Borrow or sell equity? Four capital-structure theories for SME owners

A dried-vegetable processor needs VND 3 billion for a second drying line. There is VND 0.8 billion in the safe. A bank will lend VND 2.2 billion, or an investor will put in VND 2.2 billion for 25 per cent of the business. Borrow, sell equity, or wait and save?

The processor and every number here are invented, not a real business. It is unlisted, so the textbook phrase "issue shares" means, in this article, selling equity to one investor. The article puts the four capital-structure theories onto that decision. Other doors to money are mapped in a guide to funding sources for new businesses.

Invented example, all numbers made up. The VND 2.2 billion loan runs for five years with equal principal repayments and interest of 10 per cent a year on the outstanding balance. Selling 25 per cent for VND 2.2 billion values the business at VND 6.6 billion before the investment. The project has an NPV of +VND 0.5 billion at the opportunity cost of capital. The owner values the business today at VND 9 billion, including the VND 0.8 billion of cash. Earnings before interest and tax (EBIT) after the project are VND 2.1 billion in a normal year. The 20 per cent tax rate is an assumption only.

If markets were perfect, would borrowing and selling equity differ?

No. Modigliani and Miller (1958) prove that a firm's market value equals its expected income from assets divided by one capitalisation rate for its risk class, whatever the capital structure (Modigliani and Miller, 1958, p. 268). Investors can borrow on personal account, so a levered firm cannot command a premium over an unlevered one (Modigliani and Miller, 1958, p. 270). Debt looks cheaper, but it raises the yield demanded on the shares as the debt-to-equity ratio rises, so the overall cost stays put (Modigliani and Miller, 1958, p. 271).

For the owner, a 10 per cent loan is not "cheaper" than equity once the extra risk loaded onto her own stake is counted. The way a project is financed also does not decide whether it is worth doing (Modigliani and Miller, 1958, p. 292): in this world, a project with NPV +VND 0.5 billion is worth doing whoever pays. Each of the next three theories picks one friction that breaks this neutrality: taxes and distress, information, and conflicts of interest.

Is there an optimal amount of borrowing? Taxes and distress

The trade-off theory says yes: the firm weighs the interest tax shield against the costs of bankruptcy and financial distress, borrowing more or less until firm value is highest (Myers, 1984). The 1958 paper already contains the tax piece: if interest is deductible, shareholders gain from debt even in a perfect market, but the authors call the gain small (Modigliani and Miller, 1958, p. 294). According to Myers, the 1963 correction says any tax-paying firm gains by borrowing (Myers, 1984).

In the example, 10 per cent on VND 2.2 billion is VND 220 million in year one. At the assumed 20 per cent rate, tax falls by VND 44 million and interest after tax is VND 176 million. The shield is a fifth of the interest, and only works if the firm has taxable profit to deduct it from (Myers, 1984). Distress costs sit in the bad year: principal of VND 440 million plus interest of VND 220 million makes VND 660 million in year one.

EBIT is not cash, so the table is a crude test. In the bad year EBIT does not cover principal and interest: distress costs may begin there. Modigliani and Miller observe that the difficulty of borrowing more tends to show up as tighter restrictions on management and finances rather than as a higher interest rate (Modigliani and Miller, 1958, p. 273). Myers notes that firms with valuable intangible assets or growth opportunities tend to borrow less than firms holding mostly tangible assets (Myers, 1984).

Why might an owner hesitate to sell equity when she thinks the firm is worth more?

Because investors price what they can see and the owner knows more. Myers and Majluf (1984) build a model on that: if managers act for existing shareholders and the firm is undervalued, issuing shares hands part of the value to new shareholders, and when that transfer exceeds the project's NPV the firm passes up the project (Myers and Majluf, 1984, p. 188). Issuing is itself a signal that is bad, or at least less good, than not issuing, so investors pay less (Myers and Majluf, 1984, p. 188). This is the foundation of the pecking order theory, resting on information asymmetry.

Applied to the processor (my numbers): after the project, the whole firm is worth 9 + 2.2 + 0.5 = VND 11.7 billion in the owner's eyes. Selling 25 per cent for VND 2.2 billion gives the investor 25% × 11.7 = VND 2.925 billion, a gain of VND 0.725 billion, which exceeds the NPV of 0.5.

If she sells, the owner keeps 75% × 11.7 = VND 8.775 billion, below the VND 9.0 billion of doing nothing. A fairly priced loan leaves her the whole NPV. If both sides valued the business at VND 6.6 billion, the sale would instead gain her VND 0.375 billion, which is 75% of 0.5: the damage comes from the valuation gap, not from selling equity as such.

In the model, default-free debt is as good as cash in the bank, while risky debt only eases the problem (Myers and Majluf, 1984, p. 207); an SME loan carries default risk. Modigliani and Miller saw this situation in small or new firms: existing owners may pass up a profitable venture rather than give outsiders too large a share (Modigliani and Miller, 1958, p. 292).

What if the firm has spare cash and few new projects?

Then Jensen turns the pecking order around: debt helps because it takes cash out of managers' hands. Jensen (1986) defines free cash flow as cash beyond what is needed to fund every positive-NPV project, and says conflicts between shareholders and managers are most severe when a firm generates a lot of it (Jensen, 1986, p. 323). Borrowing without retaining the proceeds turns debt into a promise to pay cash out that managers cannot take back, because creditors can take the firm to bankruptcy court if it defaults (Jensen, 1986, p. 324).

The two views collide on internal funds. Jensen says financing projects internally avoids the monitoring of the capital markets (Jensen, 1986, p. 323); Myers and Majluf say the same behaviour is, in their model, in shareholders' interest (Myers and Majluf, 1984, p. 209). An owner-manager who holds all the equity has none of the conflict Jensen describes. In my inference it appears with hired managers, with several family members sharing control, or with a minority investor who does not control spending; for the parallel question between divisions of a group, see internal capital markets. In the example, the VND 660 million of principal and interest in year one is such a promise: in a normal year it forces the processor to choose projects more carefully, and in a bad year the same sum is the distress risk above.

Four theories, four predictions: which to use?

None wins everywhere. Myers and Majluf conclude that a full description of financing behaviour will need several stories told at once (Myers and Majluf, 1984, p. 220). For a highly profitable, low-risk processor in a slow-growth industry the first two theories predict opposite things: trade-off says safe firms ought to be able to borrow more, while pecking order says an unusually profitable firm ends up with an unusually low debt ratio against its industry and does little to change it (Myers, 1984). The library also holds a fifth, market timing: among US firms, those with little debt are often the ones that raised funds when market valuations were high (Baker and Wurgler, 2002, p. 2).

Going deeper: what I read and where the limits are

Modigliani and Miller (1958), American Economic Review 48(3), pp. 261–297, has no DOI. I read the JSTOR scan hosted by a university, closely at pages 263–273 and 292–295, and only skimmed the empirical tests. I have not read the 1963 tax correction or Kraus and Litzenberger (1973); the trade-off theory here rests on Myers (1984).

Myers and Majluf (1984), Journal of Financial Economics 13(2), pp. 187–221: I read the journal version on the University of Hohenheim site, closely for the introduction, example, debt section and conclusion, skimming the general proofs. Myers (1984): I read NBER working paper 1393 (July 1984), so the published version may differ and I give no page numbers. Jensen (1986), pp. 323–329: full text, JSTOR scan. Baker and Wurgler (2002): only the introduction (pp. 1–4).

The sources concern listed or large companies, mostly American, so applying them to an unlisted Vietnamese SME is my inference. The processor and every number in the example are invented, and the article has no source on tax law or lending conditions in Vietnam.