# using the data given in the case

### Question 1: Using the data given in the case calculate contribution margin per unit for the year 2012-2016

We know,

Contribution Margin Per Unit = Sales Price Per Unit – Variables Expense Per Unit

 For 2012, Sales Price Per Unit = Sales = 1926745719 = 345.9831157 Unit        5568901 Variables Expense Per Unit = Total Variable Expense = 1197175437 = 214.9752 Unit                 5568901 So, Contribution Margin Per Unit is = 345.9831157-214.9752 = BDT 131.01 For 2013, Sales Price Per Unit= Sales = 1901444562 = 328.420481 Unit        5789665 Variables Expense Per Unit=Total Variable Expense = 1236060207 = 213.494 Unit                          5789665 So, Contribution Margin Per Unit= 328.420481 – 213.494 = BDT 114.93 For 2014, Sales Price Per Unit= Sales = 1942350752 = 270.3444058                                                            Unit        7184727 Variables Expense Per Unit=Total Variable Expense = 1219078593 =169.6763973 Unit            7184727 So, Contribution Margin Per Unit= 270.3444058 – 169.6763973 = BDT 100.67 For 2015, Sales Price Per Unit= Sales = 1704567234 = 222.5833661 Unit         7658107 Variables Expense Per Unit=Total Variable Expense = 1028435016 = 134.2936337 Unit                  7658107 So, Contribution Margin Per Unit= 222.5833661 – 134.2936337 = BDT 88.29
 For 2016, Sales Price Per Unit= Sales = 1677657674 = 201.6098762 Unit        8321307 Variables Expense Per Unit=Total Variable Expense = 1202656347 = 144.5273377 Unit                     8321307 So, Contribution Margin Per Unit= 201.6098762 – 144.5273377 = BDT 57.08

Question 2: Calculate break-even point in units for the year 2012-2016.

We know,

Break-even point in units = ????? ???????

???? ??

 For 2012, Break-even point in units= ????? ??????? = 89079122 ???? ??                     131.01 = 679952.05 ≈ 679953 UNITS For 2013, Break-even point in units= ????? ??????? = 96401390 ???? ??          114.93 = 838811.06 ≈ 83881 UNITS For 2014, Break-even point in units= ????? ??????? = 102214877 ???? ??             100.67 = 1015366.04 ≈ 1015367 UNITS For 2015, Break-even point in units= ????? ??????? = 102313047 ???? ??                  88.29 = 1158832.90 ≈ 1158833 UNITS For 2016, Break-even point in units= ????? ??????? = 174578342 ???? ??                     57.08 = 3058349.31 ≈ 3058350 UNITS

Question 3: Calculate margin of safety in units for FARR Ceramics for the year 2012-2016.

We know,

Margin of safety in units = Actual Sales in units – Breakeven Sales in units

 For 2012, Margin of safety in units = Actual Sales in units – Breakeven Sales in units = 5568901-679953 = 4888948 UNITS For 2013, Margin of safety in units = Actual Sales in units – Breakeven Sales in units = 5789665 – 838812 = 4950853 UNITS For 2014, Margin of safety in units = Actual Sales in units – Breakeven Sales in units = 7184727 – 1015367 = 616936000 UNITS For 2015, Margin of safety in units = Actual Sales in units – Breakeven Sales in units = 7658107 – 1158833 = 6499274 UNITS For 2016, Margin of safety in units = Actual Sales in units – Breakeven Sales in units = 8321307 – 3058350 = 5262957 UNITS

Question 4: Compute degree of operating leverage for the year 2012-2016. How does it help a manager to predict the change in net operating income provided the change in sales volume is given?

We know,

Degree of Operating Leverage = ???????????? ??????

??? ????????? ??????

