CAT 2025 Lesson : Caselets - Case 1

Read the following and answer the questions that follow

KK, an aspiring entrepreneur wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully gauge the demand and the likely profits before investing. Market survey indicated that he would be able to sell 1 lac units before customers shifted to different gadgets. KK realized that he had to incur two kinds of costs – fixed costs (the costs which do not change, irrespective of numbers of units of pen drives produced) and variable costs (= variable cost per unit multiplied by number of units). KK expected fixed cost to be Rs. 40 lac and variable cost to be Rs. 100 per unit. He expected each pen drive to be sold at Rs. 200.
[XAT 2009]

1) What would be the break-even point (defined as no profit, no loss situation) for KK’s factory, in terms of sales?

(1) Rs. 80 lac
(2) Rs. 100 lac
(3) Rs. 120 lac
(4) Rs. 140 lac
(5) Cannot be found with the given data

2) KK was sceptical that per unit variable cost might increase by 10% though the demand might remain the same. What will be the expected changes in profit in such a case?

(1) Profit would decrease by 10.33%
(2) Profit will increase will by 15.75%
(3) Profit would decrease by 15.75%
(4) Profit will decrease by 16.67%
(5) Profit will increase by 16.67%

3) He discussed his business plan with a chartered accountant. KK informed that he was contemplating a loan of Rs. 20 lac at simple interest of 10% per annum for starting the business. The chartered accountant informed him that in such a case KK has to pay interest, followed by 30% tax. By how much does KK’s earnings change with 20% growth in sales vis-à-vis the original sales volume, in both cases considering tax and interest on loan?

(1) 20%
(2) 16.7%
(3) 25.6%
(4) 33.3%
(5) 34.5%

Solution

1) Let us note the expected sales, expected revenue, cost incurred per unit (variable cost) and fixed cost of KK.

Expected sales = 1 lac units
Expected revenue = Rs. 200/unit
Variable cost = Rs. 100/unit
Fixed Cost = Rs. 40 lac

Let us calculate the profit for each unit (Variable Margin),

Variable Margin = Revenue – Variable cost = Rs. 200 – Rs. 100 = Rs. 100/unit

Let us calculate the number of units required to cover the fixed cost (Break even Volume),

Break even Volume = $\dfrac{Fixed cost}{Variable Margin}$=$\dfrac{40 \times 10^5}{100}$ = $40 \times 10^3$

Break even point is the amount in which we get no profit or no loss, where the cost incurred equals to the revenue generated.

Break even point = Break even Volume $\times$ Revenue per unit

Break even point = $40\times10^3\times 200$= 80 lac

Alternative Method

Let $x$ be the number of units to be sold to achieve the break even volume.

No profit and no loss is achieved when revenue equals the fixed cost and the total variable cost.

Revenue = fixed cost + variable cost

$200x = 40\times10^5 + 100x$
$100x = 40\times10^5$

$x$ = 40,000

Break even point = $40\times10^3 \times 200$= 80 lac

Answer: (1) Rs.. 80 lac

2) The expected demand is 1 lac units in both the scenarios

Scenario 1

Expected sales = 1 lac unit
Expected revenue = Rs. 200/unit
Variable cost = Rs. 100/unit
Fixed Cost = Rs. 40 lac

Total cost = Variable cost per unit $\times$ number of unit +Fixed cost

Profit = Revenue – Total cost = 200 lac – 100 $\times$ 1lac– 40 lac

= 200 lac – 140 lac
= 60 lac

Scenario 2 (10$\%$ increase in per unit variable cost)

Expected sales = 1 lac unit
Expected revenue = Rs. 200/unit
Variable cost = Rs. 110/unit
Fixed Cost = Rs. 40 lac

Total cost = Variable cost per unit $\times$ number of unit +Fixed cost

Profit = Revenue – Total cost = 200 lac – 110 $\times$ 1lac– 40 lac
= 200 lac – 150 lac
= 50 lac

If the per unit variable cost increases by 10$\%$ per unit, KK’s profit will reduce from 60 lac to 50 lac Percentage decrease = $\dfrac{60-50}{60} \times 100\%$= 16.67$\%$

Answer: (4) Profit will decrease by 16.67$\%$

3) There are two scenarios. In both the scenarios, KK has to pay interest of 2 lac (simple interest) followed by 30$\%$ tax on the profit.

Scenario 1

Expected sales = 1 lac unit
Expected revenue = Rs. 200/unit
Variable cost = Rs. 100/unit
Fixed Cost = Rs. 40 lac

Total cost = Variable cost per unit $\times$ number of unit +Fixed cost

Profit = Revenue – Total cost = 200 lac – 100 $\times$ 1lac– 40 lac

= 200 lac – 140 lac
= 60 lac

Deducting the simple interest from the profit = 60 – 2 = 58 lac

Deducting tax at 30$\%$ = (1 – 0.3) 58 lac = 0.7 $\times$ 58 lac

Scenario 2 – (20$\%$ growth in sales)

Expected sales = 1.2 lac unit
Expected revenue = Rs. 200/unit
Variable cost = Rs. 100/unit
Fixed Cost = Rs. 40 lac

Total cost = Variable cost per unit $\times$ number of unit +Fixed cost

Profit = Revenue – Total cost = 1.2$\times$200lac – 100$\times$1.2lac – 40 lac
= 240 lac – 160 lac
= 80 lac

Deducting the simple interest from profit = 80 – 2 = 78 lac

Deducting tax at 30%$\%$ = (1 – 0.3) 78 lac = 0.7$\times$78lac

KK’s earnings changed from to 0.7$\times$58lac to 0.7$\times$78lac

Change percentage = $\dfrac{78-58}{58} \times 100\%$ = $\dfrac{20}{58}\times 100\%$

= $\dfrac{10}{29} \times 100\%$(Value will be slightly greater than $\dfrac{1}{3}$) = 34.5$\%$

Answer: (5) 34.5$\%$

Answer:
1) (1) Rs. 80 lac
2) (4) Profit will decrease by 16.67%
3) (5) 34.5%