3. 1
Summary
The approached used to analyze the different scenarios and options for ChinaCarb
- Carbon Fibers Company was the Monte Carlo Simulator. The variables used in this
tool were Demand for the final good (Triangle Distribution), Yield rate of
the carbon fiber plant (Normal Distribution) and the Price of the raw material. The
model used to forecast the Price of the raw material was the Classical time series model
– AR (1) with the method OLS. These same variables were considered to be the
uncertainties that ChinaCarb was about to face for the next eleven years. Similarly,
these variables were considered to define the influence diagram and decision tree.
Given the variables and parameters mentioned above and a margin error of 1.8%
and a 95% interval of confidence we run a pilot simulator and got an optimal N of 6,500
runs. According with this number of runs we assumed the analysis will have a high
level of accuracy. It is important to mention that we considered the value of Cash Out
scenario to be equal to zero.
With uncertain demand and yield rate for 11 years, we ran the MC simulation for
acquiring the pitch plant for both 75% and 25% success probability assuming the owner
is risk neutral. The conclusion is that 75% scenario stochastically dominates 25% one.
We recommend the company to purchase the technology with at least 22% success
probability to yield a positive NPV.
With a risk tolerance of RMB 8,893,182, the risk-averse owner has an average
utility of 0.35 and a 3.83M RMB certainty equivalent for 75% success probability. In
this case, we would only suggest the management to acquire the pitch plant with a
minimum success probability of 61%.
Another scenario evaluated for this project was to consider an uncertain demand
for the first three years and then it will stay constant for the rest of the project. Under
this scenario and assuming risk neutral owner and 75% probability of success the
average NPV was 19.81 Million RMB, which represented a reduction of 0.03 Millions
RMB according with the NPV for an uncertain demand and yield rate for all the 11
years. Now assuming the European company will supply us for another 3 years, the
expected average NPV was 28.01 Million RMB representing an improvement
4. 2
of ≈41.40 % versus the scenario of “Uncertain demand for 3 years and 75% probability
of success”; and ≈41.20 % versus the scenario of “Uncertain demand and yield rate for
11 years and 75% probability of success”.
If ChinaCarb base the investment decision on the demand amount of 2013, we
recommend the management to acquire the technology even if the demand is low since
even with the minimum demand of 200 tons, the average NPV is still 28.01 Million.
Our suggestions regarding the set of opportunities mainly focus on improving the
ability of ChinaCarb to tackle the current issues and mitigate their effects on the future
plan of the company. Sharing the profit and risks with other companies in a joint
venture is firstly recommended and followed by the development of new products based
on the pitch-based carbon fiber and the substitute of the current raw materials. Lastly, a
marketing campaign is suggested to gain financial support from external parties
including private investors and government.
5. 3
Problem Analysis
Question 1
ChinaCarb produces pitch-based carbon fiber. Carbon fiber is defined as a fiber
containing at least 92 wt % carbon [1]. Pitch-based carbon fibers have been extensively
used in composites in the form of woven textiles, prepregs, continuous fibers/rovings,
and chopped fibers [2]. They have various end uses because of their high strength. In
our daily life, they are usually used as materials for sporting goods and for buildings. Its
application in sports goods ranges from the stiffening of running shoes to ice hockey
stick, tennis racquets and golf clubs. It is used in crash helmets too, for instance, for
rock climbers and in any sport where there is a danger of head injury. The uses of
carbon fiber in the home are as broad as our imagination. A shiny black bathtub, a
coffee table, iPhone cases, pens, and even bow ties can all be built from carbon fiber. In
addition, as a chemical purifier, carbon is a powerful absorbent. ChinaCarb produces
environmentally friendly, high-tech, and highly absorptive activated pitch-based carbon
fiber that could be used for air filtration, water filtration, and solvent reclamation.
ChinaCarb currently is facing a major problem. Its raw material supplier of a
particular kind of pitch discontinued its production in September 2010 due to the fact
that the pitch it produced had been declared unsuitable for its toy applications due to
toxic effects. No substitutive suppliers are available because ChinaCarb’s production
line was specially designed for this particular type of pitch. Event its two competitors in
Japan cannot provide the substitutes because of the company’s complicated, pitch-
specific design. Therefore, the alternative of selling the company to its competitors can
be clearly ruled out.
