In developed foreign capital market, second equity offering (SEO) is the main method of refinancing for listed companies. In China, SEO is also an important method of refinancing for listed companies. Private placement is an representative example of SEO with marketability restriction, and in recent years, more and more researchers have been focusing on the pricing method of private placement. The fact that there is not an ideal pricing method for private placement in China means that the research on stock pricing for private placement is of great significance. The stock price of private placement, which is a kind of SEO with marketability restriction, is based on the price discount and initial price (or inherent value) of the issuing company. Liquidity is proved an important factor accounting for stock price discount both theoretically and empirically. The price discount is mainly determined by illiquidity especially for shares with trade or marketability restriction. Pricing of illiquid stock with marketability restriction depends on not only transaction cost or bid-ask spread but also opportunity cost. Amihud and Mendelson (1986) suggest that compared with price discount corresponding with opportunity cost, the discount relating to bid-ask spread can be neglected and the price without trade restriction can be treat as the market price in a frictionless environment .
Longstaff (1995) sets the price of shares outstanding as exogenous variable, and then he deduces the upper bound of the price discount. His analysis framework is a typical opportunity cost based method . Empirical researches also reveal that price discount is very important and can’t be ignored in private placement. Shane A. Corwin (2003) investigates the price discount of SEO from 1980 to 1998 in the United States. He finds that the average price discount of the U.S. listed companies with private placement is 2.2%. Among which the listed company in New York Stock Exchange suffer lower discount rate of private placement than those in Nasdaq . On the other hand, the stock price in private placement is determined by initial price. Most researches about initial price focus on the residual income of company with the pioneering work of Ohlson (1995). Plenborg (2002) compares the residual income method with the cash flow discount method. To simplify the analysis, Plenborg releases several hypotheses and concludes that the residual income method overcomes the cash flow discount method . Song ping (2006) considers that the nature of stock represents the ownership of residual income of company. In other words, it is the ownership of equity. So the company value assessment can be based on the current value of equity and consider the earning ability and developing potential in the same time . The research work of stock pricing in private placement have been carried out for decades with a lot of research findings abroad, however, for Chinese stock market these findings may not be relevant. Chinese financial market is different in some aspects from these abroad and relative researches with pertinence are still needed especially in the area of stock pricing in private placement.
To estimate the price discount in private placement, we adopt Longstaff’s idea of opportunity cost. We further assume the return and volatility of stock price are given by independent stochastic process respectively. Then we use residual income model to estimate the initial price of stock in private placement. Monte Carlo simulation is adopted to estimate the price discount. Empirical analysis shows that the model we have developed is efficient in practice. https://arudhrainnovations.com/