THE FINANCING DECISIONS BY FIRMS: IMPACT OF CAPITAL STRUCTURE CHOICE ON VALUE

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1 IX. THE FINANCING DECISIONS BY FIRMS: IMPACT OF CAPITAL STRUCTURE CHOICE ON VALUE The capital structure of a firm is defined to be the menu of the firm's liabilities (i.e, the "right-hand side" of the balance sheet). A great variety of types of securities can be and are used in firms' capital structures. In addition to common stock equity, some typical examples are bank loans, commercial paper, secured bonds, debentures, convertible bonds, income bonds, preferred stock, and warrants. While the traditional treatment of capital structure is to examine each of these types of securities separately, the modern approach (as was suggested in Section VIII) views all these types as part of a unified theory of contingent claims pricing. That is, each of these "hybrid" securities can be represented as a "mixture" (albeit at times a complicated one) of pure" "default-free" debt and "pure" (as if %-financed by common stocks) equity. Beyond simply providing a unified theory of pricing, this approach avoids many of the pitfalls and misconceptions about the costs and benefits of different capital structure choices. Therefore, the analysis in this section of the capital structure choice and its impact on the total market value of firm will focus almost exclusively on the choice between debt and equity in providing the firm's external financing. As background, the reader should become familiar with the meaning (and effects) of financial leverage and with the distinction between financial risk and asset (or business) risk. It will be helpful to develop a feel for typical debt-to-asset ratios in various industries. In the study of the firm's investment decisions in Section VII, it was assumed that all external financing was done by issuing equity, and therefore that the firm had the simplest structure possible: namely, all claims on the firm are homogeneous equity. The fundamental question explored here is: Given the investment decision of the firm, does the financial structure of the firm "matter"? That is, for a fixed investment policy, will a change in the firm's mix between debt and equity cause a change in the market value of the firm? As one might expect, the answer to this fundamental question depends upon the assumed environment. Since, by hypothesis, the investment policy of the firm is fixed, the total cash flow generated by the firm will not be affected by the capital structure choice. Thus, if the capital structure matters (and thereby, a change in it will cause a change in the market value of the firm), 65

2 Robert C. Merton then, from the valuation formulas derived in Sections VI and VII, a capital structure change must cause a change in the cost of capital. [The only exception would be if the capital structure choice changes either the tax liabilities or the level of government subsidies to the firm, a topic addressed later in this section.] Since, as shown in Section VII, the cost of capital is used in determining the (optimal) investment decision, if the capital structure matters, then it is necessary for the manager to consider simultaneously both the investment and financing decision in making an overall optimal set of decisions for the firm. Why should the financial structure matter? With the exception of certain tax features, it is necessary to assume some type of uncertainty to give this question serious meaning because otherwise, debt and equity are essentially indistinguishable. Possibilities are:. Does the issuance of debt create a new set of securities which were previously not available? (i.e., how substitutable is personal leverage for corporate leverage?). Are there costs to bankruptcies? 3. Are there tax features unique to corporate debt? 4. What are the effects on control of the firm? 5. Does the existence of outstanding debt "induce" changes in investment policy? Other factors which are often considered by managers in deciding on the debt/equity ratio are:. growth rate of future sales. stability of future sales 3. the competitive structure of the industry 4. the asset structure of the industry 5. lender attitudes toward the firm and its industry. To analyze the problem, we begin by studying the impact of capital structure in a specific environment and use this as a benchmark for insights into why financing decisions might affect value. This environment includes the following assumptions: (A.) No income taxes (to be modified later). 66

3 Finance Theory (A.) (A.3) (A.4) (A.5) (A.6) The debt-to-equity ratio is changed by issuing debt to repurchase stock or by issuing equity to pay off debt. Moreover, a change in the capital structure is affected immediately and there are no transactions costs. The firm finances all investment by external means (i.e., dividend policy is to pay dividends equal to earnings). The expected values of the (subjective) probability distributions of future (operating) earnings for each firm are the same for all investors ("homogeneous investor beliefs"). No growth of earnings: the expected value of operating earnings for all future periods are the same. All investments that the firm considers are from the same risk class, i.e., the business risk characteristics are independent of the number of projects taken, and are taken as constant. A "Benchmark": The "Pure Equity" Case (% Financing by Equity) Let Let X average expected dollar return per period for the firm k cost of capital for % equity financed firm = expected rate of return required for the firm's particular risk characteristics, and it is assumed to be constant over time. Then, the market value of this firm is: (IX.) V = X k Let F = (expected) annual interest payments on debt outstanding B = market value of debt outstanding 67

