sou · GMB3136d2 · 1999-01-01 00:00:00 — The cash-flow constraint: In economics, we are in principle interested in the change of wealth during the accounting period. That is, the income is the maximum amount that an economic unit can spend and still be worth as much in the end of a period as in the beginning of that period. For shareholders, it is the cash flow that really matters. The distinction between reported profit and cash flow is an important one; income is the basis for companies tax payments, whereas cash is what the firm can use to service debt, fund capital expenditures, and pay dividends. Inserting (1.5)-(1.11) and (1.14)-(1.18) into (1.19) leads us to the following cash-flow constraint for the firm12 (1.24) , L) - = (1 - t) f ( M - I e - cae + cle + N e + lle In what follows we will specify various institutional constraints that must be taken into consideration when modeling the firm's decision making process. 1) The allocation to the restricted reserves must at least be a = of the NBI if the restricted reserves is less than of the share capital: (1.25) rr e ³ bNBI e Using (1.5)-(1.8), we can rewrite the constraint (1.25) as below rr e ³ b(1 - t)[ f ( M e , L) - W e L - OCe - iLLe - dT Ce ] 12 For simplicity we also assume that the price level is equal to one. iff RRe £jSCe , where j = 0.2 . If RRe > jSCe there would not be any constraints on the allocations to restricted reserves. However, we impose a non-negativity constraint on the allocations to the restricted reserves to prevent solutions where the firm have negative allocations to restricted reserves rr e ³ 0 gross dividends De cannot exceed net business income ( NBI e ), other unrestricted equity ( OURE e ) plus free reserves ( FRe ) minus allocations to the other restricted reserves ( rr e ). If dividends exceed this amount the equity base of the firm would fall. The conditions can be summarized mathematically as De £ NBI e + OURE e + FRe - rr e FRe + OURE e = M e + CAe - SCe - RRe - ASDe - LLe - CLe . Using this condition and (1.12), we can rewrite the constraint (1.28) as below (1.29) De £ NBI e - rr e + Ce + CAe - RRe - LLe - CLe If we substitute the expression for De , from (1.24), into (1.29) we obtain the following + CAe - RRe - LLe - CLe This inequality is a constraint on the use of external funds. This constraint is showing that the part of investment, the increase of current assets, free reserves and other unrestricted equity that is not covered by tax depreciation and the current increase of restricted reserves must be financed by issuing new current liabilities, new long-term liabilities or new shares. 4) The firm is not allowed to pay negative dividends: Negative dividends would mean subsidies from government in the form of tax refunds If we substitute the expression for De , from (1.24), into (1.31) we obtain the following p1 = (1 - t)[ f ( M , L) - W after tax book income or retainable net profit. Inequality (1.32) states that the sum of financing through new issues of shares, increase of current liabilities and increase of long-term liabilities must at least be large enough to finance the part of investment and the increase of current assets that cannot be financed through accelerated depreciation and retention. 5) According to the Swedish law a firm must have a share capital that is at least SC = : where a1 is the exchange rate that the firm uses to denominate its share capital at the denomination day. 6) The firms is allowed to repurchase some of their own shares: In there is a law that forbids the firm to repurchase its own shares. The reason for this is that otherwise the firm can make distributions to shareholders that are exempted from personal taxation. However, there is a possibility in the law that lets the firm reduce its share capital by a special permission by the authorities. Moreover, there is a discussion in to let the firm repurchase its shares. In this paper we will not impose any constraint on the firms ability to re-purchase its own shares, to be able to analyze the implication of a reduction of share capital by permission and/or repurchase. 7) Finally, we also impose a non-negativity condition on each and every balance-sheet item: M e ³ 0 1.4The system dynamics for the firm In what follows, we will set up an expression for the value of the firm (section 1.4.1). By using the three basic financial statements and different constraints on the financial decisions, we will (in section (1.4.2), specify the optimization problem and the optimality conditions. 