The fundamental objective of ChinaCarb is to maximize company’s profit no
matter what is going to happen to its pitch production. Since the owner’s of ChinaCarb
are unwilling to pay the high cost of hiring technicians from Europe, they have got only
two alternatives left, cashing out of the company once the current pitch supply run out,
or investing in pitch plant production technology and building their own pitch
production line in China.
As the owner of 40% of ChinaCarb’s shares, Hui Lin clearly preferred continue to
6. 4
invest in the company, yet he wants to analyze all facts before making an approach.
Question 2
Influence Diagram
We conducted the influence diagram in order to comprehend the problem
structure which includes the relevant decisions and uncertain influences. At first, the
ultimate goal was identified and all of the factors that could impact the decisions were
listed. Labor cost and depreciation were known and the selling prices of pitch and pitch-
based carbon fiber had been determined, so they were eliminated from the influence
diagram. The yield rate, demand for carbon fiber and price of raw material were the
three factors that randomized over time and had a direct effect on the goal profit.
Besides, the decision on Investment or Cash-out also affects the Profit since it led to the
different outcomes of NPV which would be analyzed in the report.
7. 5
Question 3
Decision Tree
Question 4
Since the price Pt+1 is linear dependent on Pt and the error term ε~N(0, σ), we can
apply the classical time series model – AR(1) with OLS method. Namely,
P+,- = a + b ∙ P+ + ε.
Here using OLS method:
b =
10 ∙ P+ ∙ P+,- − (5667
+85666 P+) ∙5667
+85666 ( P+,-)5667
+85666
10 ∙ P+
55667
+85666 − ( P+
5667
+85666 )5
a =
P+,-
5667
+85666
10
− b ∙
P+
5667
+85666
10
We use Stata to estimate the parameters a and b respectively. The regression results
are presented in table x and the linear function is
P+,- = 2318.174 + 0.3663×P+ + ε+,-
8. 6
Based on the linear function, P56-- = 2318.174 + 0.3663×P56-6 = 2318.174 +
0.3663×3700 = 3673.516. Analogously, the prices from 2012 to 2021 are presented
in table x+1
Year Price Year Price
2011 3673.52 2017 3658.24
2012 3663.81 2018 3658.22
2013 3660.26 2019 3658.21
2014 3658.96 2020 3658.21
2015 3658.48 2021 3658.21
2016 3658.31
Question 5
It was reported that the highest sales record of ChinaCarb was 350 tons of carbon
fiber in 2008. The actual demand at that time was not indicated; therefore, it is
reasonable to indicate that the upper limit of demand was 350 tons since the company
did achieve its highest production capacity. The following year marked the lower limit
of demand of 200 tons due to the serious impact of the worldwide financial crisis on the
demand for carbon fiber. Assuming that there are not any major changes in the market,
the projected demand provided by ChinaCarb is 250 tons with high probability. Due to
9. 7
the limited information about the demand for carbon fiber, the distribution of the
demand in ChinaCarb’s case is the triangle distribution with specific parameters:
Upper limit 350 tons
Mode 250 tons
Lower limit 200 tons
Since the historical data regarding the yield rate was not provided in the text, the
distribution for the yield rate was indicated to be normal distribution with the expected
value of 44 percent and the standard deviation of 2 percent.
Expected Value 44%
Standard Deviation 2%
Question 6 & Question 7
Assume the success probability of producing the pitch is 75% based on the
prediction of the company’s expertise. We thereby conducted a simulation model and
analyze it to generate insights as follows.
We used approximately 6,500 iterations in an attempt to report the minimum,
maximum and average NPV as well as the standard deviation. The following formula
was applied in order to determine the number of simulation runs:
with the constraint which ensures:
As can be seen from the formula, there are three important parameters, including
the estimated standard deviation of the output, the desired margin of error 𝜎 and the
critical value of the normal distribution for α/2.
For the estimated standard deviation, we used a pilot simulation of 300 outcomes
10. 8
of the total NPV with 75 percent of successfully producing the pitch and 25 percent of
failure to estimate the value of 𝜎. In particular, we applied the following equation to
compute the value of 𝜎 :
where
x = each value of the simulation
x = the mean of the values
N = the number of values
Using the outcomes of the total NPV, we calculated the mean which is equal to
RMB 19,991,051 and the estimated standard deviation which is RMB 15,484,038. (1)
For the desired margin of error , the acceptable difference between the sample
mean and the population mean was firstly determined by analyzing diverse scenarios
with the following results:
Error % Optimal N
- α = 5% -
Optimal N
- α = 1% -
1% 23,047 39,624
1.88% 6,500 11,176
2% 5,762 9,906
3% 2,561 4,403
4% 1,440 2,477
5% 922 1,585
In an attempt to have a minor error in our analysis we decided to choose the
margin error of RMB 376,429 (1.88%) with 95% of confidence interval in order to
come up with a feasible number of simulation runs (approximately 6,500) without any
negative effect in the computer performance.
