FY Math / Analytical Reasoning 101
September 30th, 2010
Agenda
•
•
•
•
•
•
Roadmap check-in
Case analysis overview
Sample case demonstration
Case math: a structured approach
Calculation best practices
Practice Time
9/30/10
Roadmap Math
2
Now is a great time to research firms
and work on distinguishing yourself
Targeted
Exceptional
• Vault/Wetfeet/company
website research
• Informal conversations w/
second years
Analytical
• Refining resumes with SY
consultants
• Behavioral interview
practice w/ CMC
• Case 101
• Math review session (today)
Today
Sep
Oct
Nov
Dec
Jan
Feb
Targeted
T.E.A.M.
Model
Exceptional
Analytical
Mature
Recruiting
Events
Presentations
Networking events
Resume drops
Interviews
9/30/10
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Your Roadmap to a consulting position
Upcoming events
• Oct 4-7: Case Team Prep
Unit 1: Behavioral
• Oct 5th: Week in cities /
Networking event 6:30pm
• Oct 21-22: Week-In-Cities
Case Prep Opportunities
• Informal case prep with
classmates
• Deloitte Case Challenge
• David Ohrvall Case Prep
Workshop
• National case competitions
Expectations
• Be prepared
• Be engaged
• Complete short feedback
surveys after events
• Contact a member of the
Roadmap team if you have
any questions
These DMCC events will facilitate your preparation for consulting interviews
9/30/10
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Today’s session covers the basics of analytical reasoning and how math appears in
cases
January
(Interviews)
Fine
Tuning
Fall 2
Accounting &
Finance
Marketing
Strategy
Economics
Subject
Areas
Confidence
& Composure
Analytical Reasoning (Math)
Fall 1
Interview
Foundation
Hypothesis Based Problem Solving (Case Basics)
“Telling Your Story” (Behavioral)
October
9/30/10
Roadmap Math
5
Case Interview feedback form
Case _______________________ Case type ______________ Interviewer ____________________
Execution
Case start time __:__
•Structure
1 2 3 4 5
Logical approach
MECE
Appropriate drive to solution
Comments:
•Quantitative Ability
Speed
Accuracy
Comfort, reaction to mistakes
•Business intuition
Practical
Insightful
Breadth & depth across multiple functions
Creativity
1 2 3 4 5
Comments:
1 2 3 4 5
Framework development ______ min
Framework explanation ______ min
Case discussion
______ min
Case end time ___:____
Overall Rating: 1 2 3 4 5
Strengths
Comments:
Communication
•Professionalism
1 2 3 4 5
Poise
Confident-Persuasive
Articulate-concise
Client ready
Comments:
Weaknesses
•Written
Clarity of writing and page layout
Ability to refer back
Comfort, reaction to mistakes
1 2 3 4 5
Comments:
Behavioral (optional)
•Quality of star stories
•Length
•Clarity
•Relevance
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
Comments:
Key: 1=Bottom 10%, 2= 10th-25th percentile, 3=
middle 50%, 4= 75th-90th percentile, 5=Top
10%
6
Agenda
•
•
•
•
•
•
Roadmap check-in
Case analysis overview
Sample case demonstration
Case math: a structured approach
Calculation best practices
Practice Time
9/30/10
Roadmap Math
7
Consultants use math analysis to develop
solutions to ambiguous problems
Problem /
Ambiguity
ID key numbers &
quantify the
situation
Develop problem
insights using the
answer & #s
Use #s/analytics
to develop
projections
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Case interviews assess a candidate’s ability to
use analysis to solve the business problem
Does the candidate:
• Develop a good
approach to reduce
complexity
• Understand when
numeric analysis is
necessary
Problem /
Ambiguity
ID key numbers &
quantify the
situation
Develop problem
insights using the
answer & #s
Does the candidate:
• Tie the numbers back to
the big picture
• Develop insights into
the problem
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Does the candidate:
• ID key numbers
• Choose the right level of
granularity
• Make sound
assumptions about
missing numbers
Use #s/analytics
to develop
projections
Roadmap Math
Does the candidate:
• ID appropriate analysis
• Have a structured math
approach
• Show comfort w/
numbers and
calculations
9
Agenda
•
•
•
•
•
•
Roadmap check-in
Case analysis overview
Sample case demonstration
Case math: a structured approach
Calculation best practices
Practice Time
9/30/10
Roadmap Math
10
Example case: Smile-Bright toothpaste
Your client, Smile-Bright toothpaste has decided that selling electronic
toothbrushes would be a great way to increase sales of it’s toothpaste;
however, they only want to do this if the electronic toothbrushes can be
profitable on their own. How would you advise them?
