Iteratioal Joural of Ecoomics ad Busiess Admiistratio Vol. 1, No. 2, 2015, pp. 59-70 http://www.aisciece.org/joural/ijeba Optimizig of the Ivestmet Structure of the Telecommuicatio Sector Compay P. N. Brusov 1, *, T. V. Filatova 2, N. P. Orekhova 3, A. P. Brusova 4, V. L. Kulik 4 1 Applied Mathematics Departmet, Fiacial Uiversity uder the Govermet of Russia Federatio, Moscow, Russia 2 Dea of GMM Faculty, Fiacial Uiversity uder the Govermet of Russia Federatio, Moscow, Russia 3 High School of Busiess, Souther Federal Uiversity, Ivestmet ad Taxatio Laboratory, Research Cosortium of Uiversities of the South of Russia, Rostov-o-Do, Russia 4 Maagemet Departmet, Fiacial Uiversity uder the Govermet of Russia Federatio, Moscow, Russia Abstract I this paper developed by the authors models of evaluatio of the depedece of effectiveess of ivestmets o debt fiacig are applied for the aalysis of ivestmets of oe of the biggest telecommuicatio compay of Russia for 2010-2012 years from the poit of view of optimal structure of ivestmet. The aalysis revealed, that oly i 2011 the compay's ivestmet structure was close to the optimal. Keywords Ivestmet Projects with Arbitrary Duratio, Effectiveess of Ivestmet Project, Optimal Leverage Level, Taxes Impact Received: May 3, 2015 / Accepted: May 28, 2015 / Published olie: Jue 30, 2015 @ 2015 The Authors. Published by America Istitute of Sciece. This Ope Access article is uder the CC BY-NC licese. http://creativecommos.org/liceses/by-c/4.0/ 1. Itroductio Ivestmets i tagible ad itagible assets play a importat role i the activities of ay compay. They are a ecessary coditio for structural adjustmet ad ecoomic growth, provide the creatio of ew ad ehacemet of existig basic fuds ad idustries. The role of ivestmet, which is always the oe of the most importat, is icreased may times at the curret stage. For example, i Russia a priority of budget will be the reduced of depedece of the price of oil ad gas. The mai issue, that help at least to start the movemet o this way are, of course, ivestmets. I this way, the role of ivestmet at the preset stage is ideed icreasig dramatically. I this regard, the role of evaluatio of efficiecy of ivestmet projects, which i the cotext of scarcity ad limited ivestmet resources allow choose for the realizatio of the most effective projects, icreases. Sice virtually all ivestmet projects use debt fiacig, the purpose of the study of impact of debt fiacig, capital structure o the efficiecy of ivestmet projects, determiig of the optimal level leverage - always actual, ad, of course, is especially actual at the preset time. Hope to determie the optimal capital structure, i which oe or more parameters of efficiecy of the project (NPV, IRR, etc.) are maximum, more tha half a cetury has ecouraged researchers to deal with the issue. Some of the major problems i the assessmet of the effectiveess of the projects are the followig : What fiacial flows ad how it is ecessary to take ito accout whe calculatig parameters of efficiecy of the project (NPV, IRR, etc. ); how may discout rate should be used for discoutig of fiacial flows associated with ivestmets; how correctly to determie these discout rate. Discussio cocerig the first two problems is still * correspodig author E-mail address: pb1983@yahoo.com (P. N. Brusov)
