FY Math / Analytical Reasoning 101 September 30 th, 2010.

FY Math / Analytical Reasoning 101September 30th, 2010

Roadmap Math 2

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 3

Now is a great time to research firms and work on distinguishing yourself

Sep Oct Nov Dec Jan Feb

Targeted

Exceptional

Analytical

Mature

Presentations

Networking events

Resume drops

Interviews

T.E.A.M.Model

RecruitingEvents

• Vault/Wetfeet/company website research

• Informal conversations w/ second years

• Refining resumes with SY consultants

• Behavioral interview practice w/ CMC

• Case 101• Math review session (today)

Targeted Exceptional Analytical

Today

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Roadmap Math 4

Your Roadmap to a consulting position

• Oct 4-7: Case Team Prep Unit 1: Behavioral

• Oct 5th: Week in cities / Networking event 6:30pm

• Oct 21-22: Week-In-Cities

• Informal case prep with classmates

• Deloitte Case Challenge• David Ohrvall Case Prep

Workshop• National case competitions

• 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

Upcoming events Case Prep Opportunities Expectations

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Roadmap Math 5

Today’s session covers the basics of analytical reasoning and how math appears in cases

January (Interviews)

9/30/10

InterviewFoundation

October

Acc

ount

ing

&

Fin

ance

Confidence& Composure

SubjectAreas

FineTuning

Fall 1

Fall 2

Hypothesis Based Problem Solving (Case Basics)

Analytical Reasoning (Math)

Eco

nom

ics

Str

ateg

y

Mar

ketin

g

“Telling Your Story” (Behavioral)

Case Interview feedback formCase _______________________ Case type ______________ Interviewer ____________________

Execution

• Structure Logical approach MECE Appropriate drive to solution

• Quantitative Ability Speed Accuracy Comfort, reaction to mistakes

• Business intuition Practical Insightful Breadth & depth across multiple functions Creativity

1 2 3 4 5Comments:

1 2 3 4 5Comments:

1 2 3 4 5Comments:

Communication

• Professionalism Poise Confident-Persuasive Articulate-concise Client ready

• Written Clarity of writing and page layout Ability to refer back Comfort, reaction to mistakes

1 2 3 4 5Comments:

1 2 3 4 5Comments:

Case start time __:__

Case end time ___:____

Framework development ______ minFramework explanation ______ minCase discussion ______ min

Behavioral (optional)

• Quality of star stories 1 2 3 4 5 Comments: • Length 1 2 3 4 5• Clarity 1 2 3 4 5• Relevance 1 2 3 4 5

Strengths

Weaknesses

Overall Rating: 1 2 3 4 5

Key: 1=Bottom 10%, 2= 10th-25th percentile, 3= middle 50%, 4= 75th-90th percentile, 5=Top 10%

6

Roadmap Math 7

Agenda


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Roadmap Math 8

Consultants use math analysis to develop solutions to ambiguous problems

ID key numbers & quantify the

situation

Problem /Ambiguity

Problem /Ambiguity

Use #s/analytics to develop projections

Develop problem insights using the

answer & #s

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Roadmap Math 9

Case interviews assess a candidate’s ability to use analysis to solve the business problem


situation

Problem /Ambiguity

Problem /Ambiguity



answer & #s

Does the candidate: • Develop a good

approach to reduce complexity

• Understand when numeric analysis is necessary

Does the candidate: • Tie the numbers back to

the big picture• Develop insights into

the problem

Does the candidate: • ID key numbers• Choose the right level of

granularity• Make sound

assumptions about missing numbers

Does the candidate: • ID appropriate analysis• Have a structured math

approach• Show comfort w/

numbers and calculations

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Roadmap Math 10

Agenda


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Roadmap Math 11

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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Roadmap Math 12

Agenda


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Case math is generally simple arithmetic

• General Arithmetic (addition, subtraction, multiplication, division)

• Ability to keep track of numbers of different magnitudes

• Use percents, fractions, proportions

• Decipher graphs / charts / diagrams

• Calculus

• Full discount cash flow analysis

• Complex finance formulas / techniques

• Accounting ratios

• Black-Schole’s ratio (see cover slide)

Definite interviewee expected

skill-setGenerally not expected*

* 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

Identify if analytics are needed • Every case doesn’t need math, work with the interviewer to determine if mathematical analysis is needed

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

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

Calculate • Work out the problem by fitting the numbers into the structure you outlined, checking in with the interviewer every few steps

Check work • Look over your work and perform a sanity check to see if everything makes sense

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

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2

3

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6

A structured approach provides a framework for sound analytics


situation

Problem /Ambiguity

Problem /Ambiguity



answer & #s

1

2

3

4

5

6

Identify if analytics are needed

Structure approach

Gather key numbers (estimate missing #s)

Calculate

Check work

Fit in big picture

A structured math approach will help candidates of all analytical abilities

• 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

• Helps a candidate show analytical skill even if mistakes are made in computation

• Keeps numbers organized, making calculations easier

• Simplifies math

Benefits for those who are “strong” at math

Benefits for those who are “weak” at 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

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= $7.56M 3 fleets* 15 ships/fleet * 5 decks/ship* 60 rooms/deck * $80/day= $1.08M

Common Math Mistakes

Miscount the Zeros!

