Capital Structure of a Firm

1 Introduction

The financing decision is the choice of how the business is funded — debt or equity, and in what proportion. It matters because the mix changes the weighted average cost of capital, and the weighted average cost of capital is the rate at which the entity's future cash flows are discounted. Change the discount rate and the value of the entity changes, even though the cash flows themselves have not moved.

Write that down before anything else, because every theory in this chapter is a variation on it. If an entity generates a constant cash flow X in perpetuity and that cash flow is discounted at the weighted average cost of capital k, then its value is:

V₀ = X ÷ k

A lower WACC therefore means a higher value, and a higher WACC a lower value. The question the capital structure theories set out to answer is whether — and how — the level of gearing changes k.

Three answers are examined: the traditional view, Modigliani and Miller without tax (1958), and Modigliani and Miller with corporate tax (1963). They differ in exactly one thing: what they say happens to the cost of equity as gearing rises.

2 The weighted average cost of capital

Before any theory, the arithmetic. The weighted average cost of capital is the cost of each source of finance weighted by its market value:

WACC = [V_E ÷ (V_E + V_D)] × k_e + [V_D ÷ (V_E + V_D)] × k_d(1 − t)

where:

• V_E and V_D are the market values of equity and debt — not the book values in the statement of financial position

• k_e is the cost of equity

• k_d is the cost of debt before tax, so k_d(1 − t) is what the debt actually costs the entity once the interest has been relieved against taxable profit

• t is the rate of corporate income tax

Two things in that formula do all the work in this chapter. The weights change as gearing changes — that much is obvious. And the cost of equity itself changes as gearing changes, because debt puts a fixed prior claim in front of the shareholders and so makes their returns more variable. The theories disagree only about the size of that second effect.

3 Traditional theory

YouTube videoLoad YouTube video

It has long been accepted that:

1. equity is a more expensive source of finance than debt — lenders take a prior claim, often with security, so they require a lower return than shareholders do, the interest attracts tax relief and the issue costs are lower; and

2. higher gearing increases the risk borne by shareholders, and therefore raises the cost of equity.

If both are true, then as gearing changes the WACC must change too. The traditional view reasons about the two effects in turn.

At low levels of gearing, shareholders are largely untroubled: the cost of equity rises only slightly, so the substitution of cheap debt for expensive equity dominates and the WACC falls. At high levels of gearing, so much profit is committed to interest that the dividend becomes genuinely uncertain; the cost of equity then rises steeply, and eventually even the lenders take fright and the cost of debt rises too. The WACC turns and rises.

Between the two there is a minimum — the optimal level of gearing. Because value is cash flow divided by the WACC, the gearing that minimises the WACC is also the gearing that maximises the value of the entity.

The graph is drawn from the arithmetic of the WACC formula in section 2, with the cost of equity rising gently at first and then steeply, and the cost of debt flat until high gearing. The WACC line is the weighted average of the other two — it must always lie between them — and it reaches its minimum at a gearing ratio of about 0.4 in this illustration. The exact position of the minimum is not the point and cannot be read off a graph; the shape is the point.

The implications are:

• since the entity should always borrow in the cheapest way available, it should raise debt finance until it reaches the optimal level of gearing;

• once there, it should hold that level of gearing by raising future finance part equity and part debt in the proportions that leave the gearing unchanged;

• while gearing up, projects should be appraised at the cost of the extra finance actually raised — the marginal cost of capital;

• once optimal gearing has been reached and is being maintained, the marginal cost of the extra finance is the WACC, so projects are appraised at the WACC.

All of that is an expression of common sense rather than a theory. It establishes that gearing matters; it does not quantify the effect, and it gives no way of finding the optimum in advance — the entity has to feel its way towards it. In the absence of any other information, assume an entity has reached its optimal gearing and is maintaining it, and appraise projects at its WACC.

It was that gap — an accepted effect that nobody could quantify — that Modigliani and Miller set out to close.

4 Modigliani and Miller

Modigliani and Miller (M&M) argued that the extra risk gearing creates for shareholders is not vague: it is measurable, and therefore the change in the cost of equity, and hence in the WACC, can be predicted rather than guessed at. They published twice, five years apart, and the two papers reach opposite practical conclusions because the second one lets in tax.

