SEPARATE APPENDIX

This separate Appendix accompanies our paper Transition Strategies in Enacting Fundamental Tax Reform, forthcoming in National Tax Journal. A¢ liations: University of St.Gallen (FGN-HSG), Varnbuelstrasse 19, CH-9000 St.Gallen. Corresponding author: Christian.Keuschnigg@unisg.ch Appendix A: Investment and Financing Decisions The Appendix derives investment and nancing choices from intertemporal optimization. The costs of debt and equity at the rm level depend on personal capital income taxes. Given tax rates tB on interest, tD on dividends and tG on capital gains, no-arbitrage dictates identical net rates of return on perfectly substitutable assets. With the residence principle of interest taxation, gross interest rates are equal across countries, i = i , leaving a net interest r = 1 tB i on internationally tradeable bonds. In a small country, the world interest i is xed. If interest on business debt is taxed at the same rate, no-arbitrage requires a gross rate iB = i which is the cost of debt to rms. Holding equity shares yields dividends and capital gains (D and r) subject to e¤ective tax rates tD and tG where V is the rm value and V N is the value of new share issues (net of share repurchases). Firm valuation must satisfy the no-arbitrage condition r V = 1 t D + 1 t r; r Vt+1 V N V: (A.1) Gross income on rm ownership is D + r. Given that dividends amount to a share of total returns, D = (D +r), while the remaining share accrues in terms of capital gains, rm valuation is equivalently written as rV = 1 tE (D +r), or 1 + i V = D V N + Vt+1; i r= 1 t ; t = t + (1 ) t: (A.2) The investors required return iE reects an average of dividends and capital gains. In turn, the marginal tax rate tE is an average of dividend and e¤ective capital gains tax rates, weighed together with the pay-out ratio . The higher the pay-out ratio, the more the rm relies on new share nancing, and the more the old view of dividend taxation applies.1 Firms maximize the present value of dividends net of new share issues, see (A.2). A rms nancial policy is constrained by the identity D+ I = + V N + BN B , i.e. dividends and gross investment must be nanced out of pro ts (gross of depreciation), new share issues and net new debt. Using the nancial identity yields net dividends = D V N = I+BN B. De ning the end of period value function by V e 1 + iE V results in a dynamic program V e K;B;KT ;KD = maxI;BN + V e t+1= 1 + it+1 subject to (1-2). Use ~ Y and in (2), de ne shadow prices K = dV e=dK, B = dV e=dB, T = dV e=dKT and D = dV e=dKD, and observe K as given in (A.3). Optimality conditions for investment and new debt are t+1= 1 + it+1 = 1 tK JI + 1 I K 1 I t+1= 1 + it+1 ; t+1= 1 + it+1 = 1 N K ; K 0tK + 1 0 t+1= 1 + it+1 ; (A.3) and envelope conditions for the four stock variables are t = 1 tK (FK JK) + EiE K + 1 B K (bm0 m) + (1 ) t+1= 1 + it+1 ; t = i B +m0 + N EiE + B iB +m0 K + (1 ) t+1= 1 + it+1 ; t = t K T + 1 T t+1= 1 + it+1 ; t = t K D + 1 + iE D t+1= 1 + it+1 : (A.4) In a steady state, the shadow price of unused deductions is D = 1 + iE tK , implying K = tK . It doesnt matter when deductions are used up, as long as they are carried forward with interest. Using this, interpretations of the other conditions are standard, see Section 2.1. Combining (A.3A.4) to eliminate B yields optimal capital structure in (3). The e¤ective tax subsidy to the purchase cost of new capital in (A.3) is Z t + 1 I T = 1 + i ; T = 1 + i = T t= i + T ; (A.5) To be more exible with respect to the old and new views of dividend taxation, we actually distinguish between marginal and average pay-out ratios, see Keuschnigg and Keuschnigg (2010) for details.