Thomas Chemmanur

Thomas Chemmanur

MF807

Topic Note - 9

1. The Financing Decision

We now come to the financing decision: how should the firm raise the money to invest in the projects it wants to undertake? Till now, when we studied the investment decision, we pretended that this decision was already made for the firm: in all the problems, part of the given data was the proportion of debt, equity or preferred stock used in financing the firm's projects. Given these proportions (usually referred to as the capital structure of the firm) we learned how to compute the cost of capital to be used in discounting cashflows and arriving at the NPV of various projects. But now we address the financing problem: what is the choice of these capital structure proportions that will maximize stockholder wealth?

Unlike in the earlier topics, however, I cannot give you a formula, which you can use to compute the optimal capital structure. Given the current state of knowledge we have in finance, the capital structure decision (and also the next topic we will discuss, the dividend decision) remains very much an art, to be made according to the specific circumstances of the firm. What I can promise you, however, is a clear understanding of the capital structure decision, and the factors that firm managers should consider in making the capital structure choice of the firm. To understand the capital structure choice of the firm clearly, we are going to study the capital structure decision in two stages: in the first stage, we will study what the capital structure of the firm ought to be in the imaginary setting of perfect capital markets. Perfect capital markets are capital markets where there are no taxes of any kind (i.e., no corporate or personal taxes), no costs to financial transactions (eg. brokerage costs, or investment banking costs for the firm when raising capital), no costs of bankruptcy, and where financing decisions do not affect managerial incentives to pursue valuable investment opportunities. Even though real world capital markets do have these 'imperfections', we will find that studying the financing decision in this setting of perfect capital markets clarifies our understanding of this decision. In the second step, however, we will introduce these market imperfections and discuss how the optimal financing mix will change as a result of these market imperfections. We will see that it is the existence of these imperfections that makes the financing decisions more of an art rather than a science.

2. Optimal capital structure under perfect capital markets

If capital markets are perfect, the financing decision of the firm is rather simple. Let us first talk about a firm whose financing choices are limited to debt and equity: the problem before the firm is the proportion of each kind of security to sell. Thus, the choice before the firm is to pick the ratios D/V and E/V. Two financial economists, Franco Modigliani and Merton Miller, studied this problem and came up with two famous propositions on how the capital structure of a firm affects the value of the firm and also the expected return on the equity in the firm.

(i) MODIGLIANI-MILLER PROPOSITION I (Effect of leverage (debt) on firm value):

If capital markets are perfect, and individuals can borrow on the same terms as the firm, the value of the firm is the same irrespective of the capital structure proportions of debt and equity.

How did they prove the above proposition? The intuition behind their proof of the above proposition is very simple: Think of two firms, identical in every way (for example, the projects they have invested in are the same) except in their capital structure: the first is financed by 100% equity, while the other is financed partly by equity and partly by riskless debt. We will refer to the first firm as the "unlevered" firm and the second as the "levered" firm (debt is often referred to as "leverage"). Since both firms have the same set of projects, their operating income (operating income refers to the income from "operations": before you take out financing charges, like interest the firm pays on debt, etc). Let us denote the operating income, common to both firms, by Y (since we are uncertain about the operating income, Y is a random variable, with a known probability distribution).

For firm 1, which is unlevered, the total firm value, VU is the same as the market value of equity, EU. On the other hand, for the levered firm, total firm value, VL = EL + DL, where EL and DL are respectively the market values of equity and debt in the levered firm. Now, to prove the above proposition I, we consider two alternative strategies an investor can take:

Strategy-I

Buy 10% of the equity in the unlevered firm.

Dollar Investment required : .1 EU = .1 VU

Payoff: .1 Y (since the investor owns 10% of the shares in the firm, he is entitled to 10% of the operating income).

Strategy-2

Buy 10% of equity and 10% of debt in the levered firm.

Dollar investment required: 0.1 EL + 0.1 DL = 0.1 VL

Payoff to holding 10% of equity: 0.1 (Y - interest on debt)

Payoff to holding 10% of debt: 0.1 interest on debt.

──────────────────

Total payoff:0.1 Y.