60 P. N. Brusov et al.: Optimizig of the Ivestmet Structure of the Telecommuicatio Sector Compay cotiuig. O the third issue, oe eeds to ote that, i recet years there has bee a sigificat progress i the more correct determiig of the cost of the equity capital of the compay ad its weighted average cost, which as time ad are the discout rate whe evaluatig the NPV of the project. The progress is associated with work performed by Brusov, Filatova ad Orekhova (Brusov P, Filatova T, Orehova N, Eskidarov M 2015; Brusov et al 2011a,b,c,d,e; 2012 a,b; 2013 a,b,c; 2014 a,b; Filatova et al 2008), i which the geeral theory of capital cost of the compay (equity cost as well as weighted average cost) was established ad its depedece o leverage ad o life-time of compay was foud for the compaies with arbitrary life-time. The mai differece betwee their theory ad theory by Modigliai ad Miller is that former oe waives from the perpetuity of the compaies, that leads to sigificat differeces of a ew theory from theory of Nobel laureates Modigliai ad Miller (Modigliai et al 1958, 1963, 1966). The lack of moder methods of evaluatio of effectiveess of ivestmet projects with accout of the debt fiacig, with the correct assessmet of discout rate, used i ivestmet models, has idetified the eed for research. The establishmet of such moder models, cosiderig problem from the poit of view of equity capital owers as well as from the poit of view of equity ad debt capital owers, with the use of moder theory by Brusov, Filatova ad Orekhova of assess of the equity capital cost ad weighted average cost of capital of the compay (Modigliai et al 1958, 1963, 1966), which play the role of discout rate i the ivestmet models, ca sigificatly cotribute to the problem of the assessmet of ivestmet projects effectiveess. 2. Ivestmet Aalysis ad Recommedatios for Telecommuicatio Compay "Nastcom Plus" Based o the method, developed by the authors (Brusov P, Filatova T, Orehova N, Eskidarov M 2015; Brusov et al 2011a,b,c,d,e; 2012 a, b; 2013 a,b,c; 2014 a, b; Filatova et al 2008) let us aalyze the efficiecy of ivestmets of oe of the leadig compaies i the telecommuicatio sector "Nastcom Plus" for 2010-2012 years from the poit of view of optimal structure of ivestmet. The source data for the aalysis are preseted i Table. 1 Table 1. Data of the compay "Nastcom Plus" for 2010-2012 years. Idicator 2010 2011 2012 Ivestmet I, millio dollars 1.124 2.05 2.763 Reveue, millio dollars 7204. 335 8232.172 9418.773 Net operatig icome for the year before taxig, NOI, 2161.3 2469.174 2826 millio dollars Equity cost at zero leverage, k 0, % 23.67 23.67 23.67 Debt cost k d, % 8.26 7.4 6.69 Retur-o-ivestmet for oe year, β = I / NOI 1.92 1.204 1.02 Amout of debt fiacig,% 35 50 50 Amout of equity, % 65 50 50 Leverage level, L 0.54 1 1 Amout of equity capital S, millio dollars 730.6 1025 1381.5 Quatity k 0 is the equity cost of fiacially idepedet compay (or equity cost at zero leverage) ad for "Nastcom Plus" is equal to 23,67% (Brusova 2011). Here are also calculated depedece of weighted average cost of capital WACC ad the equity cost keo leverage (Fig. 1 ). Fig. 1. Depedece of weighted average cost of capital WACC ad the equity cost e k o leverage: 1, 4 withi Brusov Filatova Orekhova theory; 2, 5 withi Modigliai Miller theory; 3, 6 withi traditioal approach.
Iteratioal Joural of Ecoomics ad Busiess Admiistratio Vol. 1, No. 2, 2015, pp. 59-70 61 2.1. The Depedece of NPV o Ivestmet Capital Structure Aalysis of ivestmet will be cotiued with use of the formula provided i the works (Brusov P, Filatova T, Orehova N, Eskidarov M 2015; Brusov et al 2011a,b,c,d,e; 2012 a,b; 2013 a,b,c; 2014 a,b; Filatova et al 2008): 1 1 NPV = S 1 + L (1 t) 1 + + ( 1+ kd ) ( 1+ kd ), (1) βs(1 + L)(1 t) 1 + 1 ke ( 1+ ke ) S equity capital amout; L leverage level; t tax o profit rate; k d debt cost; project duratio; β retur-o-ivestmet for oe year; k e equity cost. Aalysis of ivestmets i 2010 year Usig compay's data (Table 1 ), we compute the WACC, k e ad NVP (Tables 2 4, Figs. 1 ad 2). where NPV et preset value; Project Duratio Table 2. Weighted average cost of capital, WACC, i 2010 year. 2 0.2367 0.2284 0.2242 0.2217 0.2201 0.2189 0.2180 0.2173 0.2167 0.2163 0.2159 5 0.2367 0.2262 0.2209 0.2177 0.2156 0.2141 0.2130 0.2121 0.2114 0.2108 0.2103 7 0.2367 0.2256 0.2199 0.2166 0.2143 0.2127 0.2116 0.2106 0.2099 0.2093 0.2087 10 0.2366 0.2250 0.2190 0.2155 0.2131 0.2114 0.2101 0.2091 0.2083 0.2076 0.2071 project duratio Table 3. Equity cost k e i 2010 year. 2 0.2367 0.3096 0.3824 0.4552 0.5280 0.6008 0.6736 0.7464 0.8192 0.8920 0.9649 5 0.2367 0.3063 0.3758 0.4452 0.5147 0.5841 0.6536 0.7230 0.7925 0.8619 0.9314 7 0.2367 0.3053 0.3738 0.4423 0.5107 0.5791 0.6480 0.7165 0.7850 0.8535 0.9220 10 0.2366 0.3044 0.3720 0.4396 0.5071 0.5746 0.6422 0.7097 0.7772 0.8447 0.9122 Project duratio Table 4. Net preset value NPV i 2010 year, millio dollars. 