11. 9
Finally, applying α=5% to calculate the confidence interval which equal to 95%,
we compute the critical value of the normal distribution for as z-score:
Plug the data in (1), (2) and (3) into the formula, we have the optimal number of
simulation runs:
Figure 1-a shows the risk profile with n=6500. One can see that a probability of
total NPV exceeding zero is 75.30%, which means there is an estimated Expected
Shortfall of 24.70% (chances of when a negative NPV occurs). The total NPV varies
between -11.43 millions and 38.46 millions with a mean of 19.84 millions. This figure
also shows that the standard deviation of total NPV is 16.16 million.
The company currently faces significant risk in not being able to successfully
produce pitch plant if they chose to proceed with the plan of purchasing the technology
from their previous supplier. Therefore, we need to take a close look at different
scenario and quantify the risk for each one.
We now assume the success probability were lower, say 25%. Figure 1-b depicts
12. 10
the risk profile for both probabilities. One can see that a probability of total NPV
exceeding zero is 24.7%, which means there is an estimated high Expected Shortfall of
75.3% (chances of when a negative NPV occurs). The total NPV varies between -11.43
millions and 39.13 millions with a mean of 1.1 millions. This figure also shows that the
standard deviation of total NPV is 16.02 million.
Since a positive total NPV is preferred (because the company generates value only
if the cost of investing in the technology is smaller than the price the company is willing
to pay for its cash flows), the curve further to the right side is better. Success probability
A (75% success) stochastically dominates probability B (25% success). For any given
NPV to completion such as 28 millions, probability A has a higher probability than
probability B of meeting that value.
However, we believe that as long as the average NPV is not negative, the
company should be confident enough to invest the technology. This is because, a
positive NPV indicates that the earnings generated by this investment (in present dollars)
exceeds the anticipated costs (also in present dollars). Since we have a large amount to
simulated NPV outcomes on hand, the average outcome of the NPV is very
representative. We then adjusted the pitch product success rate to different levels and
13. 11
watched the change of the means of the NPV outcomes until we found the threshold that
the mean of NPV is just about to become negative. Eventually, we found the minimum
pitch product success rate to be 22% when the average of NPV is 0.15 million, meaning
when these is 22% chance that the company will successfully produce pitch plant after
they purchase the technology, the company is believed to make profit in the next few
years.
Question 8
From the MC simulation we yield 6500 different total NPVs. After plugging these
6500 values into the utility function , an average utility of 0.35
is generated. Now consider the average utility as the expected utility, i.e. EU=0.35. The
certainty equivalent CE has the same utility as the EU, which means
u CE = 1 − eHIJ/L,L7M,-L5
= EU = 0.35
eHIJ/L,L7M,-L5
= 1 − 0.35
ln e
H
IJ
L,L7M,-L5 = ln (0.65)
−
CE
8,893,182
= −0.4307829
CE = 3.83 Mio
Comparing the average NPV in question 6 (19.84 million) and the certainty
equivalent (3.83 million), we conclude that the company is risk-averse since the
certainty equivalent is smaller than the expected value (average NPV) of the investment.
For cash out scenario, we assume the company gains 0 RMB. As long as the
certainty equivalent yields a positive number, we could recommend the management to
acquire the technology. From above we can see that a certainty equivalent (CE) of 3.83
M RMB yields the same utility as the expected utility (EU) of the investment with 75%
success probability. We change our threshold to 50% and use the following
14. 12
methodology: if the random number (between 0 and 1) is larger than 0.5, we choose the
NPV for success, otherwise we choose the NPV for failure. Then we plug the NPV
value to the utility function and generate the average utility in this case (-0.28). Using
the same approach as before, the CE for 50% success probability scenario is equal to -
2.18 Mio RMB. Since this value is smaller than 0, we would not recommend the
investment to the management with 50% success probability. Then we change the
probability to 65% (CE= 1.00 Mio RMB), 60% (CE= -3.66 Mio RMB) and 61%
(CE=0.17 Mio RMB). So we would recommend the management to acquire the
technology with the minimum success probability of 61%.
