Question

1. murasise olekope nigeria ltd. produces single product which sells for n50 per unit. variable costs are n30 per unit and total fixed costs = n100,000.

required: answer each of the following independent questions.
(a) the net profit on a sale of n400,000
(b) the sales necessary to earn a profit of n20,000
(c) administrative salaries will increase by n12,000. what increase in sales revenue will be required to cover the increase?
(d) the sales manager thinks that sales revenue can be increased by n25,000 if he is given additional budget for sales promotion. what is the maximum amount that may be given for the promotion?
(e) the sales manager suggests cutting the present selling price by 15%. what must be the percentage increase in the number of units sold in order to off - set the decrease in selling price?
(f) variable labour cost will be increase by n2.50 per unit. how much may be budgeted for fixed costs if there is to be no change in the present break - even point?
(g) fixed costs will increase by n10,000. by how much must the present variable cost per unit be reduced if the present break - even point is to remain the same?

Explanation:

Step1: Calculate contribution margin per unit

Contribution margin per unit = Selling price per unit - Variable cost per unit = $50 - 30=\text{N}20$

Step2: Calculate number of units sold for (a)

Number of units sold when sales is N400,000 = $\frac{400000}{50}=8000$ units
Total contribution margin = Contribution margin per unit $\times$ Number of units sold = $20\times8000=\text{N}160000$
Net profit = Total contribution margin - Fixed costs = $160000 - 100000=\text{N}60000$

Step3: For (b)

Let the number of units sold be $x$.
Profit = Total contribution margin - Fixed costs
$20000=20x - 100000$
$20x=20000 + 100000$
$20x=120000$
$x = 6000$ units
Sales = Number of units sold $\times$ Selling price per unit = $6000\times50=\text{N}300000$

Step4: For (c)

If administrative salaries (fixed costs) increase by N12,000, new fixed costs = $100000+12000=\text{N}112000$
Let the increase in sales revenue be $y$.
Contribution - margin ratio = $\frac{20}{50}=0.4$
We know that increase in fixed costs = Increase in contribution margin
$12000 = 0.4y$
$y=\frac{12000}{0.4}=\text{N}30000$

Step5: For (d)

Let the maximum amount for promotion be $z$.
Increase in sales revenue = N25,000
Contribution - margin ratio = 0.4
Increase in contribution margin = $25000\times0.4=\text{N}10000$
So the maximum amount for promotion is N10,000.

Step6: For (e)

New selling price = $50\times(1 - 0.15)=50\times0.85=\text{N}42.5$
New contribution margin per unit = $42.5-30=\text{N}12.5$
Let the original number of units be $n_1$ and new number of units be $n_2$.
Original contribution margin = $20n_1$
New contribution margin = $12.5n_2$
To offset the decrease in selling - price, assume fixed costs remain the same. Let's equate the contribution margins (since fixed costs are constant and we want to maintain the same profit - level situation in terms of contribution).
Let $n_1 = 1$
$20\times1=12.5n_2$
$n_2=\frac{20}{12.5}=1.6$
Percentage increase in number of units sold = $\frac{1.6 - 1}{1}\times100\%=60\%$

Step7: For (f)

New variable cost per unit = $30 + 2.5=\text{N}32.5$
Let the new fixed costs be $F$.
Break - even point (in units) originally = $\frac{100000}{20}=5000$ units
At break - even, Profit = 0. So, $0=(50 - 32.5)\times5000-F$
$F=(17.5)\times5000=\text{N}87500$
Budget for fixed costs = N87,500
Decrease in fixed costs = $100000 - 87500=\text{N}12500$

Step8: For (g)

Original break - even point in units = $\frac{100000}{20}=5000$ units
Let the new variable cost per unit be $v$.
New fixed costs = $100000 + 10000=\text{N}110000$
At break - even, $0=(50 - v)\times5000-110000$
$(50 - v)\times5000=110000$
$50 - v=\frac{110000}{5000}=22$
$v = 50 - 22=\text{N}28$
Reduction in variable cost per unit = $30 - 28=\text{N}2$

Answer:

(a) N60,000
(b) N300,000
(c) N30,000
(d) N10,000
(e) 60%
(f) N12,500
(g) N2