1,800. In order to maintain the current profitability the tuition fee would have to increase by $9,800 or in percentage terms by 45.58%. In this case, the profit would decline by $9,800 to a loss of $7,300.
Reducing the class size and increasing the tuition by 45.58% is likely to fail because only 50% of the parents for children of ages 2 to 5 years would support a fee hike of about 50% and none of the parents for children of ages 5 to 6 years would support such a hike. In this case, it seems that demand is elastic. Prices hikes for elastic products results in a fall in demand and a reduction in revenue (Allen, Weigelt, Doherty, & Mansfield, 2012). The analysis does not justify the reduction in class sizes that will require more teachers because the move will result into a loss. Therefore, management should refrain from pursuing this strategy.
Opening up the new class from the waiting list and maintaining the current class size would require hiring an additional instructor for each class, thus instructors would increase to ten. According to Exhibit 3, total fixed cost would increase by $6,400 while variable costs would increase by $2,209.5 driving the total cost up by $8,609.5. However, the revenue increase of $8,640 slightly exceeds the rise in cost increasing the operating profit marginally from $2,500 to $2,530. In this case, the marginal or incremental profit is $30.
Implementing the new class has a marginal positive impact on the operating profits of the school. Since the decision to expand is strategic in nature, the management should consider the strategic implications of the move including the non-financial factors such as creating customer goodwill, or attaining a particular number of enrollments (Lucey, 2003). Since the school has enrolled only 80 students while it has a capacity of 120 students it means that Middlehurst House has some spare capacity and that they can increase enrollments by a further 40 children. When a business has spare capacity, they can accept new business as long as the marginal revenue exceeds marginal costs (Drury, 2012). In this case, the marginal revenue surpasses marginal costs by $30 meaning that introducing the new classes would increase the operating profit by $30.
New fee structure
Creating new classes and filling them to the maximum using the waiting list would increase the number of classes from six to eleven. According to Exhibit 4, fixed costs would increase by $8,000 while variable costs would increase by $1,971. The total costs would increase by $9,971. However, revenue would increase by $14,080 resulting in an increase in profits of $4,109.
A combination of an increase in classes and a hike in tuition fee would be the most profitable strategy since the marginal revenue would be$14,080 as compared to marginal costs of $9,971. However, while the strategy looks highly profitable on paper, it is very optimistic in that it assumes parents will be willing to pay the fee hike of 45.58% and that the day care will still be able to fill its classes at the increased tuition fee. The law of demand states that the higher the price the lower the demand (Allen, Weigelt, Doherty, & Mansfield, 2012). It is likely that the day care will face a decline in demand after hiking the school fees and they may not be able to fill even the existing classes leave alone filling the new classes. If the day care were to experience a decline in demand after introducing new classes, they would face high losses because the increase in fixed costs by $8,000 raises their break-even point. The day should not try to expand and hike the fees at the same time because the cost, volume, and profitability analysis suggest that costs will increase faster than revenues due to decreased demand following a price hike, resulting in the day care making losses.
Infant care
The infant care class would be profitable if the tuition was set at $466 equivalent to the proposed tuition for the 2-to-3 age group. According to Exhibit 5, a class of five would generate revenue of $2,329. The fixed costs would include the tutor’s salary of $1,600 and the corresponding fixed benefit of $200 adding up to $1,800 in total costs. The class would generate a contribution of $529. The variable costs would include, staff benefit of $160 (10% *$1,600) and the supplies expense of $5 (5*$1). Thus, the total cost of starting the infant care class would be $1,965 against projected revenue of $2,329. The infant care class marginal operating profit would be $364.
In evaluating the profitability of the infant care class, the analysis ignores the fixed costs because they are irrelevant (Hansen, Mowen, & Guan, 2009). The day care will continue to incur the fixed costs irrespective of whether they start the infant care class or not. However, the variable costs that include staff benefit and supplies expense are relevant because they are incremental and would not be incurred if Middlehurst house does not offer the infant care class. Therefore, the management should open up the infant care class because it will be profitable.
References
Allen, W., Weigelt, K., Doherty, N., & Mansfield, E. (2012). Managerial Economics. xxx:
W. W. Norton & Company.
Drury, C. (2012). Cost and management accounting. Andover: Cengage Learning.
Hansen, D., Mowen, M., & Guan, L. (2009). Cost management. Mason, Ohio: South-Western.
Lucey, T. (2003). Management accounting. London: Continuum.
Exhibit 1
Exhibit 2
Exhibit 3
Exhibit 4
Exhibit 5
