Determing company value

Summary: The value of a business entering bankruptcy is determined by the asset, income, or market approach and creditors are repaid according to their risk.

Bankruptcy of a business occurs when the business is legally declared insolvent (its assets are less than its liabilities). If the debtor files a bankruptcy petition, it is called a voluntary bankruptcy. However, if creditors force the debtor into bankruptcy, then it is called an involuntary bankruptcy. Most bankruptcies are voluntary. In either case, the value of the business needs to be determined for legal purposes. The standard of the value used in the valuation is the fair market value (the value of the price of the firm that a rational buyer is willing to pay to a willing seller in a free market). There are three basic approaches for valuating the business: the asset approach, the income approach, and the market approach. The hierarchy of the creditor in a bankruptcy is determined by the amount of risk the creditor bears: the creditor who bears least amount of risk will have priority to receive payment after liquidation.

Asset Approach

The asset approach determines the value of a company by adjusting its book value of assets to the current market value. It is based on the economic principles of substitution: a rational investor will not pay more for a business asset than the price of a different asset that provides similar utility. There are two methods associated with the asset approach: the adjusted book value method and the replacement cost method.

In the adjusted book value method, the assets and liabilities on the balance sheet are examined item by item by professionals to determine the business’s current market value. Once the assets and liabilities have been adjusted to the current market value, the value of the company is calculated as the difference.

In the replacement cost method, the value of each asset and liability on the balance sheet is first determined as the cost to replace it. Then, the value the company is determined as the difference of its assets and liabilities.

The asset approach is not reliable for companies with significant intangible assets because the approach involves professional judgment. It is more suitable for companies that have many tangible assets and few intangible assets.

Income Approach

The income approach determines the fair market value of a firm by discounting its expected cash flows at an appropriate discount rate assuming the firm will continue to operate without liquidation. The discount rate is often chosen to be the firm’s weighted average cost of capital (WACC). The procedure is completely analogous to that of determining the net present value of a firm in corporate finance theory. Mathematically, the fair market value under the income approach can be written as

where FMV is the fair market value, E(C) is the expected cash flows under the assumption that the firm will continue to operate, and WACC is the weighted capital of cost.

In corporate finance theory, WACC is often calculated as the weighted average of the cost of debt of the firm and the cost of equity of the firm

where T_c is the corporate tax rate, r_D is the cost of debt, r_E is the cost of equity, B is the market value of the firm’s bonds, and S is the market value of the firm’s stocks.

WACC takes into consideration the facts of leverage and taxes and thus is the appropriate discount rate used for income approach. The income approach assesses the value of the debtor to the creditors. However, it fails to take account of the value inherent in the flexibility of decision making, which is often valued using a mathematical tool called “decision tree.”

Market Approach

The market approach assesses a company’s value by comparing it with similar companies in the market. The rationale behind this approach is that the price of the subject company should be very close to the values of the similar companies in the market. There are two methods associated with the market approach: the guideline public company method, and the comparable transaction method. In the guideline public company method, a peer group of public companies with similar sizes, natures, operations, and financial characteristics is first selected. Next, the enterprise value of each company in the group is calculated as

where EV is the enterprise value, P_s is the stock price per share, N_s is the number of outstanding shares, D is total debt, and C_E is excess cash.

Then market multiples, such as enterprise value/revenue and enterprise value/earning before interest and tax, will be calculated using the enterprise value. Finally, the value of the subject company is determined by applying the calculated market multiples. For example, if the enterprise value/revenue is used, then the value of the subject company can be calculated as

where V is the value of the subject company and R is the revenue of the subject company.

In the comparable method, the value of the subject company is determined in a similar fashion as in the guideline public company method. In other words, market multiples are derived, and then they are applied to the subject company to determine its value. However, in the comparable method, public data of comparable transactions are used to calculate the market multiples.

Thus, the comparable method also consists of three steps: selecting a group of comparable transactions, calculating market multiples, and applying the market multiples.

The biggest drawback to the guideline public company method is that it is not applicable for nonpublic companies. The challenge with the comparable method is finding appropriate and reliable comparable transactions.

Paying Creditors

When a company declares bankruptcy, its creditors must be paid, but the creditors receive only some of the money they are owed. For example, if a bankrupt company is ordered to pay 10 cents on the dollar, this means for every dollar the company owes a creditor, it will pay only 10 cents. This is a proportional solution that is easy to arrive at using simple algebra. However, this is not the only payout strategy. There are several mathematical methods that can be used to determine how much money each creditor should receive. In the total equality method, available capital is simply divided equally among debtors, regardless of how much they are owed. A variation, traced back to medieval philosopher Moses Maimonides, proposes giving every debtor as equal a share as possible but never more than they are owed. In modern terms, this is a constrained optimization problem that can be solved using methods such as linear programming. Other decision methods are logically and analytically more complex, like the Shapely value, which considers paying a sequence of creditors their full amounts owed, to the extent of available funds, for all possible orderings. This game-theory approach is named for American mathematician and economist Lloyd Shapely.

Bibliography

Brealey, Richard A., Stewart C. Myers, and Allen Franklin. Principles of Corporate Finance. 9th ed. New York: McGraw-Hill, 2008.

Copeland, Thomas E., Fred J. Weston, and Shastri Kuldeep. Financial Theory and Corporate Policy. 4th ed. Upper Saddle River, NJ: Pearson Education, 2005.

Newton, Grant W. Practice and Procedure. Vol. 1, Bankruptcy and Insolvency Accounting. Hoboken, NJ: Wiley, 2010.

Ratner, Ian, Grant Stein, and John C. Weitnauer. Business Valuation and Bankruptcy. Hoboken, NJ: Wiley, 2009.