# Investigating Two Aspects Of Equity Issues

SEO Initial public offering (IPO) underpricing, is a phenomenon common to stock markets in both developed and economies on the rise. An initial public offering is when a company first issues shares to the public. They are regarded as underpriced when the percentage difference between the first day closing bid price is lower than the initial offer price. When the same company issues shares after the initial public offering, the issue is called a Seasonal Equity Offering (SEO). Unlike IPOs, SEOs do not appear to be underpriced.

A common discernment is that underpricing of IPOs is a contradiction to market efficiency and creates problems for firms trying to raise finance for expansion. In order to raise finance, via an IPO or SEO issue, firms must first be valued. Firms are valued in order to set a price for their new share issue that will reflect the market’s expectation of the firm’s future profitability. Thus an equity underpricing puzzle arises from IPO firms being valued differently from SEO firms.

In an effort to solve the equity underpricing puzzle, this paper focuses firstly on determining how stock markets value firms and secondly examining if Initial public offerings really are underpriced relative to Seasonal equity offerings.

Numerous theories of IPO underpricing have been tested against data of a range of stock markets. Prior research undertaken on underpricing by Gary Koop (2001) and J Hunt-McCool et al (1996) uses a stochastic frontier model. Our research applies an alternative approach to test this hypothesis. We employ an ordinary least squares (OLS) multivariate regression model which efficiently uses the data available to us to obtain reliable results from our small sample. Like Koop we include information on SEOs in order to answer the question “Are IPOs undervalued relative to SEOs”. Most previous research tends to focus solely on IPOs and thus is limited to only answering the question “Are IPOs underpriced”.

Using a sample of 83 IPO and 226 SEO U.S. firms during 1996, we find that stock markets value a firm depending on their level of sales, debt and issue type. We also confirm Koop’s findings that IPOs are underpriced relative to SEOs.

Confirming the accuracy of previous results and partially determining how stock markets value firm’s advances prior literature. However, there are further unknown explanatory variables for firm value that this paper does not establish. Additional research should be conducted to fully determine how stock markets values firms. Fully answering this could be the key to solving this equity underpricing puzzle.

The rest of the paper is organised as follows: section two looks at the review of literature; section three is dedicated to data analysis and explains the methodology used to interpret the data, section four highlights the results obtained from regressions ran; whilst section five draws conclusions on results obtained, and looks at possible areas to advance the research. Finally, the reference section outlines papers which we reviewed throughout our study.

## Literature Review

Valuation of equity involves estimating the worth of a firm from historical data and is a necessary action in determining the price of a new share issue. It is unknown how stock markets, traders of company stock, value issuing firms. There are many methods of firm valuation but they all have the same aim, to reflect the “firm’s expected future profitability” Koop (2001). The variation in these methods is caused by the use of alternative historical data variables to proxy for future profitability.

Debt is one variable that is believed to affect the value of a firm and thus is used in valuation methods. Lina and Chang (2009) find that “debt…prompts managers to find the optimal capital structure’ that maximizes firm value”. Koop (2001) also notes the impact of debt on valuation and believes the “market value of a firm is negatively associated with its debt level”

Ritter (1984) finds that accounting information has a positive relationship with firm value and may therefore be used in valuation methods. Other methods of valuation involve the calculation of future cash flows, supporting evidence from Teoh et al. (1998a).

Koop (2001) finds that most valuation methods however commonly use “measures of profitability, level of operations and risk and underwriter fees to value equities”.

Determining the method of valuation employed by stock markets, however, is the key to solving the equity underpricing puzzle. This puzzle has arisen because stock markets value IPO firms differently from SEO firms. That is, IPOs are claimed to be undervalued and therefore underpriced relative to SEOs.

It is known that “IPOs are underpriced in virtually all countries” (Ljungqvist, 2004). Koop (2001) documents evidence of IPO underpricing and SEO efficient pricing when examining “2969 IPO and 3771 SEO” firms over a 13 year period. His paper is very similar to our own in that he additionally compares IPOs relative to SEOs. Koop (2001) however uses a stochastic frontier model in his research. A stochastic frontier model has the benefit that it can “measure the extent of underpricing without using aftermarket information” (Koop 2001). Hunt McCool et al (1996) also use a stochastic frontier model in their research, which also finds evidence of underpricing. Though, like the majority of research papers, McCool et al (1996) is limited to observing IPOs only and are unable to examine IPOs relative to SEOs.

