Leverage Costs Research Articles

Leverage and the Cost of Capital: Some Tests Using Nepalese Data

This paper is devoted to test the MM’s propositions about the relationship between leverage and cost of capital in the context of Nepalese capital markets. The main objective of the study is to determine whether the firms' overall cost of capital and cost of equity decline with the increasing use of leverage. The results showed a negative but insignificant beta value of the relationship between leverage and the overall cost of capital. Therefore the leverage may not be regarded as contributing variable to the cost of capital function for Nepalese firms. But finding contradicts with the traditional approach of the capital structure theories. It is further concluded that the cost of capital declines not only with leverage because of the tax deductibility feature of interest charge. The relationship between the cost of equity and leverage is also strongly negative. Besides leverage, the size, and D-P Ratio are other important variables that affect the cost of capital in Nepalese context.Journal of Nepalese Business Studies 2006/III/1 pp. 85-91

Cost of Equity and Leverage Under 'Fair' Rate-of-Return Regulation

A rate-of-return regime characterized by fairness satisfies two criteria: the total allowed return on the rate base is equal to the cost of capital, and the regulated firm should be able to raise capital without either gain or loss to existing equity holders. Assuming a monopoly firm with a single product, a single-period state-preference world, risk-free debt, corporate (but not personal) tax, and perfectly price inelastic demand; this paper shows that in such a regime the tariff of a regulated firm will have to be reset with leverage. This resetting arises because unlike in a Modigliani-Miller world where firm (and equity) value is enhanced by the leverage (because of interest tax shields), fairness implies that interest tax shield benefits accrue to consumers, after ensuring equity holders receive a return on equity commensurate with systematic risk. If demand is not perfectly inelastic, a change in tariff consequent upon change in leverage will also lead to a change in equilibrium output. With the assumption that there is a single driver of systematic risk (that of output), the cost of equity-leverage relationship obtained with perfectly inelastic demand is shown to still hold.

South East Asian Corporate Board Size

There are few papers that analyse the determinants of South East Asian firm board size, though there is a literature focusing on the impact of board characteristics on firm value. This paper adds to this former literature, focusing on the determinants of board size for firms listed in Hong Kong, Indonesia, Malaysia, the Philippines, Singapore and Thailand. While it is apparent that large firms have large boards there is also more subtle cross-country variation concerning the impact of leverage and agency costs on board size. Finally, using pooled analysis there is evidence of a decrease in average board size for firms in the Philippines and Singapore over the sample period, 1999 to 2002, with increases in average board size evident for Indonesian firms over the same period.

Valuing Companies with a Fixed Book-Value Leverage Ratio

We develop valuation formulae for a company that maintains a fixed book-value leverage ratio and claim that it is more realistic than to assume, as Miles-Ezzell (1980), a fixed market-value leverage ratio. The value of tax shields depends only on the present value of the net increases of debt. The value of tax shields in a world with no leverage cost is the tax rate times the current debt plus the present value of the net increases of debt. We also show that the appropriate discount rates for the equity cash flows and for the expected value of the equity are different. It is more realistic to assume that a company maintains a fixed book-value leverage ratio than to assume, as Miles-Ezzell (1980) do, that the company maintains a fixed market-value leverage ratio because the amount of debt does not depend on the movements of the stock market, it is easier to follow for non quoted companies, and managers should prefer so because the value of tax shields is more valuable.

The Value of Tax Shields Depends Only on the Net Increases of Debt

The value of tax shields depends only on the nature of the stochastic process of the net increases of debt. The value of tax shields in a world with no leverage cost is the tax rate times the current debt plus the present value of the net increases of debt. By applying this formula to specific situations, we show that Modigliani-Miller (1963) should be used when the company has a preset amount of debt, Fernandez (2004) when the company maintains a fixed book-value leverage ratio, and Miles-Ezzell (1980) when the company maintains a fixed market-value leverage ratio.

The Value of Tax Shields with a Fixed Book-Value Leverage Ratio

The value of tax shields depends only on the nature of the stochastic process of the net increases of debt. The value of tax shields in a world with no leverage cost is the tax rate times the current debt plus the present value of the net increases of debt. We develop valuation formulae for a company that maintains a fixed book-value leverage ratio and show that it is more realistic than to assume, as Miles-Ezzell (1980) do, a fixed market-value leverage ratio. We also show that Miles-Ezzell assume that the increase of debt is proportional to the increase of the free cash flows.

The Value of Tax Shields Depends Only on the Stochastic Process of the Net Increase of Debt

The value of tax shields depends only on the nature of the stochastic process of the net increase of debt. The value of tax shields in a world with no leverage cost is the tax rate times the current debt, plus the tax rate times the present value of the net increases of debt. By applying this formula to specific situations, we show that Myers (1974) should be used when the company has a preset amount of debt, Fernandez (2004) when the company maintains a fixed book value leverage ratio, and Miles-Ezzell (1980) when the company maintains a fixed market value leverage ratio.