 For 2012, Degree of Operating Leverage = ???????????? ?????? = 729570282 ??? ????????? ??????  640491160
 For 2013, Degree of Operating Leverage = ???????????? ?????? = 665384355 ??? ????????? ??????  568982965 = 1.17 Times For 2014, Degree of Operating Leverage = ???????????? ?????? = 723272159 ??? ????????? ??????  621357282 = 1.16 Times For 2015, Degree of Operating Leverage = ???????????? ?????? = 676132218 ??? ????????? ??????  573819171 = 1.18 Times For 2016, Degree of Operating Leverage = ???????????? ?????? = 475001327 ??? ????????? ??????  300422485 = 1.58 Times

Operating leverage examines how a company’s cost structure can affect its profitability and its operating risk. This relationship assesses how sensitive a company’s operating income is to a change in sales. It’s helpful to managers because they need to predict how a change in sales will affect operating income. It also helps managers see how external users view their company.

To determine a compny’s degree of operating leverage, its cost structure must be examined. Cost structure refers to the proportion of fixed costs incurred by a company in relation to the amount of variable costs it incurs. Companies with large costs tied up in production equipment will often have relatively small amounts of assembly labor costs. While investments in machinery generate depreciation—a fixed cost, fewer production employees result in lower labor costs—which are variable. Because fixed costs are incurred regardless of the level of sales, companies with higher fixed costs find it difficult to reduce these costs in the short-run. As a result, companies with higher proportions of fixed costs have higher operating leverage and are considered to have more risky operations. Companies with a cost structure consisting of significant amounts of production labor with fewer capital assets have lower fixed costs and higher variable costs. Variable costs are easier to reduce on a short-term basis, which in turn, implies lower operating leverage and less risky operations

The DOL indicates the number of times that the contribution margin exceeds the company’s net operating income. A company with higher DOL has more extreme fluctuations in operating income than a company with a lower DOL when a change in sales revenue occurs. A high DOL implies a riskier operating structure because of the volatility of the change in profit. Conversely, a lower DOL amount implies a less risky operating structure. The following table summarizes the relationship between cost structure, risk, profit fluctuations, and the degree of operating leverage.

The DOL can be used to predict the effect that a specified increase in sales will have on operating income. One approach to determine the effect is to prepare a revised income statement that reflects the increase in sales, though time consuming and unnecessary. Using the operating leverage approach, you can quickly estimate the percentage change in operating income by multiplying the DOL by the anticipated percentage change in sales.

Why Does Profit Change More Than Sales? The greater the percentage of fixed costs in a company’s structure, the greater the increase/decrease in operating income from a stated percentage increase or decrease in revenue. Operating leverage is higher near the breakeven point and decreases with an increase in sales. This is because once a company reaches its breakeven point, every unit sold thereafter contributes directly to an increase in profit, as sales up to the breakeven point have already covered fixed costs. Once a company with a higher proportion of fixed costs reaches breakeven, each sales dollar beyond breakeven generates a higher contribution to profit. A company with lower fixed costs, results in a lower contribution out of each sales dollar once breakeven has been achieved.

The Risk Element -Companies with a higher DOL are riskier because profit is more volatile, i.e., more likely to change. This can be favorable for managers and investors due to a specified change in sales producing higher earnings in a company with high operating leverage. However, on the flip side, managers and investors will see a larger decline in profit if the company has high operating leverage than if the company has a lower DOL.

Managers need to know how investors perceive their company in terms of operating leverage. Investors often compare potential stock investments with competitors to assess which company is the less risky. More conservative investors will likely choose to invest in companies that maintain a lower DOL, which aggressive investors may prefer investments in companies with higher DOLs because of the larger return these companies will generate if sales increase.

Once identified, managers have some ability to reduce their company’s operating leverage risk by reducing fixed costs, often by offsetting with an increase in variable costs. This is sometimes accomplished through outsourcing. An increase in variable costs also increases forecasting accuracy because variable costs are more predictable.

Question 5: What is the main difference between gross margin and contribution margin? Which one is the main focus of CVP analysis? Explain briefly.

