Cost of equity (COE) is one of the most important financial metrics firms and investors consider when evaluating potential investments. There is an enormous academic literature that either proposes measures of cost of equity or uses it to study asset prices or corporate decisions. Further, practitioners employ discount rates ubiquitously, including for discounted cash flow (DCF) analysis to value firms or investment projects. However, despite the fundamentally important role that discount rates play in finance, our understanding of how finance professionals construct and use cost of equity is still limited. Existing research on discount rates in practice largely comes from insightful survey evidence. Our recent paper provides new evidence by analyzing actual cost of equity estimates computed by investment banks.
We aim to shed light on two main research questions. First, how do investment banks construct cost of equity estimates in their valuation analyses? Specifically, what firm attributes do banks consider? Second, how do banks’ incentives impact their cost of equity estimates? We take advantage of one important institutional detail to empirically study these questions. In an acquisition of a publicly traded U.S. firm, the target firm almost always hires an investment bank to provide a valuation analysis called a “fairness opinion.” Details of the valuation analysis must be disclosed in merger documents, which allow us to collect banks’ cost of equity estimates. Moreover, compared to voluntarily self-disclosed data from other sources, our unique data have several advantages. First, information required to be disclosed in mandatory Securities and Exchange Commission (SEC) filings is potentially more credible. Moreover, the nature of the disclosures alleviates concerns about sample selection, as target firms are almost always required to file merger documents. Finally, our data allow us to uncover how sophisticated finance professionals (i.e., investment banks) estimate the cost of equity and how incentives affect their estimates.
Using hand-gathered data from SEC filings for a randomly generated sample of M&A deals from 1993 to 2017, we begin by studying how well academically motivated risk factors or firm characteristics explain banks’ cost of equity estimates. We show that cost of equity values from banks are significantly positively related to firm beta, financial distress, return volatility, and leverage, and they are negatively related to firm size and stock returns from the previous year. COE also varies by industry, as stable industries like utilities have the lowest discount rates and more volatile industries such as medical devices and pharmaceuticals have the highest rates. We further compare investment bank COE estimates with those implied from commonly employed asset pricing models, such as the CAPM or the Fama-French models. Bank COE estimates are substantially higher, with the difference ranging from 2.1 to 5.5 percentage points. Moreover, the correlation between cost of equity values constructed by banks and expected returns from the asset pricing models is positive but relatively low, ranging from 0.12 and 0.28.
In some ways, banks’ incorporation of risk differs from the empirical academic literature. For example, past returns are negatively related to bank COE, while the literature documents a robust positive relation between returns from the previous year and subsequent returns (i.e., the momentum effect). Similarly, distress risk, volatility, and leverage are all positively related to bank COE, though the literature finds evidence of a negative relation between these characteristics and expected returns. Further, other common predictors of expected return, including the market-to-book ratio, profitability, and investment, do not seem to affect banks’ cost of equity calculations.
We next examine incentive effects and value implications associated with banks’ choice of cost of equity. We continue to exploit our sample of target firm valuations in M&A transactions. Given uncertainty about the true model of discount rates as well as imprecision in estimating the chosen mode, the bank has considerable flexibility to choose a rate that either underestimates or overestimates target firm value. On the one hand, the bank and its client may overestimate the target value by using relatively low discount rates to negotiate a higher price with bidding firms. On the other hand, since advisory fees are usually contingent on deal completion, the bank may construct high discount rates to underestimate target value so that the final sales price looks more attractive for target shareholder approval.
A recent study by Eaton et al. (2022) find that in another popular valuation approach, the comparable companies analysis (CCA), banks first identify a pool of potential peers with similar business and product profiles as the target firm. Banks also tend to match on other firm characteristics, but when peers do differ, they are larger and have higher valuation multiples than the target. The authors interpret their findings as consistent with banks’ choosing high-multiple peers to boost the target firm value for premium negotiation purposes. One possibility is that banks use alternative valuation approaches, such as DCF and CCA, to provide robust estimates that align with each other. In that case and given the findings in Eaton et al (2022), we would expect banks to adjust the discount rate downward to produce a higher target valuation when selecting highly valued peers.
However, it is possible that the cost of equity and ultimately DCF provide valuation estimates that diverge from those given by other valuation approaches. Compared to the comparable companies approach, the DCF approach offers more flexibility for banks to operate. As previously discussed, banks have substantial leeway to determine the discount rate, which has a substantial effect on the valuation output given the sensitivity of discount rates on present values. However, it would generally be difficult for banks to present to shareholders a group of underperforming peers with substantially lower valuations than the target. Thus, discount rates and DCF may sometimes give valuation estimates that differ from less flexible approaches, and it is possible that the former better aligns with investment bank incentives. We find that peer choice in CCA and the cost of equity choice in DCF have conflicting incentive effects on target valuation. Banks choose a higher discount rate when they select peers with higher valuations than the target. This effect is absent when banks select peers with lower valuations.
Given investment banks’ incentives effects, we further investigate their cost of equity estimates in management buyouts (MBO), which are deals where the target firm’s managers have incentives to purchase the firm from shareholders at the lowest possible price. We find that banks’ cost of equity estimates is substantially higher in MBOs compared to other M&A transactions, even after controlling for firm and deal characteristics as well as industry fixed effects. We interpret these results as consistent with managers and the banks they hire increasing discount rates in valuation analyses to negotiate a lower purchase price with the target shareholders who are bought out in MBOs.
We next explore the potential value implications of banks’ COE estimates. We find a negative association between cost of equity and takeover premiums, especially when banks’ COE estimates are precise. However, we suggest caution in interpreting our premium results as our analyses examine associations, not causal relations. Lastly, we explore bank reputation and bank fixed effects in COE estimates. We find that the top 5 investment banks tend to use significantly lower cost of equity estimates. However, we find substantial variation in cost of equity estimates among top banks.
In summary, our paper connects the extensive asset pricing literature with evidence from the field. Moreover, our unique setting allows us to investigate potential incentive effects that affect banks’ cost of equity estimates, which adds to the literature on managerial conflicts of interest in corporate takeovers.
Gregory Eaton is Ed Keller Associate Professor of Finance at Oklahoma State University.
Feng (Jason) Guo is an Assistant Professor of Accounting and Dean’s Fellow in Accounting at Iowa State University.
Tingting Liu is an Associate Professor of Finance and John and Connie Stafford Professor in Finance at Iowa State University.
Danni Tu is an Assistant Professor of Finance at Southern Illinois University, Carbondale.
This post is adapted from their paper, “The cost of equity: Evidence from investment banking valuations,” available on SSRN.