Question

3-19 Multiproduct breakeven point (LO 5) Andrew Sinclair operates a lawn care business. He offers customers a choice of two services. The first service, basic lawn care, includes mowing and trimming of all lawn areas. Andrew bills these customers $30 per hour, and his variable cost for providing this service is $22 per hour. Andrew also offers deluxe lawn care services, which includes flower bed maintenance in addition to basic lawn care. He bills his customers $60 per hour for this service, and his variable cost for providing this service is $28 per hour. Andrew currently spends 1 hour of his time providing deluxe lawn care services for every 4 hours of basic lawn care services. Andrew also incurs $140,800 in fixed costs per year running his business.

Required

a.What is Andrew's profit equation?

b.How many hours of each service type must Andrew provide in a year to break even?

c.Andrew believes that with a little persuasion, he could convert many of his basic lawn care customers to the deluxe service. If he is able to convert enough customers so that he spends an equal amount of time providing basic and deluxe services, how many hours will he need to work to break even?

Answer 1

Contribution from Basic Lawn Care = Sale Price - Variable Cost

                                           = 30-22

                                            = $8

Contribution from Deluxe Lawn Care = 60 - 28 = $32

fixed costs = $140,800

a)Let Andrew currently spends x hour of his time providing deluxe lawn care services

hence time spent for providing basic lawn care services = 4x

Hence Andrew's profit equation will be as follows:

$32(x) + $8(4x) - 140,800 = Operating Profit

b) At Break even point, Profit = 0

So, $32(x) + $8(4x) - 140800 = 0

    32x + 32x -140800 = 0

   64x = 140,800

     x = 140,800 / 64

     x = 2,200 hours ( Deluxe Care Serive Hours)

   4x = 2200*4 = 8,800 hours ( Basic Care Serive Hours)

So Andrew must provide 2200 hours of deluxe Lawn Care and 8800 hours of basic Lawn Care service in a year to break even

c) Lets assume Andrew provides x hours of basic and deluxe lawn care services

Hence the For Break even, the equation will be

32x + 8x -140,800 = 0

40x = 140,800

x = 140,800 / 40

x = 3520 hours

Total Hours = 3520 (Basic) + 3520 (deluxe) = 7040 Hours.

So he will he need to work 3520 hours of basic service and 3520 hours of deluxe care servive i. e. total 7040 hours to break even.