McCool et al (1996) find that IPO underpricing happens deliberately. There are numerous possible explanations for this. One main theory is that asymmetric information exists between the issuer (investment banker) and investors. Baron (1982) finds that the “investment banker is better informed about the capital market than is the issuer” and thus they underprice to compensate for using their expertise and reputation. Welch (1989) discovers that underpricing IPOs leads to a higher SEO price because of this asymmetry of information. He finds that underpricing is a way for which “High-quality firm owners can signal their superior information to investors”. This gives rise to the signalling theory that firms use IPO underpricing as a signalling tool. Benveniste-Spindt (1989) additionally emphasise that IPO underpricing is necessary if underwriters are to derive relevant pricing information in order maximize issuer’s gains.

Ruud (1993) however challenges this theory that IPO underpricing occurs deliberately. He finds that “underwriter price support” can account for this underpricing. That is, he believes it is the inefficiencies experienced in the aftermarket caused by underwriter price support which leads to IPOs prices deviating from their intrinsic values. Hughes (1986) finds that firms that suffer most from the asymmetric information problem have higher underwriter compensation.

Speculative bubbles are another inefficiency to be experienced in the aftermarket. That is “Prices of IPOs have shown a striking tendency to jump up dramatically as soon as the after-market trading begins” (Shiller, 1990). Shiller’s theory for these speculative bubbles or fads is that underpricing IPOs generates high initial returns which gives investors the impression that the “stockbroker or underwriter is giving good investment advice”. That is, underwriters underprice IPOs in order to produce high initial returns that will “generate publicity and good will for the IPO's” Shiller (1990).

Though there are many theories as to why underpricing of IPOs occurs, not all research conducted actually agrees that IPOs are underpriced. Purnanandam and Swaminathan (2004) find that IPOs are actually “overvalued at the offer and price” and “tend to run up in the aftermarket” in the period between 1980 and 1997. These results discredit the theory of asymmetric information in IPO pricing as it expects that the IPOs with the largest first day return would be those that are most overvalued. Purnanandam and Swaminathan’s (2004) results are consistent with that of Daniel, Hirshleifer and Subrahmanyam (1998) who finds that “investors will overreact to private information signals and under react to public information signals” which leads to initial overvaluation. Purnanandam and Swaminathan (2004) find that overvalued IPOs are less profitable than undervalued IPOs because investors are “deceived by optimistic growth forecasts”.

## Data analysis

The initial sample includes data on 309 firms who sold new shares in 1996 in the USA. Of the sample 226 of the share issues are SEOs and the remaining 83 are IPOs. The data on the new share issues was provided by Mr Barry Quinn lecturer of Time Series Financial Econometrics. For inclusion in our final sample we have used the data provided by Quinn to generate financial ratios in order to further analyse the data given. A summary of the data can be seen in Table 1 (appendix). Included within Table 1 are the summary statistics for each variable, as well as their meaning and relevance to our study. All variables except SEOs are measured annually in millions of US dollars.

The summary statistics shows a very high figure of 38396.6 million US dollars as the maximum Value of a share issue. This lies more than 16 standard deviations away from the mean. For this reason we have included a stem plot of the Value variable in Table 2 (appendix), which shows the data has one major outlier.

This major outlier is one limitation of the data as it will skew the results and will lead us to question their validity. Another limitation of the data provided is that as it is based on unidentified firms we are unable to obtain additional relevant data. Increasing our sample size and making our data set evenly spread across IPOs and SEOs would make our results more reliable. As there is always an IPO issue before an SEO issue, it would be helpful to have the value of this IPO for easy comparison between each valuation and this would also increase the accuracy of our results. The inability to distinguish whether the value of intangible assets has been included in the firms issue also creates a limitation. Dimovski and Brooks (2006) note that intangible assets are a large contributor to IPO undervaluing. Share prices are very reactive to major events such as corporate scandals, natural disasters etc. In order to account for share price volatility this study should look at more than one time period, so results are not misleading.

## 3.1 Methodology

From the data outlined we wish to determine how stock markets value firms and if IPOs are undervalued relative to SEOs.

To answer these questions we will use an ordinary least square multivariate regression consisting of dummy (D) variables and our significant non-dummy (X) explanatory variables. The method of Ordinary Least Squares (OLS) is accredited to the German Mathematician Carl Friedrich Gauss. It is a method which estimates the unknown parameters in a linear regression model by minimising the sum of squared residuals. Its estimators can be shown to have desirable properties that are consistent, unbiased and efficient.

