# Debt Irrelevance Proposition Assumptions And Critical Thinking

## When Are Dividends Irrelevant? (The Miller Modigliani Proposition)

There is a school of thought that argues that what a firm pays in dividends is irrelevant and that stockholders are indifferent about receiving dividends. Like the capital structure irrelevance proposition, the dividend irrelevance argument has its roots in a paper crafted by Miller and Modigliani.

## The Underlying Assumptions

The underlying intuition for the dividend irrelevance proposition is simple. Firms that pay more dividends offer less price appreciation but must provide the same total return to stockholders, given their risk characteristics and the cash flows from their investment decisions. Thus, there are no taxes, or if dividends and capital gains are taxed at the same rate, investors should be indifferent to receiving their returns in dividends or price appreciation.

For this argument to work, in addition to assuming that there is no tax advantage or disadvantage associated with dividends, we also have to assume the following:

· There are no transactions costs associated with converting price appreciation into cash, by selling stock. If this were __not__ true, investors who need cash urgently might prefer to receive dividends.

· Firms that pay too much in dividends can issue stock, again with no flotation or transactions costs, to take on good projects. There is also an implicit assumption that this stock is fairly priced.

· The investment decisions of the firm are unaffected by its dividend decisions, and the firm’s operating cash flows are the same no matter which dividend policy is adopted.

· Managers of firms that pay too little in dividends do not waste the cash pursuing their own interests (i.e., managers with large free cash flows do not use them to take on bad projects).

Under these assumptions, neither the firms paying the dividends nor the stockholders receiving them will be adversely affected by firms paying either too little or too much in dividends.

## A Proof of Dividend Irrelevance

To provide a formal proof of irrelevance, assume that an LongLast Corporation, an __unlevered__ firm manufacturing furniture, has a net operating income after taxes of $ 100 million, growing at 5% a year, and a cost of capital of 10%. Further, assume that this firm has net capital expenditure needs (capital expenditures in excess of depreciation) of $ 50 million, also growing at 5% a year, and that there are 105 million shares outstanding. Finally, assume that this firm pays out residual cash flows as dividends each year. The value of LongLast Corporation can be estimated as follows:

Free Cash Flow to the Firm = EBIT (1- tax rate) - Net Capital Expenditures

= $ 100 million - $ 50 million = $ 50 million

Value of the Firm = Free Cash Flow to Firm (1+g) / (WACC - g)

= $ 50 (1.05) / (.10 - .05) = $ 1050 million

Price per share = $ 1050 million / 105 million = $ 10.00

Based upon its cash flows, this firm could pay out $ 50 million in dividends.

Dividend per share = $ 50 million/105 million = $ 0.476

Total Value per Share = $ 10.00 + $ 0.48 = $10.476

To examine how the dividend policy affects firm value, assume that LongLast Corporation is told by an investment consultant that its stockholders would gain if the firm paid out $ 100 million in dividends, instead of $ 50 million. It now has to raise $ 50 million in new financing to cover its net capital expenditure needs. Assume that LongLast Corporation can issue new stock with __no flotation cost__ and __no adverse signaling implications__ to raise these funds. If it does so, the firm value will remain unchanged, since the value is determined not by the dividend paid but by the cash flows generated on the projects. The stock price will decrease, because there are more shares outstanding, but stockholders will find this loss offset by the increase in dividends per share. In order to estimate the price per share at which the new stock will be issued, note that after the dividend payment, the old stockholders in the firm will own only $1000 million of the total firm value of $ 1050 million.

Value of the Firm = $ 1050 million

Dividends per share = $ 100 million/105 million shares = $ 0.953

Value of the Firm for existing stockholders after dividend payment = $ 1000 million

Price per share = $ 1000 million / 105 million = $ 9.523

Value accruing to stockholder = $ 9.523 + $ 0.953 = $ 10.476

Another way of seeing this is to divide the stockholders into existing and new stockholders. When dividends are increased by $ 50 million, and new stock is issued for an equivalent amount, the existing stockholders now own only $1000 million out of the firm value of $ 1050 million, but their loss in firm value is offset by their gain in dividends. In fact, if the operating cash flows are unaffected by dividend policy, we can show that the firm value will be unaffected by dividend policy and that the average stockholder will be indifferent to dividend policy since he or she receives the same total value (price + dividends) under any dividend payment.

To consider an alternate scenario, assume that LongLast Corporation pays out no dividends and retains the residual $50 million as a cash balance. The value of the firm to existing stockholders can then be computed as follows:

Value of Firm = Present Value of After-tax Operating CF + Cash Balance

= $ 50 (1.05) / (.10 - .05) + $ 50 million = $1100 million

Value per share = $ 1100 million / 105 million shares = $10.48

Note that the total value per share is unchanged from the previous two scenarios, as shown in Table 10.1, though all of the value comes from price appreciation.

