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

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

2 September 2004 © Scholtes 2004Page 2 Where are we? I. Introduction II. The forecast is always wrong I. The industry valuation standard: Net Present Value II. Sensitivity analysis III. The system value is a shape I. Value profiles and value-at-risk charts II. SKILL: Using a shape calculator III. CASE: Overbooking at EasyBeds IV. Developing valuation models I. Easybeds revisited

2 September 2004 © Scholtes 2004Page 3 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

2 September 2004 © Scholtes 2004Page 4 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”

2 September 2004 © Scholtes 2004Page 5 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

2 September 2004 © Scholtes 2004Page 6 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

2 September 2004 © Scholtes 2004Page 7 Logical structure of the model Added value Added revenues - Added costs Additional bookings * Unit price Max(bookings - capacity,0) Min(demand, booking limit) # bumped customers Unit cost * Max(bookings – no-shows - capacity,0) Conceptual “parts” of the system Data driving the systemControl variables

2 September 2004 © Scholtes 2004Page 8 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!

2 September 2004 © Scholtes 2004Page 9 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!

2 September 2004 © Scholtes 2004Page 10 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)

2 September 2004 © Scholtes 2004Page 11 Sensitivity Analysis w.r.t. Demand

2 September 2004 © Scholtes 2004Page 12 Sensitivity Analysis w.r.t. Demand Interpret non-linearity points: - What causes them? - Will they lead to NPV based on average larger or smaller than average NPV?

2 September 2004 © Scholtes 2004Page 13 Sensitivity Analysis w.r.t. No-shows

2 September 2004 © Scholtes 2004Page 14 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

2 September 2004 © Scholtes 2004Page 15 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

2 September 2004 © Scholtes 2004Page 16 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

2 September 2004 © Scholtes 2004Page 17 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

2 September 2004 © Scholtes 2004Page 18 Where from here? I. Introduction II. The forecast is always wrong I. The industry valuation standard: Net Present Value II. Sensitivity analysis III. The system value is a shape I. Value profiles and value-at-risk charts II. SKILL: Using a shape calculator III. CASE: Overbooking at EasyBeds IV. Developing valuation models I. Easybeds revisited V. Designing a system means sculpting its value profile

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