1. Real Option in design and operation of an automotive assembly line
Kaushik Sinha
Dept. of Aeronautics and Astronautics
Massachusetts Institute of Technology
Dec. 9, 2008

2. Contents: Introduction Uncertainty Definition
Flexible and Inflexible assembly line
Two-stage decision analysis
Lattice Analysis
Simulation-based method
Conclusions

3. Introduction: Questions posed
Assume there are two car models, the second being a length-modified version of the first. The fist model is popular and has a positive growth rate. The demand for the length-modified version is less but it has the same positive growth-rate but with a high volatility.
A new assembly line is being built and the question is whether to build it only for the first model or there should be embedded flexibility in the line so as to be able to built any one model depending on the market scenario. Initially first model is produced but production switches to second model if it shows higher profit. Once started, only second model can be produced from the flexible assembly line – flexibility valuation using Decision analysis and Lattice analysis
Question 2:
In this case, the second car model do not exist initially. It can be manufactured only after two years. This length-modified version is predicted to have a higher growth-rate but also higher volatility. It is assumed that once launched, it would capture 90% of the market share of the existing model.
A new assembly line is being built and the question is whether to build it only for the first model or there should be embedded flexibility in the line so as to be able to switch to new model based on market conditions. The production switches to new model if present model cannot generate a certain net revenue margin. Once changed, the flexible assembly line can only produce the new model – flexibility valuation using Simulation-based method

4. Introduction:
An automotive manufacturer is planning to built with a new assembly line for an existing and successful model.
The question is whether to go with a customized of inflexible line or a flexible line that can churn out vehicle with modified length. A length-modified model depicts the scenario of changing customer preference over a period of time.
Front-view of body-in-white (BIW) [1]
A product platform essentially tries to standardize components across different product variants (different car models in our case) and thereby reduces cost and increases efficiency.
But platform design based on a forecasted point design is not nimble and cannot adapt to uncertain changes in the marketplace. Adding flexibility to some elements of the product platform will make it nimble and introduce an element of adaptability to the platform over a longer period of time. This is a case of “in” system flexibility.

5. Real option valuation framework
For the purpose of the class project, we are considering embedding the flexibility to produce same class of cars from an assembly line with body-in-white length modified to match changing customer needs.
We will consider a single assembly line producing a mid-size sedan that is part of a platform and embed a specific flexibility of length change. Therefore the flexible line would be able to produce vehicles with varying length of the body while the inflexible line can produce vehicles of a specific size only.
A generic real options analysis framework [2].

6. Uncertainty Definition
We can represent the set of uncertainties as: Uveh = [Dveh(t) ; Sveh(t)],
where Dveh(t) refers to the demand scenario for a model and Sveh(t) refers to the variation in customer perception with time which manifests in increasing premium for the updated model and also impacts the demand scenario of the modified model.
Demands for both models are assumed to be correlated in a sense that if the demand for present model increases the same happens for the modified model.
During development of simulation based method of option valuation, a scenario is analyzed where introduction of a new model introduces a ‘jump’ in the demand scenario.
The time horizon for this assembly line is assumed to be 12 years for the analysis purpose (but this number is purely hypothetical and may not bear resemblance to real data).
This assumption (2) has been made while performing lattice analysis to reduce complexity and be able to apply the binomial method for option valuation but may not represent realistic situation where the market share for two models may pan out to be very different.

7. Flexible and Inflexible assembly line
Flexible assembly line: Can produce vehicles with passenger compartment of different lengths. It has the capability to switch from producing the present model to the new model but there is an additional cost to be paid upfront in terms of initial capital expenditure to embed this flexibility in design.
Inflexible assembly line: The inflexible line is capable of producing a fixed model only.
It is assumed that once the option to produce the new model from the assembly line is exercised it is permanent until the end of its life. The reason for this important requirement is the necessary condition of path independency for the lattice valuation that is to come.

8. Cost and Revenue structure
Vehicle type
Present mid-size sedan model
Length-modified version
Yearly growth rate 3%
15%
Yearly volatility in demand
45%
Initial demand (per year)
62,500 units
12,500 units
Fixed cost (per year)
$240,000,000
Sale price per unit
$20,000
$25,000
Marginal cost per unit
$12,000
$12,200
Limiting capacity (# of units per year)
300,000
Initial Capita expenditure
$800 million
$880 million
Net revenue is calculated as:
Net Revenue, R = (SP-MC)*MIN (demand, capacity) – FC
where SP stands for sale price of a car, MC stands for manufacturing cost of a car and FC stands for fixed cost of running the assembly line.

9. Two-stage decision analysis
Each state of high and low is assumed to be equally probable. Hence probability of all chance events in the decision tree shown below is 0.5.
The value or net revenue for present model is based on the demand evolution.

10. Two-Stage decision analysis
Statistic
Inflexible line
Flexible line
Which line?
E(NPV)
$2.79 billion
$3.06 billion
Flexible
Max (NPV)
$5.44 billion
$7.16 billion
Min (NPV)
$0.8 billion
$0.7 billion
Inflexible
CAPEX
$0.88 billion
B/C ratio = E(NPV)/CAPEX
3.49
3.48
E (value of flexibility)
$0.19 billion
The flexible assembly line takes advantage of upside opportunities. This is a very coarse grained analysis, but still shows the value of flexible line in this case.
VARG curve

11. Lattice Model
Assumes demand increases exponentially period to period. Lognormal Binomial Distribution for demand over 12 years which has been divided into 6 periods of 2 years each.
Two demand lattices for developed corresponding to two car models.
The growth rate (μ) and volatility (σ) are to be adjusted so that they reflect corresponding growth rate and volatility. The relations for adjusting (μ, σ) are as follows (since Δt = 2):
These new parameters are then used above to derive parameters (p,u,d) for the lattice.