Thus, we find that the portfolios held by the investor in the two strategies given above have the same payoff and the same riskiness (the riskiness is simply that of Y, the operating income). Then, by the law of one price, which we learned earlier in the course, the investment required (ie., the market value) of the two portfolios have to be the same (if not, we can make arbitrage profits). Thus, 0.1 VU = 0.1 VL, or VU = VL. Thus, we see that in perfect capital markets, the market value of the firm is the same regardless of the capital structure.

ILLUSTRATION-1

We can illustrate Proposition-I using a simple numerical example. Consider two firms, as in the case above, which are identical in every respect except in their capital structure. Let the distribution of their operating income per year be as follows:(Assume that this is a perpetual stream of cashflows).

YProbability

1,500,0000.5

1,100,0000.5

Therefore, expected operating income per year = 1,500,000(0.5) + 1,100,000(0.5) = 1,300,000

Since the firm has no debt, this entire operating income goes to equity holders (assume that the firm pays out this entire amount in dividends every year). Thus, expected cashflow to equity holders = 1,300,000

Assume for simplicity that the firm has no systematic risk: ßA = ßEU = 0. (ßA is the asset beta of this firm. The asset beta, as you may remember, measures the business risk of the firm, and does not change with the way the firm is financed. ßEU is the equity beta of this unlevered firm. For unlevered or all-equity firms, the equity beta is the same as the asset beta).

Thus, we can discount the cashflows of the firm at the risk-free rate, say RF = 10%.

Value of the equity in the unlevered firm, EU = 1,300,000/0.1 = 13,000,000.

Since there is no debt, VU = EU = 13,000,000

Now, let us consider the levered firm. If the levered firm has issued 5,000,000 in debt with 10% interest (assume this debt is a perpetuity for convenience).

Yearly interest payment = 5,000,000(0.1) = 500,000.

Market value of debt, DL = 500,000/0.1 = 5,000,000

Cashflow to equity holders = Operating income - Interest payment (I)

probabilityYI(Y - I)

0.51,500,0005,00,0001,000,000

0.51,100,0005,00,000600,000

Expected cashflow to equity holders = 1,000,000(0.5) + 6,00,000(0.5) = 800,000.

Value of equity in the levered firm, EL = 800,000/0.1 = 8000,000

(Now, since the debt on the firm is riskless, ßD = 0, ßEL, the equity beta of this levered firm, is given by ßEL = ßA/(E/V) = 0/(E/V) = 0, since ßA=0, so that rE = rF = 10%).

Total value of levered firm, VL = EL + DL = 8000,000 + 5000,000 = 13,000,000

Thus the value of the levered firm is the same as that of the unlevered firm.

We can understand Proposition-I once we realize that by issuing debt, all the firm is doing is slicing up the stream of operating income accruing to the firm into two parts: a cash flow stream going to equity holders and a cash flow stream going to debt holders. If, on the other hand, there were no debt, the entire cashflow from the firm goes to the equity holders. Clearly, the value of the total cashflow (ie., the market value of the unlevered firm) should be equal to the sum of the parts: the value of the cashflow to debt in a levered firm and the value of the cashflow to equity in a levered firm, provided no value is gained or lost in the cutting up process: we will study later on that sometimes there are such losses or gains due to market imperfections.

Some of you may wonder: why should equity holders worry about total firm value? Shouldn't they be concerned just with the value of equity? The answer to that is, under fairly general conditions, the financing policy which maximizes firm value will also maximize equity value. This is because, since debt is fairly priced, debt holders will pay for exactly what they get, and any additional value left over goes to the equity holders (similarly, any loss in value is also borne by equity holders!). Thus a capital structure which maximizes the value of the firm will also maximize the value the equity in the firm.

We can generalize the above intuition to all kinds of different security combinations. For example, under perfect capital markets, the value of the firm is the same irrespective of whether the firm issues common stock, preferred stock, or some combination of these. Similarly, under perfect capital markets, firm value will be the same irrespective of whether the firm issues short term or long term debt; alternatively, firm value is the same irrespective of whether the firm issues riskless or risky debt.

ii) MODIGLIANI-MILLER PROPOSITION II (Effect of leverage (debt) on the expected return on equity):

Consider a levered firm (i.e., the firm has issued debt as well as equity). Further, think of the firm as a portfolio of debt and equity. Then, the return on the assets of the firm as a whole is given by the weighted average of the returns on debt and equity:

(1)

Rearranging the above equation, we can write,

(2)

i.e., Expected return on equity = Expected return on assets + (Debt/Equity Ratio)(Expected Return on Assets - Expected Return on Debt)

This is Modigliani-Miller Proposition-II. This merely states that the return you can expect from equity goes up with the debt-to-equity ratio, and gives the relationship between the two. However, this does not translate to a change in total firm value (as we know from Proposition I) because the riskiness of the equity in the firm also goes up.

