Question

Beball camp example covered in the class, let's assume the segment size is 9000, price per participant is $90, frequency is 1, variable cost per person is $5, TFC = $9,000. Based on the assumption provided above, what percentage of the segment should participate if the program wants to make $1500 profit?

Answer 1

Answer:

About 1.37

Explanation:

Given that

Segment size = 9000

TFC = $9000

VC per person = 5

Price per person = 90

Profit = 1500

Let y he number of participants in the camp

Thus,

Variable cost = variable cost per person × no. Of participants

VC = 5 × y

VC = 5y

Also,

TC = TFC + TVC

TC = 9000 + 5y

The next thing to calculate for is total revenue

Total revenue of the program = Price per person × No. of participants + Profit

Total revenue of the program = 90 × y + 1,500

Total revenue of the program = 90y + 1,500

For break even

TC = price per person × no. of participants

9000 + 5y = 90y

9000 = 90y - 5y

9000 = 85y

y = 9000/85

y = 105.88

y = 106 approximately.

For $ 1,500 of profits:

Number of participants at break-even + Profits/Price per participant

106 + 1,500/90

= 106 + 16.7 = 123

= 123/1,500

= 0.0137

= 1.37% (Rounding to two decimal places)

Answer 2

Answer:

1.38%

Explanation:

to solve this question we can use a formula very similar to the break even point formula:

% of the segment needed to participate to generate $1,500 profit

= (total fixed costs + expected profit) - contribution rate

= ($9,000 + $1,500) / ($90 - $5) = $10,500 / 85 = 123.53 ≈ we round up to 124 participants

124 participants / 9,000 segment size = 1.38%