2 910.5 1181.8 1358.3 1458.5 1496.3 1482.8 1426.6 1334.6 1212.4 1064.5 894.5 5 2371.6 2979.2 3347.7 3547.1 3624.5 3612.4 3533.6 3404.2 3236.1 3038.0 2816.2 7 2939.0 3594.8 3955.1 4121.6 4157.6 4103.6 3981.6 386 3619.9 3397.1 3155.1 10 3444.5 4086.2 4396.9 4509.1 4497.4 4405.3 4258.9 4074.9 3863.8 3632.7 3386.5 Fig. 2. Depedece of NPV o leverage L at t = 20% i 2010 year: 1 for two-year icome from ivestmets; 2 for five-year icome from ivestmets (the term hardware depreciatio); 3 for seve years of ivestmet icome; 4 for te years of ivestmet icome.
62 P. N. Brusov et al.: Optimizig of the Ivestmet Structure of the Telecommuicatio Sector Compay I the compay's ivestmet i 2010 equity capital accouted for 65 %, ad debt - 35 %, i.e. the leverage level was equal to L = 0.54. The term hardware depreciatio, ito establishmet of which ivestmet were doe, was five years. Curve 2 (Fig. 2 ) correspods to depedece of NPV o leverage level for the five-year project. Optimum NPV is achieved whe L = 2. At this leverage level NPV = 3 624.5 millio dollars. The level leverage with which compay "Nastcom Plus" has carried out its ivestmet projects (L = 0.54), was lyig far from optimum ad provided NPV = 2.979.2 millio dollars, that is approximately 645 millio dollars less tha optimal NPV value. oe ca estimate the NPV ad for a more log-term perspective. For example, seve-year project the optimal leverage value is L = 2.0, whe the NPV = 4,157.6 millio dollars, that is for 562.8 millio dollars more tha ooptimal values of NPV = 3,594.8 millio dollars, obtaied by the compay. For the te-year project the optimal leverage level L = 1.5, with NPV = 4,509.1 millio dollars, that is for 422.9 millio dollars more tha o-optimal values of NPV = 4, 086.2 millio dollars, obtaied by the compay (Fig. 2, Tables 2 4). Aalysis of ivestmets i 2011 year Usig compay's data, we compute the WACC, k e ad NVP (Tables 5 7, Fig. 3). Sice the equipmet ca be operated ad after depreciatio, project duratio Table 5. Weighted average cost of capital WACC i 2011 year. 2 0.2367 0.3096 0.3824 0.4552 0.5280 0.6008 0.6736 0.7464 0.8192 0.8920 0.9649 5 0.2367 0.3063 0.3758 0.4452 0.5147 0.5841 0.6536 0.7230 0.7925 0.8619 0.9314 7 0.2367 0.3053 0.3738 0.4423 0.5107 0.5791 0.6480 0.7165 0.7850 0.8535 0.9220 10 0.2366 0.3044 0.3720 0.4396 0.5071 0.5746 0.6422 0.7097 0.7772 0.8447 0.9122 project duratio Table 6. Equity cost k e i 2011 year. 2 0.2367 0.3142 0.3916 0.4690 0.5464 0.6239 0.7013 0.7787 0.8561 0.9335 1.0110 5 0.2367 0.3110 0.3853 0.4595 0.5338 0.6080 0.6822 0.7565 0.8307 0.9049 0.9791 7 0.2367 0.3100 0.3833 0.4565 0.5297 0.6029 0.6761 0.7493 0.8230 0.8963 0.9695 10 0.2366 0.3091 0.3813 0.4536 0.5258 0.5980 0.6702 0.7424 0.8146 0.8868 0.9589 project duratio Table 7. Net preset value, NPV, of the compay i 2011 year, millio dollars. 2 418.8 460.5 415.8 302.3 133.3 80.9 332.5 615.0 923.5 1254.0 1 603.1 5 1704.2 2025.4 2131.8 2089.9 1943.2 1721.0 1443.5 1124.7 774.8 400.9 8.5 7 2203.4 2558.0 2650.5 2576.1 2392.2 2134.4 1825.6 1480.7 1105.7 715.0 309.8 10 2648.2 2982.3 3028.1 2907.1 2685.2 2399.5 2071.6 1715.0 1338.0 946.0 542.9 Fig. 3. Depedece of NPV o leverage L at t = 20% i 2011 year: 1 for two-year icome from ivestmets; 2 for five-year icome from ivestmets (the term hardware depreciatio); 3 for seve years of ivestmet icome; 4 for te years of ivestmet icome.
