Appendix: Mathematics of the Mean–Variance Model
I. A.5 Basics of Capital Structure
Steven Bishop1
I.A.5.1 Introduction
How should a business be funded? How much debt? What form of debt? How much equity?
Does it matter? Answering these questions is at the heart of capital structure choice. The answer must be assessed relative to the overall objective of a business enterprise, and we view this as being to maximise the value of the business for its shareholders. Consequently, capital structure choice requires an understanding of the relationship between capital structure and business value.
This chapter focuses on the capital structure decision primarily from the perspective of an industrial company determining the most appropriate financing for its long-term assets and working capital. This is relevant for a lending institution considering the appropriate level of debt for its customers.
Financial institutions, particularly banks, face the same issues when considering their own capital structure. There are, however, additional complexities. Banks have a unique perspective on funding because of their role as deposit-taking institutions. Deposits are a source of low-cost funding, but are, at the same time, a ‘product’ that is offered to the public.
In addition, the indirect costs of financial distress for a bank are likely to be significantly larger than for an industrial company and, as a result, there are regulatory requirements that influence the capital structure decision. That is, there are minimum equity requirements and strict restrictions on the extent to which hybrid securities may qualify as capital for regulatory purposes. For most banks, however, these regulatory constraints are not binding; banks choose to hold more capital than regulators require. It is likely that while the specifics may vary, the general issues affecting capital structure for banks mirror those of other listed companies. The specific issues relevant for determining risk capital for banks are discussed in Section III of The PRM Handbook.
A key determinant of capital structure choice for any business is the risk or variability of the operating earnings stream. Generally, the higher this risk the less debt can be supported, essentially due to the exposure to distress and bankruptcy costs. Many firms will select a desired credit rating or probability of distress based on the volatility of the earnings stream and use this
1 Visiting Fellow, Macquarie Applied Finance Centre, Macquarie University; Director and Principal, Education and Management Consulting Services Pty Ltd.
The PRM Handbook – I.A.5 Basics of Capital Structure
to establish the interest bill, or amount of debt that can be supported. Further, hedging risks can reduce risk and enable additional debt financing and adding value. We expect banks to have lower operating earnings volatility than industrials, and therefore higher debt levels.
We know that funding decisions affect the behaviour of managers under certain circumstances and that this will affect the value of a business. Exactly what the best funding mix is for a particular business is a little imprecise. There are, however, a number of key guidelines that we can provide to help directors make decisions in this area that create shareholder value. The objectives of this chapter are to identify differences between debt and equity and present the drivers of choice between them for a corporation.
As noted above, the underlying assumption in the analysis is that the primary objective of a business is to maximise its value for shareholders. For the purposes of this chapter we will view maximising the value of the operating cash-flow stream as also maximising the value of the equity cash-flow stream.2
The value we focus on is the present value of operating free cash flows over time.
¦
f1 1
t
t t
WACC
V OFCF (I.A.5.1)
where
x V is the value of the business and is equal to the value of debt (D) plus the value of equity (E);
x OFCFt is expected operating free cash flow after tax in period t (i.e., revenue less operating expenses and capital expenditure), that is, it is the mean of a probability distribution of possible operating free cash-flow outcomes in period t; and
x WACC is the weighted average cost of capital and is equal to the weighted average of the cost of debt and the cost of equity,
2 The value of the firm (V) can be viewed as the sum of the value of debt (D) plus the value of equity (E), that is, V = D + E. Since there is a limit to the claim debt has on the value of the company, maximising V is effectively maximising E. However, E could be maximised by transferring value from D. Thus maximising V and E might not be the same. In fact the text will examine ways management might transfer wealth from D to E and, in so doing, provide explanations for the existence of covenants, aspects of corporation law and the reason for auditing of the books. Nevertheless, our primary focus is on how V changes with changes in the debt–equity mix because of the contractual arrangements which minimise wealth transfers.
Copyright© 2004 S. Bishop and the Professional Risk Managers’ International Association 2 For Evaluation Only.
The PRM Handbook – I.A.5 Basics of Capital Structure
V r E V t D r
WACC d 1 e (I.A.5.2)
where
x rd is the cost of debt (interest rate);
x re is the cost of equity, assumed to be determined using the capital asset pricing model (see Chapter I.A.4);
x D/V is the proportion of debt financing and E/V is the proportion of equity financing;
and
x t is the effective tax rate.
For the purposes of this chapter we will assume that the expected future cash flow can be expressed as a perpetuity and therefore its value is:
WACC
V OFCFt (I.A.5.3)
Our concern is with how V changes with the proportion of debt (to equity) financing, if it changes at all. The effect can be analysed by examining the impact of D/V changes on WACC and/or the operating free cash flow. As we will see, both WACC and cash-flow effects can arise from changing the capital structure decision.
This chapter presents both the beneficial and detrimental effects of changing the debt–equity mix to tease out the considerations in capital structure choice. The analysis of this trade-off starts with an assumption of all-equity financing and then examines how value changes as debt is progressively substituted for equity. What becomes evident is that there are benefits of debt financing that increase the value of a business up to a point where the costs begin to offset them.
This point/range corresponds to an optimal capital structure, as is illustrated in Figure I.A.5.1.
The shape of the curve and the optimal point/range depend upon many factors that are likely to be similar for businesses in the same industry, with some ‘uniqueness’ for a particular business.
These factors or determinants are discussed in subsequent sections.
Copyright© 2004 S. Bishop and the Professional Risk Managers’ International Association 3 For Evaluation Only.
Figure I.A.5.1: Value changes with the proportion of debt financing
Benefits of Debt Costs of Debt Value
Debt / Equity Highest Value
All Equity Funding
Progressively substituting more debt for equity
Benefits of Debt Costs of Debt Value
Debt / Equity Highest Value
All Equity Funding
Progressively substituting more debt for equity
The chapter proceeds as follows:
It discusses agency costs to shareholders that arise when a business appoints professional managers to operate on their behalf and, particularly, the incentives such managers have to transfer wealth from debt-holders to shareholders. This explains why we see arrangements like restrictive covenants, dividends limited to earnings, and restrictions around issuing higher-ranking debt.
x
x x
x
It characterises debt and equity and identifies some of the variables that distinguish different forms of debt.
Under the heading ‘Choice of Capital Structure’ it firstly demonstrates that it is easy to be misled into thinking that debt is ‘cheap’ because the interest rate is lower than the cost of equity. Debt is not ‘cheap’. For debt to be attractive it must provide benefits other than an apparent lower interest rate. The sources of such benefits are examined next. This is followed by a discussion of the source of additional costs of debt that limits its attractiveness and therefore leads to an optimal mix of debt and equity financing.
It finishes by presenting some guidelines for selecting the debt-equity mix and by showing what chief financial officers (CFOs) say they focus on when making this important decision.
Copyright© 2004 S. Bishop and the Professional Risk Managers’ International Association 4
The PRM Handbook – I.A.5 Basics of Capital Structure