Let us see how the beta of equity in the firm, ßE, changes as the firm takes on higher debt. We know that the beta of the firm as a whole, ßA, is given by, ßA = (E/V) ßE + (D/V)ßD = [E/(D+E)]ßE + [D/(D+E)]ßD. Re-arranging this expression, we get:

(3)

Thus, the riskiness of the equity increases as the firm takes on more debt.

This is why, as the firm takes on more debt, the required return on equity also goes up in equilibrium (as stated by proposition II). Since the risk of the firm's equity increases as the proportion of debt in its capital structure increases, the required return on this equity also increases, because the higher the risk, the higher the return has to be for investors to hold the equity in equilibrium).

The above figure plots Proposition II (i.e., equation (2)), which gives the expected return on equity as a function of the debt equity ratio. Notice that (a) rA is constant, irrespective of the debt to equity ratio (b) rD is constant, as long as debt is riskless, but increases with D/V oce the debt becomes risky (c) rE increases linearly with D/V as long as the debt is riskless, but increases at a slower rate once the debt becomes risky (this is because the second term in (2) starts getting smaller as soon as rD starts getting bigger, which happens once the debt becomes risky).

ILLUSTRATION - 2

Proposition-II can be illustrated with a simple example. Consider a firm with the following probability distribution of the operating income, Y (this cashflow is a perpetual income stream: ie. the firm generates a cashflow of $Y per year in perpetuity). Assume further that the firm is all equity financed (no debt in the capital structure). Assume that the number of shares outstanding is 100,000.

YProbabilityEarnings per share (eps)

100,0000.25$1.00

250,0000.50$2.50

400,0000.25$4.00

Since the firm has no debt, the entire earnings of the firm go to the equity holders. Therefore,

Expected cashflow to equity = 100,000 (0.25) + 250,000 (0.5) + 400,000 (0.25) = $250,000.

The earnings per share under each possible scenario is also listed above.

Total cashflow to equity holders

Earnings per share (eps) =------

Total number of shares

Expected cashflow to equity holders

Expected earnings per share =------

Total number of shares in the firm.

= 250,000/100,000 = $2.50 per share.

Let us now assume that the asset beta of the firm, ßA = 1. Since the firm is all equity financed, the equity beta, ßEU = 1 also. If rF = 10%, and rM = 12.5%, we can use the CAPM to find the expected return on equity:

rE = rF + ßEU (rM - rF) = 12.5%.

Then, Value of equity in the firm, EU = Present Value of the expected cashflow to equity = Expected cashflow to equity/The discounting rate, rE = 250,000/.125 = 2,000,000.

(Using the fact that the cash flow stream to equity is a perpetuity).

Total value of this unlevered firm, VU = EU = 2,000,000.

Price per share = EU/total number of shares = 2,000,000/100,000 = $ 20 per share.

Let us now see what happens if we change the capital structure of this firm. Assume that the management wants to change the capital structure to 50% debt and 50% equity. To do this, they buy back half the existing number of shares: ie., they buy back 50,000 shares, leaving only 50,000 shares outstanding, and issue debt instead.

Value of shares bought back = 50,000 (20) = 1000,000

The above amount 1,000,000 was generated by issuing debt. Assume that the face value of debt issued is 1000,000, and offers perpetual interest of 10%.

Interest payment per year = 1,000,000 (0.1) = 100,000

Clearly, this debt is riskless, since the firm will be able to pay this interest with probability 1.

Therefore market value of this debt, DL = 100,000/0.1 = 1,000,000

Let us now compute the distribution of the cashflow to equity. Remember, the operating income of the firm remains the same as before.

YProbabilityInterest payment(I)(Y - I)eps

100,0000.25100,00000

250,0000.50100,000150,0003.00

400,0000.25100,000300,0006.00

Expected cashflow to equity holders = E [Y - I] = 0(0.25) + 150,000(.5) + 300,000 (0.25) = $ 150,000.