Iteratioal Joural of Ecoomics ad Busiess Admiistratio Vol. 1, No. 2, 2015, pp. 59-70 63 I the compay's ivestmet i 2011 equity capital accouted for 50 %, ad debt capital - 50 % as well, i.e. the leverage level was equal to L = 1. The term hardware depreciatio, ito establishmet of which ivestmet were doe, was five years. Curve 2 (Fig. 3) correspods to depedece of NPV o leverage level for the five-year project. Optimum NPV is achieved approximately at L = 1. More accurate calculatios show that optimal value NPV = 2,133.7 millio dollars is achieved whe L = 1.1. carried out its ivestmet projects (L = 0.1), was lyig i the viciity of optimum ad provided NPV = 2,131.8 millio dollars, that is just 2 millio dollars less tha optimal NPV value. You ca take it that, i 2011, ivestmet i "Nastcom Plus" compay have bee carried out with almost optimal structure. Aalysis of ivestmets i 2012 year Usig compay's data, we compute the WACC, k e ad NVP (Tables 8 10, Fig. 4). The level leverage with which compay "Nastcom Plus" has Table 8. Weighted average cost of capital WACC i 2012 year. project duratio 2 0.2367 0.2298 0.2264 0.2243 0.2229 0.2219 0.2212 0.2206 0.2202 0.2198 0.2195 5 0.2367 0.2278 0.2234 0.2207 0.2189 0.2176 0.2167 0.2159 0.2153 0.2148 0.2144 7 0.2367 0.2272 0.2224 0.2195 0.2176 0.2162 0.2152 0.2143 0.2137 0.2132 0.2127 10 0.2366 0.2265 0.2213 0.2183 0.2162 0.2147 0.2136 0.2127 0.2120 0.2115 0.2110 project duratio Table 9. Equity cost k e i 2012 year. 2 0.2367 0.3180 0.3992 0.4805 0.5617 0.6430 0.7242 0.8055 0.8867 0.9680 1.0492 5 0.2367 0.3150 0.3933 0.4715 0.5497 0.6279 0.7062 0.7844 0.8626 0.9408 1.0190 7 0.2367 0.3140 0.3913 0.4685 0.5457 0.6229 0.7001 0.7772 0.8544 0.9316 1.0088 10 0.2366 0.3130 0.3892 0.4653 0.5415 0.6177 0.6938 0.7699 0.8461 0.9222 0.9983 project duratio Table 10. Net preset value NPV i 2012 year, millio dollars. 2 267.0 200.9 33.4 214.0 525.3 888.3 1293.4 1733.4 2202.4 2695.8 3209.9 5 1734.8 1968.9 1954.6 1771.8 1472.1 1089.6 647.1 160.6 358.9 903.4 1467.2 7 2304.7 2566.9 2528.9 2304.4 1960.4 1537.2 1060.3 545.9 4.7 556.0 1131.2 10 2812.6 3041.6 2945.5 2667.4 2281.9 1829.9 1335.0 811.1 266.8 292.2 862.1 Fig. 4. Depedece of NPV o leverage L at t = 20% i 2012 year: 1 for two-year icome from ivestmets; 2 for five-year icome from ivestmets (the term hardware depreciatio); 3 for seve years of ivestmet icome; 4 for te years of ivestmet icome. The compay's ivestmet structure i 2012 year was the same as i 2011: equity capital accouted for 50 %, ad debt capital - for 50 %, i.e. the leverage level was equal to L =1. The term hardware depreciatio, ito establishmet of which ivestmet
64 P. N. Brusov et al.: Optimizig of the Ivestmet Structure of the Telecommuicatio Sector Compay were doe, was five years. Curve 2 (Fig. 4) correspods to depedece of NPV o leverage level for the five-year project. Optimum NPV is achieved whe L = 0.5. More accurate calculatios show that optimal value NPV = 1. 