MBA 8415Dr. D.A. Stangeland
Capital Structure and TheoriesPage 1 of 8
MBA 8415Dr. D.A. Stangeland
Capital Structure and Theories
Definition: Capital Structure refers to the mix of securities used to finance the firm’s investment projects. Note: this is the mix of all securities of the firm outstanding, not just new securities issued to finance new projects. When considering capital structure we always look at the market values of debt and equity and the market rates of return on each. If market values are not available, then estimates of market values should be used.
A. Miller and Modigliani (M+M) Theories with no taxes.
Miller & Modigliani’s Proposition 1
In a world with no taxes, the firm’s capital structure does not matter.
The firm’s value is determined by its real assets, not by the securities issued against them.
See “pies”
Miller & Modigliani’s Proposition 2:
The expected rate of return on common stock of a levered firm (firm with debt financing) increases in proportion to the debt/equity ratio. (Note: D/E ratios must be using market values, not book values.)
E.g., if a firm’s debt has its expected rate of return held constant at RD, then as the proportion of debt increases, the expected rate of return on equity must increase.
Recall firm is due to the firm’s assets, firmdoesn’t change as financing changes.
firm = X EE+(1-XE)D
If X E 1-X E
E to maintain firm. For moderate levels of debt, D does not change.
Note: X D = proportion of firm financing which is debt = (1-XE)
When XD = 1, so there is no equity and the debt risk must be the same as the overall risk of the firm’s assets.
Now, look at firm’s WACC (no taxes) with changes in capital structure:
Assets = A
Assets = E +D
Rearranging terms we get
In the example below we assume debt is risk free. With this simplifying assumption, D = 0 and thus we get a simpler form for the equity beta as follows: E=V/E A
The equity beta increases relative to the asset beta because of financial risk– i.e., risk due to leverage. Note that asset beta is the result of cyclicality of output and revenues and the degree of operating leverage – these two determine the operating risk or asset risk.
E[rE] = rf + E[E(rm) - rf]
Firms WACC =
If (for simplicity) D = 0, we can replace E[rD] with rf. Now we can also substitute in the CAPM (somewhat rearranged) for E[rE]:
WACC =
=
= E[rm]A-A rf + rf
= rf + A[E(rm) - rf] independent of proportion in E or D
We have seen that with zero taxes, WACC of the firm doesn’t change with changes in the firm’s mix of securities because betas of securities change so as to keep the of the firm constant.
Summary:
As D/E increases, the value of the firm doesn’t change, the WACC doesn’t change, and the asset beta doesn’t change. However, as D/E increases, the market values of D and E obviously change, and the risk and expected return of equity both increase. For very high levels of debt, the debt beta will also increase.
Do investors prefer to hold stock in firms with different capital structures?
Assumptions: perfect capital markets
- no transaction costs, no taxes
- lending & borrowing rates are same
- competitive markets
Let rf = .10 [E[rm]-rf] = .09
Two firms hold exactly same assets is same overall for firms.
Firm 1 / Firm 2assets / 1.2 / 1.2
% in Equity / 75% = X = .75 / 50% = X = .50
% in Debt / 25% / 50%
of debt / 0.1 / 0.1
Note: of equity is solved from assets = X(e) + (1-X)D so 1.2 = Xe + (1-X)0.1
e / 1.5 / 2.3
E[re] = rf+e(E[rm]-rf)
E[re] = / .24 / .307
Suppose an investor currently has a well diversified portfolio with = 1.56. Suppose the investor prefers a portfolio with = 1.56, will the investor pay a premium for firm 1’s stock because it possesses that whereas firm 2 stock has a higher ?
No. Why? The investor can achieve the same desired using either stock.
E.g.Using Firm 1:just buy the stock, = 1.5 E[rp] = .24
Using Firm 2:Want = 1.5, then buy a combination of firm 2’s stock & risk-free asset.
p = X(2) + (1-X)0 rf
1.56 = X(2.3)
X =
So, for each additional dollar invested in the portfolio, invest $.678260870 in firm 2’s stock and $.32173913 in risk free asset.