Mistake Example

Johnny’s Apple Company sold 20M barrels of seed in 2010 Each barrel has 100 seeds Therefore Johnny’s Apple Co. sold:

20,000,000*100 or 200M seedsWRONGRIGHT

Confuse terms

WRONG

RIGHT

20,000,000*100 or 2000M or 2B seeds

Calculate the payback period if a machine costs $260,000 and the total lifetime revenue for the machine is $30,000/year

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!

Common Math Mistakes

Silent math

Mistake Example

What is the average revenue per elderly customer? (Silence)

I don’t do division

WRONG

RIGHT

WRONG

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”

“I should divide 260,000 by 30,000, but I didn’t practice division. How about another question?”

RIGHT

Smile-Bright breakdown

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

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2

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Potential Revenue Cost structure

Smile-Bright breakdown

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

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

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

Potential Revenue Cost structure

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Roadmap Math 21

Agenda


9/30/10

Percents and fractions are very common in case interviews

• Get comfortable converting between percents, #/100 or #/1000 and fractions

• Ask a friend to quiz you

.75 = 75% = 75 out of 100 = 3/4

.33 = 33% = 33 out of 100 = 1/3

4 Calculation Best Practices

TIP

S

Roadmap Math 23

Interviewees can represent numbers in any way, but are best served to be consistent

Good: 1M, .01M, 20M

Caution: 1,000,000, 10K, 20M


• 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 youTIP

S

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Roadmap Math 24

Case math can greatly simplify if you choose the correct units

Good: $ / cubic feet / mile

Caution: $ / boat


• 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…

TIP

S

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Roadmap Math 25

Rounding may be used to simplify complex math

Good: 1.37*66% = 1.5*2/3 = 1

Caution:1.4*66% =lots of math


• 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%)T

IPS

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Roadmap Math 26

Distilling case problems into formulas shows structure and allows for graphing

Cost = FC + VC * Q

$1m

$3m

Num of toothbrushes

Mexico

China


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Tables are very useful for keeping track of numbers and details

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

Manufacture in China Manufacture in Mexico


• Whenever there are multiple options think table!• Write big on the paper, keep your number legible

TIP

S

Other tips: Division and Multiplication decomposition

• Use decomposition to “cross-out” numbers in the numerator / denominator

Example:

72 / 16= (8 * 9) / (8 *2)= 9 / 2

• Use mathematical decomposition to speed up multiplication

Example:

72 * 8= 70*8 + 8*8= 420 + 64 = 484

Division decomposition Multiplication decomposition

Keep your eyes out for other tips while working with students

Other tips: Rule of 72 & Averages

• The amount of periods it takes to double a number is 72 divided by the rate

Example:

How long will it take to double $5 if the annual interest rate is 9%

= 72/9 = 8 years

• Watch out for averages they are trickier than they appear

Examples:

Average cost of items at a retailer

Average effectiveness of a drug

Rule of 72 Averages

Keep your eyes out for other tips while working with students

Other tips: 1% and 10% 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!)

1% rule

Simplify whenever possible

• 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%)

10, 20, 25% rule

Other tips: % of round numbers and division simplification

• When calculating percentages of round numbers:

x% of y = y% of x

Example: Cabinet Pro LLC has profits that are

28% or sales of $400,000. What are CP’s profits?

= 28% of 400,000= 400,000% of 28

• Simplify to 4000*28 and then 4*28• 4*28= 112

• Then add back the zeros• $112,000

% of round numbers

Simplify whenever possible

• Simplify tough division questions by splitting the division into two easier steps

Example: • One step: 960/6 = not fun

• Two step: • 960/2= easier (480)• 480/3 = also easy (160)• Answer = 160!

Division simplification

Roadmap Math 32

Agenda


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Roadmap Math 33

Practice TimeYou 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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Roadmap Math 34

Practice TimeYour 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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FY Math / Analytical Reasoning 101 September 30 th, 2010.

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Transcript of FY Math / Analytical Reasoning 101 September 30 th, 2010.