987.7 millio dollars is achieved whe L = 0.7 (Table 11, Fig. 5). Table 11. Net preset value NPV at leverage level from 0.5 up to 1.05 i 2012 year, millio dollars. project duratio 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 2 200.9 188.3 174.8 160.2 144.8 128.4 111.1 92.9 73.9 54.1 33.4 12.0 5 1968.9 1977.0 1982.8 1986.3 1987.7 1987.0 1984.2 1979.5 1973.0 1964.6 1954.6 1942.8 7 2566.9 2574.2 2578.8 2580.6 2580.0 2576.9 2571.5 2563.9 2554.2 2542.5 2528.9 2513.5 10 3041.6 3043.5 3042.4 3038.5 3032.0 3023.1 3011.7 2998.2 2982.6 2965.0 2945.5 2924.3 Fig. 5. Depedece of NPV o leverage L at t = 20% i 2012 year i the viciity of optimum: 1 for two-year icome from ivestmets; 2 for five-year icome from ivestmets (the term hardware depreciatio); 3 for seve years of ivestmet icome; 4 for te years of ivestmet icome. The level leverage, with which compay "Nastcom Plus" has carried out its ivestmet projects (L = 0.1 ), did ot correspod to optimum value (L=0.7) ad provided NPV = 1,954.6 millio dollars, that is 31.7 millio dollars less tha optimal NPV value (Figs. 4 ad 5 ; Tables 10 ad 11). Sice the equipmet ca be operated ad after depreciatio, oe ca estimate the NPV ad for a more log-term perspective. For example, for seve-year project the optimal leverage value is L =0.65, whe the NPV = 2,580.6 millio dollars, that is for 51.7 millio dollars more tha o-optimal values of NPV = 2,528.9 millio dollars, obtaied by the compay. For the te-year project the optimal leverage level L = 0.55, with NPV =3,043.5 millio dollars, that is for 98 millio dollars more tha o-optimal values of NPV = 2,945.5 millio dollars, obtaied by the compay. 2.2. The Depedece of NPV o the Equity Capital Value ad Coefficiet β Let us ivestigate the depedece of NPV o the equity capital value ad coefficiet β (Tables 12 15, Figs. 6 9). Table 12. Net preset value NPV at β = 1.02, millio dollars. Equity. S 1382 1734.8 1968.9 1954.6 1771.8 1472.1 1089.6 647.1 160.6 358.9 903.4 1467.2 1000 1255.7 1425.2 1414.8 1282.5 1065.6 788.7 468.4 116.2 259.8 653.9 1062.0 1200 1506.8 1710.2 1697.8 1539.0 1278.7 946.4 562.1 139.5 311.8 784.7 1274.4 1600 2009.1 2280.3 2263.7 2052.0 1705.0 1261.9 749.5 186.0 415.7 1046.3 1699.2 1800 2260.3 2565.3 2546.7 2308.5 1918.1 1419.7 843.2 209.2 467.6 1177.1 1911.6 Equity. S Table 13. Net preset value, NPV, at β = 0.5, millio dollars. 1382 146.1 71.8 411.5 833.8 1313.3 1833.5 2383.1 2954.2 3541.6 4141.1 4750.2 1000 105.7 52.0 297.9 603.5 950.7 1327.2 1725.0 2138.4 2563.6 2997.6 3438.4 1200 126.9 62.4 357.4 724.2 1140.8 1592.6 2070.0 2566.1 3076.3 3597.1 4126.1 1600 169.2 83.2 476.6 965.6 1521.0 2123.5 2760.0 3421.5 4101.7 4796.1 5501.4 1800 190.3 93.6 536.2 1086.3 1711.2 2388.9 3105.0 3849.2 4614.4 5395.6 6189.1
Iteratioal Joural of Ecoomics ad Busiess Admiistratio Vol. 1, No. 2, 2015, pp. 59-70 65 Fig. 6. Depedece of NPV o leverage at differet values of equity cost S at β=1.02, millio dollars: 1 S = 1,382. 2 millio dollars; 2 S = 1 000 millio dollars; 3 S = 1 200 millio dollars; 4 S = 1 600 millio dollars; 5 S = 1 800 millio dollars. With icrease of the equity value, optimum is observed for all of the values S whe leverage level is approximately equal to L = 0.7, ad the optimum value, as well as the NPV value is growig with icreasig S, as log as the project remais effective (up to the leverage level approximately L = 3.7 ). With decrease of the retur o ivestmet (β = 0.5) the depedece of the NPV o leverage chages sigificatly: ow NPV mootoically decreases with the leverage at all values of equity capital S (Fig. 7 ). Fig. 7. Depedece of NPV o leverage at differet values of equity cost S at β=0.5, millio dollars: 1 S = 1 382, 2 millio dollars; 2 S = 1 000 millio dollars; 3 S = 1 200 