*Table 10.1: Value Per Share to Existing Stockholders from Different Dividend Policies*

Value of Firm | Dividends | Value to Existing | Price | Dividends | Total Value |

(Operating CF) |
| Stockholders | per share | per share | per share |

$1,050 | $ - | $1,100 | $ 10.48 | $ - | $ 10.48 |

$1,050 | $ 10.00 | $1,090 | $ 10.38 | $ 0.10 | $ 10.48 |

$1,050 | $ 20.00 | $1,080 | $ 10.29 | $ 0.19 | $ 10.48 |

$1,050 | $ 30.00 | $1,070 | $ 10.19 | $ 0.29 | $ 10.48 |

$1,050 | $ 40.00 | $1,060 | $ 10.10 | $ 0.38 | $ 10.48 |

$1,050 | $ 50.00 | $1,050 | $ 10.00 | $ 0.48 | $ 10.48 |

$1,050 | $ 60.00 | $1,040 | $ 9.90 | $ 0.57 | $ 10.48 |

$1,050 | $ 70.00 | $1,030 | $ 9.81 | $ 0.67 | $ 10.48 |

$1,050 | $ 80.00 | $1,020 | $ 9.71 | $ 0.76 | $ 10.48 |

$1,050 | $ 90.00 | $1,010 | $ 9.62 | $ 0.86 | $ 10.48 |

$1,050 | $ 100.00 | $1,000 | $ 9.52 | $ 0.95 | $ 10.48 |

When LongLast Corporation pays less than $ 50 million in dividends, the cash accrues in the firm and adds to its value. The increase in the stock price again is offset by the loss of cash flows from dividends.

It is important to note though that the irrelevance of dividend policy is grounded on the following assumptions.

· The issue of new stock is assumed to be costless and can therefore cover the cash shortfall created by paying excess dividends.

· It is assumed that firms that face a cash shortfall do not respond by cutting back on projects and thereby affecting future operating cash flows.

· Stockholders are assumed to be indifferent between receiving dividends and price appreciation.

· Any cash remaining in the firm is invested in projects that have zero net present value (such as financial investments) rather than used to take on poor projects.

## Implications of Dividend Irrelevance

If dividends are, in fact, irrelevant, firms are spending a great deal of time pondering an issue about which their stockholders are indifferent. A number of strong implications emerge from this proposition. Among them, the value of equity in a firm should not change as its dividend policy changes. This does not imply that the price per share will be unaffected, however, since larger dividends should result in lower stock prices and more shares outstanding. In addition, in the long term, there should be no correlation between dividend policy and stock returns. Later in this chapter, we will examine some studies that have attempted to examine whether dividend policy is in fact irrelevant in practice.

The assumptions needed to arrive at the dividend irrelevance proposition may seem so onerous that many reject it without testing it. That would be a mistake, however, because the argument does contain a valuable message: Namely, a firm that has invested in bad projects cannot hope to resurrect its image with stockholders by offering them higher dividends. In fact, the correlation between dividend policy and total stock returns is weak, as we will see later in this chapter.

The **Modigliani–Miller theory (of Franco Modigliani, Merton Miller) is a theorem on capital structure, arguably forming the basis for modern thinking on capital structure. The basic theorem states that in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed.^{[1]} Since the value of the firm depends neither on its dividend policy nor its decision to raise capital by issuing stock or selling debt, the Modigliani–Miller theorem is often called the**

*capital structure irrelevance principle'*.

The key Modigliani-Miller theorem was developed in a world without taxes. However, if we move to a world where there are taxes, when the interest on debt is tax deductible, and ignoring other frictions, the value of the company increases in proportion to the amount of debt used.^{[2]} And the source of additional value is due to the amount of taxes saved by issuing debt instead of equity.

Modigliani was awarded the 1985 Nobel Prize in Economics for this and other contributions.

Miller was a professor at the University of Chicago when he was awarded the 1990 Nobel Prize in Economics, along with Harry Markowitz and William F. Sharpe, for their "work in the theory of financial economics", with Miller specifically cited for "fundamental contributions to the theory of corporate finance".

## Historical background[edit]

Miller and Modigliani derived the theorem and wrote their groundbreaking article when they were both professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon University. The story goes that Miller and Modigliani were set to teach corporate finance for business students despite the fact that they had no prior experience in corporate finance. When they read the material that existed they found it inconsistent so they sat down together to try to figure it out. The result of this was the article in the *American Economic Review* and what has later been known as the M&M theorem.

Miller and Modigliani published a number of follow-up papers discussing some of these issues. The theorem was first proposed by F. Modigliani and M. Miller in 1958.

