Wednesday, July 4, 2012

Application of Pascal’s Triangular plus Monte Carlo Analysis to Find the Least Squares Fitting for a Limited Area: The Case of Constant – Growth (Gordon) Model


Following to article of “Application of Pascal’s Triangular plus Monte Carlo Analysis to Find the Least Squares Fitting for a Limited Area” on link: http://emfps.blogspot.com/2012/05/application-of-pascals-triangular-plus_23.html, some professional people asked me about the application of the Least Squares Fitting for a Limited Area. In this article, I am willing to bring a simple example which is the case of constant – growth model.

The Case of Constant – Growth (Gordon) Model

As an example, I would like to refer you to my article of “Case Analysis of GAINESBORO MACHINE TOOLS CORPORATION (CON): A New Financial Simulation Model” on link: http://emfps.blogspot.com/2012/04/case-analysis-of-gainesboro-machine.html. The case issue is: How can we cope with the Constant- Growth Model as our dividend policy and our decision making?
Lawrence J. Gitman (2009) in his book of “Principles of Managerial Finance (Twelfth edition)” stated:
“The most widely cited dividend valuation approach, the constant – growth model, assumes that dividends will grow at a constant rate, but a rate that is less than the required return.”
If we simplify the equation of the constant – growth model, we will have below formula:
P0 = D1 / (rs – g)
Where:
P0 = value of common stock
D1 = the most recent dividend per – share
rs = required return on common stock ( In this case, I consider it as the Cost of Capital (WACC) for GAINESBORO MACHINE TOOLS CORPORATION)
g = the constant – growth rate
If we multiply all outstanding shares to above equation, the formula shows us the enterprise value of Gainesboro.
We can re-write above formula as follows:
WACC = (D1/ EV) + g
Where:
WACC = Gainesboro’s Cost of Capital
D1 = total dividend projected in 2005
EV = enterprise value in accordance with financial model mentioned on link: http://emfps.blogspot.com/2012/04/case-analysis-of-gainesboro-machine.html
In the reference with the article of “Application of Pascal’s Triangular plus Monte Carlo Analysis to Find the Least Squares Fitting for a Limited Area” on link: http://emfps.blogspot.com/2012/05/application-of-pascals-triangular-plus_23.html, we can define the area as follows:
WACC = y
 D1/ EV = b
g = x
m = 1
Then we have:
y = x + b
Referring to the article of “Case Analysis of GAINESBORO MACHINE TOOLS CORPORATION (CON): A New Financial Simulation Model” posted on link: http://emfps.blogspot.com/2012/04/case-analysis-of-gainesboro-machine.html, I obtained the range for “WACC” and “g” as follows:
4% <= WACC <= 11%
And
0 <= g <= 3%
It means that, our definition for area is:
0.04 <= y <= 0.11
0 <= x <=3
Now, I try to calculate “b” as the Least Squares Fitting for a Limited Area by using the application of Pascal’s Triangular and Monte Carlo Simulation (referred to link: http://emfps.blogspot.com/2012/05/application-of-pascals-triangular-plus_23.html) below cited:



As we can see:
D1/ EV = 0.06
Since the range of “g” is between 0 and 3%, WACC should be always equal or more than 6% and equal or less than 9%. Therefore we have:
WACC = g + 0.06, If and only if 6% < = WACC < = 9%
In this case, I have made four scenarios which will cover all results.
Now, I am ready to use from Financial Model posted on link: http://emfps.blogspot.com/2012/04/case-analysis-of-gainesboro-machine.html :
How can we work with this financial model for this example?
1) I added the item D1/ EV on my spreadsheet (financial model)
2) I used from sensitivity analysis for D1 as independent variable and  D1/ EV as dependent variable and I obtained D1 for each scenario for D1/ EV = 0.06
3) I added D1 for 2005 year as dividend payout and formula = D1 * (1+g) for 2006 to 2011.
The final results of each scenario are as follows:

Scenario (1)
WACC = 6%
g = 0%




Scenario (2)

WACC = 7%
g = 1%























Scenario (3)

WACC = 8%
g = 2%



Scenario (4)

WACC = 9%
g = 3%




As we can see, the range of changes for D1 and current share price (P0) in the all scenarios are negligible.

Conclusion

The final answer to the issue of this case is that the Constant – Growth (Gordon) Model as a dividend policy and decision making for Gainesboro should be completely rejected, if the range of “WACC” is between 4% to11percent and so the range of “g” is between 0 to3percent. Because by using of Constant – Growth (Gordon) Model, expected share price will go down under current share price that the average is equal to $29.15 for 2004 year.

Let me start another case as the new example as follows:

The Case of Terminal Value

One of the most crucial problems to use the discounted cash flow analysis is to find the appropriate the Terminal Value because this methodology is very sensitive to the Terminal Value Growth Rate and the firm’s Cost of Capital. The formula for terminal value is as follows:
Terminal value = [FCFn * (1+g)] / (WACC – g)


Note:  “All spreadsheets and calculation notes are available. The people, who are interested in having my spreadsheets of this method as a template for further practice, do not hesitate to ask me by sending an email to: soleimani_gh@hotmail.com or call me on my cellphone: +989109250225. Please be informed these spreadsheets are not free of charge.”

To be continued……..