4 Robert C. Merton E = (expected) annual earning available to shareholders = X - F S = market value of equity outstanding F k i = cost of debt = required (expected) return by investors to B hold this amount of debt in the firm k e E = cost of equity = required (expected) return by investors S to hold this amount of equity in the firm = S + B V k X F + E k + = = B k S V V V i e or (IX.) B S B + = + S k = k i k e k i k V V B + S B + S e. k is called the "weighted" cost of capital and is the relevant number to use in the investment (capital budgeting) decision of Sections VI and VII. The question "Does financial structure `matter'?" can be restated as "does k change for different mixes of debt and equity (given a fixed investment policy)?" Or, for a given level of business or asset risk, does changing the financial risk of equity change the total value of the firm? 68

5 Finance Theory "Extreme" Classical Theory: The "Net Income" Approach Assumption: k e and k i are constants with k e > ki Example: k e= % and k i = 5%; net operating earnings = $ Case : B = $3 which implies F = $5 and so, B S Net Operating Earnings $ k = k i + k V V 3 85 minus interest payments (5) = (.5)+ (.) 5 5 e Earnings available to equity $ 85 = 8.7% 5 k =. e Market Value of Equity ( S ) $85 Leverage Factor + Market Value of Debt ( B ) 3 =.35 Market Value of Firm ( V ) $5 B S 3 = 85 Case : B = $6 which implies F = $3, so 6 7 Net Operating Earnings $ k = (.5) + (.) 3 3 minus interest payments (3) = 7.7% 3 Earnings available to equity $ 7 k e=. 69

6 Market Value of Equity ( S ) $7 Leverage Factor + Market Value of Debt ( B ) 6.86 Market Value of Firm ( V ) $3 B S 6 = 7 Robert C. Merton Classical Approach (generally) as is illustrated in figure above. Assumes that there is an optimal capital structure and hence, through the appropriate choice of leverage, the value of the firm can be increased.. Assumes that beyond some point of leverage, k e rises at an increasing rate. 3. Assumes that beyond some point of leverage, k i may rise. 7

7 Finance Theory Modigliani-Miller (as is illustrated in figure above) Assume perfect capital markets: equal information; no transactions costs; investors are rational and believe everyone else is; free access to borrowing and lending; no taxes; firm debt is default-free. Their basic propositions are: () The total market value of the firm and its cost of capital,, k are independent of its capital structure (the total market value of a firm is calculated by capitalizing the expected stream of operating earnings at a discount rate appropriate for its risk class). 7

8 Robert C. Merton () The required expected return on equity,, k e is equal to the capitalization of a "pure" equity stream, plus a premium for financial risk which equals the difference between the "pure" equity capitalization rate and k i, times the leverage factor ( B / S ). (3) Therefore, the "cut off" rate for asset selection (investment policy),, k is independent of the financing decision. Graphically, under the assumption that the debt has no risk of default (hence, k i is constant), the M - M result is: Proposition can be derived formally from equation (IX.) as follows: k = e V S B k = V k - B S i S k i + V S k = ( B + S ) k e k - B S k i or (IX.3) k = k + e B ( k - k i) S 7

9 Finance Theory (First) Proof of M M result by arbitrage Suppose the borrowing and lending rates are equal and the same for all investors and corporations, i.e., k i = constant r, rate of interest; (the debt is default-free). Consider two companies with identical anticipated earnings, i.e., X = X = X. Suppose that company # has no debt (financed completely by equity) and company # has some debt. Company # Company # Earnings: Debt: X = X Earnings: X = X B = at rate k i = r Debt: B > at rate k i = r Equity: S (=V ) Equity: S Firm Value: V Firm Value: V (= B + S ) Consider an investor who currently owns S dollars of stock in company #. If α = % of total shares of company # held by this investor, we have that S = α S. Suppose that V > V, i.e., by the "right" choice of leverage, company # will have a larger value than #. If the investor continues to hold his present portfolio, his return in dollars,, Y will be his fractional claim, α, times the portion of earnings available to shareholders, X - rb. I.e., (IX.4) Y = α (X - r B ) The investor could sell out his present holdings and choose an alternative portfolio as follows: Step : sell his current holding for S (= α S ) dollars. Step : borrow ( α B ) dollars. Step 3: with the proceeds from steps and, buy shares in company #. If S = number of dollars invested in company #'s shares, then S = α S + α B = α( S + B )= α V. 73