E[rp] = X(E(re2)) + (1-X)rf
= .67826087(.307) + (.32173913)(.10) = 0.24
With no transaction costs, etc., the investor is indifferent between the two possibilities, therefore no premium will be paid for a particular capital structure of a firm.
B. Taxes in the M&M analysis
Previously with taxes we saw the WACC decreases as the proportion of the firm financed through debt increased because interest expenses are tax deductible.
WACC = D/VE[rD](1-TC) + E/VE[rE]
Assume over moderate levels of debt that E[rD] does not change. Then as increases, E[rE] will increase as before (similar to the no tax case) but unlike the no tax case, the higher proportion of financing with tax-subsidized debt results in WACC decreasing.
Note: E[rD] cannot always be constant; as D/V approaches 1, the debt becomes as risky as the firm.
MM adjust their proposition one in the presence of taxes to …
MM Proposition I corrected to reflect corporate income taxes
Value of firm = value if all equity financed + PV tax shield from debt interest payments
VL = Vu+TcD
Why? Because in after tax cash flows, introducing debt will incur interest charges but part of these will be paid by government through reduced taxes more of the firm’s financing cash flows are paid by the government. In effect, more of EBIT is available for security holders and less goes to the government. Thus the total value of the firm (D+E) goes up.
E.g. for simplicity assume a risk free firm with EBIT of $100,000 per year in perpetuity.
Before tax: EBIT = $100,000 (assume risk free)
Tc = 40% Let rf = 10%
Consider an all-equity financed firm, all income (after taxes) is paid out as dividends.
Income before tax = 100,000, tax = 40,000, therefore Income after tax = 100-40 = 60,000.
PVdiv = 100,000(1-TC)/rf = 60,000/0.10 = 600,000 = VU = E
Now consider a levered firm …
Consider afirm that has perpetual bond financing with interest per year = 20,000
Earnings before interest and tax (EBIT) = 100,000
Earnings after interest = 80,000
Tax = 32,000
Earnings after interest and tax = 48,000
PVdiv = 48,000/0.10 = 480,000 = value of equity = E
PVint = 20,000/0.10 = 200,000 = value of debt = D
PVfirm = Value of firm = 680,000 = D+E = VL
Or using M+M revised Proposition 1:
VL = Vu+TcD
PVfirm= 600,000 + PVinterest tax shields
The annual tax shield is the change in tax due to the interest, 40,000-32,000, or calculated as
TC Interest = 8,000/yr.
PVinterest tax shield = 8,000/0.10 = 80,000
PVfirm= 600,000 + 80,000 = 680,000
C. Other Considerations
Why not finance the firm entirely with debt? WACC drops and MM say value increases.
Personal taxes
Investors generally face higher tax rates on interest income than on capital gains or dividend income.
-interest income is taxed at the investor’s personal tax rate.
-tax on capital gains can be deferred until the capital gain is realized (when the stock is sold)
-tax on dividend income is reduced by the dividend tax credit.
Counterargument to personal tax reason:
Some investors (e.g. pension funds, RRSP’s) are exempt from paying tax on interest income (or any other income) firms could increase their value by financing with debt placed to these tax exempt investors and the firmsstill get a tax reduction because of interest payment more funds available to be paid out.
But . . .
Merton Miller - Debt & Taxes,Journal of Finance, May 1977, argues that all firms will try to exploit the ability to issue debt to zero-tax investors. As there are fewer tax exempt institutions left to buy the firms debt, firms will try to place their debt with low-tax investors. In order to entice more investors to the firm’s debt, the firm will have to raise the interest payments (yield or return) on the debt. As firms try to place more debt, the tax rates of the “newly enticed” investor will creep up and the firm will have to pay even higher interest rates to entice these investors. Eventually, the point will be reached where the tax advantage to the firm of debt is offset by the high rate of interest required … resulting in indifference to debt or equity financing.
