Solution 4.12

Workings

	Product 1	Product 2	Product 3	Product 4	Total
Volume	15,000	5,000	10,000	7,500	37,500
Total sales revenue	€37,500	€16,250	€43,000	€13,125	€109,875
Contribution per unit *	€1.55	€2.00	€2.30	€1.10
Total contribution	€23,250	€10,000	€23,000	€8,250	€64,500

*Contribution per unit is found by dividing sales revenue by volume to get sales price per unit and then deducting variable costs.

a) Calculate the total revenue required to break-even based on the current sales mix

Fixed cost: 37,500 units x 50p = €18,750

C/S ratio: €64,500 / €109,875 x 100 = 58.7% (average based on mix ratio)

Break-even: €18,750 / 0.587 = €31,942 revenue

b) Calculate the number of units of each product required to break-even based on the current sales mix

Average selling price: €109,875 / 37,500 = €2.93

Total units to break-even: €31,942 / €2.93 = 10,902 units

Ratio: 15 : 5 : 10 : 7.5

Product 1:	10,902 / 37.5 x 15	4,361 units
Product 2:	10,902 / 37.5 x 5	1,454 units
Product 3:	10,902 / 37.5 x 10	2,907 units
Product 4:	10,902 / 37.5 x 7.5	2,180 units

c) Calculate the margin of safety in revenue

€109,875 - €31,942 = €77,933 revenue

d) Calculate the break-even point and margin of safety if the business follows a strategy of increasing advertising by €15,000 which is forecast to increase sales by 10 per cent

	Product 1	Product 2		Product 3		Product 4		Total
Volume	15,000	5,000		10,000		7,500		37,500
New volume + 10%	16,500	5,500		11,000		8,250		41,250
Contribution per unit	€1.55	€2.00		€2.30		€1.10
New contribution	€25,575	€11,000	€25,300		€9,075		€70,950

New sales:	€109,875 x 110% = €120,863
C/S ratio:	€70,950 / €120,863 x 100 = 58.7%
New fixed cost:	€18,750 + €15,000 = €33,750
Break-even:	€33,750 / 0.587 = €57,493
Margin of safety:	€120,863 - €57,493 = €63,370

e) Should the increase in advertising be implemented?

Existing profit: €64,500 - €18,750 = €45,750

New profit: €70,950 - €33,750 = €37,200

NO, although the proposal increases volume the proposal should not be implemented as the profit will fall from €45,750 to €37,200 the break-even revenue will increase and the margin of safety decrease.