10 Robert C. Merton Step 4: as an owner of $ S worth of shares of company #, he will have claim on ( S / S ) percent of #'s earnings. Because # has no debt, S = V and so, he has claim on ( S / S )X =( S / V )X dollars of return. The return in dollars on his new portfolio,, Y will be ( ) S αv Y = X r αb = X rαb, from step 3 V V V V V = α X rb α X rb αx = + V V (IX.5) ( ) or Y V + αx V = Y V so for V >V, Y >Y. Hence, we have demonstrated that for the same number of dollars invested in either case, if V >V, then the investor can earn a higher return in the second portfolio than in the first, for every possible outcome of earnings, X. Therefore, rational investors will "switch" to portfolio # from portfolio # until V V. The argument goes through in precisely the same way, if it was assumed that V >V. Therefore, to avoid arbitrage or dominance, (IX.6) V =V. A second proof of the M - M proposition using the same notation and company data as in the first proof is as follows (where firm # has no debt and firm # has some debt): Case I: Hold as an investment: $ S of shares of company # = α S = α V. The return from the investment will be =α X. 74

11 Finance Theory Alternative Investment: Transaction Investment Return () (sell $ S of # and) buy the same fraction α of the shares of # ( ) ( α X - rb ) αs α V B () buy α percent of the bonds of firm # α B rα B Total α V α X So, if V > V, the investor gets the same return for α(v - V ) fewer dollars invested. Case II: Hold α% of shares of firm #: $S of shares of # = α(s = α(v-b). The return will be α (X-rB ). Alternative Investment: Transaction Investment Return () buy fraction α of the shares of # () borrow ( B ) α dollars αs ( αv ) α X αb - α rb Total ( α V B) α ( X - rb ) If V > V, then the investor gets the same return for α(v-v ) fewer dollars. Hence, to avoid dominance or arbitrage, V = V. 75

12 Robert C. Merton Thus, given their assumptions, M-M demonstrate, by a powerful arbitrage argument, that the capital structure or financing decision among alternative instruments does not affect the market value of the firm or its (average) cost of capital for determining which assets to purchase. The intuition is that a purely financial transaction for a fixed amount of real assets should not affect any "real" decisions or values. Or, if personal borrowing is a perfect substitute for corporate borrowing, then M-M holds because investors will not pay more for firms that borrow for them if they can do it themselves. The classical view of the capital structure simply assumes that leverage "matters." M-M showed why it does not. To disagree with the conclusions of M-M one must therefore disagree with their assumptions. Items that could affect the M-M Conclusion. Tax deductibility of interest payments by the firm.. The risks of personal versus corporate leverage (limited liability and bankruptcy). 3. Cost of borrowing may be higher for the investor than the firm. 4. Institutional restrictions may prevent institutional investors from "levering". Margin requirements restrict individuals. 5. Transactions costs in establishing the arbitrage position. 6. Moral Hazard: management makes decisions in the best interests of the shareholders that may conflict with the interests of the bondholders, and therefore, reduce the overall market value of the firm. Of these items, by far, the most important are () and (). In the proofs of M-M, it is assumed that both corporate debt and personal borrowing is default-free, and therefore, investors who levered equity by personal borrowing could exactly replicate the payoffs to investors who held shares levered by corporate borrowing. As was already demonstrated in Section VIII, this will no longer be the case when there is a possibility of default on the debt of the firm. To review the difference between personal and corporate borrowing, we maintain the assumption 76

13 Finance Theory that personal borrowing is default-free and briefly reexamine the case of a pure discount term loan: Consider a personal term loan (with no interim interest payments) with a face value of B dollars due at time T in the future. Let the firm (unlevered) have a current value of V. Then the value of levered equity, Ep, would be Ep = V B/[ + R(T)] T, and at time T in the future if the firm is worth V(T), the payoffs to the debt and levered equity will be Consider a corporate loan with the same terms except limited liability for the shareholders. The payoffs are: 77

