مقایسه مدل قیمت گذاری گزینه مرتون در ارزش گذاری اوراق قرضه شرکتی برای استفاده از ارزش دفتری

Many studies use the book value of debt as a proxy for its market value because most corporate debt does not trade. I call this practice the book value of debt (BVD) approximation, and it appears to be justified by the observation that the average market value of debt is close to its book value. Many corporate bonds, however, trade at values significantly different from their book values, and consequently the BVD approximation can create important biases. I compare the accuracy of the BVD approximation to Merton's option pricing (OPT) model of corporate debt valuation, and find consistent evidence that the Merton model provides more accurate estimates. I also show that this model is an easily estimated alternative to the BVD approximation. In short, the BVD approximation not only creates significant biases, but it is also an unnecessary simplification.

Nearly all firms have debt outstanding and most of it does not trade. This dearth of trading creates a problem for many researchers because they need market values of debt for their empirical tests. A common solution to this problem is to use the book value of debt as a proxy for its market value. I call this solution the book value of debt (BVD) approximation, and it appears to be justified by the observation that the average market price of debt is close to its book value. As Sweeney et al. (1997) report, however, many corporate bonds trade at values significantly different from their book values and the consequences of these differences can be notable. For example, previous studies documenting the existence of a diversification discount use the BVD approximation (e.g., Berger and Ofek (1995)).1Mansi and Reeb (2002) reexamine the existence of this discount by analyzing a sample of firms with publicly traded debt. Their sample selection permits them to use the market value of debt instead of the BVD approximation. They find that diversification does destroy shareholder wealth but it increases bondholder wealth by an approximately equal amount because it decreases default risk. They conclude that there is no destruction of (total) firm value (i.e., the sum of the firm's market value of equity and debt) associated with diversification. What appears to be a diversification discount is actually a wealth transfer from shareholders to bondholders, and the BVD approximation prevents previous studies from observing this wealth transfer effect.2 In short, there is extensive evidence that the BVD approximation can create important biases and yet its widespread use ignores this evidence. These results are even more notable when one considers that the kinds of firms with traded debt (i.e., large, well-established firms) are the least likely to have large differences between their book and market values of debt. In other words, previous studies documenting the bias created by the BVD approximation most likely understate the extent of the bias because their samples are limited to firms with traded debt. Notwithstanding these problems, the BVD approximation might be viewed as a necessary simplification because it permits researchers to conduct large sample tests (requiring debt values) without having to go through a cumbersome and involved valuation of each firm's debt. There is, however, an alternative to the BVD approximation that can be estimated easily using standard data available in Compustat and the Center for Research in Security Prices (CRSP) files: Merton's (1974) option pricing (OPT) model of corporate debt valuation (also called a structural bond valuation model). Despite the long history of this model, I am unaware of any previous study that conducts a comprehensive comparison of this model to the BVD approximation. One of the main contributions of this paper to the literature is to make such a comparison using two primary series of tests. My two test series differ mainly in their estimation of the underlying firm value and return volatility, two important inputs to the Merton model that are not directly observable for most firms because most corporate debt does not trade. My first series of tests use exogenous estimates of firm values and return volatilities. The advantage of these tests is that I can compare the stock value estimates implied by the Merton model, and by the BVD approximation, to actual stock prices. So, I am not limited to examining the small percentage of firms with traded debt (around 10 percent of firms with traded stocks have traded bonds). With these tests, I subtract the Merton OPT model estimate of the firm's debt value from my underlying firm value estimate to arrive at the OPT estimate of the firm's stock value. The put-call parity theorem shows that this approach is equivalent to estimating the value of equity as a call option on the underlying firm value (I call this the OPT equity valuation approach). I next compare the OPT equity valuation approach to the traditional discounted cash flow (DCF) equity valuation approach. The DCF approach uses the same firm value estimate as the OPT approach, but it uses the BVD approximation; that is, the DCF stock value estimate is defined as the firm value estimate minus the firm's book value of debt.3 Whenever the Merton OPT debt value estimate differs from its book value, the OPT stock value estimate differs from the DCF estimate.4 Therefore, comparing the DCF equity valuation approach to the OPT approach is ultimately a test of the Merton OPT model of corporate debt valuation to the BVD approximation.5 If the Merton model is more accurate than the BVD approximation, then the OPT stock price estimates will be more accurate (i.e., closer to actual stock market prices) than the DCF estimates. I compare the DCF equity valuation approach to the OPT approach and find that the OPT approach is more accurate. Most important, the greater the difference between the OPT debt value estimate and its book value, the greater the accuracy of the OPT approach relative to the DCF approach. For example, I sort my sample firms into deciles according to the absolute percentage difference between their OPT debt value estimates and their book values. For firms in the top decile (i.e., firms with the greatest difference between their OPT debt value estimates and book values), the absolute DCF stock valuation error (i.e., the absolute value of the percentage difference between the DCF stock value estimate and the actual stock market price) is more than 10 percentage points higher, on average, than the absolute OPT stock valuation error. My sample for these tests consists of firms with complete cash flow forecasts available in the Value Line Investment Survey (i.e., Value Line) any time (as of the end of each June) between 1988 and 2000. I use these cash flow forecasts to generate my exogenous estimates of firm values. I also examine an alternative sample of firms that does not require cash flow forecasts to estimate firm values (i.e., my Overall sample). With my second series of tests, I use the market value of each firm's common stock and stock return volatility to infer the underlying firm value and return volatility, and consequently to infer the Merton OPT debt value estimate. Hence, these “market-based” OPT debt value estimates do not depend on the accuracy of my exogenous firm value and return volatility estimates. This method for estimating the Merton model is the easiest to use because it can be quickly estimated using standard data that is available in CRSP and Compustat. This method also illustrates an important advantage of the Merton model over other structural bond valuation models (as I discuss in more detail below). As with the OPT debt value estimates based on with my exogenous firm value and return volatility estimates, I find that there are often significant differences between these “market-based” OPT debt value estimates and their book values. I also compare these “market-based” OPT debt value estimates to actual bond market prices, and find that these estimates are more accurate than the BVD approximation. In summary, this paper makes two primary contributions to the literature. First, I perform two series of tests comparing the Merton model to the BVD approximation. Using stock and bond data, I find consistent evidence that the Merton model provides more accurate debt value estimates than the BVD approximation. Second, I show that the Merton model is an easily estimated alternative to the BVD approximation (it only requires standard data available in CRSP and Compustat). Therefore, not only does the BVD approximation create important biases, but it is also an unnecessary simplification. I present the DCF and OPT approaches to common stock valuation in the next section. In Section 3, I discuss the data and descriptive statistics. I present the results from my tests that compare the DCF and OPT approaches in Section 4. In Section 5, I compute the “market based” Merton OPT debt value estimates and compare them, and the BVD approximation, to actual bond prices. I present the summary and conclusions in Section 6.