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Agenda
•
•
•
•
•
•
Roadmap check-in
Case analysis overview
Sample case demonstration
Case math: a structured approach
Calculation best practices
Practice Time
9/30/10
Roadmap Math
12
Case math is generally simple arithmetic
Definite interviewee expected
skill-set
• General Arithmetic (addition,
subtraction, multiplication, division)
Generally not expected*
• Calculus
• Full discount cash flow analysis
• Ability to keep track of numbers of
different magnitudes
• Complex finance formulas / techniques
• Use percents, fractions, proportions
• Accounting ratios
• Decipher graphs / charts / diagrams
• Black-Schole’s ratio (see cover slide)
* Exceptions:
• Every firm is a little different. Make to sure to
follow up with second years/firm
representatives late in Term 2 to see the
differences
Example Exceptions
• ZS: Derivatives
• LEK: Some finance/valuation math
• Deloitte: Financial ratios
Like a case, the analytics should be
structured
1
Identify if analytics are needed
• Every case doesn’t need math, work with the interviewer to
determine if mathematical analysis is needed
2
Structure approach
• Start by developing a structure/game-plan for analysis (To
calculate expected profit I am going to subtract our total costs from
our projected revenue)
• Review the approach with the interviewer
3
Gather key numbers (estimate
missing numbers)
• After identifying the key numbers you need in your structure ask
your interviewer if they have them
• If not, ask if an estimation would be appropriate
4
Calculate
• Work out the problem by fitting the numbers into the structure you
outlined, checking in with the interviewer every few steps
5
Check work
• Look over your work and perform a sanity check to see if
everything makes sense
6
Fit in big picture
• Place the information back into the context of the case and
determine next steps
At no point should an interviewee go heads down or silent for more than 15-20 seconds.
Analysis should be an interactive process
A structured approach provides
a framework for sound analytics
1
Identify if analytics are needed
Problem /
Ambiguity
6
Fit in big picture
Develop problem
insights using the
answer & #s
2
Structure approach
3
Gather key numbers
(estimate missing #s)
ID key numbers &
quantify the
situation
Use #s/analytics
to develop
projections
4
Calculate
5
Check work
A structured math approach will help
candidates of all analytical abilities
Benefits for those who are “strong” at
math
• Keeps the focus on describing analysis
instead of doing analysis
• Demonstrates the ability to tie numbers
back to the big picture
• Keeps a candidate from getting too deep
into the numbers
Benefits for those who are “weak” at
math
• Helps a candidate show analytical skill
even if mistakes are made in
computation
• Keeps numbers organized, making
calculations easier
• Simplifies math
A good practice for good “casing” is to always explain what you are going to do before you
do it, and walk your interviewer what you’re doing every step of the way
Common Math Mistakes
Mistake
Miscount the Zeros!
Confuse terms
Example
 Johnny’s Apple Company sold 20M barrels of seed in 2010
 Each barrel has 100 seeds
 Therefore Johnny’s Apple Co. sold:
WRONG  20,000,000*100 or 200M seeds
 20,000,000*100 or 2000M or 2B seeds
RIGHT
 The price per standard room on a cruise ship is $560/week
The RowBoat Luxury Shipping Company has the following assets:
 3 fleets of luxury cruise boats
Each fleet has 15 ships
Each ship has on average 5 decks
 Each deck has on average 60 rooms
 How much does RowBoat make per day?
 3 fleets* 15 ships/fleet * 5 decks/ship* 60 rooms/deck * 560=
WRONG
$7.56M
RIGHT
 3 fleets* 15 ships/fleet * 5 decks/ship* 60 rooms/deck *
$80/day= $1.08M
Common Math Mistakes
Mistake
Silent math
Example
WRONG
RIGHT
 What is the average revenue per elderly customer?