14 Robert C. Merton By inspection, the payoff to the debtholders in the corporate case is less favorable than in the personal case. Correspondingly, the payoff to the equityholders in the corporate case is more favorable than in the personal case. Therefore, the current value of the corporate-levered equity will exceed the current value of the personal-levered equity, i.e., Ec > Ep. Correspondingly, the current value of the corporate debt will be less valuable than the current value of the personal debt, i.e., Dc < Dp. Inspection of the payoffs to Ep versus Ec shows that, in the event that V(T) < B, Ec(T) Ep(T) = B V(T). As noted in Section VIII, the corporate-levered equityholders are "insured" against losses that would occur for the personal-levered equityholders if V(T) < B. So, we can write the value of the corporate-levered equity as E = E + g c = V - B/[+R(T)] + g where g is the value of this "downside insurance" (i.e., the put option insurance premium). Similarly, the corporate debtholder is not only lending money but, in addition, is "insuring" the equityholder, i.e., we can write the value of corporate debt as D = D - g = B/([ + R(T)] - g c p where g is the "liability" associated with issuing the put insurance (its cost). If V is the value of the unlevered firm and if g = g, then M-M holds even when bankruptcy is possible. That is, even in the presence of default possibilities, M-M will hold if either put options on the stock exist or if these options can be created by low-transaction cost investment strategies. Of course, if there are significant "dead-weight" losses to the firm's liability holders from a bankruptcy (e.g., attorney fees, disruption of the operations of the firm), then corporate leverage can matter. This analysis should serve to underscore once again (as noted in Section VIII) that one cannot compare the "true" or "economic" cost of the debt of one firm with that of another by simply comparing promised yields on debt. That is, by definition, the promised yield (for the period) is simply [B/Dc] which can be rewritten (for T = ) as p T T 78

15 Finance Theory (IX.7) g(+ R) Promised yield = R + B - (+ R)g where g is the value of the (implicit) put option. If the value of the put option on one firm is larger than the value of a corresponding put option on the other, then it is entirely possible that the debt with the higher promised yield could have a lower economic cost than the debt with the lower promised yield. The analysis also makes clear why the promised yield on a personal loan will be lower than on a (comparable) corporate loan because in the former, the investor pledges all his assets and in the latter (with limited liability) he pledges only his share of the corporate assets. Effect of Corporate and Personal Taxes on the M-M Result The federal tax law allows corporations and individuals to deduct interest payments from their income before computing taxes. This tax shield is a subsidy to borrowers and may induce corporations and individuals to borrow when they otherwise might not. Taxation in the M-M Model Let X = operating income (before interest and taxes) and XT = after-tax earnings before interest; Tc = corporate tax rate; Tp = personal tax rate; Bc = "long-run" amount of debt outstanding and R = interest payments. V = value of unlevered firm and V = value of levered firm. Let k = required pre-tax expected return on the unlevered firm. Then X( - T c )( - T p ) ( - T c )X (IX.8) V = =. ( - T p )k k On the levered firm, X T =(X - R)( - T c )+ R =( - T c )X +T c R 79

16 Robert C. Merton ( - T p )r Bc If the debt is riskless, MM argue that R = rbc, then the value of the debt is = Bc, ( - T p )r and they show, by their arbitrage argument, that (IX.9) ( - T c )X T c R V = + k r =V +T c Bc In essence, because of the tax subsidy, the levered firm is equivalent to the unlevered firm plus a certain number (TcBc) of riskless bonds. MM assume that all earnings are paid out as dividends which are taxable at Tp. Moreover, they assumed that the magnitude of the tax shield is certain which need not be so if Bc is "pegged" to V. The latter is not of substantive importance because the value of the tax shield can be shown to equal TcBc, even if there is a possibility of default. Alternatively to corporate borrowing, let all the flows be riskless and let Y = after-tax income to an investor who maintains a fixed total leverage (corporate + personal borrowing = constant) position. Let Bp = amount of personal borrowing. Then, (IX.) Y = [( X -r Bc )(-T c )(-T p ) - r B p (-T p )] and the value of this stream will be (IX.) V(Y )=V r[ Bc( - T c )( - T p )+ B p( - T - ( - T p )r =V - Bc( - T c ) - B p p )] If Bc + Bp = constant, then dbc = dbp and (IX.) dv = - ( - T c )+=T c as MM dbc claim. However, suppose that one pays capital gains on the income of the firm, then 8

