Case 024Sector economicsWarm up

Sudhira Home Care raises prices 6%, volumes fall 2%, and gross margin moves from 45% to about 48%. What are revenue growth and gross profit growth?

The situation

Sudhira Home Care sells detergents and surface cleaners. Revenue is Rs 1,000 crore at a 45% gross margin, so cost of goods is Rs 550 crore. It raises prices 6% across the range; volumes fall 2% as some shoppers trade down. Input costs per unit do not change.

Your task

What happens to revenue, gross profit and gross margin, and why does gross profit grow so much faster than revenue?

Quick check

Revenue grows about 3.9%. Roughly how fast does gross profit grow?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Revenue grows 3.9% and gross profit 11.1%, with the margin rising to 48.1%. Revenue is 1.06 x 0.98 of the old level, Rs 1038.8 crore. Cost of goods falls with volume to Rs 539 crore, so gross profit is Rs 499.8 crore. Every rupee of price rise is pure gross profit, while lost volume costs only its margin, so a price-led quarter grows profit almost three times as fast as sales.

Step 1Why does a price rise lift gross profit faster than revenue?

A tea stall that raises its price from Rs 10 to Rs 11 does not need more milk or sugar to earn the extra rupee. Price increases arrive with no extra cost, so all of the extra revenue drops to gross profit; volume changes move revenue and cost together, so they move gross profit only by the margin. That asymmetry is why companies with pricing power show margin expansion when they take price, and why analysts split revenue growth into price and volume before anything else.

Step 2How do the numbers work?

Revenue: 1,000 x 1.06 x 0.98 = Rs 1038.8 crore, up 3.88%. Cost of goods moves only with volume: 550 x 0.98 = Rs 539 crore. Gross profit is Rs 1038.8 crore less Rs 539 crore, Rs 499.8 crore, up 11.1%, and the margin is 48.1%. The case's 'about 48%' is this 48.1%, a useful check that unit costs really did stay flat.

Price goes straight to gross profit; volume takes only its marginRevenue: +3.9%1,000Start+58.8Price +6%-20Volume -2%1,038.8EndGross profit: +11.1%450Start+58.8Price +6%-9Lost margin499.8EndBars start at 85% of each opening value so the steps can be seen
Sudhira's 6% price rise adds Rs 58.8 crore to both revenue and gross profit, but the 2% volume loss takes Rs 20 crore of revenue and only Rs 9 crore of gross profit, so revenue grows 3.9% while gross profit grows 11.1%.
Rs croreBeforeAfterChange
Revenue1,000.01,038.8+3.9%
Cost of goods(550.0)(539.0)-2.0%
Gross profit450.0499.8+11.1%
Gross margin45.0%48.1%
A 6% price rise with 2% lower volume takes Sudhira's revenue up 3.9% to Rs 1038.8 crore and its gross profit up 11.1% to Rs 499.8 crore, lifting the gross margin from 45.0% to 48.1%.
Step 3How much volume could Sudhira lose before the price rise stops paying?

Per unit, gross profit rises from 45 to 51 on a price of 100 that became 106. Gross profit holds at Rs 450 crore until volume falls to 45/51 of its old level, a fall of about 11.8%. Sudhira lost 2%, far inside that. The limitation: this ignores what happens next year. If shoppers who traded down do not come back, or rivals hold price and gain share, the volume loss can keep growing after the gain has been booked.

Where candidates lose it

The fast wrong answer adds the percentages: 6% minus 2% is 4% for revenue, and then says gross profit grows 4% too. Revenue is roughly right; gross profit is not, because price and volume act on it differently.

The other miss is treating the margin as fixed at 45% and computing gross profit as 45% of new revenue. The margin itself moves when price changes and unit costs do not.

What the interviewer asks next

  • Input costs rise 4% at the same time. What price rise keeps gross profit growth at 11%?
  • Why might Sudhira's advertising spend rise after a price increase?
  • How would you tell from reported results whether growth came from price or volume?

Company names and figures are illustrative.