Many finance researchers examine samples of hundreds or thousands of firms, and the market value of each firm's debt is a common variable that is required for their empirical tests. Because most corporate debt does not trade, nearly all of these studies use the book value of debt as a proxy for its market value (i.e., the BVD approximation). The BVD approximation appears to be justified by the observation that the average and typical traded bond has a market price close to its book value, and that it is impractical to perform a separate valuation of individual firm debt values for large sample studies. Recent studies, however, show that the BVD approximation can create important biases, and these studies probably understate the extent of the problem because they do not analyze the kinds of firms that are most likely to have the greatest difference between the market value of their debt and its book value (i.e., small firms because they are less likely to have traded debt). Moreover, the Merton (1974) OPT bond valuation model is an alternative to the BVD approximation that is easy to estimate. In this study, I compare the accuracy of the Merton OPT model to the BVD approximation using two primary series of tests. My two test series differ mainly in their estimation of the underlying firm value and return volatility, the two key inputs into the Merton OPT debt value estimation that are not directly observable for most firms. With my first series of tests, I use exogenous estimates of firm values and return volatilities. The advantage of this approach is that I can compare the stock value estimates implied by the Merton model, and by the BVD approximation, to actual stock prices. So, I am not limited to examining the small percentage of firms with traded debt. My test results provide consistent evidence that the Merton model is more accurate than the BVD approximation. My second test series uses the market value of each firm's common stock and return volatility to infer the underlying firm value and return volatility (and consequently to infer the Merton OPT estimate of each firm's debt value). I then compare these “market-based” OPT debt value estimates to actual bond prices, and I make a similar comparison for the BVD approximation. These results provide consistent evidence that the Merton OPT model provides more accurate debt value estimates than the BVD approximation. In summary, this paper makes two primary contributions to the literature. First, I find consistent evidence that the Merton OPT approach provides more accurate debt value estimates than the BVD approximation. Second, I show that the OPT approach is an easily estimated alternative to the BVD approximation, and that it only requires standard data available in CRSP and Compustat. Therefore, not only does the BVD approximation create important biases, but it is also an unnecessary simplification.