The Value of Tax Shields is Not Equal to the Present Value of Tax Shields: A Correction

I correct some expressions of Fernandez (2004) and provide a more general expression for the value of tax shields. This expression is the difference between the present values of two different cash flows, each with its own risk: The present value of taxes for the unlevered company and the present value of taxes for the levered company. The value of tax shields in a world with no leverage cost is the tax rate times the current debt, plus the tax rate times the present value of the net increases of debt. The value of tax shields depends only on the nature of the stochastic process of the net increase of debt; it does not depend on the nature of the stochastic process of the free cash flow.

The Value of Tax Shields and the Risk of the Net Increase of Debt

The value of tax shields depends upon the nature of the stochastic process of the net increase of debt, and does not depend upon the nature of the stochastic process of the free cash flow. The value of tax shields in a world with no leverage cost is the tax rate times the debt plus the tax rate times the present value of the net increases of debt. This expression is the difference between the present values of two different cash flows, each with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For perpetual debt, the value of tax shields is the debt times the tax rate. When the company forecast to repay the actual debt without issuing new debt, the value of tax shields is the present value of the interest times the tax rate, discounted at the required return to debt.

The value of tax shields is NOT equal to the present value of tax shields

The value of tax shields is the difference between the present values of two different cash flows, each with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For constant growth companies, the value of tax shields in a world with no leverage cost is the present value of the debt, times the tax rate, times the unlevered cost of equity, discounted at the unlevered cost of equity. This result arises as the difference of two present values and does not mean that the appropriate discount for tax shields is the unlevered cost of equity.

The Value of Tax Shields is NOT Equal to the Present Value of Tax Shields

The value of tax shields is the difference between the present values of two different cash flows, each with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For constant growth companies, the value of tax shields in a world with no leverage cost is the present value of the debt, times the tax rate, times the unlevered cost of equity, discounted at the unlevered cost of equity. This result arises as the difference of two present values and does not mean that the appropriate discount for tax shields is the unlevered cost of equity.

Reconciling the Two Definitions of the Present Value of the Tax Shield (PVTS)

There are two ways to define the present value of the tax shield (PVTS). First, the (present) value of the tax shield VTS is simply the tax shield, discounted by y, which is the appropriate discount rate for the tax shield. Second, the (present) value of the tax shield VTS is the difference in the present values of the tax payments for the unlevered firm and the levered firm, where the risk profiles of the two tax payments are different. Happily, in this note, we show that both definitions of the present value of the tax shield are equivalent. To reconcile the two definitions of VTS, it is important to specify the risk profile of the free cash flow (FCF) and estimate the appropriate discount rates for the different cash flow profiles. We use a simple binomial model to specify the risk profile of the FCF and present simple numerical examples to illustrate the equivalence between the two definitions of the present value of the tax shield. The growth rate of the FCF and the leverage cost are zero. We assume that the reader is familiar with risk-neutral valuation. In Section One, we present a numerical example with risk-free debt. In Section Two, we present a numerical example with risky debt.

The Correct Value of Tax Shields

For constant growth companies, we prove that the value of tax shields in a world with no leverage cost is the present value of the debt, times the tax rate, times the required return to the unlevered equity, discounted at the unlevered cost of equity. Please note that this does not mean that the appropriate discount for tax shields is the unlevered cost of equity, since the amount being discounted is higher than the tax shield (it is multiplied by the unlevered cost of equity and not the cost of debt). Rather, this result arises as the difference of two present values. We also show that the value of tax shields is the difference between the present values of two different cash flows with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. This is the difference between the present values of two separate cash flows each with its own risk.

Beta Levered and Beta Unlevered

We claim that in a world without leverage cost the relationship between the levered beta (BL) and the unlevered beta (Bu) of a company depends upon the financing strategy. For a company that maintains a fixed book-value leverage ratio, the relationship is Fernandez (2004): BL = Bu + (Bu - Bd) D (1 - T) / E. For a company that maintains a fixed market-value leverage ratio, the relationship is Miles and Ezzell (1980):BL = Bu + (D / E) (Bu - Bd) [1 - T Kd / (1 + Kd)]. For a company with a preset debt in every period, the relationship is Modigliani and Miller (1963):BL = Bu + [Bu - Bd] (D-VTS) / E, being the Value of Tax Shields (VTS) the present value of the future tax shields discounted at the cost of debt. We also analyze alternative valuation theories proposed in the literature to estimate the relationship between the levered beta and the unlevered beta (Harris and Pringle (1985), Damodaran (1994), Myers (1974), and practitioners) and prove that all provide inconsistent results.