Expected cashflow to equity holders

Expected earnings per share = ------

Number of shares

= 150,000/50,000 = $3 per share.

Let us now compute the value of equity. For this we need to find the expected return on equity, rE. We can do this in two ways: we can either use the CAPM or the Modigliani-Miller Proposition II (Both should give the same answer).

Using CAPM: To do it this way, we need to find the ßEL, the beta of the levered equity. We know that the asset beta of the firm, ßA = 1 = ßEL (E/V) + ßDL (D/V), where ßEL and ßDL are respectively the betas of the debt and equity of this levered firm. Since debt is riskless here, ßDL = 0. Further, E/V = 0.5 (since the firm has now 50% equity in its capital structure). Thus, ßA = 1 = 0.5 ßEL ßEL = 1/0.5 = 2.

Then, from CAPM, rE = 10 + 2 (12.5-10) = 15%.

Using Modigliani-Miller Proposition II: We know that for the all equity firm, rA = rE = 12.5 %. Once the capital structure is changed, rA remains the same at 12.5%. Now, for the levered firm, rD = rF = 10% since the debt is riskless. Then, from Proposition II, rE = rA + D/E (rA - rD) = 12.5 + 1 (12.5 - 10) = 15%. (Remember that E/V = D/V = 0.5, so D/E = 1).

Thus both methods produce the same answer: rE = 15%.

Thus, value of equity in the firm = Expected cashflow to equity/rE = 150,000/0.15 = 1,000,000.

Price per share = 1,000,000/50,000 = $20 per share.

Total value of the levered firm, VL = EL + DL = 1,000,000 + 1,000,000 = 2,000,000.

Summary of Illustration-2:

Value of the firm : same for both levered and unlevered firm.

Expected return on equity: Higher for levered firm.

Expected earnings per share : Higher for levered firm.

Riskiness of equity ; Higher for levered firm.

Price per share of equity : Same for both levered and unlevered firm.

An interesting point to note from the above illustration is that, when times are bad (ie., when the operating income of the firm is low) the levered firm has lower earnings per share compared to the unlevered firm; when times are good, the levered firm has higher earnings per share than the unlevered firm; however, on average, the earnings per share of the levered firm is higher than the unlevered firm. This, however, does not translate into a higher price per share for the levered firm because the risk of the equity also goes up correspondingly, so that the rate of return required by investors on this equity also goes up correspondingly, leaving the price per share remains the same.

In the light of the Modigliani-Miller Proposition-II, consider the following argument: The expected return on debt of a certain firm is only 10%; the expected return on equity is 15%. So the firm should use debt to finance the next project it plans to undertake. This argument is wrong because if the firm issues more debt, the riskiness of its equity will go up, hence the expected return on its equity will go up even further, to such an extent that it actually doesn't matter whether the firm issues debt or equity. In fact, given the assumptions under which the Modigliani-Miller propositions hold (i.e., ignoring taxes), the cost of capital remains the same irrespective of whether the firm issues debt or equity, and irrespective of the capital proportions of debt or equity used to finance its next project![1]

Problem to be worked out at home

Company C is financed entirely by common stock and has an equity ß of 1. The stock of the company has a price earnings multiple of 10 and is priced to offer a 10% expected return. The company decides to repurchase half the common stock and substitute an equal value of debt. If the debt yields a risk-free 5%, and capital markets are perfect,

a) Give:

i) The beta of the common stock after the refinancing.

ii) The beta of debt.

iii) The beta of the company (ie., stock and debt combined)

b) Give:

i) The required return on the common stock before the refinancing.

ii) The required return on the common stock after the refinancing.

iii) The required return on the debt.

iv) The required return on the company (ie., stock and debt combined) after the refinancing.

c) Assuming that the operating profit of the company remains the same after refinancing give:

i) percentage increase in earnings per share

ii) The new price-earnings multiple.

[1]Under the assumption of perfect capital markets, Tc is 0. Therefore, this result is quite consistent with the cost of capital formula we developed in earlier classes. We will show later that if we take taxes and other market imperfections into consideration, the effective cost of capital of a project will depend on the way the project is financed.