Question

Futaba photo shop has three services, print, enlargement, frame. The shop owner thinks these two services can be sold as a bundle, Print 3, Enlarge 4 and Frame 1. The company spends 10% of selling price as variable advertising expenses. Fixed cost for the shop is $129,320. The following information related to these three services is given.

		Print	Enlarge	Frame
Selling price		0.8	1.2	4.5
Direct material and labor costs per unit		0.17	0.31	1.8
Variable manufacturing costs		0.10	0.22	0.5
Expected sales units		45,000	60,000	15,000

Determine the contribution margin per unit of each product

Compute the breakeven point volume for each service. Present supporting calculations

What is the total sales units required to earn profit of $252,000 on after tax, the above assumption and a tax rate of 40%?

Answer 1

Computation of contribution margin per unit of each product

	Print ($)	Enlarge ($)	Frame ($)
Selling price	0.8	1.2	4.5
(-) direct material and labour costs	0.17	0.31	1.8
(-) variable manufacturing costs	0.10	0.22	0.5
(-) variable advertisement expenses	0.08 (0.8*10%)	0.12 (1.2*10%)	0.45 (4.5*10%)
Contribution margin per unit	0.45	0.55	1.75

Contribution margin per unit is the difference between the selling price and all the variable expenses. This is what has been done in the above table.

Break even point volume for each service

Break even point volume means break even point in dollars. We can find out the break even point volume by computing the break even point in units of each product first and multiplying it by the respective selling price. But to do this we must find the combined contribution per unit as shown below:

The sales mix of (print: enlarge: frame) is given to be 3:4:1.

Combined contribution per unit= total contribution for sales mix/total units

= [(3*0.45)+(4*0.55)+(1*1.75)]/(3+4+1)

=$0.6625 per unit

Break even point (units)= fixed cost/combined contribution per unit

= 129320/0.6625= 195200 units

Sales mix

	Print	Enlarge	Frame
Break even units (195200 in 3:4:1) (units)	73200	97600	24400
Selling price per unit($)	0.8	1.2	4.5
Break even point volume for each service($)	58560	117120	109800

Total sales for profit after tax of $252000

To compute the sales to get a desired profit, we must use the equation for desired profit as shown below:

Total sales units= (fixed expenses+desired profit)/contribution per unit

Fixed expenses= $129320

Desired profit= (252000*100)/60= $420000

The desired profit is given after tax. We have to convert it to before tax profit to be able to use it in the desired profit equation.

Contribution per unit= $0.6625 per unit

Applying all this is the desired profit equation,

Total sales units= (129320+ 420000)/0.6625= 829162 units (rounded off)

Total sales units to earth an after tax profit of $252000 is, 829162 units.