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 - offset 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 sales of N400,000

Number of units sold = $\frac{400000}{50}=8000$ units

Step3: Calculate total contribution margin for (a)

Total contribution margin = Contribution margin per unit $\times$ Number of units sold = $20\times8000=\text{N}160000$
Net profit = Total contribution margin - Fixed costs = $160000 - 100000=\text{N}60000$

Step4: For (b), set up profit - equation

Let the number of units sold be $x$. Profit = Total contribution margin - Fixed costs. We want a profit of N20,000. So, $20000 = 20x-100000$.
Adding 100000 to both sides gives $120000 = 20x$. Then $x=\frac{120000}{20}=6000$ units. Sales = $6000\times50=\text{N}300000$

Step5: For (c), new fixed costs

New fixed costs = $100000 + 12000=\text{N}112000$. Increase in fixed costs = N12000. Since contribution - margin ratio = $\frac{20}{50}=0.4$, increase in sales revenue needed = $\frac{12000}{0.4}=\text{N}30000$

Step6: For (d), new sales revenue

New sales revenue = $400000 + 25000=\text{N}425000$. New number of units sold = $\frac{425000}{50}=8500$ units. Total contribution margin = $20\times8500=\text{N}170000$. Current contribution margin for 8000 units (sales of N400,000) is $20\times8000=\text{N}160000$. Maximum promotion budget = $170000 - 160000=\text{N}10000$

Step7: For (e), new selling price

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 $n_2$. We want to keep total contribution margin the same. Let $n_1 = 1$ (for simplicity of ratio - calculation). Original contribution margin = $20\times1$. New contribution margin = $12.5n_2$. So, $20\times1=12.5n_2$, and $n_2=\frac{20}{12.5}=1.6$. Percentage increase in units sold = $\frac{1.6 - 1}{1}\times100\%=60\%$

Step8: For (f), new variable cost per unit

New variable cost per unit = $30 + 2.5=\text{N}32.5$. New contribution margin per unit = $50-32.5=\text{N}17.5$. At break - even, fixed costs = Total contribution margin. Let fixed costs be $F$. $F = 17.5x$ (where $x$ is the number of units at break - even). Original break - even units = $\frac{100000}{20}=5000$ units. New fixed costs $F$ can be $17.5\times5000=\text{N}87500$. Budget for fixed costs = N87500

Step9: For (g), original break - even units

Original break - even units = $\frac{100000}{20}=5000$ units. New fixed costs = $100000 + 10000=\text{N}110000$. Let new variable cost per unit be $v$. Contribution margin per unit = $50 - v$. At break - even, $110000=(50 - v)\times5000$. Divide both sides by 5000: $22 = 50 - v$. Then $v = 50 - 22=\text{N}28$. 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) N87,500
(g) N2