 (Silence)
 Talk through each step!
 “You mentioned elderly customers make up 2/3 of total
customer base but 1/3 of total revenue. With a total customer
base of 1M, that means there are ~.67M elderly customers. Total
revenues are 50M. If revenues were 100M, elderly revenues
would be 33M. Since revenues are 50M, or half of 100M, elderly
revenues are half of 33M, or around 16.67M. That means
average revenue per customer is 16.67/..67. To put this in easier
terms, lets multiply be 3/2 rather than divide by 2/3. So 16.67
divided 2 is 8.33, then times 3 equals 25. So average revenue
per elderly customer is $25”
 Calculate the payback period if a machine costs $260,000 and the
total lifetime revenue for the machine is $30,000/year
I don’t do division
WRONG
RIGHT
 “I should divide 260,000 by 30,000, but I didn’t practice
division. How about another question?”
 Simplify, then divide. 260,000/30,000= 26/3 (much easier)
 3 goes into 24- 8 times with 2 remaining. So the answer is 8
and two thirds!
Smile-Bright breakdown
Potential Revenue
1
2
Cost structure
Identify if analytics
are needed
• Math analysis needed to estimate
revenue
• Math analysis need to scope costs
Structure approach
• Demand = US population * Health
conscious individuals * % with enough
disposable income * electronic
toothbrush purchases per year
• Cost = FC + VC
Gather key numbers
(estimate missing
numbers)
• Health conscious individuals = 60%
• Average electronic toothbrush lasts 5
years
• Average price is 30$
• Estimated level of wealthy individuals,
US pop
• Recorded costs for:
• US rollout
• Setup costs
• Materials
• Labor
• Taxes
• Transportation
3
Smile-Bright breakdown
Potential Revenue
Cost structure
4
Calculate
• 300M * 2/3 * 1/4 * 1/5 = 10m p.a.
• 10m * 1/10 addr market = 1m potential
customers
• 1m * $30 = $30,000,000
• China: 5M + 3M + 1M*(5 + 4 + 1+ 15) =
33Million
• Mexico: 5M + 1M + 1M*(6 + 5 + 2 + 10)
= 29M
5
Check work
• 30 million is about 10 cents for every
American, that sounds about right
• 29 million dollars is around the right
magnitude, this number looks good
6
Fit in big picture
• $30,000,000 in total revenue sounds
shows that this presents a sizeable
opportunitiy
• Overall, Mexico has the better cost
structure and is the only option that
would allow for a profitable roll-out
Agenda
•
•
•
•
•
•
Roadmap check-in
Case analysis overview
Sample case demonstration
Case math: a structured approach
Calculation best practices
Practice Time
9/30/10
Roadmap Math
21
Percents and fractions are very common
in case interviews
4
Calculation Best Practices
.75 = 75% = 75 out of 100 = 3/4
TIPS
.33 = 33% = 33 out of 100 = 1/3
• Get comfortable converting between percents, #/100 or #/1000 and
fractions
• Ask a friend to quiz you
Interviewees can represent numbers in any
way, but are best served to be consistent
4
Calculation Best Practices
Good: 1M, .01M, 20M
TIPS
Caution: 1,000,000, 10K, 20M
9/30/10
• Use whatever feels natural but your best to keep it consistent
• Be ready for a mix of millions, billions, and thousands find an
approach that works for you
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Case math can greatly simplify if you
choose the correct units
4
Calculation Best Practices
Good: $ / cubic feet / mile
TIPS
Caution: $ / boat
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• Think small: what is the smallest unit of comparison you can use to
compare all the different options
• Look out for units involving: time (per year), weight (kg, pound),
distance (miles), etc…
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Rounding may be used to simplify
complex math
4
Calculation Best Practices
Good: 1.37*66% = 1.5*2/3 = 1
TIPS
Caution:1.4*66% =lots of math
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• Always ask your interviewer if you can round!