Market value will therefore be our dependent variable. Our explanatory variables can be outlined as debt, total assets, income and sales. In addition, we will manipulate the data we have been given in order to create ratios. The three ratios which we will use are: Return on Assets, Debt Ratio and Sales to Assets Ratio. These ratios will therefore become additional explanatory variables which we can use to determine the best model for valuing SEOs and IPOs. Firm’s shares should reflect investor’s expectations about the firm’s future profitability. As data on expected future profitability is non-existent we will use our explanatory variables outlined instead.

We will then use the Wald test (~F[m, T-k]) , to test the significance of each of our explanatory variables. The Wald test is preferable because it is sensitive to the sample size. If the Wald test does not prove significant for any explanatory variable, i.e. their p value is not significant; we will omit it from our model. Our model will then consist of any significant explanatory variables and, therefore, give us the model of best fit for valuing firms. The model with the best fit will exhibit the highest R-squared value. R-squared is the movement in the value of the issue that can be explained by movements in the explanatory variables. We will confirm our findings using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values which highlights the best model via the information criteria selection rule. The AIC and BIC values are indicative of the amount of information that is lost between the actual data set and the predicted value. Thus the optimal model will therefore have the lowest AIC and BIC values and highest R-squared value. Our main objective is to build a parsimonious model that is statistically adequate and satisfies the assumptions of the Classical Linear Regression Model.

After determining which explanatory variables are to be included in the regression, we must therefore test that the 5 assumptions for the classical linear regression model are not violated. These are known as the Gauss-Markov assumptions. We note that the assumptions are assumptions on the unobservable error terms. The assumptions of proper functional form, no outliers, residual normality, homoskedasticity, and no multicollinearity must be satisfied in order for the model to be valid. If these assumptions are violated the coefficient estimates of Beta and the standard error will be incorrect and the distributions assumed for the test statistic will be inappropriate.

The 5 assumptions the OLS model is based on are outlined below:

## The model is linear in the parameters: yi = β0 + β1xi + ei for all i = 1, ...,N

The first assumption that arises is that of proper functional form – Is the model linear? In order to analyse this assumption we will need to test the distribution of the data, testing if we need to transform the dependent variable to make the data more ‘normal’. Transformations could include logs and squared or cubic functions.

## The standard errors are equal to zero: E(ei) = 0

Assumption 2 is used to ensure that the regression function has a meaningful interpretation. This assumption ensures that β0, β1 etc. are unbiased. However, if the model being tested has an intercept above zero, i.e. has a constant term in the regression equation, assumption 2 cannot be violated. In testing this assumption we aim to prove that the mean standard errors of the regression equal zero.

There are adverse consequences to not having an intercept. R squared may be negative, meaning that the sample mean does a better job of explaining the change in Value than our explanatory variables. There also could be severe biases in our slope coefficient estimates and the R squared value therefore may also be worthless.

## The model exhibits homoskedacity - var(ei) = σ2 is constant for all i

Assumption 3 assumes homoskedasticity (constant variance). In order to test for homoskedasticity the Breusch-Pagan test is performed with a null hypothesis of constant variance. If Assumption 3 is violated, then the error term is said to be heteroskedastic (non-constant variance). If the variance is constant, that is, the variance of the error term does not depend on the explanatory variables, then the error term is said to be homoskedastic. Problems when using the OLS model arise if the error term proves to be heteroskedastic. Although the OLS estimators will still give unbiased and consistent estimates, the OLS model is no longer the best linear unbiased estimator. The standard formula for the OLS standard errors is also no longer correct and any conclusions made therefore may be misleading.

## The model exhibits no significant multicollinearity

Assumption 4 implies that two or more repressors’ are not highly correlated with each other as this would undermine the statistical influence of the model. Multicollinearity does not bias the estimates of the dependent variable; therefore if our study only takes into account the predictive accuracy of the model then this assumption does not affect it. However, it does affect the conclusion about the significance of the collinear variables. To test the level of multicollinearity between variables, we will use the variance inflation factor (VIF) test. VIF is a measure of how the change in standard errors is caused by collinearity between explanatory variables. “Not uncommonly a VIF of 10 or even one as low as 4 (equivalent to a tolerance level of 0.10 or 0.25) have been used as rules of thumb to indicate excessive or serious multicollinearity” (Robert O’Brien 2007). Therefore, if the values for VIF are low enough we can then assume no multicollinearity. Higher correlation between explanatory variables reflects greater multicollinearity.

