Question

Suppose that Nash Daycare provides two different services: full-time childcare for preschoolers, and after-school care for older children. The director would like to estimate an annual cost per child in each of the daycare programs, ignoring any facility-sustaining costs. She is considering expanding the services and wants to know whether full-time or after-school care is more profitable.

The following activities and annual costs apply to the daycare centre. Salaries and wages are $140,000. Full-time children arrive between 8:00 and 9:00 a.m. Older children arrive about 3:00 p.m. All the children are gone by 6:00 p.m. Employees estimate that they spend about 30% of their time on meal-related activities, 30% supervising naps or recreation, 10% in greeting children or sending them home, and the rest of the time presenting educational experiences to the children. Meals and snacks cost about $19,000. Preschoolers receive 2 snacks and 1 meal per day, and the older children receive 1 snack per day. On average, snacks and meals do not differ in cost. Supplies cost $9,000 for the full-time childcare program and $7,000 for the after-school program.

Currently, 30 children participate in full-time care and 15 children in after-school care. Because Nash Daycare maintains a waiting list for openings in its programs, the number of children in each program remains steady.

Assuming 200 days of daycare for a year, estimate the annual cost per child in each program

Answer 1

Total No. of Children-days:

• 30 preschoolers x 200 days = 600 child day
• 15 older children x 200 days 300 child day
  Total = 900

Total Hours Spent by each group

• Pre-schoolers arrive between 8 and 9 am. Averaged at 8:30. They leave by 6 pm. Time spent: 9:30 hours.
  Total hours for pre-schoolers = 9:30 hours x 600 = 5,700 hours
• Older children arrive by 3 pm. They leave by 6 pm. Time spent: 3 hours.
  Total hours for older children = 3 hours x 300 = 900 hours
  Total = 5,700 + 900 = 6,600 hours

Snacks:

• 2 snacks and 1 meal for preschoolers = 3 x 600 = 1,800
• 1 snack for older children = 1 x 300 = 300
  Total = 2,100 numbers.

Total Unallocated Cost:

• Salaries and Wages: $140,000
• Meals and Snacks: $19,000

Allocation of Salaries and Wages of $140,000:

• 30%, being $42,000 on meal related activities:
  • Pre-schoolers: $42,000 x 1800 / 2100 = $36,000
  • Older children: $42,000 x 300 / 2100 = $6,000
• 30% being $42,000 on supervision:
  • Pre-schoolers: $42,000 x 5700 / 6600 = $36,273 (rounded)
  • Older children: Balance of $5,727
• 10% being $14,000 in greeting children:
  • Pre-schoolers: $14,000 x 600 / 900 = $9,333
  • Older children: Balance of $4,667
• Balance 30% being $42,000 on education:
  • Pre-schoolers: $42,000 x 5700 / 6600 = $36,273 (rounded)
  • Older children: Balance of $5,727

Allocation of Meals and Snacks Costs of $19,000:

• Pre-schoolers: $19,000 x x 1800 / 2100 = $16,286
• Older children: Balance of $2,714

Supplies:

• Pre-schoolers: $9,000
• Older children: $7,000

TOTAL

• Pre-Schoolers: $36,000 + $36,273 + $9,333 + $36,273 + $16,286 + $9,000 = $143,165
• Older Children: $6,000 + $5,727 + $4,667 + $5,727 + $2,714 + $7,000 = $31,835

Note: I have rounded the figures to the nearest whole dollar.
Note: Different interpretations can be taken regarding allocation. I have worked out in detail based on the interpretations used.
Note: Allocation of Salaries and Wages could be done differently as well, to see which is more profitable, by assuming that they are fixed costs, and hence do not change even if they allow more children in, from any category. If this is the interpretation you are taught to take, kindly make note of the same and I can rework the entire problem accordingly. Feel free to inform.

Hope this helps.
Thank you!