Result: there will be an optimal debt/equity ratio for the economy, but individual firms will be indifferent to debt or equity financing.
Miller shows that with both corporate and personal taxes, the following holds:
where the subscripts on the tax rates T refer to tax on the following kinds of income:
C = corporate income
PE = personal equity income
PD = personal debt income
Bankruptcy Costs and Costs of Financial Distress
The likelihood of bankruptcy costs or costs of financial distress (being perceived as unlikely to be able to meet debt obligations) increases as debt levels increase.
It is more likely the firm won’t be able to meet fixed obligations (i.e. coupon or interest payments) as the fixed obligations increase.
Investors may then value firm as
VL = VU + PVnet interest tax shields- PVexpected costs of financial distress
Costs of financial distress:
Direct costs:Legal and admin (e.g., 5.3% of pre-bankrupt market value for railways)
Indirect costsLoss of value of intangible assets
Lost ability to invest in + NPV projects; not able to finance them – less flexibility
Loss of preferential terms given by suppliers
Loss of customers (when after sales support is important)
Loss of best employees
There will be higher bankruptcy costs for firms with intangible assets, e.g., reputation, brand names, human capital, etc. vs. tangible assets, e.g., buildings, land, etc.
Limit to debt financing
Want to increase debt until the marginal benefit from the increase in PV of interest tax shields equals the marginal cost from the increase in the PV of bankruptcy costs.
More Indirect Costs of for firms in financial distress:
Adverse incentive problems
1. Select high risk projects
-shareholders benefit as there is a chance of a payout to them butbondholders are hurt because what is left for them is more risky and there is a greater chance of even less being available for them. (When near bankruptcy, it is best to view the equity as an out-of-the money call option on the firm’s assets. As the assets are more variable, there is more value for the option holder – the stockholders.)
2. Pass up +NPV projects because shareholders won’t provide financing.
- the benefits would only (or mainly) go to the bondholders
3. Pay a large dividend
-shareholders benefit by receiving cash they otherwise would not get; bondholders are hurt by having less left to pay to them.
Agency Costs and Capital Structure
Recall the Stockholder - Manager conflict
- If the manager owns less than 100% of the firm, then less than a 100% proportion of the cost will be borne by the manager if perquisites or shirking are done
e.g.Manager owns 50% of firm
Manager consumes $100 of perquisites
Cost to manager personal shares drop by $50
total firm’s shares drop by $100
There is an incentive for a non-owner manager to consume perquisites or to shirk on his/her duties.Jensen, 1986, states that this problem is more severe when managers control a greater amount of “free cash flow” from the firm. If “free cash flow” at management’s discretion can be reduced, the costs of undesired perquisites and shirking can be reduced too and thus the total value of the firm can be increased. Jensen states that higher debt levels reduce discretionary cash flow and thus reduce these costs.
M&M irrelevancy assumes operating cash flows of the firm are unaffected by capital structure. The argument now is that capital structure can affect the size of the operating cash flows, EBIT.
Signalling
Information about firms is not symmetric between the firm’s managers and investors in the capital markets. With asymmetric information, managers’ actions can be analyzed to try to infer additional information about their firms.
Capital structure changes may signal what managers think about the future or what they think about the current market values of their securities. E.g., an increase in debt usually signals that managers think the debt payments can be supported by better performance in the future. A stock issue may signal that managers think the stock is currently overvalued.
This leads to the pecking order theory of financing in that managers will (if possible) first finance with retained earnings, then with debt, and, as a last resort, with equity.
D. Setting Debt Policy — putting it all together
Each firm (or industry) will likely have a different optimal capital structure. The optimal structure depends on balancing benefits of interest tax shields and reduced agency costs of equity against expected costs of financial distress & bankruptcy and the lack of flexibility that results from too high debt levels. The following equation helps to illustrate this:
VL = / VU / + PVnet benefit from
interest tax shields / + PV
of expected reduction of
agency costs of equity / – PV
of expected financial
distress costs
Copyright © 2002 David A. Stangeland