Chapter 3, Problem 40E

1.

To determine

Find out the total cost of renting space if 100 people and attend and calculate the average cost.

Explanation of Solution

Costs: In accounting terms, costs refer to the monetary value expended to produce a product. Costs are generally classified based on the purpose it is incurred for. Costs are classified based on the necessity for preparation of cost statements for various purposes. Classification of costs based on the nature is known as subjective classification; and classification of costs based on the purpose is known as objective classification.

Calculate the amount of fixed cost:

$\begin{array}{c}\text{Total}\text{cost}\text{=}\text{Fixedcost}\text{of}\text{rental}\text{space}\text{+}\text{Variable}\text{cost}\text{of}\text{refreshments}\\ \text{=}\text{\$1,500+}\text{\$1,500}\left(\text{\$15}\text{×}\text{100}\text{people}\right)\\ \text{=}\text{\$3,000}\end{array}$

Calculate the amount of average cost:

$\begin{array}{c}\text{Average}\text{cost}\text{=}\frac{\text{Total}\text{cost}}{\text{Number}\text{of}\text{people}}\\ \text{=}\frac{\text{\$3,000}}{\text{100}\text{people}}\\ \text{=}\text{\$30}\text{per}\text{person}\end{array}$

Therefore, the amount of fixed cost is $3,000 and average cost is $30 per person.

2.

To determine

Find out the total cost of renting space if 200 people and attend and calculate the average cost.

Explanation of Solution

Calculate the amount of fixed cost:

$\begin{array}{c}\text{Total}\text{cost}\text{=}\text{Fixedcost}\text{of}\text{rental}\text{space}\text{+}\text{Variable}\text{cost}\text{of}\text{refreshments}\\ \text{=}\text{\$1,500+}\text{\$3,000}\left(\text{\$15}\text{×}2\text{00}\text{people}\right)\\ \text{=}\text{\$4,500}\end{array}$

Calculate the amount of average cost:

$\begin{array}{c}\text{Average}\text{cost}\text{=}\frac{\text{Total}\text{cost}}{\text{Number}\text{of}\text{people}}\\ \text{=}\frac{\text{\$4,500}}{\text{200}\text{people}}\\ \text{=}\text{\$22}\text{.50}\text{per}\text{person}\end{array}$

Therefore, the amount of fixed cost is $4,500 and average cost is $22.50 per person.

3.

To determine

Explain the reason for which average total cost differs with changes in total attendance.

Explanation of Solution

Decrease in fixed cost per person is $7.50$\left[\$15(1)-\$7.50(2)\right]$ and average cost for 200 people is $22.50 (3). Therefore, as attendance increases, average costs decrease since the fixed cost component of total costs is now spread over 100 additional people.

Working notes:

(1)Calculate the amount of fixed cost per person for 100 people:

$\begin{array}{c}\text{Fixed cost per person for 100 people}\text{=}\frac{\text{Fixed}\text{cost}\text{of}\text{space}\text{rental}}{\text{Number}\text{of}\text{people}}\\ \text{=}\frac{\text{\$1,500}}{\text{100}\text{people}}\\ \text{=}\text{\$15}\end{array}$

(2)Calculate the amount of fixed cost per person for 200 people:

$\begin{array}{c}\text{Fixed cost per person for 200 people}\text{=}\frac{\text{Fixed}\text{cost}\text{of}\text{space}\text{rental}}{\text{Number}\text{of}\text{people}}\\ \text{=}\frac{\text{\$1,500}}{\text{200}\text{people}}\\ \text{=}\text{\$7}\text{.50}\end{array}$

(3)Calculate the average cost of 200 people:

$\begin{array}{c}\text{Average}\text{cost}\text{of}\text{200}\text{people}\text{=}\left(\begin{array}{l}\text{Average}\text{cost}\text{for}\text{100}\text{people}-\\ \text{Decrease}\text{in}\text{fixed}\text{cost}\text{of}\text{per}\text{person}\end{array}\right)\\ \text{=}\text{\$30}-\text{\$7}\text{.50}\\ \text{=}\text{\$22}\text{.50}\end{array}$