## The theorem[edit]

Consider two firms which are identical except for their financial structures. The first (Firm U) is **unlevered**: that is, it is financed by **equity** only. The other (Firm L) is levered: it is financed partly by equity, and partly by debt. The Modigliani–Miller theorem states that the value of the two firms is the same.

## Without taxes[edit]

### Proposition I[edit]

where

*is the value of an unlevered firm* = price of buying a firm composed only of equity, and *is the value of a levered firm* = price of buying a firm that is composed of some mix of debt and equity. Another word for levered is *geared*, which has the same meaning.^{[3]}

To see why this should be true, suppose an investor is considering buying one of the two firms, U or L. Instead of purchasing the shares of the levered firm L, he could purchase the shares of firm U and borrow the same amount of money B that firm L does. The eventual returns to either of these investments would be the same. Therefore the price of L must be the same as the price of U minus the money borrowed B, which is the value of L's debt.

This discussion also clarifies the role of some of the theorem's assumptions. We have implicitly assumed that the investor's cost of borrowing money is the same as that of the firm, which need not be true in the presence of asymmetric information, in the absence of efficient markets, or if the investor has a different risk profile than the firm.

### Proposition II[edit]

here

*is the expected rate of return on equity, or cost of equity.**is the expected rate of return on borrowings, or cost of debt.**is the debt-to-equity ratio.*

A higher debt-to-equity ratio leads to a higher required return on equity, because of the higher risk involved for equity-holders in a company with debt. The formula is derived from the theory of weighted average cost of capital (WACC).

These propositions are true under the following assumptions:

- no transaction costs exist, and
- individuals and corporations borrow at the same rates.

These results might seem irrelevant (after all, none of the conditions are met in the real world), but the theorem is still taught and studied because it tells something very important. That is, capital structure matters precisely because one or more of these assumptions is violated. It tells where to look for determinants of optimal capital structure and how those factors might affect optimal capital structure.

## With taxes[edit]

### Proposition I[edit]

where

This means that there are advantages for firms to be levered, since corporations can deduct interest payments. Therefore leverage lowers tax payments. Dividend payments are non-deductible.

### Proposition II[edit]

where:

The same relationship as earlier described stating that the cost of equity rises with leverage, because the risk to equity rises, still holds. The formula, however, has implications for the difference with the WACC. Their second attempt on capital structure included taxes has identified that as the level of gearing increases by replacing equity with cheap debt the level of the WACC drops and an optimal capital structure does indeed exist at a point where debt is 100%.

The following assumptions are made in the propositions with taxes:

- corporations are taxed at the rate on earnings after interest,
- no transaction costs exist, and
- individuals and corporations borrow at the same rate.

## Notes[edit]

## Further reading[edit]

- Brealey, Richard A.; Myers, Stewart C. (2008) [1981].
*Principles of Corporate Finance*(9th ed.). Boston: McGraw-Hill/Irwin. ISBN 978-0-07-340510-0. - Stewart, G. Bennett (1991).
*The Quest for Value: The EVA management guide*. New York: HarperBusiness. ISBN 0-88730-418-4. - Modigliani, F.; Miller, M. (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment".
*American Economic Review*.**48**(3): 261–297. JSTOR 1809766. - Modigliani, F.; Miller, M. (1963). "Corporate income taxes and the cost of capital: a correction".
*American Economic Review*.**53**(3): 433–443. JSTOR 1809167. - Miles, J.; Ezzell, J. (1980). "The weighted average cost of capital, perfect capital markets and project life: a clarification".
*Journal of Financial and Quantitative Analysis*.**15**: 719–730. doi:10.2307/2330405. JSTOR 2330405. - Sargent, Thomas J. (1987).
*Macroeconomic Theory*(Second ed.). London: Academic Press. pp. 157–162. ISBN 0-12-619751-2. - Suresh P. Sethi, Extension of the Miller and Modigliani theory to allow for share repurchases, Mathematical Finance Letters, Vol 2017 (2017), Article ID 3 http://scik.org/index.php/mfl/article/view/3138
- Sethi, S.P.; Derzko, N.A.; Lehoczky, J.P. (1991). "A Stochastic Extension of the Miller-Modigliani Framework".
*Mathematical Finance*.**1**(4): 57–76. - Sethi, S.P. (1996). "When Does the Share Price Equal the Present Value of Future Dividends?".
*Economic Theory*.**8**: 307-319.

## External links[edit]

Proposition II with risky debt. As leverage (D/E) increases, the WACC (k0) stays constant.

**^**MIT Sloan Lecture Notes, Finance Theory II, Dirk Jenter, 2003**^**Fernandes, Nuno. Finance for Executives: A Practical Guide for Managers. NPV Publishing, 2014, p. 82.**^**Arnold G. (2007)

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