Risk Management & Real Options IV. Developing valuation models Stefan Scholtes Judge Institute of Management University of Cambridge MPhil Course 2004-05

Risk Management & Real Options

IV. Developing valuation models

Stefan ScholtesJudge Institute of Management

University of Cambridge

MPhil Course 2004-05

2 September 2004 © Scholtes 2004 Page 2

Where are we?

I. IntroductionII. The forecast is always wrong

I. The industry valuation standard: Net Present Value

II. Sensitivity analysisIII. The system value is a shape

I. Value profiles and value-at-risk charts

II. SKILL: Using a shape calculator

III. CASE: Overbooking at EasyBedsIV. Developing valuation models

I. Easybeds revisited


What is a good model?

A good model cannot be made simpler without loss of relevance and cannot be made more relevant without loss of simplicity

Relevance

Complexity


What is a good model?

A good model cannot be made simpler without loss of relevance and cannot be made more relevant without loss of simplicity

Relevance

Complexity

“good models”

“bad models”


There is no right model!

Real-life decision situations are too complex to be captured in ONE model

Key to success:

• BEGIN WITH AN OVERLY SIMPLISTIC MODEL WHICH CAPTURES OBVIOUS INTUITION

• IMPROVE RELEVANCE

• DON’T LOOSE INTUITION AS YOU WORK UP THE COMPLEXITY LADDER!

>̵ You have to be able to communicate your model to a wide audience


Decouple model logic from uncertainty

Step 1: What drives the value?

Try to understand the logic of value creation first! Don’t worry too much about exact numbers in this phase

• Added value = added revenue minus added costs• Added revenue = additional bookings * unit price• Additional bookings = max(bookings – 150, 0)• Bookings = min(demand, booking limit)• Added costs = number of bumped customers * unit cost of bumping• Number of bumped customers = maximum(bookings minus no-

shows minus capacity,0)

What is under our control? Booking limit

What drives this model?• Demand, unit price• Number of no-shows, unit cost of bumping


Logical structure of the model

Added value

Added revenues - Added costs

Additional bookings *

Unit price

Max(bookings - capacity,0)

Min(demand, booking limit)

# bumpedcustomers

Unit cost*

Max(bookings – no-shows - capacity,0)

Conceptual “parts” of the systemData driving the system Control variables


Demand projection

Last year’s average booking was 139 Based on this figure, overbooking has no value!

• Problem: bookings do not give us an idea of demand on fully booked days

Use Enquiries as proxy: • Average number of enquiries: 1253• Average conversion rate of enquiries to bookings when not fully

booked: 11.6%• Average demand: 11.6%*1253 = 146

Based on this figure, overbooking still has no value!

What is missing?• Variation in demand gives value to overbooking!


Two demand scenarios

Scenario I: Demand below capacity Added value from overbooking = 0

Scenario II: Demand above capacity

If scenario II occurs in, say 50% of days then

Expected value of overbooking = 50% added value if demand above capacity

Projected demand if demand is above capacity:• Average number of enquiries on fully booked days: 1415• Demand projection = conversion rate * enquiries =

11.6%*1415=164

This model shows that overbooking can have value!


The impact of uncertainty

Are there asymmetries that could lead to “imbalance” and thus to flaw of averages?

• Additional revenues: Negative impact of low demand scenario is not balanced out by positive impact of high demand scenario

>̵ Sales from high demand scenarios are capped at booking limit>̵ Additional sales from low demand scenarios are zero if demand is below

capacity

• Additional costs: Positive impact of low no-show number is not balanced out by negative impact of high no-show numbers

>̵ Costs from high no-shows are capped at zero if there is no bumping

Clear indications of potential asymmetries: • Use of max or min functions in spreadsheet model• Non-linearity of sensitivity graph (not a line)


Sensitivity Analysis w.r.t. Demand

No-shows fixed at 23

-200

0

200

400

600

800

1000

1200

1400

130 140 150 160 170 180 190

Demand

Ad

ded

Val

ue


Sensitivity Analysis w.r.t. Demand

No-shows fixed at 23

-200

0

200

400

600

800

1000

1200

1400

130 140 150 160 170 180 190

Demand

Ad

ded

Val

ue

Interpret non-linearity points:- What causes them?- Will they lead to NPV based on average larger or smaller than average NPV?


Sensitivity Analysis w.r.t. No-shows

Demand fixed at 164

-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 5 10 15 20 25 30 35 40

No-shows


Which uncertainties are important?

Intuition: The value of overbooking is driven by • Fluctuating commercial capacity is sometime larger than physical

capacity• Fluctuating demand

Both fluctuations have a non-linear effect on the added value• Sensitivity charts

Incorporate them both, first in the easiest possible way• Sample enquiries and multiply by conversion rate to generate demand• Sample no-show rate and multiply by bookings to generate no-shows

Result is much different from average-based analysis• Expect additional revenue of 1.5% (instead of 4.5% based on

averages)• Best overbooking limit is around 160


Drilling deeper

There are other issues that may have an effect on the outcome• Marginal room rate• Conversion rate from enquiries to demand fluctuates• Demand growth• Etc.

A more complex model can be developed to take all these issues into account

If you do so, you will see that the additional complexity does not give you more insight or change the story

• It is important to have done this, though, because how will you know o/w

KEY: Communicate the analysis on the basis of the simplest possible model that conveys the main message

• BUILD INTUITION


Every model tells a story

Intuition is often explained through a set of “stories”• Often based on historic parallels, war stories (“Remember what

happened to IBM in the late 80ies…”) Valuation models are another source of “stories”

• Models provide a rigid quantitative framework within which you can develop a story to explain where value lies

No story gets it right, but they all contribute to our understanding of the possible consequences of our decision

A model that you don’t understand is as useful as a story told in a language you don’t understand

• “Understanding” is not necessary on a very detailed level but “assumptions and limitations environment” must be understood in the same way as the historic environment of a “war story” must be understood to make it useful

Consequence: Build models that can be communicated!

BOTTOMLINE: Business modelling is about building simple models and eliciting the stories behind the models


Main Lessons

Build your models step-by-step• Be prepared to discard your models and start fresh (now that you

know what you actually wanted to model in the first place)• Use many models

Begin with the system logic, then incorporate data and uncertainty

Make sure you validate your model well • Through intuitive interpretation of the output (graphical / numbers)• By plugging in possibly unrealistic scenarios for which you know how

the system should perform

Climbing up the complexity ladder will give yourself confidence in the relevance of your analysis

BUT: Climb down again for your presentation• Explain your analysis in intuitive terms• Use a few key pictures that convey the story


Where from here?

I. IntroductionII. The forecast is always wrong

I. The industry valuation standard: Net Present Value

II. Sensitivity analysisIII. The system value is a shape

I. Value profiles and value-at-risk charts

II. SKILL: Using a shape calculator

III. CASE: Overbooking at EasyBedsIV. Developing valuation models

I. Easybeds revisitedV. Designing a system means sculpting its value profile

Documents

Risk Management & Real Options IV. Developing valuation models Stefan Scholtes Judge Institute of Management University of Cambridge MPhil Course 2004-05