Question 9
a) & b)
Assume that the demand for carbon fiber will be uncertain for the next three years
after which it will stay constant at its level in 2013. Figure 2-a shows the new risk
profile for the scenario above. One can see that a probability of total NPV exceeding
zero is 75.3%, which means there is an estimated Expected Shortfall of 24.7%. The total
NPV varies between -11.43 millions and 46.07 millions.
Now we assume that the European supplier will be able to continue its operations
for another 3 years, and ChinaCarb wait to acquire its technology at the end of 2013 at
15. 13
the same price of RMB 11,800,000. Figure 2-b depicts the risk profiles for both
"without Real option" and "with Real option" to wait. One can see that if the company
choose to wait until 3 years to purchase the technology, the total NPV varies between
9.19 millions and 48.67 millions, meaning it is always good to invest if the company
actually have the chance to invest it after 3 years. Thus, the company on condition of
Real option to wait stochastically dominates when they do not have the Real option.
As we mentioned before, the curve further to the right side is preferred. The range
of total NPV narrows with when the company choose to wait and the risk of loss on the
investment is 0%. Therefore, we recommend the company to invest the technology at
the end of 2013.
c)
With the assumption that the demand after 2013 stays constant as the level of
2013 while the demand for 2011-2013 still randomizes with triangle distribution (lower
limit: 200 ton; upper limit: 350 ton; mode: 250 ton), the management chooses to invest
if the demand in 2013 is larger than a threshold and otherwise he chooses to cash out.
We should keep in mind that he still faces 75% success probability if he chooses to
invest. We set the threshold to different demand amount and found the one amount
16. 14
yielded the maximum average NPV. We first set the threshold as the same amount as
the mode (250 ton) and generated an average NPV of 19.85 Mio.. We changed the
threshold to the minimum demand amount and yielded 28.01 Mio.. We tried some other
demand numbers and came up with the following result:
We can conclude from the table above that the investment generates positive NPV
with any demand amount between 200 ton and 350 ton with the maximum NPV of
28.01 Mio. (appearing at 200 ton). If the demand is lower than 200 ton, it yields the
same average NPV as 200 ton. Therefore we suggest the management to acquire the
technology even if the demand is low.
Question 10
In order to increase the set of opportunities for ChinaCarb, there are some relevant
alternatives which can support the company to continue operating in the market and
reduce the company’s exposure to the risk of cash out. The first option is that
ChinaCarb can participate in a business arrangement with the Japanese competitors
to pool the resources and share profits as well as possible losses. This joint venture will
help ChinaCarb to have enough resources to stay in its own market in the next ten years
and generate plans for new products after the pitch-based carbon fibers are replaced.
According to the context, it is essential that ChinaCarb prepares for its operations when
new materials are introduced into the market. Therefore, the second option for the
company initializes from creating a R&D team which will be responsible for looking for
substitutes for the current raw materials which is pitch. The process of developing
new products based on new materials requires time and effort but it will ensure the
operations and even the profitability of ChinaCarb after ten years. Moreover, in order to
continue to utilize the available pitch-specific design and production technology,
Demand
(Ton)
150 200 250 300 340
Average
NPV
(Mio.RMB)
28.01 28.01 19.85 5.78 0.30
17. 15
ChinaCarb can use the pitch-based carbon fiber to produce finished products instead
of just selling carbon fiber directly in the market. With the strong position in the
original market, the company will be able to introduce a new range of products into the
current market in a short-time. Another option is based on the characteristics of pitch-
based carbon fiber which is environmentally friendly and high-tech. By launching a
marketing campaign to emphasize the unique characteristics of the products, the
company will draw the attentions of private investors and governmental parties to the
current situation and possibly receive more money through investments. With this new
finance resource, the company will manage to earn back the money spent on the
investment of RMB 6.8 million and have the incentive to invest into new projects.
18. 16
Appendix
1. Fitzer, E.; Edie, D.D.; Johnson, D.J. Carbon fibers-present state and future
expectation; Pitch and mesophase fibers; Structure and properties of carbon fibers. In
Carbon Fibers Filaments and Composites, 1st ed.; Figueiredo, J.L., Bernardo, C.A.,
Baker, R.T.K., Huttinger, K.J., Eds.; Springer: New York, NY, USA, 1989; pp. 3–41,
43–72, 119–146.
2. Huang, X., Fabrication and Properties of Carbon Fibers, Materials, 2009.