4.1 M&M without tax (1958)

Ignoring tax, M&M state that higher gearing does create more risk for shareholders and the cost of equity does rise — but it rises in exact proportion to the amount of debt taken on, so that the increase in the cost of equity precisely offsets the benefit of the cheaper debt.

The two effects cancel, and so:

• Proposition I — the total market value of the entity (equity plus debt) is unaffected by its capital structure;

• Proposition II — the cost of equity rises linearly with the ratio of debt to equity, and the weighted average cost of capital is constant however the entity is financed.

The cost of equity line is straight, which is the whole of Proposition II: plotted against the debt-to-equity ratio, the risk premium the shareholders demand is directly proportional to the gearing. The WACC line is flat.

The implications are:

1. it is irrelevant how an entity raises finance — the overall cost of its capital is unaffected;

2. every investment should be appraised at the WACC, however it happens to be financed.

That the total market value is unchanged is, on reflection, unsurprising. However the entity is financed, the total cash available for distribution is the same; if more goes to lenders then less goes to shareholders, and the total does not move. Why should the total value be any different?

The 1958 paper caused a great deal of interest and had very little practical relevance, because it ignored all taxes.

4.2 M&M with corporate tax (1963)

Five years later M&M reworked the theory with corporate income tax in it, still ignoring personal taxation.

Debt interest is deductible in computing taxable profit; a dividend is not — it is a distribution of profit that has already been taxed. Borrowing therefore reduces the entity's tax bill, and the saving belongs to the shareholders. The cost of equity still rises with gearing, but by less than the tax relief is worth, so the two effects no longer cancel:

• the WACC falls as gearing rises;

• the total market value of the entity rises as gearing rises;

• so the entity should raise as much debt as it possibly can.

The gap between the two cost-of-debt lines is the tax relief, and it is the entire reason the WACC falls. In this illustration an ungeared cost of equity of 12% and a pre-tax cost of debt of 6% at a 30% tax rate take the WACC from 12% at zero gearing to 9.84% at a debt-to-equity ratio of 1.5.

The rise in total value is equally logical. The more the entity borrows, the more interest it pays, the less tax it pays on the same pre-interest profit, and so the more there is to distribute in total to lenders and shareholders together. On M&M's assumptions the whole of that gain is the tax saved on the interest, capitalised:

V_g = V_u + V_Dt

where V_g is the value of the geared entity, V_u the value of the same entity if it were all-equity financed, and V_Dt the value of the tax shield — which takes that simple form only because the debt is assumed to be irredeemable and the relief certain.

4.3 The M&M assumptions

The theories hold only so far as their assumptions do, and the assumptions are the most heavily examined part of this section. They are:

• shareholders have perfect information about the entity and about the effect of the gearing on it;

• shareholders act rationally with regard to risk — nobody panics at the sight of a little debt;

• a perfect capital market exists: no transaction costs, no issue costs, and securities correctly priced, so that a change in the WACC feeds straight through to the market value;

• there are no costs of financial distress or bankruptcy, however high the gearing;

• debt interest is tax allowable, and the entity has enough taxable profit to use the relief — a loss-making or already sheltered company gets nothing from the tax shield;

• investors can borrow personally on the same terms as the entity, so that corporate gearing and personal gearing are perfect substitutes;

• the debt is irredeemable;

• the entity is liable to tax but its investors are not — personal taxation is ignored throughout, in both papers.

5 The M&M formulae

YouTube videoLoad YouTube video

M&M expressed the effect of gearing on the cost of equity and on the WACC as two formulae. Both are given on the formula sheet in the examination, so they do not have to be memorised — but they do have to be applied accurately, and the symbols have to be read correctly.

5.1 The cost of equity of a geared entity

k_eg = k_eu + (k_eu − k_d) × [V_D(1 − t) ÷ V_E]

where:

Read it as an addition. Start from the return shareholders would require if there were no debt at all; then add a premium for the financial risk the debt creates. The premium is larger the wider the gap between k_eu and k_d, and larger the more debt there is relative to equity.

