Question

KK, an aspiring entrepreneur, wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully judge the demand and the likely profit before investing. A market survey showed he could sell 1 lac (100000) units before customers moved to other gadgets. KK had to bear two kinds of cost: fixed cost (the cost that does not change no matter how many units are made) and variable cost (variable cost per unit times the number of units). He expected the fixed cost to be Rs. 40 lac and the variable cost to be Rs. 100 per unit. He expected to sell each pen drive at Rs. 200.

He discussed his business with a chartered accountant. KK said he was thinking of a loan of Rs. 20 lac at simple interest of \(10\%\) per year to start the business. The chartered accountant told him that in this case KK has to pay interest, followed by \(30\%\) tax. By how much does KK's earnings change with a \(20\%\) growth in sales as against the original sales volume, in both cases considering tax and interest on the loan?

• A. 20%
• B. 16.7%
• C. 25.6%
• D. 34.5%

Hint:

Work out net profit (after loan interest and 30% tax) at the original 1 lac units, then again at 1.2 lac units, and compare the two.

Answer 1

The Correct Option is D

Step 1: Find the profit before interest and tax at the original sales volume.
The market survey shows KK can sell up to \(100000\) pen drives, so the original sales volume is \(100000\) units.
Revenue \( = 100000 \times 200 = \text{Rs. } 2{,}00{,}00{,}000\).
Variable cost \( = 100000 \times 100 = \text{Rs. } 1{,}00{,}00{,}000\).
Contribution (revenue minus variable cost) \( = 2{,}00{,}00{,}000 - 1{,}00{,}00{,}000 = \text{Rs. } 1{,}00{,}00{,}000\).
Fixed cost is Rs. \(40{,}00{,}000\) and does not change with sales, so profit before interest and tax (EBIT) \( = 1{,}00{,}00{,}000 - 40{,}00{,}000 = \text{Rs. } 60{,}00{,}000\).

Step 2: Bring in the loan interest and tax to get the original net profit.
The loan is Rs. \(20{,}00{,}000\) at \(10\%\) simple interest a year, so the yearly interest is \(0.10 \times 20{,}00{,}000 = \text{Rs. } 2{,}00{,}000\). This interest depends only on the loan amount, not on how many units are sold, so it stays the same at both sales levels.
Profit before tax \( = 60{,}00{,}000 - 2{,}00{,}000 = \text{Rs. } 58{,}00{,}000\).
Tax at \(30\%\) takes away \(0.30 \times 58{,}00{,}000 = \text{Rs. } 17{,}40{,}000\), so net profit \( = 58{,}00{,}000 - 17{,}40{,}000 = \text{Rs. } 40{,}60{,}000\).

Step 3: Repeat the same working for sales that are 20% higher.
New sales volume \( = 100000 \times 1.2 = 120000\) units.
Revenue \( = 120000 \times 200 = \text{Rs. } 2{,}40{,}00{,}000\), variable cost \( = 120000 \times 100 = \text{Rs. } 1{,}20{,}00{,}000\), so contribution \( = 1{,}20{,}00{,}000\).
Fixed cost is still Rs. \(40{,}00{,}000\), so new EBIT \( = 1{,}20{,}00{,}000 - 40{,}00{,}000 = \text{Rs. } 80{,}00{,}000\).
The loan and its interest do not change, so profit before tax \( = 80{,}00{,}000 - 2{,}00{,}000 = \text{Rs. } 78{,}00{,}000\), and net profit after \(30\%\) tax \( = 0.70 \times 78{,}00{,}000 = \text{Rs. } 54{,}60{,}000\).

Step 4: Find the percentage change in net profit.
Increase in net profit \( = 54{,}60{,}000 - 40{,}60{,}000 = \text{Rs. } 14{,}00{,}000\).
Percentage change \( = \dfrac{14{,}00{,}000}{40{,}60{,}000} \times 100 \approx 34.5\%\).
The fixed cost and the loan interest stay the same while sales grow, so almost all the extra revenue drops straight into profit. That is why a \(20\%\) rise in sales turns into a much bigger, about \(34.5\%\), rise in net earnings, and why options A, B and C, which understate this effect, are wrong. \[ \boxed{34.5\%} \]