Circularity problems

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A Practical Approach to Solving the Circularity Problem in Estimating the Cost of Capital
Pitabas Mohanty
XLRI Jamshedpur

While valuing a company using the DCF approach, we face the well-known circularity problem, where we need to know the cost of capital to value a company, and we need to know the value of the company (in particular the market debt-to-equity ratio) to find the cost ofcapital. Usually, analysts use the market capitalization and the book value of debt (if the market value of debt figure is not available) while estimating the cost of capital. Since the final equity value that one gets often turns out to be different from the initial value (market capitalization) used to estimate the cost of capital, this raises questions about the very valuation method itself. In thispaper we suggest a simple and practical approach that can be used to solve this circularity problem. In particular we suggest an iterative method that can be used to find the actual value of equity that one should use to estimate the cost of capital and subsequently value a company even when the market value of equity figure is not available or is not reliable.

This paper can be downloadedwithout charge from the Social Science Research Network Electronic Paper Collection at: http://ssrn.com/abstract=413240

A Practical Approach to Solving the Circularity Problem in Estimating the Cost of Capital Abstract While valuing a company using the DCF approach, we face the well-known circularity problem, where we need to know the cost of capital to value a company, and we need to know thevalue of the company (in particular the market debt-to-equity ratio) to find the cost of capital. Usually, analysts use the market capitalization and the book value of debt (if the market value of debt figure is not available) while estimating the cost of capital. Since the final equity value that one gets often turns out to be different from the initial value (market capitalization) used toestimate the cost of capital, this raises questions about the very valuation method itself. In this paper we suggest a simple and practical approach that can be used to solve this circularity problem. In particular we suggest an iterative method that can be used to find the actual value of equity that one should use to estimate the cost of capital and subsequently value a company even when the marketvalue of equity figure is not available or is not reliable.

A Practical Approach to Solving the Circularity Problem in Estimating the Cost of Capital Introduction Though DCF approach is hailed as one of the most scientific methods available to value a company, it has certain inherent limitations1. We face a circularity problem while estimating the cost of capital used to value a company. When weestimate the cost of capital, we require an estimate of the market value of debt-to-equity ratio. But the market leverage ratio can be estimated only if we know both the market value of debt and the market value of equity. But we cannot know these values unless we value the company (and debt and equity) in the first place. Most analysts either ignore this problem, or they do not address this issueproperly. In most valuation reports, the analysts use the market capitalization figure as a proxy for equity, and the book liability figure as a proxy for the market value of debt to estimate the market leverage ratio2. This approach creates further problems when one finally gets a value of equity (let’s call it the DCF equity value) that is different from the market capitalization figure one hasused in the first place to estimate the cost of capital. Which number should be taken as equal to the market value of equity? If the DCF equity value is to be used as the true value of equity, then does it mean that the market capitalization figure is wrong? But we obtain the DCF equity value based on the market capitalization figure in the first place. The problem becomes more serious when we...
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