Question

Julianna Abdallah owns and operates FirstCakes, a bakery that creates personalized birthday cakes for a child’s first birthday. The cakes, which sell for $40 and feature an edible picture of the child, are shipped throughout the country. A typical month’s results are as follows:

Sales revenue $840,000

Variable expenses 630,000

Contribution margin 210,000

Fixed expenses 112,000

Operating income $ 98,000

a) Assuming a 30% tax rate, how many cakes will Julianna Abdallah have to sell if she wants to earn $115,150 in net income each month? (Round answer to 0 decimal places, e.g. 5,275.)

Answer 1

Solution:

As per the information given in the question we have

Sales revenue = $ 840,000 ; Sales price per unit = $ 40

Thus No. of units of sales = Sales revenue / Sales price per unit = $ 840,000 / $ 40

= 21,000 units

Further as per the information given in the question we have

Variable expenses = $ 630,000 ; No. of units of sales = 21,000

Thus variable expense per unit = Variable expenses / No. of units of sales

= $ 630,000 / 21,000

= $ 30

Thus variable expense per unit = $ 30

Calculation of Sales units required to make a profit of $ 115,150 :

The net income required is $ 115,150 at a tax rate of 30 %

The tax rate = 30 % = 0.30 ; Fixed expenses = $ 112,000

The formula for calculating the Net Income

( Sales – Variable costs – Fixed costs ) * ( 1 – Tax rate ) = $ 115,150

Let the number of sales units = “ x “ units

Thus the Total sales = No. of sales units * Sales price per unit

= x * 40 = 40 x

Thus the Total variable expenses = No. of sales units * Variable expense per unit

= x * 30 = 30 x

Applying the available information in the equation below we have

( Sales – Variable costs – Fixed costs ) * ( 1 – Tax rate ) = $ 115,150

( 40x – 30x – $ 112,000 ) * ( 1 – 0.30 ) = $ 115,150

( 40x – 30x – $ 112,000 ) * 0.70 = $ 115,150

( 10x – $ 112,000 ) * 0.70 = $ 115,150

7 x - $ 78,400 = $ 115,150

7 x = $ 78,400 + $ 115,150

7 x = $ 193,550

x = $ 193,550 / 7

x = 27,650 units

Thus, assuming a 30% tax rate, the number of cakes that Julianna Abdallah will have to sell if she wants to earn $115,150 in net income each month = 27,650 units