If the model ignores the presence of multicollinearity our significance tests may give inappropriate results. Parameter confidence intervals will be very wide and although R squared will be high, standard errors of individual coefficients will also be high.

## The model is ‘normal’ and has no outliers

Assumption 5 assumes normality in our data set. We will test our model for normality and outliers, which will show if there is a need to include a dummy variable in order to remove the impact of a large outlier. Outliers have to be detected, identified, and analysed. We will be using the Jarque-Bera test with a null hypothesis that our model does display normality and has no outliers. Assuming normality means we can easily test hypotheses about our parameter estimates.

## The model errors are not auto correlated

Assumption 6 is irrelevant to our study. As our data only captures one period it is unnecessary to test for correlation of error terms.

Once the assumptions have been satisfied we can proceed with using the regression model to answer our research questions.

Firstly we will conclude from our regression results which explanatory variables have the greatest impact on the issue value. This will give an indication of how stock markets value equity issues therefore answering our first research question.

We will interpret the results further to conclude if IPOs are undervalued relative to SEOs. Examining the SEO dummy variable coefficient will provide the answer to this second research question. If the coefficient is significant and positive we can conclude that IPOs are undervalued relative to SEOs.

We must acknowledge that there are however limitations to using the OLS method. The model is sensitive to the presence of outliers, which can sometimes seriously skew the results of the model and can lead to questioning its validity. However, removing outliers means our results are no longer a true representation of the sample.

## 4. Results

In Table 3(appendix) the Wald test shows that the best model for accurately predicting the value of a company’s share issue is Reg 11. This model includes debt, sales, income, SEO (dummy) and d1 (dummy) as they all have a significant relationship with value. Assets, return on assets, debt ratio and sales to assets ratio have been removed from the model as their inclusion did not prove to be statistically significant. If all variables had been included in the model, we would have formed a model that has the highest R-squared of 0.923, meaning that 92.3% of the change in issue value is due to the change in our explanatory variables, however we cannot call this the best model for the data as the goodness of fit would have been increased by the quantity of variables rather than their quality and significance.

Reg 9 and Reg 11 have the lowest Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values. AIC is lowest in Reg 9 but BIC is lowest in Reg 11. In a conflict such as this, the BIC value is deemed a more important measure by the parsimony principle, since it is more consistent. This therefore indicates that the result of Reg 9 is influenced by the use of too many variables. The parsimony principle and information criterion selection rule therefore confirm that Reg 11 is the best model for the study.

The R-squared value of this model is 0.92, meaning that 92% of the change in issue value is due to the change in our explanatory variables. All variables in the model (Reg 11) are significant to at least 5%. The F test displays the highest value for Reg 11 meaning that this model shows the highest level of statistical significance.

We will now test that the model of best fit does not violate any of the assumptions of the classical linear regression model.

## The model is linear in the parameters: yi = β0 + β1xi + ei for all i = 1, ...,N

From Table 4 (appendix), the log transformation of the dependent variable (value) is shown to have the least significant departure from a normal distribution. A graphical depiction of this can be seen in Figure 1 (appendix). Consistent with Koop (2001), we are taking logs of our dependent variable will mean that we are using a model that displays normality, therefore fitting with the assumptions of OLS regression.

We can now change our model to –

LogValue = β0 + β1Debt + β2Sales + β3Income + β4SEO + β6D1 + e

This model will be used to continue testing the other assumptions.

## The standard errors are equal to zero: E(ei) = 0

The test statistics below show that we can strongly reject the null hypothesis that there is no constant in the regression. This presence of a constant means we can be sure that our regression does not violate the first assumption.

Testing: Constant = 0

F-statistic: 1842.19

P value: 0.0000

## The model exhibits homoskedacity - var(ei) = σ2 is constant for all i

The results showed a p-value of 0.4971 on a chi2 distribution. This means there is a 49.71% chance that we got a result as extreme as the viewed dataset, given that the null is true. This percentage is too high for us to reject the null hypothesis. Therefore, we can surmise that the errors do not appear to be heteroskedastic.

## The model exhibits no significant multicollinearity

Table 5 (appendix) shows the largest correlation value to be 0.6384. Although this is not large enough to assume multicollinearity in the data, we will perform another test to clarify that multicollinearity is not present.

