Growth Options, Unwritten Call Discounts and Valuing the Small Firm

45 Pages Posted: 11 Jun 2004

See all articles by Michael S. Long

Michael S. Long

Rutgers University at Newark

Jingfeng Zhang

University of Muenster - Institute of Materials Physics

Date Written: March 15, 2004


Why do small firms sell at lower multiples of earnings than large firms? Are small firms being consistently undervalued or is there some other rational explanation? We develop a rationale why valuing the smaller firm is not the same as valuing a smaller scaled, large firm in much the same way that a child is not a miniature adult. We have identified a factor we name the "real unwritten call" against the firm's value. The unwritten call refers to the ability of potential competition to enter the product market and destroy value. Firms do not operate in a static environment, but rather in a dynamic ever changing one. For example, when Wal-Mart opens a new store that destroys a traditional local retailer's value, it is a dynamic change. Thus, for a small firm merely projecting past financial data into the future is extremely naive. While a changing environment affects large firms also, larger firms have more resources that enable them to better adjust to changes and thus avoid permanent losses in value. Considering real market attributes is a major contribution to understanding and improving the pricing of small public firms. While it is well known that the lack of information about small firms creates the information asymmetry and liquidity costs that increase the investor's required return on the right hand side of the balance sheet, the cost of real market changes also affect the firm's ability to produce future cash flows from their investments. These smaller firms have fewer resources with which to create barriers to entry and react to changes in the real markets. We present empirical evidence consistent with our premise. We find evidence of a real call option against value. The option is greater for smaller firms. Finally, our results are consistent with some, and help explain other, anomalies such as the pricing of equity carve-outs relative to their parent, and the low earnings multiples at which closely held firms are actually sold.

Suggested Citation

Long, Michael S. and Zhang, Jingfeng, Growth Options, Unwritten Call Discounts and Valuing the Small Firm (March 15, 2004). Available at SSRN: or

Michael S. Long (Contact Author)

Rutgers University at Newark ( email )

111 Washington Avenue
Newark, NJ 07102
United States
973-353-5471 (Phone)

Jingfeng Zhang

University of Muenster - Institute of Materials Physics

Schlossplatz 2
Muenster, D-48149

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