millio dollars; 4 S = 1 600 millio dollars; 5 S = 1 800 millio dollars. Table 14. Net preset value NPV at β = 1.5, millio dollars. Equity. S 1382 3201.2 3852.6 4138.6 4176.9 4043.3 3787.8 3444.2 3035.8 2578.9 2085.3 1563.3 1000 232 2788.7 2995.8 3023.5 2926.8 2741.8 2493.1 2197.5 1866.7 1509.4 1131.6 1200 2780.7 3346.5 3594.9 3628.2 3512.1 3290.2 2991.7 2637.0 2240.1 1811.3 1357.9 1600 3707.5 4462.0 4793.2 4837.6 4682.8 4386.9 3989.0 3515.9 2986.8 2415.1 1810.6 1800 4171.0 5019.7 5392.4 5442.3 5268.2 4935.3 4487.6 3955.4 3360.1 2716.9 2036.9 Fig. 8. Depedece of NPV o leverage at differet values of equity cost S at β=1.5, millio dollars: 1 S = 1382. 2 millio dollars; 2 S = 1000 millio dollars; 3 S = 1200 millio dollars; 4 S = 1600 millio dollars; 5 S = 1800 millio dollars.
66 P. N. Brusov et al.: Optimizig of the Ivestmet Structure of the Telecommuicatio Sector Compay With icrease of the retur o ivestmet (β = 1.5) the NPV of the project has a optimum at all values of equity capital S at leverage level L=1.5 ad NPV(L) curve is goig up with the icrease i S util the project remais effective (up to the leverage level approximately L = 7). The optimum positio (value L 0 ) is almost does ot deped o the equity value S (L 0 = 1.5). This meas the possibility of a tabulatio of obtaied results by the kow values k 0 ad k d for large values β 1, whe i depedece of NPV(L) there is a optimum. Table 15. Net preset value, NPV, at β = 2.0, millio dollars. Equity. S 1382 4728.8 5814.9 6413.7 6682.3 6721.7 6598.5 6357.9 6030.8 5639.2 5198.5 4720.0 1000 3423.0 4209.1 4642.6 4837.0 4865.5 4776.3 4602.2 4365.4 4081.9 3762.9 3416.6 1200 4107.5 5050.9 5571.1 5804.4 5838.6 5731.6 5522.6 5238.5 4898.3 4515.5 4099.9 1600 5476.7 6734.5 7428.1 7739.2 7784.8 7642.1 7363.4 6984.7 6531.1 6020.6 5466.6 1800 6161.3 7576.4 8356.6 8706.6 8757.9 8597.4 8283.9 7857.8 7347.4 6773.2 6149.9 Fig. 9. Depedece of NPV o leverage at differet values of equity cost S at β=2, millio dollars: 1 S = 1 382, 2 millio dollars; 2 S = 1 000 millio dollars; 3 S = 1 200 millio dollars; 4 S = 1 600 millio dollars; 5 S = 1 800 millio dollars. With further icrease of the retur o ivestmet (β = 2) NPV of the project has a optimum for all values S at leverage level which is already approximately equal to L = 1.8, ad the value of optimum as well as of NPV i geeral is growig with icreasig S, util the project remais a effective (up to leverage level of order L=8.5, see Fig. 9). I this way, the aalysis of the depedece of NPV o the equity value S ad o the retur o ivestmet β allows us coclude, that i cotrast to the parameters I ad NOI the chage of parameters S ad β, both idividually ad simultaeously, ca sigificatly chage the ature of the depedece of NPV o leverage level. With icrease of retur o ivestmet (with the icreased β) there is a trasitio from the mootoic decrease of NPV of the project with leverage (Fig. 7 ) to the existig of the optimum at all values of S (see fig. 6 ad 8 ). The growth of β leads to growth of NPV as well as to growth of the limit leverage value, up to which project remais a effective. This meas the iability of tabulatio of the results, obtaied i the geeral case of a costat value of equity capital: i this case, it is ecessary to use the obtaied by authors i the works (Brusov et al 2011a,b,c,d,e; 2012 a,b; 2013 a,b,c; 2014 a,b; Filatova et al 2008) formulas to determie the NPV at the existig leverage level, as well as for optimizatio of existig ivestmet structure. Tabulatio is possible oly i the case of large β values ( β 1), whe there is a optimum i the depedece of NPV o the leverage level. 