Question

Hunter & Sons sells a single model of meat smoker for use in the home. The smokers have the following price and cost characteristics. Sales price Variable costs Fixed costs $ 77 per smoker 36 per smoker 315,700 per month Hunter & Sons is subject to an income tax rate of 40 percent. Required: a. How many smokers must Hunter & Sons sell every month to break even? b. How many smokers must Hunter & Sons sell to earn a monthly operating profit of $68,880 after taxes? a. Break-even sales in units b. Number of units to be sold

Answer 1

Solution:

a.Calculation of Break-Even sales in units :

The formula for calculating the Break-Even sales in units is

Break-Even sales in units = Fixed costs / Contribution margin per unit

= Fixed costs / ( Sales price per unit – Variable cost per unit )

As per the information given in the question we have

Variable cost per unit = $ 36 ;   Sales price per unit = $ 77 ; Fixed costs = $ 315,700

Applying the above information in the formula we have

= $ 315,700 / ( $ 77 - $ 36 )

= $ 315,700 / $ 41

= 7,700 units

Thus the Break-Even sales in units = 7,700 units

b.Number of units to be sold to earn a monthly operating profit of $ 68,880 after taxes

The formula for calculating the number of units to be sold to earn a monthly operating profit of $ 68,880 after taxes :

= [ Fixed costs + ( Operating Profit after tax / ( 1 – tax rate ) ) ] / ( Sales price per unit – Variable cost per unit )

As per the information available in the question we have

Fixed costs = $ 315,700 ;   Operating Profit after tax = $ 68,880   ; Tax rate = 40 % = 0.40   ;

Variable cost per unit = $ 36 ;   Sales price per unit = $ 77 ;

Applying the above information in the above formula we have

= [ $ 315,700 + ( $ 68,880 / ( 1 – 0.40 ) ) ] / ( $ 77 – $ 36 )

= [ $ 315,700 + ( $ 68,880 / 0.60 ) ] / ( $ 77 – $ 36 )

= [ $ 315,700 + ( $ 68,880 / 0.60 ) ] / ( $ 41 )

= [ $ 315,700 + $ 114,800 ] / $ 41

= $ 430,500 / $ 41

= 10,500

Thus the number of units to be sold to earn a monthly operating profit of $ 68,880 after taxes = 10,500 units