1.4.1The Value of the Firm and Its Cash Flow Constraint The fundamental condition for equilibrium in the capital market is that the yield in SEK on investing in any particular asset will be the same as the yield in SEK on all other assets, taking into account taxes:13 (1 - tp )a2iV e (u) = (1 - td )a3 De (u) + (1 - tc )(a4V&e - a5 N e (u)) where V e (u) is the value of the firm in euro at time u, a2V e (u) is the value of the firm in SEK at time u, a2 is the exchange rate used to convert the value of the firm in SEK to euro, N e (u) is the value of the new issue in euro at time u, a3 De (u) is the dividend (cash flow) in SEK paid by the firm, V&e is the derivative of the firm's value with respect to time, td is the dividend tax, tc is the tax on accruing capital gains, i is the market interest rate, tp is the marginal rate of income tax on bond income. The hypothesis in this paper is that an investor that has chosen to buy shares in euro compare the return on shares (converted into SEK) with 13 See King (1977) Section 4.1 pages 90-91, (1992) chapter 5, Poterba & Summers (1985) pages 232-233, and (1987) pages 63-65. the return on a euro-bond converted into SEK. We assume that the investor wants to invest V e (u) euro in either euro-bonds or euro-shares. His return of investing this amount in euro-bonds is iV e (u) euro. This return in euro converted into SEK gives ia2V e (u) . The after-tax return in SEK for investing in euro-bonds is then (1 - tp )a2iV e (u) . the investor can instead buy euro-shares. In that case, the shareholders after-tax return in SEK is equal to the after-tax dividends in SEK paid at time u plus the after-tax accrued capital gains in the same period. value of the invested amount in euro (V e (u) ) increases by V&e euro. Converting this amount to SEK gives a value increase by a4V&e , where a4 is the exchange rate used for conversion. However, the firm may have issued new shares during this period which decreases the value increase for old shareholders by a5 N e (u) SEK. The after-tax accrued capital gains for the shareholder is (1 - tc )(a4V&e - a5 N e (u)) SEK. Expression (1.42) represents the non-arbitrage condition. By integrating (1.42) we can then obtain the value of the firm at time t: (1.43) Ve (t) = òr[qa3 De - a5 N e ]e- r(u - t)du u = t dividends (the cash flow constraint), net of profit tax, are defined from the firms budget constraint (1.24). g> 1 means that the exchange rate used to convert the return in euro on a euro-bond to SEK is higher than the exchange rate used to convert the accrued capital gains in euro to SEK. 1.4.2The optimization problem and the optimality conditions. We assume that the interest rate and the wage rate are exogenously given. The firm will choose the time path of employment, net increase in current- and long-term liabilities, new issues of shares, net increase in free and restricted reserves, net increase of current assets and net investment so that the market value of it's shares is maximized. The state variables of the optimization problem are the stock of machinery and equipment, the firm's tax residual value of machinery and equipment, current assets, share capital, the stock of current and long- term liabilities, the stock of free- and restricted reserves, the stock of accumulated supplementary depreciation. The firms objective is then to maximize (1.43) subject to (1.24), (1.18), (1.13), (1.15)-(1.17), (1.10)-(1.11), (1.6), (1.14), (1.30), (1.32), (1.26)-(1.27), and(1.33)-(1.41) and the initial conditions CAe (t) = CA0e , M e (t) = M0e , FRe (t) = FR0e , ASDe (t) = ASD0e , LLe (t) = LLe0 , and CLe (t) = CLe0 this problem is: F = rqa3{(1 - t)[ f (a1 M e , L) - The current-value Hamiltonian for - i B LL ] + t d - I e - cae + cle + N e + lle} - ra e ( I e - dM e ) + mCe ( I + mSC e N + mRR e rr + mASDe (dM - lle + cae - cle + Ce + CAe - SCe - RRe - LLe - CLe ] + nf {N e + lle - t)[ f ( M , L) - n ( N e + where mM e , mCe , mCAe , mSCe the shadow prices for the stock variables, while nr , n2 , n3 , n4 , n5 , n6 , n7 , n8 , n9 and n10 are the shadow-price of (1.30), (1.32), (1.35)-(1.36), RRe > jSCe , (1.33) (1.37)-(1.41) and (1.34). The first order necessary conditions are: I e : - rqa N e : r(qa L: f L rr e : m fr e : m = (r + - (1 - M e : m = (r + d )mCe - t){rqa3 + n f }+ LLe : m LLe i(1 - nr : [I e - dT Ce - rr e - N e - lle + ca e - cle + Ce + CAe - SCe - RRe - LLe - CLe ] ³ 0, nr ³ n f : {N e + lle - ca e + cl e - I e + dT Ce + (1 - t)[ f (a1 M e , L) - i B LL ]} ³ 0, n f ³ 0, n f n : M e ³ 0, n ³ 0, n n : CAe ³ 0, n ³ 0, n ³ 0, n ³ 0, n n : SCe - n : RRe - jSCe ³ 0, n ³ 0, n ³ 0, n ³ 0, n n : Ce ³ 0, n ³ 0, n n : ASDe ³ 0, n ³ 0, n n8 : LLe ³ 0, n8 ³ n9 : CLe ³ 0, n9 ³ n : (N e + e ) ³ 0, n ³ 0, n 2 The Financial Decisions The corporate taxation system considered in this paper can be characterized by the following parameterization (1- t p) > (1- tc)(1- t) > (1- td )(1- t) which implies that debt dominates retention, which in turn dominates new share issues as