2.3. Coclusios I 2010, the compay "Nastcom Plus" worked at leverage level L = 0.54 istead of optimal value L = 2.0. The NPV loss amouted to 645 millio dollars. I 2012, the compay worked at leverage level L = 1.0 istead of optimal value L = 0.7. The NPV loss amouted from 32 to 98 millio dollars, depedig o the term of operatio of equipmet. The authors have evaluated effectiveess of ivestmet at existig level of debt fiacig ad have developed recommedatios o the optimum level of leverage for the Russia compay "Nastcom Plus" i 2010-2012. The results idicate that, if i 2011 fiacial structure of ivestmet of compay " Nastcom Plus" was close to the optimal ad NPV was oly 2 millio dollars less tha the optimal value, i 2010, whe the leverage level was L = 0.54, NPV was 645 millio dollars less tha optimal value (the
Iteratioal Joural of Ecoomics ad Busiess Admiistratio Vol. 1, No. 2, 2015, pp. 59-70 67 optimal leverage level should be equal to L = 2). I 2012 the leverage level, with which compay "Nastcom Plus" has carried out its ivestmet projects (L = 0.1 ), did ot correspod to optimum value (L=0.7) ad provided NPV = 1,954.6 millio dollars, that is 31.7 millio dollars less tha optimal NPV value (Tables 10 ad 11; Figs. 4;5). Sice the equipmet ca be operated ad after depreciatio, oe ca estimate the NPV ad for a more log-term perspective. For example, for seve-year project the optimal leverage value is L =0.65, whe the NPV = 2,580.6 millio dollars, that is for 51.7 millio dollars more tha o-optimal values of NPV = 2,528.9 millio dollars, obtaied by the compay. For the te-year project the optimal leverage level L = 0.55, with NPV =3,043.5 millio dollars, that is for 98 millio dollars more tha o-optimal values of NPV = 2,945.5 millio dollars, obtaied by the compay. positio while it exists (chage optimum positio is chaged for two-years ad te-years projects i 2010, ad for the fiveyear project i the 2012 year (for 0.5-1 (i L uits)), evertheless the optimum positio turs out to be sufficietly stable. 3. Effects of Taxatio o the Optimal Capital Structure of Compaies i the Telecommuicatio Sector Fig. 11. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for five-year project i 2010. We cotiue the aalysis of activity of the compay "Nastcom Plus". I this paragraph we examie the effect of chage of tax o profit rate, both i the case of its icrease as well as decrease, o optimal structure of ivestmets at differet project duratios. Fig. 12. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for seve-year project i 2010. Fig. 10. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for two-year project i 2010. It is show, that icreasig of tax o profit rate leads to degradatio (decreasig) of NPV, ad degradatio is reduced with a icrease project duratio. I particular, for the fiveyear project (amortizatio period) whe the tax o profit rate decreases o 1%, NPV decreases o 1.5% - 2.34% i differet years. Impact of chage of tax o the profit rate o the optimum Fig. 13. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for te-year project i 2010.
