Part 1 - AL-Tax
Share Embed Flag
Download ePaper

Part 1 - AL-Tax

Part 1 - AL-Tax Part 1 - AL-Tax

eduart0.tripod.com
from eduart0.tripod.com More from this publisher
12.07.2015 Views

Chapter 2of an optimal investment path is contingent upon the determination of an optimalcapital path, a more useful expression is obtained by determining the optimalsize of the latter. Concisely, without personal taxes, owners’ wealth is maximizedwith respect to K t :W e ρ∫ t ( btF ( K ) t τY qtI )d t t st . . (2.2),0(2.3)where ρ is the financial cost or the firm’s discount rate, which will be clarifiedbelow. Additionally, b t is the price of output, q t the price of capital goods, τ thestatutory tax rate (0 τ1) and Y is taxable income.Taxable income is defined as output less depreciation allowances, immediateexpensing or free depreciation and tax credits permitted by the tax authorities(A l ). Therefore,Y b t F(K t ) A l q t I t . (2.4)Substituting the above equation in the firm’s optimization problem (2.3) and denotingA τA l , the Euler condition, which must hold at the optimum yields:Ct⎛ i ⎞qt q F( Kt) 1 Aδρ btqt⎝⎜⎠⎟1 τ .The term C t is the cost of capital, expressing the shadow price of capital at time t.Hence, the firm will carry investment until the rate of return of the marginalinvestment is equal to the cost of the investment (the right-hand side of the equation).If inflation is neutral in the sense that q/q t b/b t πand q t b t 1, theexpression above reduces to:Ct A F( Kt) ( δρπ ) 1 1 τ .(2.5)When the rate of allowances (A) or inflation (π) increases, the cost of capitaldeclines. And when the depreciation rate (δ) or the discount rate (ρ) increases, thecost of capital follows the same direction. Additionally, an increase in the tax ratewill raise the cost of capital, although it also raises A.In the absence of taxes, equation (2.5) implicitly defines the demand for capitalas a function of real interest rate (K(r)). 2 The firm will invest until the net returnto one unit of capital equals the rate of return to savings:F( K )δ r.t15

International Taxation HandbookrS′(r)S(r)MRRr *sK(r)K′(r)S * K *K, SFigure 2.2Capital demand and supply functionsSimilarly, let us define capital supply as a function of real interest rate (S(r)), 3 andassume that the economy is small and open, implying that the real interest rate isdetermined internationally.In Figure 2.2 we illustrate the situation of a capital importing country, 4 wheredomestic capital demand is K*, funding given by residents is S*, and the differenceis supplied by foreigners.If the return to capital is taxed, the real rate of return will differ from r* and thecapital demand curve will usually shift leftwards, reflecting the distortion in domesticinvestments. This tax distortion on the marginal investment can be observed byrearranging equation (2.5) to obtain:( τ A rF( Kt) r )( δ )δ,(1 τ)where the second term measures the difference between the net return to capital andthe real rate of return, indicating the extra earnings the company must achieve topay the investor a return r. Nevertheless, this wedge is not necessarily positive, sincea tax system may provide allowances and investment incentives causing a negativetax liability.Like the capital demand, the capital supply curve will move left after the impositionof a personal tax on interest income, and savers will receive a post-tax realrate of return s. The presence of taxes imposes a wedge between the gross marginalrate of return (MRR) and the after-tax real rate of return, which could be disaggregatedbetween the wedge generated by the corporate tax (w c MRR r*) and thewedge generated by personal tax on savings (w p r* s).16

International <strong>Tax</strong>ation HandbookrS′(r)S(r)MRRr *sK(r)K′(r)S * K *K, SFigure 2.2Capital demand and supply functionsSimilarly, let us define capital supply as a function of real interest rate (S(r)), 3 andassume that the economy is small and open, implying that the real interest rate isdetermined internationally.In Figure 2.2 we illustrate the situation of a capital importing country, 4 wheredomestic capital demand is K*, funding given by residents is S*, and the differenceis supplied by foreigners.If the return to capital is taxed, the real rate of return will differ from r* and thecapital demand curve will usually shift leftwards, reflecting the distortion in domesticinvestments. This tax distortion on the marginal investment can be observed byrearranging equation (2.5) to obtain:( τ A rF( Kt) r )( δ )δ,(1 τ)where the second term measures the difference between the net return to capital andthe real rate of return, indicating the extra earnings the company must achieve topay the investor a return r. Nevertheless, this wedge is not necessarily positive, sincea tax system may provide allowances and investment incentives causing a negativetax liability.Like the capital demand, the capital supply curve will move left after the impositionof a personal tax on interest income, and savers will receive a post-tax realrate of return s. The presence of taxes imposes a wedge between the gross marginalrate of return (MRR) and the after-tax real rate of return, which could be disaggregatedbetween the wedge generated by the corporate tax (w c MRR r*) and thewedge generated by personal tax on savings (w p r* s).16

logo

products

Resources

Company

Terms of service
Privacy policy
Cookie policy
Cookie settings
Imprint
Change language
Made with love in Switzerland
© 2024 Yumpu.com all rights reserved

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!