Global Value Investing

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A multifaceted approach to value investing with stock valuation based on intrinsic value estimated from cash returns, appraised value of assets, and other facets of value.

 

 

Example Stock Valuation

 

General DCF Model   |   Spreadsheet   |   Graphs   |   Questions


General DCF Model

The following example is designed to display the elements of the calculation of the net present value per share (absolute safety margin) and its percentage of the purchase price basis (relative safety margin) for a company with publicly-traded common stock. The DCF Valuator include examples of the estimation of economic intrinsic value and internal rate of return. These valuation models, unlike pricing models, calculate absolute value -- not comparative price relative to another company or group or index. A hypothetical company is chosen to avoid limiting the stock selection to one particular circle of competence.

The General Discounted Cash Flow (DCF) model is appropriate for this case. It is the most broadly applicable model and thus requires the most input data. The most general DCF model allows any number of input line items, any desired input line items, any number of input periods, and any unique values of each input line item in each input period. This will work for negative cash flows and for irregular cash flows that can't be well approximated by a growth pattern. Usually, annual total dividend distributions are estimated for at least five years. If a company is not expected to pay regular dividends, then annual free cash flow to equity would be estimated. For the sake of convenience only, the stock price basis is here assumed to double in five years.

The U.S. federal income tax rate is assumed at the highest marginal rate on ordinary income, in this case portfolio income from dividends. In addition, the investment is assumed to be held for longer than 18 months, and thus the capital gains and losses are classified as long-term for income tax purposes. Generous U.S. trading and other costs are included for the sake of completeness. These assumptions can be modified for other tax and trading regimes.

In addition to using a general DCF model, the example uses a static or deterministic as opposed to a dynamic or stochastic (probabilistic) analysis. The estimate of value per share is a single point estimate rather than a more comprehensive interval estimate of a range of values based on a probability distribution provided by the estimator. The point value in the range of values that is the best single estimate of value is the mean value. In the spreadsheet, pa means per annum, and n/a means "not applicable". Graphs of the more important items in the calculation are presented below. Other abbreviations in the spreadsheet and graphs are explained in the questions.


Spreadsheet

(please wait while the table loads ...)

General DCF model for a company with stock basis expected to double in 5 years.

Estimate of deterministic single value as opposed to probabilistic range of values.

 

Value per Share

$65.83

             
NPV per Share $15.83 24%            

Company

ATOZ

             

Stock Issue

Common

             

Market

NYSE

             

Currency Unit

US $

             

Share Price: Buy

$49.00

             

Share Price: Sell

$101.00

             

Number of Shares

100

             

Date:

10.15.97

             

Year

1997

1998

1999

2000

2001

2002

Total

Percent

End of Year

0

1

2

3

4

5

   

Discount Rate

7.25%

7.25%

7.25%

7.25%

7.25%

7.25%

   

Discount Factor

1.00000

0.93240

0.86937

0.81060

0.75581

0.70471

   

Income Tax:

               

Dividends

39.6%

             

L.T. Cap.Gains

20.0%

             
 

Capital Account:

               

Investment-Price

4,900

n/a

n/a

n/a

n/a

10,100

   
Trade Cost 100 n/a n/a n/a n/a 100    

Investment-Basis

5,000

n/a

n/a

n/a

n/a

10,000

5,000

 

Income Account:

               

Other Costs

50

n/a

n/a

n/a

n/a

50

100

 

Dividends/Share

n/a

1.00

1.10

1.20

1.30

1.40

6.00

 

Total Dividends

n/a

100.00

110.00

120.00

130.00

140.00

600.00

 
 

Cash Flow:

               

NCF-BFIT:

-5,050

100

110

120

130

10,090

5,500

100%

Capital

-5,000

n/a

n/a

n/a

n/a

10,000

5,000

91%

Income

-50

100

110

120

130

90

500

9%

Income Taxes

-20

40

44

48

51

1,036

1,198

 

NCF-AFIT:

-5,030

60

66

72

79

9,054

4,302

100%

Capital

-5,000

n/a

n/a

n/a

n/a

9,000

4,000

93%

Income

-30

60

66

72

79

54

302

7%

 

Present Value:

               

NPV-BFIT:

-5,050

93

96

97

98

7,111

2,445

100%

Capital

-5,000

n/a

n/a

n/a

n/a

7,047

2,047

84%

Income

-50

93

96

97

98

63

398

16%

Income Taxes

-20

37

38

39

39

730

862

 

NPV-AFIT:

-5,030

56

58

59

59

6,381

1,583

100%

Capital

-5,000

n/a

n/a

n/a

n/a

6,342

1,342

85%

Income

-30

56

58

59

59

38

240

15%

 

Div. Growth:

               

End of Year

0

1

2

3

4

5

   

Dividends/Share

0.90

1.00

1.10

1.20

1.30

1.40

   

Average Rate

n/a

11.11%

10.00%

9.09%

8.33%

7.69%

9.25%

 

Compound Rate

n/a

n/a

n/a

n/a

n/a

n/a

9.24%

 

Regression Trend

n/a

n/a

n/a

n/a

n/a

n/a

-0.85%

 
 

Note 1: Compound Rate increases the Year 1 dividend to the Year 5 dividend.

Note 2: Regression Trend is the best linear fit of the Average Rate series.

 

End of Year

0

1

2

3

4

5

   

NCF-AFIT

-5,030

60

66

72

79

9,054

   

NPV-AFIT

-5,030

56

58

59

59

6,381

   

 

Graphs

. . .

 

Questions for Thought

1. What proportion of the total net cash flows (NCF) is attributable to estimated dividends (DIV) and what proportion is attributable to estimated capital gains/losses (CG)? What are the two extremes of the range of proportions? Are dividends more certain or less certain than future selling price? Why is this important?

2. What proportion of the total net present value after federal income tax (NPV-AFIT) is attributable to estimated dividends (DIV) and what proportion is attributable to estimated capital gains/losses (CG)? How are these proportions different from the NCF-AFIT proportions? Why is this important?

3. In light of the answers to the above questions, how important is the assumed pattern or growth rate of total annual dividend distributions (total dollars per share and total dollars per year) over the years of the appraisal? Why is the dividend pattern or growth rate important?

4. The interest rate of 7.25 percentage per annum each year in this example is intended to be the estimated yield on U.S. Treasury bonds of 30-year term. This is assumed to be the particular investor's economic opportunity cost of capital for the particular investor's time horizon for this particular investment opportunity at this particular time. Given the same estimates of future economic conditions, under what circumstances might this investor use a different discount rate to appraise the pure, true, intrinsic economic value of this company?

5. How would a probability distribution for a range of estimated values be superior to a single point estimate of value that implicitly assumes one hundred percent probability? How would this impact the single point estimate of the margin of safety or investment value minus buy price?

6. How would a sensitivity analysis of either the estimated single point value or the mean value of the distribution improve the appraisal of intrinsic economic value? Which assumptions, factors, or variables in the appraisal would benefit most from a sensitivity analysis? Note: The input factors that are required for appraising the intrinsic economic value of a company relate and interact with each other in a complex dynamic process. They should not be varied over a large range independently of each other.

7.
Would a sensitivity analysis be best performed by calculating in terms of absolute factor-specific units (e.g. U.S. Dollars), relative unit independence (e.g. percentage), or relative standardized unit independence (e.g. standard deviation)?

8. When would it be more appropriate to calculate rate of return and intrinsic value using opportunity cost and other factors under the following conditions:

  • after instead of before adjustments for price-level inflation?

  • after instead of before personal income taxes?


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