Table 6 (appendix) shows that the VIF test values are low enough to confirm that the model exhibits no significant multicollinearity.

## The model is ‘normal’ and has no outliers

The results from the Bera-Jarque test below show that the Chi2 value is reduced when adding the dummy variable, indicating that the dummy variable increases the normality of the model. The p-value increases from 0.7893 to 0.8514 when the dummy variable is included. As the p-value increases we can have more confidence when accepting the null hypothesis of normality.

Jarque-Bera test for model without d1:

Chi2: 0.4733

p-value: 0.7893

Jarque-Bera test for model with d1:

Chi2: 0.3218

p-value: 0.8514

After testing all the assumptions we can now answer our research questions using the following model -

## LogValue = β0 + β1Debt + β2Sales + β3Income + β4SEO + β6D1 + e

## 4.1 How do stock market values share issue?

From running our regression to estimate the value of stock market issues our findings show that debt, sales, income, SEO (dummy) and a dummy variable for outliers creates a suitable estimator, results shown in Table 7 (appendix). The R-squared value is 0.369 meaning that 36.9% of the change in issue value is influenced by our explanatory variables. Although a higher value would have been preferred, models predicting stock markets valuations typically exhibit low R-squared statistics.

The coefficients of the variables in the regression show a positive relationship between all the explanatory variables and the value of the issue. Intuitively, this means that with increasing levels of debt, sales and income, the value of the share issue increases. However, the coefficient of income is not statistically significant meaning that we cannot place any relevance on this coefficient. Meanwhile, sales is significant to a 5% level and debt is significant to a 1% level. This means that the value of a share issue is dependent on debt and sales. The SEO variable is also significant to a 1% level, meaning that the type of issue is also taken into consideration when the market determines the value of share issues.

## 4.2 Are IPOs undervalued relative to SEOs?

Our regression results show that the coefficient for the SEO dummy variable is positive when the model is used to estimate issue value. A positive coefficient of 1.026 indicates that when the dummy variable is 1 (an SEO) the value of an issue increases. Due to the statistical significance of this result, we can be confident in concluding that IPOs are undervalued.

## 5. Conclusion

In this paper we use an OLS multivariate regression model to examine how stock markets value firms and if IPOs are undervalued relative to SEOs. The advantage of our model is that it is the best linear unbiased estimator. Data for analysis comprised of a sample of 83 IPO and 226 SEO U.S. firms during 1996. Our results show that stock markets use a firm’s sales, debt and issue type when valuing a firm. Consistent with prior research carried out by Koop (2001) we also find that IPOs are less valuable than SEOs i.e. they are undervalued.

Originally in our paper we proposed the method of using financial ratios as a means to further examine our data. They were to act as additional explanatory variables in order to give us the best fit model for pricing IPOs relative to SEOs. However, after we conducted the Wald test we found that the use of financial ratios where insignificant, and therefore they were omitted from our regression, as was the assets variable. Our conclusion to omit financial ratios from our data is consistent with the findings of Miller-Modigliani (1958), who suggest that ‘The value of a firm is independent of its debt ratio and the cost of capital will remain unchanged as the leverage changes’. However, this theory does not hold up in the real world. In the real world, where taxes, default risk and agency costs exist; it is no longer correct that debt and value are unrelated. In many cases it is in fact found that increasing debt can raise the value of some firms and in other cases it may reduce the value of a firm.

In this study we found debt and sales to have a significantly positive relationship with value meaning that with higher levels of debt and sales the value of the equity issue increases. Income is shown to be positively related to firm value, however this result was not significant and, therefore, is not reliable and cannot be included as an accurate predictor of the equity issue.

Finally, the SEO dummy variable has a significant and positive relationship with firm value. This result completes our model for valuing equity issues and answers the question of IPO undervaluing. As this is a positive result, the value of a firm is increased when it is listed as an SEO, therefore proving that IPOs are undervalued.

Although we can show confidence in our results, we are aware of certain limitations with our study. We have already outlined the limitations surrounding our data set in that we require more variables and a larger number of observations to improve the accuracy and reliability of our results. Multivariate regression does not allow for outliers in the data set, therefore a different method of analysis could be used to cater for a dynamic data set. Future research should additionally examine the effect of intangible assets on valuation as it is a large contributor to IPO undervaluing (Dimovski and Brooks, 2006).

Therefore our paper can conclude that, ‘The price is NOT right’.

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