The essential difference between the contribution margin and gross margin is that fixed overhead costs are not included in the contribution margin. This means that the contribution margin is always higher than the gross margin. The classic measure of the profitability of goods and services sold is gross margin, which is revenues minus the cost of goods sold. The cost of goods sold figure is comprised of a mix of variable costs (which vary with sales volume) and fixed costs (which do not vary with sales volume).

Typical contents of the cost of goods sold figure in the gross margin are:

• Direct materials
• Direct labor
• Variable overhead costs (such as production supplies)
• Fixed overhead costs (such as equipment depreciation and supervisory salaries)

An alternative to the gross margin concept is contribution margin, which is revenues minus all variable costs of sales. By excluding all fixed costs, the content of the cost of goods sold figure now changes to the following:

• Direct materials
• Commission expense

Most other costs are excluded from the contribution margin calculation (even direct labor), because they do not vary directly with sales. For example, a certain minimum crew size is needed to staff the production area, irrespective of the number of units produced, so direct labor cannot be said to vary directly with sales.

The gross margin concept is the more traditional approach to ascertaining how much a business makes from its sales efforts, but tends to be inaccurate, since it depends upon the fixed cost allocation methodology. The contribution margin concept is the recommended method of analysis, since it yields a better view of how much money a business actually earns from its sales, which can then be used to pay off fixed costs and generate a profit.

In general, the contribution margin tends to yield a higher percentage than the gross margin, since the contribution margin includes fewer costs. This can lead to an erroneous assumption that a company’s profitability has surged, when all the business has done is switch from the gross margin method to the contribution margin method, thereby shifting all fixed costs into a separate classification lower down in the income statement. In fact, total company profits are the same, no matter which method is used, as long as the number of units sold has not changed.

Question 6: Determine the possible impact of the followings on margin of safety calculation assuming other things remains constant and each of the situation is independent.

• Increase in fixed cost
• Increase in per unit variable cost
• Increase in per unit sale price

Margin of Safety is the excess of budgeted or actual sales taka over the breakeven volume of sales in taka. It is the amount by which sales can drop before losses are incurred. The higher the margin of safety, the lower the risk of not breaking even and incurring a loss. We calculate margin of safety using the following formula:

Margin of Safety in Taka = Actual Sales – Break-Even Sales

Increase in fixed cost: By looking at the formula for calculating BEP Sales,

BEP Sales = ????? ????? ???? ↑

?? ?????

We can see that an increase in Total Fixed Cost on the right-hand side of the equation will result in the increase in BEP sales on the left-hand side of the equation. So, the higher the fixed cost of FARR ceramics, the higher will be their breakeven point in sales. The higher the breakeven point of sales, all things remaining constant, the margin of safety of FARR Ceramics Limited will decrease.

Increase in per unit variable cost: We know that if sales remain the same and variable cost increases, the contribution margin will decrease. Looking at the formula to calculate BEP Sales again,

BEP Sales = ????? ????? ???? ↑

?? ?????

We can see that a decrease on the CM Ratio on the right-hand side of the equation will inversely increase the BEP Sales on the left-hand side of the equation. Therefore, an increase in per unit variable cost will increase the Break-Even Point in Sales. The higher the breakeven point of sales, all things remaining constant, the margin of safety of FARR Ceramics Limited will decrease.

Increase in Per Unit Sales price: We know that if Variable Cost remains the same, an increase in Per Unit Sales Price will increase the Contribution Margin. Looking at the formula to calculate BEP Sales again,

BEP Sales = ????? ????? ???? ↑

?? ?????

We see that an increase on the Contribution Margin on the right-hand side of the equation will inversely decrease the Break-Even Point in sales. The lower the breakeven point of sales, all things remaining constant, the margin of safety of FARR Ceramics Limited will increase.

Question 7: Please discuss why the fixed costs were steadily increasing from the year 2012 to 2015.