17 Finance Theory (IX.3) Y = [( X -r Bc )(-T c )(-T g )- r B p (-T p )], and if we capitalize at ( Tp)r, then (IX.4) (IX.5) r[ Bc(- Tc)(- T g) + Bp(- T p)] V(Y ) = V and r(- T p ) dv ( - T c )( - T g ) < = - depending on T c,t g,t dbc ( - T p ) > > if T p <T c p In summary, while the theoretical and empirical evidence is hardly conclusive on whether or not capital structure matters, it is probably a reasonable conclusion that generally, the effects of capital structure on the firm's cost of capital will not be large enough to make a capital budgeting project worth undertaking when it would not have been undertaken if financed entirely by equity. There are, of course, exceptions to this general rule especially when projects are subsidized by government and the subsidy takes the form of below-market interest rate loans, loan guarantees, or tax exemption for corporate debt. In completing this section, we present another example of the care that must be exercised in computing the cost of borrowing. The example is that of a bank loan with compensating balances and line fees. Problem IX.. On the Cost of Bank Borrowing Loan Commitment = Maximum that can be Borrowed = "Line" L Principal Amount Borrowed = Gross Borrowings B Stated Interest Rate on Loan R = r + δ where r = "prime" rate and δ amount "over prime" charged. 8

18 Robert C. Merton CB required (by the bank) amount to be kept on deposit in free balances in the form of noninterest-bearing demand deposits. ("Compensating Balances") P = cl + cb (i.e., a fraction of the line plus a fraction of the principal) penalty charged for not maintaining sufficient compensating balances = Rp[CB CB] where Rp penalty rate and CB compensating balances actually maintained. D d amount of noninterest-bearing demand deposits maintained by firm amount of noninterest-bearing demand deposits which would have been maintained by the firm even if there were no loans. Of each $ deposited, $.6 must be maintained at the Federal Reserve, so that only $.84 represent free-balances. Therefore, CB =.84D or D = CB/.84.9CB Fee is payable to the bank for the unused part of the line [i.e., L B]. Let RL rate paid as a line fee M actual amount of money available for corporate purposes (IX.6) M = B - D + d I $ charges paid for money (IX.7) I = R B + RL (L - B)+ R p [CB-CB] Let R T the "true" interest rate cost of borrowing = I/M 8

19 Finance Theory (IX.8) T = { + C L + L + C P P P } R R R R B R R L R CB M / (IX.8') R = { R + R C R B + R + R L R D C } [ B D + d ].84 / P P T L L P Should the firm maintain the compensating balance or pay the penalty? [i.e., which D should be chosen for d D.9CB + d]. Holding fixed the amount of money available for corporate purposes, M, how is RT R affected by the choice of D? R drt = R+ Rpc RL db RpdD M db dd M {[ ].84 } [ ] But dm = db = dd. Therefore, dr dd (IX.9) = ( ) ( ) Mfixed R R L.84 c R p / M ( R RL ) ( ) dr T < if R > Doptimum =.9CB + d dd.84 c p M [ R R L ] ( ) dr T = if R > indifference w.r.t. choice of D dd.84 c p M [ R RL ] ( ) dr T > if R > Doptimum = d dd.84 c p M A Numerical Example: Prime = r = 8%; δ = % so that R = % 83

20 Robert C. Merton Compensating Balance Requirement: % of the Line plus % of the Principal [i.e., c = c =.] Compensating Balance Penalty Rate: Rp = [R RL]/[.84 c] Line fee: RL =.5%; Payments of interest and fees once a year. Line = L = $,,; d =. Since Rp is such that for fixed M, the level of deposits has no effect upon R T, assume that D is chosen such that D = CB /.84 (i.e., no penalties) Amount for Corporate Purposes (M) "True" Interest Cost R T $,, 53.49%,, ,, ,, ,, 8.4 6,, ,, 6.6 8,, 6.5 9,, 5.6,, 5.7 This R T should be compared with "stated" rate of R = % R T Note:.5 r [i.e., an increase in prime of basis points will cause (at least) a 5 basis point increase in the cost of the loan.] 84