Section 4 Case Study
4.1 Price Competition Industry
Although much evidence shows that the laptop OEM/ODM industry is a price competition industry, the competitive type of the industry still needs to be proved by numbers. Bulow, Geanakoplos, and Klemperer (1985) and Sundaram, John, and John (1996) indicated that the variable of Competitive Strategic Measure (CSM) is a direct proxy of the second derivative of profit with respect to its own quantity and the competitor’s quantity. By computing the coefficient of correlation between the change in a firm’s profit margin (Δ
π
f /Δ ) against the change in its competitor’s outputS
f ( ), the market competitive type can be found. If CSM is greater than zero, the market is defined as strategic complements (a price competition market); otherwise, the market is defined as strategic substitutes (a quantity competition market).S
cΔ
In the laptop OEM/ODM industry of Taiwan, the coefficient of correlation between the profit margin of Quanta and the output of Others is 0.1033, so the market is regarded as a price competition market. However, because of the highly seasonal variation of the revenue in this industry, we use the approach of seasonal differential to eliminate the strong seasonal variation.
4.2 Case Study
4.2.1 Assumptions
Firstly, based on the estimation of MIC, Quanta uses the CMOS technology of PixArt Imaging Inc.4, so the invested capital for touch panel laptops in this study includes the R&D expenses of Quanta and PixArt. TABLE 4.1 shows the R&D expenses of Quanta and PixArt for the touch panel laptop project in 2007 and 2008, and this study assumes that 50 percent of the total R&D expenses are used in inventing touch panel laptops.
(TABLE 4.1 is about here)
Secondly, this study assumes that the first mover (the company which invests in the project first) can earn 5 percent additional quantity when the market moves up and earn 3 percent additional quantity when the market moves down.
4.2.2 Estimation of Parameters
Equation (4.1) supposes that the demand for the touch panel laptops is linear in prices5:
( , , )
i i j it it i j
Q P P θ =θ −bP + dP
, = Quanta or Others (4.1) i
where the quantity which is sold by company is related to its price and the competitor’s price . By putting the historical data ofi P
iP
j Pi, Pj, and Qi (where
4 PixArt Imaging Inc., one of the leading companies of CMOS imaging sensors and related IC design, research, production, and sales.
i = Quanta and j = Others or = Others and i j = Quanta) into regression model, the
coefficients and d can be estimated. These two estimated coefficients and are 599.5746 and 572.3002. The time period of data starts in the third quarter of 2003 and ends in the fourth quarter of 2008. Equation (4.1) becomes:
b b
d
Q P Pi( i, j,θit)=θit −599.5746Pi+572.3002Pj
, = Quanta or Others (4.2) i
After that, Pi, Pj, and Qi are put into the equation (4.2), a series ofθ
i t,(where = Quanta or Others) can be gained. The market demand for touch panel laptops in 2008 is 82,573,618 when equals Quanta; the market demand for touch panel laptops in 2008 is 107,666,161 when
i equals Others. Besides, the annual
volatility of the growth rate of the laptop market demand (i
i
σ ) is 0.4465.
According to this statistic, the up moves (u) and down moves (d) are:
exp( ) exp(0.4465 1) 1.5628
u
=σ T
= × = , and4.2.3 Cash Flows of the Last Period
Equation (4.3) describes the cash flow of the last period under different outcomes, including Cournot Nash price competition equilibrium outcome, monopolist outcome, Stackelberg price leader/follower outcome, and abandon.
Cash flow of the project ( * ) e stim a te d
i i i
P c Q I
= − × − (4.3)
where Pi* is the competition price of different outcomes, is the variable cost, is the estimated quantity of the touch panel laptops, and is the invested capital for the project. In this project,
ci
e stim a te d
Qi I
I
equals NT$ 6,239(million). The average operating costs of Quanta and Others are NT$41,290 and NT$44,091 respectively.TABLE 4.2 illustrates the estimated quantity of touch panel laptops in the last period (2011) under different nature moves.
(TABLE 4.2 is about here)
4.2.4 Backward Induction
If Quanta decides to invest in the project at the beginning (2008), the sequential game will be formed.
(FIGURE 4.1 is about here)
FIGURE 4.1 illustrates the cash flow of the last period if the market moves up three times in the past three years. Since Quanta invested in the project, Others has to
decide whether it should invest in the last period (2011). If Others chooses to invest, Quanta will become the Stackelberg leader and Others will become the Stackelberg follower. The cash flow of Quanta is NT$ 19,969,659(million), and the cash flow of Others is NT$ 25,350,106(million). If Others decides not to invest, then Quanta will become the monopolist. The cash flow of Quanta is NT$ 154,182,726(million), and the cash flow of Others is NT$ 0. After that, the option value can be obtained through the backward induction. On the other hand, a similar result can be obtained when the market moves down (d).
0.412 19,969,659,434,487 +(1-0.412) 2,515,880,963,735
9,514,334,503,328 (1 0.02)
× ×
+ =
If Quanta decides to defer in the project at the beginning (2008), then the simultaneous game will be formed. There exists two equilibrium of the simultaneous
game, one is pure strategy equilibrium, and the other is mixed strategy equilibrium.
(FIGURE 4.2 is about here)
FIGURE 4.2 shows the simultaneous game with the extensive and normal form in 2011 when the market moves up three times in the past three years. There exists pure strategy equilibrium in this situation. If Quanta chooses invest in the project, Others will decide to invest in it. However, if Quanta choose not to invest in the project, Others will still decide to invest in the project, because Others will gain more profits. Namely, no matter if Quanta invests in the project, investing in the project is
the optimal decision for Others. Under this decision from Others, Quanta will decide to invest in it finally since Quanta can earn more cash flow through investing in the multi-touch panel laptop project.
The other equilibrium is mixed strategy equilibrium. The derivation process is showed in the Appendix 2.
According to the ultimate value, which is computed through the options game methodology, the result shows that investing in the multi-touch panel laptop project is optimal decision for Quanta, and the option value is NT$ 2,082,601(million). FIGURE
4.3 illustrate the route of the decision tree for the project. FIGURE 4.4 and FIGURE 4.5 show the decision route if the market moves up and down respectively.
(FIGURE 4.3 is about here) (FIGURE 4.4 is about here) (FIGURE 4.5 is about here)