12. Lattice Analysis: Inflexible assembly line

13. Lattice Analysis: Flexible assembly line

14. Lattice Analysis Statistic Inflexible line Flexible line Which line?
E(NPV)
$3.117 billion
$3.431 billion
Flexible
Max (NPV)
$7.15 billion
$5.44 billion
Min (NPV)
$0.8 billion
$0.78 billion
Inflexible
CAPEX
$0.88 billion
B/C ratio = E(NPV)/CAPEX
3.9 --
E (value of flexibility)
$0.314 billion
E (net value of flexibility)
E (value of flexibility) – cost of flexibility = $0.234 billion
NPV (no variability, inflexible case)
$0.526 billion
E(NPV) inflexible
$3.117 billion
E(NPV) flexible
$3.431 billion
E (value of flexibility)
$0.314 billion
Price of flexibility
$80 million
E (Net value of flexible line)
$234 million

15. Lattice Analysis: Sensitivity Studies
As the growth rate and/or the volatility increases, so does the value of the option.
The volatility in demand is the primary driver for deriving value out of embedded flexibility. The results make sense qualitatively, given that in general flexible strategies increase in value in scenarios of greater uncertainty.
The same is true for price premium achieved from updated model.

16. Simulation method
Monte-Carlo simulation is arguably the most generic but computationally intensive method for calculation option value. There are no restrictive assumptions that are required to be satisfied before this method could be applied and any kind of demand scenario (continuous or discontinuous) can be modeled.
The disadvantage associated to this approach is the computational cost.
In this case, at year zero, there is no demand for the new model since the model simply does not exist. Now along the way, if the demand for present model fails to generate more than a target minimum net revenue, the new model is introduced at time T = t and there is a jump in demand and the demand curve is changed entirely beyond time T>t and so does the realized revenue from the flexible assembly line.
The demand model is based on Geometric Brownian Motion (GBM) while using the simulation approach.
We will analyze such a ‘jump’ in the demand due to introduction of a new model.

17. Simulation method
For new model: growth 5%, volatility 25%
For new model: growth 5%, volatility 20%
As we change the volatility from 25% to 20% , the lower the volatility actually mitigated the left tail of the CDF for flexible case. The minimum NPV for flexible case has reduced and the width of distribution of NPV also reduced.
The value of flexibility increased marginally but the distribution of NPV got more compact thereby reducing the potential upside as well.

18. Simulation method
Case 1: New model with growth 5% and volatility of 25%
Statistic
Inflexible line
Flexible line
Which line?
E(NPV)
$1.84 billion
$2.63 billion
Flexible
Median (NPV)
$1.65 billion
$2.16 billion
Max (NPV)
$8.99 billion
$12.67 billion
Min (NPV)
-$0.85 billion
-$1.21 billion
Inflexible
B/C ratio = E(NPV)/CAPEX
2.3
2.99
E (value of flexibility)
$0.78 billion
E (net value of flexibility)
E (value of flexibility) – cost of flexibility = $0.7 billion
Case 2: New model with growth 5% and volatility of 20%
Statistic
Inflexible line
Flexible line
Which line?
E(NPV)
$1.85 billion
$2.65 billion
Flexible
Median (NPV)
$1.65 billion
$2.26 billion
Max (NPV)
$8.96 billion
$11.9 billion
Min (NPV)
-$0.91 billion
-$0.72 billion
B/C ratio = E(NPV)/CAPEX
2.312
3.01
E (value of flexibility)
$0.8 billion
E (net value of flexibility)
E (value of flexibility) – cost of flexibility = $0.72 billion

19. Conclusions:
The results support the notion that the value of an option in a flexible strategy tends to increase with increasing uncertainty.
Simulation-based methods seem very natural for handling demand discontinuity in terms of ‘jumps’ introduced in the system by the introduction of a new model. Pure decision analysis could be applied in this case, but involves a lengthy process of developing a rather large decision tree and it gets very complex quite fast.
Since the industry in question comprises a wide variety of products produced from the same platform to take advantages due to part commonality, some sort of framework would have to be developed to account for product diversity manufactured out of platform that would typically consist of multiple assembly lines.
Doing the application portfolio is a necessary exercise to truly understand what flexible design has to offer under exogenous uncertainty. Thus, the opportunity to develop this application portfolio in the context of class material has helped in gaining a better appreciation for the very valuable tools that this kind of analysis has to offer.

20. References:
1. de Weck O.L., Suh E.S., “Flexible Product Platforms: Framework and Case Study”, DETC , Proceedings of IDETC/CIE 2006 ASME 2006
2. de Weck, O.L., de Neufville R. and Chaize M., “Staged Deployment of Communications Satellite Constellations in Low Earth Orbit”, Journal of Aerospace Computing, Information, and Communication, 1 (3), , March 2004. 3.
4. de Weck, O., 2006, "Determining Product Platform Extent", Product Platform and Product Family Design: Methods and Applications, T. W. Simpson, Z. Siddique and J. Jiao, eds., Springer, New York, pp