Some math help please... adjusting price and solving for volume

Felicia asked on Aug 19, 2018

Hi Everyone, I got the below from a casebook. The way I solved it was to use an assumption for volume, say volume = 100 units. Is there a more elegant way to do so though?

One option that our client has is to give in to its customers’ demands for a price discount. However our client is concerned about the impact this will have on its profits. If we were to cut prices 5%, how much would we have to increase volumes to maintain the same amount of profits?

In this case the gross margin is 20%. So if the original price is 100, then per unit costs are 80 and profits 20. A 5% decline in price makes it 95. Costs remain at 80 and profits are now 15. To make the profits the same, you need to increase volume by one third. So cutting prices to take back market share, requires that it sell 33.3% more product simply to keep profits constant. Given its high market share levels, this is unlikely.

3 answers

  • Upvotes
  • Date ascending
  • Date descending
Best Answer
Anonymous A updated his answer on Aug 19, 2018

20% margin means C = 0.8*P.

If new price is 0.95*old price, then new margin is 0.95*P - 0.8*P=0.15*P, so your new margin is 15%.

New volume * P * 0.15 = Old volume * P * 0.2 (price is same here in both sides),

New volume / Old volume = 0.2/0.15 = 1.33. So your new profit has to be 33% higher than old.

To arrive at non-number equations, once you have calculated the solution in numbers, replace numbers with words.

(edited)

Alessandro
Expert
replied on Aug 19, 2018
Bain & Company | University of Cambridge | CV/Resume writing | 770 GMAT
Book a coaching with Alessandro

100% Recommendation Rate

60 Meetings

789 Q&A Upvotes

USD 139 / Coaching

Anonymous answer is correct. However, there is nothing wrong with using your approach of 100 units - and if it helps you, you shouldn't be worried about using it.

That said, practice algebraic equations like this (e.g. by doing GMAT problem solving) to get more used to solving problems like this in an algebraic way.

Matthew
Expert
replied on Sep 06, 2018
Former McKinsey Consultant, graduate of Harvard and MIT, FastMath author
Book a coaching with Matthew

100% Recommendation Rate

6 Meetings

5 Q&A Upvotes

USD 509 / Coaching

Hi Felicia,

Using a base price of 100 is fine to do. I have an online course that covers how to solve this, and similar problems quickly and efficiently. I have some practice problems here (check out he sections labled Inverse Proporation): http://www.fastmath.net/ace-the-case/practice-problems/?pc=preplounge_bc_001 .

Related BootCamp article(s)

Which companies are currently using written tests ?

All major firms like McKinsey, BCG and Bain use tests to assess a candidate's analytical skills. However the design of those tests can differ a lot.

Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

Guide to Improving Speed in Written Tests such as the PST

Follow these instructions to significantly improve your performance and speed in solving problem solving tests used at McKinsey, BCG and Bain.

Related case(s)

REA Reinsurance

Solved 8.6k times
4.1 5 882
| Rating: (4.1 / 5.0)

Your client, REA, is a reinsurance company. REA recently acquired another reinsurance company (approximatively same size): the choice of this company was notably based on its product portfolio as well as its market presence which appeared complement with REA. However, the acquisition is not well r ... Open whole case

AirService

Solved 3.5k times
3.8 5 706
| Rating: (3.8 / 5.0)

Your client AirService is the service provider for a number of airports. The management realized a decrease in profits that is linked to increasing costs. How would you help them? Open whole case