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The Black Scholes and binomial pricing models were originally developed for valuing traded options with relatively short lives and are based on complex mathematical formulas Option values derived under these models are sensitive to both the expected stock volatility and the expected dividend yield Exhibit 398 illustrates the relative effect of changes in expected volatility and dividend rates using a generalized Black-Scholes option-pricing model Software packages that include option pricing models are readily available from numerous software vendors As demonstrated in Exhibit 398, option values increase as expected volatility increases, and option values decrease as expected dividend yield increases It is interesting to note that in instances where higher expected volatility is coupled with higher dividend yields, the binomial model generally produces higher option values than the Black-Scholes model due primarily to increased sensitivity to compounded dividend yields in the binomial model Nevertheless, FASB Statement No 123 permits the use of either model (i) Expected Volatility Volatility is the measure of the amount that a stock s price has uctuated (historical volatility) or is expected to uctuate (expected volatility) during a speci ed period Volatility is expressed as a percentage; a stock with a volatility of 25 percent would be expected to have its annual rate of return fall within a range of plus or minus 25 percentage points of its expected rate about two-thirds of the time For example, if a stock currently trades at $100 with a volatility of 25 percent and an expected rate of return of 12 percent, after one year the stock price should fall within the range of $87 to $137 approximately two-thirds of the time (using simple interest for illustration) Stocks with high volatility provide option holders with greater economic up-side potential and, accordingly, result in higher option values under the Black Scholes and binomial option pricing models FASB Statement No 123 suggests that estimating expected future volatility should begin with calculating historical volatility over the most recent period equal to the expected life of the options Thus, if the weighted-average expected life of the options is six years, historical volatility should be calculated for the six years immediately preceding the option grant FASB Statement No 123 provides an illustrative example for calculating historical volatility Companies should modify historical stock volatility to the extent that recent experience indicates that the future is reasonably expected to differ from the past Although historical averages may be the best available indicator of expected future volatility for some mature companies, there are legitimate exceptions including: (1) a company whose common stock has only recently become publicly traded with little, if any, historical data on its stock price volatility, (2) a company with only a few years of public trading history where recent experience indicates that the stock has generally become less volatile, and (3) a company that sells off a line of business with signi cantly different volatility than the remaining line of business In such cases, it is appropriate for companies to adjust historical volatility for current circumstances or use the average volatilities of similar companies until a longer series of historical data is available FASB Statement No 123 does not allow for a company with publicly traded stock to ignore volatility simply because its stock has little or no trading history A company with only publicly traded debt is not considered a public company under FASB Statement No 123 Subsidiaries of public companies are considered public companies for purposes of applying FASB Statement No 123 s provisions (ii) Expected Dividends The assumption about expected dividends should be based on publicly available information While standard option pricing models generally call for expected dividend yield, the model may be modi ed to use an expected dividend amount rather than a yield If a company uses expected payments, any history of regular increases in dividends should be considered For example, if a company s policy has been to increase dividends by approximately three percent per year, its estimated option value should not assume a xed dividend amount throughout the expected life of the option Some companies ith no history of paying dividends might reasonably expect to begin paying small dividends during the expected lives of their employee stock options These companies may use an average of their past dividend yield (zero) and the mean dividend yield of an appropriately comparable peer group. vb.net pdf page count PDF File Pagecount - VB.NET | Dream.In.Code PDF File Pagecount: PDF Files. ... 09, Public Class PageCount. 10, 'function for getting the total number of pages in a PDF file. 11. 12, Public ... vb.net get pdf page count Count number of pages in a PDF file - Visual Basic , VB.NET Sep 9, 2017 · Find Code: All Words, Any of the Words ... 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