a source of finance. In what follows, we will assume that relation (2.1) holds (which means that the firm would like to substitute debt for retained earnings and to new share issues) and investigate whether the firms dividend-ceiling, dividend-floor and other constraints are binding. Mathematically, we will try to establish whether the shadow prices nr , n f , n1 , n2 , n3 , n4 , n5 , n6 , n7 , n8 , n9 and n10 will be strictly positive or not (section 2.1 and 2.2). No adjustment costs have been introduced in this model, so that the adjustment procedure occurs instantaneously. Therefore, we impose stationary constraints on (1.52)-(1.60), i.e. = mCe = m LLe = mCAe = mSCe = mFRe = m ASDe (2.2) together with (1.52)-(1.60) give the values of mRRe , mFRe , mASDe , mLLe , and mCLe (1 - t) f M e (rqa3 + n f ) + (r + d) n f t) + nr i(1- t){rqa3 + n f }+ n3 - nr - n4j mRR = n4 -r nr 2.1Pair wise comparisons between different financial nstruments In this section, we will compare the three long term financial instruments in pair to determine the firms preferences.14 Preference relations that are obtained by comparing any two financial instruments hold everywhere in the solution space. The substitution between two financial instruments gives rise to changes in the market value of the firm. To be able to see this change we use the Hamiltonian function, F. The Hamiltonian function describes a plane above the solution space because F is linear in lle and N e . This means that the overall financial optimum can be found by mapping out the preference relations between any two financial instruments. 2.1.1The Comparison Between New Share Issues and Retained Profit To be able to find out whether the firm chooses new issues of shares or retained profit to finance investment, we use the first order condition with regard to N e , (1.46). We assume that I e and lle are exogenously- given values. We also assume that the firm distributes an amount that is both positive and less than net business income, other unrestricted equity plus free reserves minus allocations to the other restricted reserves. ( nr = 0 ). We also assume that the firm pays positive dividends ( n f = 0 ). Finally, we also assume that n10 It can than be showed = r(qa where NI stands for new issues of shares and RP denotes retained profits. NI f RP means that new share issues are superior to retention 14 It is worth mentioning that financial preferences should not be mixed up with preferences in the sense of utility levels, because such preferences are not important according to 's separation theorem. NI ~ RP the Expression (2.12) measures the marginal advantage of substituting new share issues for retention. The substitution does not effect the market value of the firm, because the stock of equity does not change when one euro of net profit is replaced by one euro of new issues of shares. The substitution only creates gross advantages and disadvantages for the shareholders.15 To clarify this statement we rewrite expression (2.12) as follows: [a3 (1 - td ) + a5 (tc - 1)]í=ý0 Substitution between one euro (or a3 SEK) new issues of shares and retention gives rise to three advantages. First of all, a5tc SEK is saved because of reduced capital gains tax. Secondly, If the firm choose to substitute new share issue with one euro retained profit, it would be possible for the firm to raise dividends payments by a3 (1 - td ) SEK, after personal taxes on dividends. The disadvantage of the substitution is that one euro (or a5 SEK) has to be paid for the new issues. The net advantage thus becomes [a3 (1 - td ) + a5 (tc - 1)] SEK. Substitution is favorable if and only if the net advantage in euro [a3 (1 - td ) + a5 (tc - 1)] ) to the shareholder is positive. Expression (2.12) can be interpreted in another way. i(1 - tp ) purpose we multiply both sides of (2.12) by td )(1 - t) (1 - t p)a2i (1 - t p)a2i a5 (1 - tc)(1 - t) (1 - td )(1 - 15 This part is based on (1987), page 80. The left hand side of equation (2.14) is the cost of retention in SEK. This is the cost in SEK that the firm saves when it substitutes new share issues for retention. The right hand side is the cost of new share issues in SEK. For instance, if the cost of retention that the firm saves because of the substitution exceed the cost of new share issues then it will prefer to substitute new issues of shares for retain profits. The net advantage of the substitution for the case of accounting in home currency can be found by assuming that a2 = a3 = a5 = 1 , as follows i(1 - t p) i(1 - t p) - tc)(1 - (1 - td )(1 - t) (2.1), i(1 - t p) i(1 - t p) NI p RP . (1 - tc)(1 - td )(1 - t) firm prefer to retain its profits instead of issuing new shares at the (with regard to the Swedish tax system formalized in (2.1)). The comparison between the net advantage of substitution in the case of SEK accounting with the net advantage in the case of euro accounting (see (2.14)) imply that the choice at the between new share issues and retained profits can indeed be altered because of the conversion method used to convert dividends and capital gains in euro to SEK. For example, if the exchange rate at the time of new issues of shares is lower than the exchange rate at the time of dividend payment than the marginal cost relation specified above (in the case of SEK) can be altered. If the difference between these two exchange rates are high than the initial tax incentive can be disturbed. This means that NI f RP (which means that new issues of shares can become more favorable than retain earnings) if the home currency depreciate between the time of new share issues and the dividend payment. Theoretically, this problem could be solved by using the same exchange rate so that a2 = a3 = a5 (for example the average exchange rate during the year). However, the Swedish tax law does not permit such method. According to the tax law shareholders should be taxed for the amount they receive at the dividend payment day. Shareholders receive dividends in euro at the dividend payment day which they exchange to euro at the same day. This means that the taxation must be based on the exchange rate at the time of dividend payment. However, if we like to give the firm the opportunity to have its accounting in euro and pay dividends in euro, than we must accept that this firms financial decisions can be altered because of exchange rate movements. Another way of accomplishing exchange rate neutrality is to abandon the principle that taxation of dividends (that is paid in foreign currency) should be based on exchange rate at the time of dividend payment. However, Such legislation could be adopted on dividends that are paid by a Swedish firm (and who has decided to have its accounting in euro). But, can not adopt such rules on dividends paid by a foreign firm. This means that such legislation would create non-neutrality between a Swedish and a foreign owned firm.16 The conclusion is that the exchange rate neutrality can be obtained if we accept the non- neutrality between the exchange rules regarding the taxation of dividends paid by a Swedish and a foreign owned firm. Another problem concerns the risk taking by shareholders. A legislation that force shareholders to pay taxes on their dividend income in euro, which are converted to SEK by adopting the average exchange rate during the year, create a new risk for the shareholders. It is possible that the exchange rate appreciate from the end of the year and the dividend payment day. This means that shareholders will receive an mount in SEK but taxed for a higher amount (which is based on the average exchange rate during the year). One way to solve this is to force the firm pay dividends in SEK. By this method, we let the firm take the exchange rate risks. One could argue that the firm have better opportunities to manage exchange rate exposures during this period. However, can not adopt such legislation on a foreign owned firm. This means that those shareholders that own shares in foreign companies will have to manage exchange rate exposures by themselves, while shareholders that own shares in Swedish companies are protected by laws. This implies that a Swedish firm will have to manage exchange rate risks which a foreign firm is let of. 2.1.2The Comparison Between Debt and Retained Profit 16 However, this problem can be solved by follwing rules. Swedish shareholders that receive dividends for their ownership in foreign companies are usually taxed for this income in foreign countries. In , these shareholders get reduction for foreign taxes. These foreign taxes paid are today converted to SEK using the exchange rate at the dividend day. However, we could instead use the average exchange rate for conversion purposes. This method would create neutrality between the taxation of dividens paid by the foreign and Swedish firms. To be able to find out whether the firm chooses debt or retained profit, we use the first order condition with regard to lle , (1.45). that I e and N e are exogenously-given values. We also assume that the firm distributes an amount that is both positive and less than net business income, other unrestricted equity plus free reserves minus allocations to the other restricted reserves. In other words nr = 0 and n f = 0 . It can be than be showed that where DF stands for debt financing. Thus (2.16) measures the marginal advantage of substituting debt financing for retention. It is important to mention that the policy, dlle < 0 Û DF p RF , implies that we get a solution at the