5.2 The weighted average cost of capital of a geared entity

k_adj = k_eu × [1 − V_Dt ÷ (V_E + V_D)]

With no debt, V_D is nil, the bracket is 1, and the WACC equals k_eu — an all-equity entity's WACC is its cost of equity. As debt is introduced the bracket falls below 1 and the WACC falls with it; the whole of the fall is the tax relief on the interest.

The two formulae are not alternatives. Put the k_eg from section 5.1 into the ordinary weighted-average formula of section 2 and the answer is exactly k_adj. Example 3 does it both ways to show that.

5.3 Ungearing and regearing

In practice the formula is usually needed backwards. An entity moving into an industry it is not already in has no cost of equity of its own for that business risk, so it borrows one from a quoted company that is already in the industry — a proxy. The proxy's cost of equity reflects the proxy's business risk and the proxy's gearing, and only the first of those is wanted. Two steps:

1. Ungear — strip the proxy's financial risk out of its cost of equity to leave k_eu, the return for the business risk alone.

2. Regear — put your own gearing in, to get the k_eg you should be using.

Rearranging the formula in section 5.1 for k_eu gives the ungearing step:

k_eu = [k_egV_E + k_dV_D(1 − t)] ÷ [V_E + V_D(1 − t)]

6 The effect of capital structure on the financial statements

Choosing debt rather than equity, or the reverse, changes the reported figures as well as the value of the entity, and the reported figures are what covenants and analysts are measured against.

The book gearing that comes out of the statement of financial position is not the market gearing the theories in this chapter are about, and the two can be a long way apart — a company whose shares trade far above their book value has much lower market gearing than book gearing. Covenants are normally written on the book figures; the value argument runs on the market ones.

7 Structuring debt and equity within a group

A group is not one borrower. The same finance can be raised by the parent, by an intermediate holding company or by the operating subsidiary that will use it, and where it is raised changes five things.

• Who the lender can look to. Debt raised by a subsidiary is a claim on that subsidiary's assets and cash flows, and on nothing else, unless the parent guarantees it. Debt raised at the parent is a claim on the parent — whose only route to a subsidiary's cash is a dividend the subsidiary has to declare, and only after the subsidiary's own lenders have been paid.

• What the debt costs. A group with a strong credit standing can usually borrow more cheaply at the centre and on-lend to the subsidiary than the subsidiary could borrow alone. The price of that is a parent guarantee, which extends the parent's risk over borrowing it does not control.

• Where the tax relief lands. Interest is relieved against the taxable profit of the company that pays it. Debt pushed into a subsidiary with little taxable profit, or into a low-tax jurisdiction, wastes relief; debt in a profitable, highly taxed company is worth more. Many tax regimes restrict this deliberately, through thin-capitalisation and interest-restriction rules and through transfer-pricing rules on the rate charged on intra-group loans.

• Currency. Borrowing in the currency of the assets and cash flows a subsidiary generates hedges the group's translation exposure without a derivative — the matching technique of chapter 9. Borrowing centrally in one currency and lending on in another does not.

• What the accounts show. Intra-group loans cancel on consolidation, so consolidated gearing shows only external borrowing. A covenant tested at subsidiary level is nevertheless tested on that subsidiary's own accounts, so a structure that looks conservative for the group can be tight in one of its companies.

The practical consequence is that the group sets a target capital structure, and the individual companies' structures are then arranged so that the group reaches it at the lowest cost, with the tax relief usable and the covenants met at every level at which they are tested.

8 What the theories leave out

The three theories differ in one respect only — what they say the cost of equity does as gearing rises — and they share a long list of things they do not contain: the costs of financial distress and of an actual insolvency; the restrictions lenders impose through covenants and the loss of freedom that goes with them; issue costs; the limited debt capacity created by the assets available as security; and the plain fact that relief on interest is worth nothing to an entity with no taxable profit to relieve.

Which is why real capital structures sit well below M&M 1963's “as much as possible”, and why the traditional picture — a range of gearing within which the WACC is low, rather than a single point at which it is lowest — remains the better description of what finance directors actually do.

9 Test your knowledge

Two quick checks before you move on: work through the flashcards to fix this chapter’s terms and definitions, then sit the objective questions for exam-style practice. Both mark themselves and explain the answers as you go.