• Don’t be afraid to ask though and use it to your advantage
• Don’t ask to round easy numbers (75%  100%)
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Distilling case problems into formulas
shows structure and allows for graphing
4
Calculation Best Practices
Cost = FC + VC * Q
China
$3m
Mexico
$1m
Num of toothbrushes
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Tables are very useful for keeping track
of numbers and details
4
Calculation Best Practices
Manufacture in Mexico
Materials
5 $ / unit
6 $ / unit
Labor
4 $ / unit
5 $ / unit
Taxes
1 $ / unit
2 $ / unit
Transportation
15 $ / unit
10 $ / unit
Total Var costs
25 $ / unit
23 $ / unit
US Rollout
$4,000,000
$4,000,000
Setup costs
$3,000,000
$1,000,000
Total fixed cost
$7,000,000
$5,000,000
TIPS
Manufacture in China
• Whenever there are multiple options think table!
• Write big on the paper, keep your number legible
Other tips: Division and Multiplication
decomposition
Division decomposition
Multiplication decomposition
• Use decomposition to “cross-out”
numbers in the numerator / denominator
• Use mathematical decomposition to
speed up multiplication
Example:
Example:
72 / 16
= (8 * 9) / (8 *2)
=9/2
72 * 8
= 70*8 + 8*8
= 420 + 64 = 484
Keep your eyes out for other tips while working with students
Other tips: Rule of 72 & Averages
Rule of 72
Averages
• The amount of periods it takes to double
a number is 72 divided by the rate
• Watch out for averages they are trickier
than they appear
Example:
Examples:
How long will it take to double $5 if the
annual interest rate is 9%
Average cost of items at a retailer
= 72/9 = 8 years
Average effectiveness of a drug
Keep your eyes out for other tips while working with students
Other tips: 1% and 10% rule
1% rule
10, 20, 25% rule
• When faced with tough
percentages, put things in terms of
10%, 5%, and/or 1%
Example:
LifeJacket Ventures makes 17%
margins on revenue of $88M. How
much profit do they make?
= 10%= 8.80
5%= 4.40
1%= 0.88
1%= 0.88
=
14.96M (yeah addition!)
• 10% rule: drop the last digit
Example:
10% of 156= 15.6
• 20% rule: drop last digit and double the
number
Example:
20% of 16,300= 1630*2= 3260
• 25% rule: half the number twice
Example:
25% of 244M= 122M (50%) = 61M (25%)
Simplify whenever possible
Other tips: % of round numbers and
division simplification
% of round numbers
Division simplification
• When calculating percentages of
round numbers:
x% of y = y% of x
• Simplify tough division questions by
splitting the division into two easier
steps
Example:
Cabinet Pro LLC has profits that are
28% or sales of $400,000. What are
CP’s profits?
Example:
• One step: 960/6 = not fun
= 28% of 400,000= 400,000% of 28
• Two step:
• 960/2= easier (480)
• 480/3 = also easy (160)
• Answer = 160!
• Simplify to 4000*28 and then 4*28
• 4*28= 112
• Then add back the zeros
• $112,000
Simplify whenever possible
Agenda
•
•
•
•
•
•
Roadmap check-in
Case analysis overview
Sample case demonstration
Case math: a structured approach
Calculation best practices
Practice Time
9/30/10
Roadmap Math
32
Practice Time
You are the captain of your first year campout team. Despite many requests, you
have limited your team to 20 people. You are traveling to Costco to purchase beer
and water for the weekend. You received the following data from informed
second years:
•Begins on Friday at 7pm and goes to Sunday at 7am
•Average beer consumption: 1.5 beers/hour/person
• Each beer has 12 ounces and comes in cases of 24 beers
• Due to the new campout rules, you must have 2 ounces of water per ounce of
beer
•Each water bottle has 20 ounces and comes in packages of 12
How many cases of beer and how many packages of waters do you need to
buy?!
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Practice Time
Your client wants to commercialize a new chemical that improves the quality of
apples. What is the maximum price the charge for a hectoliter of the chemical?
• Market = Maine
• Maine = 800 orchards
• Average orchard = 100 acres
• Average revenue =$30,000 / orchard
• 25% of revenue is full apples
• 75% of revenue comes from juice
• The chemical improves apple yield by 10% and juice yield by 5%
• Each hectoliter can cover 200 acres
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