Question

David is a local barber who operates his own mobile barber business in the Canarsie area of Brooklyn. The total fixed costs for running the company car and David's wages are S3,200 per month. The price for a haircut is $18 with a variable cost of $6.75 per cut. In a typical month, David makes 365 cuts. Due to his success, other mobile barbers are entering the market with lower prices, so David is considering a 5% price reduction . Assuming no changes in his variable or fixed costs, what would be the %BE and unit BE required to be profitable? 2. Fortunately for David, since he's been doing this for a while, he's managed to identify a way to reduce his variable costs by $0.25 per cut. What would be his %BE and unit BE given this new information? 3. David is considering an expansion into the next neighborhood to increase his territory. However, he would need a new car and some new equipment. He estimates that it would require incremental semi-fixed costs of $6,600 (a) Calculate the BE sales volume required (to the nearest whole unit) to recover the incremental investment (b) Calculate the %BE sales change AND the unit BE to account for BOTH the 5% price cut and the incremental fixed costs

Answer 1

Current scenario:

Fixed cost is $3200 per month

variable cost is $6.75 per cut

income is $18 per cut and he does 365 cuts a month.

His BE at this point is

(income * BE ) = (fixed cost) + (variable cost * BE)

18*BE = 3200 + (6.75* BE)

This puts the BE at 284.44 or roughly 285 to get profitable.

With a 5% reduction in charges, the income would drop to $17.1 per cut

Thus,

1. assuming he needs to have X cuts to be break even, the formula becomes

(Income per cut * X ) = fixed cost + (variable cost per cut * X)

(17.1 *X) = 3200 + (6.75*X)

10.35 X = 3200 and hence X becomes is 3200 / 10.35 = 309.17

This means that to become profitable, David needs to do at least 310 cuts per month.

This is about 8.77% more than what is was without a price reduction

2. The variable cost comes down by $0.25 per cut, so the formula values change

(17.1 * X ) = 3200 + (6.5 * X)

10.6 X = 3200 and hence X becomes 301.88

This means that to become profitable, David needs to do at least 302 cuts per month

This is about 5.96% more than what it was without a price reduction

3. Now, with new car costing about $6600 (semi-fixed)

a) without factoring in the 5% reduction in price, the BE sales volume to recover the cost of the new car would be:

(income per cut * X ) = fixed cost + semi fixed cost for new car + (variable cost * X)

(18 * X) = 3200 + 6600 + (6.75 * X)

11.25 * X = 9800

therefore the value of X which is the break even sales volume is 9800 / 11.25 = 871.11

Thus, David needs to do at least 872 cuts to recover the cost of the new car.

b) The BE point would change and the formula would be

(income per cut * X) = fixed cost + semi fixed cost for new car + (variable cost * X)

(17.1 * X ) = 3200 + 6600 + (6.75*X)

10.35*X = 9800

therefore X becomes 9800/10.35 = 946.85 or roughly 947

Thus, 947 cuts are needed to recover the cost of the new car.