Question

Crest Industries sells a single model of satellite radio receivers for use in the home. The radios have the following price and cost characteristics: Sales price $80.00 per radio Variable costs $32.00 per radio Fixed costs $360,000.00 per month Crest is subject to an income tax rate of 40.00% a. How many receivers must Crest sell every month to break even? b. How many receivers must Crest sell to earn a monthly operating profit of $90,000.00 after taxes?

2. Cesar's Bottlers bottle soft drinks in a factory that can operate either one shift, two shifts, or three shifts per day. Each shift is eight hours long. The factory is closed on weekends. The sales price of $2.00 per case bottled and the variable cost of $0.90 per case remain constant regardless of volume. Cesar's Bottlers can increase volume by opening and staffing additional shifts. The company has the following three choices: Daily Volume Range Total Fixed (# of cases bottled) Costs per Day 1 Shift 0 - 2,000 $1,980.00 2 Shifts 2,001 - 3,600 $3,740.00 3 Shifts 3,601 - 5,000 $5,170.00 a. Calculate the break-even point(s). b. If Cesar's Bottlers can sell all the units it can produce, should it operate at one, two or three shifts?

Answer 1

1. Selling price per unit = $ 80 per radio

variable cost per unit = $ 32

Contribution margin per unit = 80 - 32

= $ 48

Fixed Costs = $ 360000

BEP in Units = Fixed Cost /(Selling price per unit - variable cost per unit)

= 360000/(80-32)

= 360000/48

= 7500 units

BEP in $ = 7500*Selling price per unit

= 7500*80

= $ 600000

1. (b) Required Monthly operating profit after taxes = $ 90000

To earn $ 90000 monthly operating profit after tax, need to earn before tax 90000/0.60(1-tax rate) = $ 150000

to earn $ 90000 after tax means suppose before tax = $ x

then x - 0.40x = 90000

0.60x = 90000

x = 90000/0.60 = 150000

now Required sales = (desired income + fixed cost)/contribution margin

= (150000+360000)/48

= 510000/48

= 10625 units

Required sale in dollars = 10625*80

= $ 850000

2. Selling Price per unit = $ 2.00

Variable cost per unit = $ 0.90

Contribution margin = sales - variable cost

= 2 - 0.90

= 1.10

contribution margin ratio = Contribution Margin per unit / selling price per unit

= 1.10/2

= 55%

(a) (i) BEP if it run only 1st shift = Fixed Cost / Contribution margin ratio

= 1980/55%

= $ 3600

(ii) BEP if it run two shifts = 3740/55%

= $ 6800

iii) BEP if it run all shift(three shifts) = 5170/55%

= $ 9400

(b) (i) total sales if it operates only 1st shift = 2000*2 = 4000

Margin of safety in that case = Actual sales - BEP sales

= 4000 - 3600

= $ 400

(ii) total sales if it operates only 2 shifts = 3600*2 = 7200

Margin of safety in that case = Actual sales - BEP sales

= 7200 - 6800

= $ 400

(iii)

total sales if it operates only 3 shifts = 5000*2 = 10000

Margin of safety in that case = Actual sales - BEP sales

= 10000 - 9400

= $ 600

so from analysis all the three option Cesar's bottlers should operate all the three shifts as MOS is greater if it run all shifts.

Please check with your answer and let me know.