The Value of Tax Shields is the Difference of Two Present Values with Different Risk

We show that the value of tax shields is the difference between the present values of two different cash flows with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For perpetuities without costs of leverage, the value of tax shields is equal to the tax rate times the value of debt. For any company, we claim that the value of the tax shield in a world with no leverage cost is the present value of the debt (D) times the tax rate (T) times the required return to the unlevered equity (Ku), discounted at the unlevered cost of equity (Ku): VTS = PV[Ku; D T Ku]. Please note that it does not mean that the appropriate discount for the tax shields is the unlevered cost of equity. We discount D T Ku, which is not the tax shield. This expression arises as the difference of two present values each with different risk.

The Correct Value of Tax Shields. An Analysis of 23 Theories

Although Copeland et al. (2000) claim that finance literature does not provide a clear answer about which discount rate for the tax benefit of interest is theoretically correct, we show that we can provide some clear answers on that topic. This paper provides clear, theoretically sound, guidelines to evaluate the appropriateness of different valuation methods to estimate the present value of tax shields. We first show that the discounted value of tax shields is the difference between the present values of two different cash flows with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. This implies as a first guideline that, for the particular case of a perpetuity and a world without costs of leverage, the discounted value of tax shields is equal to the tax rate times the value of debt (i.e. Modigliani-Miller). The discounted value of tax shields can be lower, when costs of leverage exist. In that case, we show that, since the existence of leverage costs is independent of taxes, a second guideline for the appropriateness of the valuation method should be that the discounted value of tax shields when there are no taxes is negative. We then look at the case of constant growth and derive similar implications. Second, we identify 23 valuation theories proposed in the literature to estimate the present discounted value of tax shields and show their performance relative to the proposed guidelines. Eight of these theories do not satisfy the two proposed guidelines for the case of perpetuities. Only one of the valuation methods is consistent with these restrictions when we look at the case of constant growth and no leverage costs. Three theories provide consistent valuations when we allow for leverage costs and growth. Finally, we use the 23 theories to value a hypothetical firm and show remarkable differences in the obtained values suggesting the importance of using a method consistent with the proposed guidelines.

Strategic parameter-driven routing models for multidestination traffic in telecommunication networks

We present mathematical models that determine the optimal parameters for strategically routing multidestination traffic in an end-to-end network setting. Multidestination traffic refers to a traffic type that can be routed to any one of a multiple number of destinations. A growing number of communication services is based on multidestination routing. In this parameter-driven approach, a multidestination call is routed to one of the candidate destination nodes in accordance with predetermined decision parameters associated with each candidate node. We present three different approaches: (1) a link utilization (LU) approach, (2) a network cost (NC) approach, and (3) a combined parametric (CP) approach. The LU approach provides the solution that would result in an optimally balanced link utilization, whereas the NC approach provides the least expensive way to route traffic to destinations. The CP approach, on the other hand, provides multiple solutions that help leverage link utilization and cost. The LU approach has in fact been implemented by a long distance carrier resulting in a considerable efficiency improvement in its international direct services, as summarized.

Diversification: How Much is Enough?

Diversification in the fund of funds industry is at present not thorough enough. A model of random stock-picking, combined with empirical data, shows how the benefits of diversification vary among asset classes. This is the result of differing costs of leverage and differing levels of diversifiable and nondiversifiable risk. A comparison of the costs and benefits of diversification for funds of CTAs and hedge funds indicates that typical portfolio sizes are suboptimally low.

Communication and the Oslo Negotiation: Contacts, Patterns, and Modes

AbstractThis essay contends that Oslo, as a back-channel negotiation, grew out of and was implemented within a complex communication system. This system consists of six elements: the roles of multiple agents, the patterns of interaction among the agents, communication across the sides, overlapping inputs from negotiation channels, the roles of mediators, and the use of communication modes. Back-channel negotiations are characterized by concerns for legitimacy, secrecy, keeping the talks moving, and leveraging both sides to remain at the table. The Oslo system evolved through the use of multiple agents to enhance legitimacy and the use of chain patterns to filter information and persuade principals. The Norwegian mediators acted as facilitators to build relationships between the sides, leverage costs and benefits of working together, and accelerate the speed of the talks through using multiple modes of communication. Overall, the communication system preserved the secrecy of the process through special codes for telephone conversations and through traveling to multiple sites outside of Oslo for meetings. Ironically, the secrecy and expediency of the process also created an insular system, one in which the principals experienced selective bias and illusions of unanimity.

An empirical study of interest rate swap usage by nonfinancial corporate business

This study examines the relationship between the probability and extent of a firm's participation in interestrate swap markets and the magnitude of some of its operating and financial ratios. These ratios are selected to proxy incentives to reduce agency costs of leverage and information asymmetry in credit markets. The data on swap usage are obtained from disclosures mandated by SFAS 105. The results suggest that fixed-rate payers, compared to non-swap-users, have more leverage, greater profitability, more growth options, less operating risk, lower ratios of fixed to total assets, and more divergent earnings estimates. On the other hand, floating-rate payers do not seem to have financial and operating characteristics significantly different from non-swap-users, although they do have less divergent earnings estimates.