lower boundary of the solution space. This solution is characterized by De = 0 , which also means that the market value would become negative or equal to zero if N e ³ 0 . For this reason, we exclude such non-optimal solution when the firm issues new shares (or when they abstain from issuing shares).17 However, in this model, we let the firm to repurchase its own shares ( N e < 0 ). In such case the policy mentioned above can become value increasing for the firm. We need to rewrite the first term of (2.16) to be able to interpret this It can be shown that (2.16) can be re-written as (1 - t (1 - tp )a2i - td )(1 - t)i a4 (1 - tc ) ï ïa4 Assume that a representative shareholder is indifferent between borrow-and-distribute policy within the firm. If the firm now chooses to substitute one euro of debt with one euro of retained profit, it would be possible for the firm to raise the dividend payments by one euro, 17 The interested reader is referred to , page 82. which represents a3 SEK. Thus, a3 (1 - td ) SEK is the dividends after personal taxes.18 Dividend payments also raise the market value of the DV e euro, so that the tax debt on capital gains becomes SEK. The shareholder thus receive a3 (1 - td ) - tca4 DV e SEK. To ensure that the shareholder remains indifferent between retention and debt, two claims must be fulfilled: The market value has to fall so that selling the shares would neither give capital gains nor losses, thus DV e = - a (1 - t DV e = - So the initial amount that the shareholder becomes a3 (1 - a3 (1 - a3 (1 - a4 (1 - a3 (1 - td ) (1 - tc ) Using debt instead of retention implies interest payments in future. the Future dividend cuts that arise because of interest payments must be at least as high as the amount shareholders receive if they invest the initial dividend amount in the capital market. If shareholders invest the initial amount that they receive in the capital market, then they will receive (net of income tax) (1 - tp )a (1 - td ) (1 - tc ) 3 (1 - 4 (1 - reduction of dividends that arises from the interest payments is equal to 3 (1 - td )(1 - t)i If (2.18) is higher than (2.19) then it is profitable for the firm to issue bonds. 18 The corresponding figure in euro is a3 (1 - td ) . Equation (2.17) can also be interpreted in another way. For this purpose we re-write equation (2.17) as follows (1 - t p)a2i ì> ü a4 (1 - tc)(1 - t) î=þ (2.20) is the (1 - t p)a2i tc)(1 - t) financing through retain profit. This is the cost that the firm saves when it substitutes debt for retention. If the cost of financing through retention exceed the cost of debt financing then the firm will prefer to substitute between these two financial instruments. The net advantage of the substitution for the case of accounting in home currency can be found by assuming that a2 = a3 = a4 = 1 . (1 - t p)i ì> ü Using (2.1), we can conclude (1 - t p)i (1 - tc)(1 - t) î=þ > i Û RP p DF . This means that the firm prefers (1 - tc)(1 - issuing debt instead of retaining its profits at the (with regard to the Swedish tax system formalized in (2.1). The comparison between the net advantage of substitution in the case of SEK accounting with the net advantage in the case of euro accounting (see (2.20)) imply that the choice at the between debt and retained profits can indeed be altered because of the conversion method. The only way to accomplish exchange rate neutrality in this case compared to the case where the firm has its accounting in SEK is to let a2 = a3 = a4 . However, as we explained in our previous section, this is associated with different practical problems, which implies that we must accept that the firms choice at the between debt and retain profit may be disturbed. This means that the original intention of the tax legislation may be disoriented because of non-neutrality with regard to the conversion method. 2.1.3 The Comparison Between Debt and New Issues of Shares To be able to find out whether the firm chooses new issues of shares or debt, we differentiate the Hamiltonian function with respect to N e , given I and the constraint N e + lle = const. . Using (2.12) and (2.16) we obtain the following expression positive nr = n f as: N e + lle = const. Assume now that the firm distributes an amount that is both and less than the accounting profit. We assume that = n10 = 0 . (2.21) can, by using (2.12) and (2.16), be re-written = r(qa3 - a5 ) - rqa3 N e + lle = const. i(1 - t)ra3 By a few simplifications (and the fact that i = i B) we obtain19 (1 - t )(1 - t)a i (1 - tp )a N e + lle = const. (2.23) measures the marginal advantage of substituting new issues of shares for debt financing. Let us rewrite (2.23) as below (1 - t )(1 - t)a i ì=ü (1 - tp )a3i NI f DF is again an existence problem. ll e = const.