Accounting For Value: A Quantitative Securities Research, Inc. Presentation for Residual Earnings Method of Stock Valuation:

This page illustrates how a HUGIN model in combination with the HUGIN Web Service API can facilitate Accounting For Value[Penman, 2011] based on the Residual Earnings Method for stock valuation. Our example is from Accounting for Value, page 67, Cisco Systems, Inc: (NasdaqGS: CSCO) fiscal year end July 31, but updated for July 31, 2012. Model inputs are 2013 and 2014 Wall Street forecasts for earnings per share (EPS), 2012 Book Value Per Share (BPS), assumed cost of equity capital r1 and g is the growth rate of residual earnings implied by Cisco's stock price of $15.95 on July 31, 2012. Given the implied g for any stock price, that stock price will increase annually by the required rate of return r as demonstrated in the CSCO seven year forecast of fair value price per share.

Residual Earnings Method variable inputs may be changed for the investor to explore the effect on g embedded in any stock price and speculative growth. Fair value price per share is the calculated per share value at the end of each fiscal year given the variable model inputs of r, g, and EPS. The calculation of fair value price per share may be simulated in a Bayesian network using Monte Carlo simulation to show probable outcomes of buying CSCO at any price per share given the model inputs. The Monte Carlo simulation also ranks CSCO Buy, Hold, or Sell.

The Cisco example is a proof of concept, but this model can be used to analyze any stock if the investor inputs the current market price per share and the specified r and EPS inputs for that stock. The investor has to decide if positive g building blocks showing positive speculative growth indicate the stock is overpriced or if negative g building blocks showing negative speculative growth indicate the stock is underpriced. If the investor inputs the stock price for g equals zero (Book Value + Value from short-term accounting building blocks) that sometimes helps decide the answer. The commercial product will be driven by the input of the stock symbol for any global stock, automatically update daily, and have the capacity to rank stocks by g or other variables.

VariableValue (constant)
Enter Current Market Price
Enter BPS_12A
VariableValue (Variable)
Enter r
Enter EPS_13E
Enter EPS_14E

Press the button below to update the remaining parts of the page

Determining Speculative Growth g

Growth (g)

Building Blocks That Identify the Market's Valuation of Speculative Growth

Building Block Value per share Relative Block Size
Current Market Price ($)
Value from long-term growth (g) ($)
Value from short-term accounting for EPS ($)
Book Value ($)


Fair Value Price Per Share (PPS) Growth in EPS

Price Per Share (PPS)Growth in EPS
Fair Value PPS 2012A
Fair Value PPS 2013E
Fair Value PPS 2014E
Fair Value PPS 2015F
Fair Value PPS 2016F
Fair Value PPS 2017F
Fair Value PPS 2018F
Fair Value PPS 2019F

Accounting For Uncertainty In Accounting For Value

This part of the web site illustrates how it is possible to account for uncertainty in Accounting For Value using a Bayesian network in combination with Monte Carlo simulation (using 10000 samples).

The Monte Carlo simulation is performed assuming a Normal distribution for each input parameter; i.e., g, r, EPS_13E and EPS_14E. For each input parameter the mean value is set equal to the value entered above while the variance can be changed below. A default value for the variance is specified.

The variance represents the uncertainty in each input parameter. The default values for the variances are determined as a percentage deviation from the (initial) mean values defined above (i.e., the initial values for g, r, EPS_13E and EPS_14E). For g and r the default variance is calculated as ten per cent of the mean squared while for EPS_13E and EPS_14E the default variance is calculated as five per cent of the mean squared.

Variable nameMean (from above)Variance

Select output variable (i.e., variable to simulate)

The simulation model contains all seven years (i.e., 2013 to 2019) and in each iteration it computes the Fair Value PPS for each year based on a simulation of the input parameters. The button below is used to specify the year to monitor for Fair Value PPS simulation.

Monte Carlo simulation of 10,000 stock prices based on inputs.

Maximum Price (+2 STD)
Sell Threshold (+1 STD)
Mean: Target Price
Buy Threshold (-1 STD)
Minimum Price (-2 STD)
Standard Deviation (STD)
Action Today
Market Price

The frequency distribution over the selected output value will be shown above. Each of the samples generated by the simulation will produce a value of the selected output variable. The frequency distribution is constructed by defining 20 bins for selected output variable. The bins are determined based on the lowest and highest values produced. The range from the lowest to the highest value is divided into 20 bins (i.e., intervals) of equal size. The values computed for the output variable are mapped to the bins producing the frequency distribution.

The frequency distribution can be used to assess the probability (according to the simulation model and input values) of getting a value of the output variable in one of the intervals defined by the bins. The frequency count in each bin reflects the probability of achieving a value of the output value in the corresponding interval.

Accounting For Uncertainty Using Bayesian Networks and Simulation

Using a Bayesian network it is possible to model different types of distributions and correlations between input parameters of the Accounting For Value model. Here we assume for simplicity that BPS_12A is known whereas the r, g, EPS_13E and EPS_14E are assumed to follow a normal distribution (with mean and variance as defined by the values specified above).

The figure below shows how a HUGIN model encodes the valuation (for seven years).

In each step of the simulation process, the Bayesian network model is used to generate a set of values for the input parameters of the valuation model. This set of values for the input parameters is a scenario. The valuation model is applied to this scenario producing one value of the selected output variable. The set of values obtained by evaluating the valuation model on each scenario is the distribution over the output variable shown in the table.

The Bayesian network model only simulates the input parameters of the valuation model.


[Penman, 2011] Accounting For Value, Stephen H. Penman, Columbia University Press, 2011.  Stephen H. Penman is the George O. May Professor of Accounting at Columbia University Graduate School of Business. Stephen H. Penman's Curriculum Vitae may be downloaded here. Accounting For Value in hard cover and (eBook) may be ordered at: Amazon.


[1] Dividends are not included as a model input because value is not affected by dividend payout policy, Accounting For Value[Penman, 2011], page 18.