Question

QUESTION 4 CVP Analysis

Guide to marks: 20 marks – 4 for a, 4 for b, 4 for c, 8 for d
Show all calculations to support your answers.

A manufacturer can make two products, A and B. The following data are available:B

Product	A	B	Total
Sales price per unit	$12	$15
Variable cost per unit	$8	$10
Total fixed costs/month			$5000

(a)Calculate the unit contribution margin for each product.
(b)This month the manufacturer will specialise in making only Product B. How many does he need to sell to break even?
(c)If they specialise in making only A what is the breakeven sales volume for the month in sales dollars?
(d)He now decides to manufacture both A and B this month in the ratio of 3 of A to 1 of B.
(i)How many of each product must be sold to earn a profit of $3,500 before tax for the month?
(ii)How many of each product must be sold to earn a profit of $8,400 after tax (of 30c in the dollar) for the month?

Answer 1

a) Unit Contribution for each product:-

Unit contribution margin = Sales Price per unit - Variable Cost per unit

Product A = 12 - 8

= $4 per unit

Product B = 15 - 10

= $5 per unit

b) If manufacturer produces only product B,

Contribution margin = Contribution per unit/Sales price per unit *100

= 5/15 * 100

= 33.33%

So, BEP Sales (dollars) = Fixed Cost/Contribution margin

= 5000/33.33%

= $15,000

BEP Sales (Units) = Fixed Cost/Contribution per unit

= 5000/5

= 1,000 units

c) If manufacturer produces only product A,

Contribution margin = Contribution per unit/Sales price per unit *100

= 4/12 * 100

= 33.33%

So, BEP Sales (dollars) = Fixed Cost/Contribution margin

= 5000/33.33%

= $15,000

BEP Sales (Units) = Fixed Cost/Contribution per unit

= 5000/4

= 1,250 units

d) He now decides to manufacture both A and B this month in the ratio of 3 of A to 1 of B.

Ratio = A:B = 3:1

So, 3B = A

(i) If manufacturer needs profit of $3,500

Contribution = Profit + Fixed Cost

= 3500 + 5000

= 8,500

Unit contribution for A = $4

Unit contribution for B = $5

Overall contribution margin ratio = 33.33%

So, Total sales required = 8,500/33.33%

= $25,500

Now, A + B = 8,500

Since, A = 3B

3B + B = 8,500

4B = 8,500

B = $2,125

So, Units = 2125/5 = 425 units

Now A = 8500 - 2125 = 6,375

A = 6,375/4

= 1594 units approx

A = 1,594 units

B = 425 units

(ii) After tax profit = $8,400

Tax rate = 30c of $1 = 30%

So, Before Tax = 8400/0.70

= $12,000

So, contribution = 12,000 + 5,000

= $17,000

Now, 4B = 17,000

B = 4,250

Units = 4,250/5

= 850 units

A = 17000 - 4250

= 12,750

Units = 12750/4

= 3187.50 units

A = 3187.5 units

B = 850 units