68 P. N. Brusov et al.: Optimizig of the Ivestmet Structure of the Telecommuicatio Sector Compay Table 16. Depedece of optimum positio of ivestmet structure i 2010 o tax o profit rate ad project duratio. 2010 t\ 2 5 7 10 15% 3 2 2 2 20% 2 2 2 1.5 25% 2 2 2 2 Table 19. Absolute ad relative chage of NPV with icrease/decrease of tax o profit rate o 5% (1%) i 2011. 2011 t=20%-15% t=25%-20% O 5% O 1% =2 119 118 25.8% 5.16% 5 222 223 10.2% 2.04% 7 236 239 8.75% 1.75% 10 238 242 7.7% 1.54% Table 17. Absolute ad relative chage of NPV with icrease/decrease of tax o profit rate o 5% (1%) i 2010. 2010 t=20%-15% t=25%-20% O 5% O 1% =2 418/487 204 34% 6.8% 5 266 273 7.45% 1.49% 7 263 271 6.88% 1.37% 10 245 256 5. 56% 1.11% Table 18. Depedece of optimum positio of ivestmet structure i 2011 o tax o profit rate ad project duratio. 2011 t\ 2 5 7 10 15% 0.5 1 1 1 20% 0.5 1 1 1 25% 0.5 1 1 1 Fig. 16. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for seve-year project i 2011. Fig. 14. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for two-year project i 2011. Fig. 17. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for te-year project i 2011. Fig. 15. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for five-year project i 2011. Fig. 18. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for two-year project i 2012.
Iteratioal Joural of Ecoomics ad Busiess Admiistratio Vol. 1, No. 2, 2015, pp. 59-70 69 Table 21. Absolute ad relative chage of NPV with icrease/decrease of tax o profit rate o 5% (1%) i 2012. 2012 t=20%-15% t=25%-20% O 5% O 1% =2 104 103 39% 7.8% 5 229 229 11.7% 2.34% 7 253 256 9.9% 1.98% 10 269 271 8.9% 1.74% It is show, that icreasig of tax o profit rate leads to degradatio (decreasig) of NPV, ad degradatio is reduced with a icrease of project duratio. Note, that for the five-year project (amortizatio period) whe the tax o profit rate decreases o 1%, NPV decreases o 2.34% i 2012, o 2.04% - i 2011 ad o 1.49 - i 2010. Fig. 19. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for five-year project i 2012. 4. Coclusios Paper is devoted to optimizig of the ivestmet structure of the telecommuicatio sector compay "Nastcom Plus". We examie the effect of chage of tax o profit rates, both i the case of its icrease as well as decrease, o optimal structure of ivestmets at differet project duratios. All calculatios have bee doe withi moder theory of capital cost ad capital structure by Brusov-Filatova-Orekhova. The aalysis of ivestmets carried out by the formula, obtaied by us earlier for the case of costat value of equity capital. Cosideratio has bee doe from the poit of view of owers of equity capital. Fig. 20. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for seve-year project i 2012. It is show that icreasig of tax o profit rates leads to degradatio (decreasig) of NPV, ad degradatio is reduced with a icrease project duratio. I particular, for 5-year project (amortizatio period) with icrease of tax o profit rate o 1% NPV decreases o 1,5%-2,34% for differet years. Ifluece of chage of tax o profit rate, while there is, (optimum for 2-years ad 10-years projects i 2012 is chaged (o 0,5-1 (i leverage uits)), evertheless the optimum positio is stable Refereces [1] Brusov P, Filatova T, Orehova N, Eskidarov M (2015), Moder corporate fiace, ivestmets ad taxatio, Spriger Iteratioal Publishig, Switzerlad, 373 p. Fig. 21. Depedece of NPV o leverage level L for three values of tax o profit rate: T=15%;20%;25% for te-year project i 2012. Table 20. Depedece of optimum positio of ivestmet structure i 2010 o tax o profit rate ad project duratio. 2012 t\ 2 5 7 10 15% 0 1 0.5 0.5 20% 0 0.5 0.5 0.5 25% 0 0.5 0.5 0.5 [2] Brusov P, Filatova T, Orehova N, Brusova A (2011a) Weighted average cost of capital i the theory of Modigliai Miller, modified for a fiite life time compay. Applied Fiacial Ecoomics 21(11): 815-824 [3] Brusov P, Filatova P, Orekhova N (2013a) Absece of a Optimal Capital Structure i the Famous Tradeoff Theory! Joural of Reviews o Global Ecoomics 2: 94-116 [4] Brusov P, Filatova P, Orekhova N (2014a) Mechaism of formatio of the compay optimal capital structure, differet from suggested by trade off theory. Coget Ecoomics & Fiace 2: 1-13 http://dx.doi.org/10.1080/23322039.2014.946150
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