Methodology of identification optimal capital structure

One of the largest and the most important events of new Novatek was launching of the Purovsky Plant that became core organization's production facility. In the same 2005 company decided to become public and conducted IPO on two stock exchanges - London stock exchange and further Moscow stock exchange.

According to annual financial reports, the latest (considering two previous years) significant strategic solutions concerning investments, acquisitions and disposals include the following events:

· Joint company of Novatek and Gazprom acquired 60% of Artic Russia B.V. in 2013. Simultaneously, Novatek made an agreement with Rosneft for exchange of 51% of Sibneftegas to acquire 40% of Artic Russia B.V.

· Novatek sold 20% of equity shares of Yamal LNG to China National Petroleum Corp. in 2013

· Novatek acquired additional share in LLC Nortgas increasing its ownership from 49% to 50% in 2013.

· Novatek gained share of 100% in LLC Novatek-Kostroma by increasing shares number on 15% in 2014.

· Novatek acquired 100% of JSC Office's shares in 2014.

· Novatek acquired LLC NovaEnergo by purchase of 100% of the company in 2014.

· Novatek reduce groups' ownership share in Artic Russia B.V. by disposal of 20% in 2014.

· Novatek sold 9.9% in Yamal LNG to Chinese fund in 2015; whereas remains share of 50.1%,which gives ownership of the project in cooperation with Total SA and China National Petroleum Corp.

One of the latest significant events that highly affected operations of Novatek was inclusion of the company into sanction list of the Office of Foreign Asset Control [U.S. Department of the Treasury, 2014]. This organization is connected directly with the US Government. Inclusion in this list means that company has no access to long-term debts in western financial organizations. The following situation was caused by political isolation of the Russian Federation concerning to Crimea. Novatek was included as representative of the Russian Energy Sector, although company has no operations in Ukraine. However, this affected current operations of Novatek significantly. New projects of liquid natural gas deposits development in Yamal suffer seriously from lack of funds [The Moscow Times, 2014]. As these projects were developed on cooperation with foreign partners - Total SA and China National Petroleum Corp. - companies had to seek fund in China financial market [Marson and Williams, 2015].

The joint project with Russian government and several companies was aimed to develop port Sabetta to the ability to export by sea. However, in conditions of budgets' shortage Novatek had to sell share of equity in Yamal LNG to Chinese investment funds. According to consolidated interim condensed financial statements for the first three months of 2016, company disposed of 9.9% of share to support activities of the project. In general, Novatek and its subsidiaries use the following ways of finance:

· Internal borrowings.

Companies ruled by the shareholders' agreement are able to provide different subsidiaries with internal credit lines both in rubles and in US dollars.

· Eurobonds.

The group of companies issued Eurobonds with different termination dates.

· Bank loans.

Novatek has available in Russian bank credit lines for long-term and short-term periods. Each opportunity has negotiable interest rate and temporary restricted contract for the implementation of the credit line.

3.3 Model implementation

3.3.1 Case of Lukoil company

Firstly, as it was described in the proposed algorithm it is needed to estimate the proxy values for every year. The information about the company was taken from the company reports for the respective years. The information about capitalization and volatility of the company's equity was taken from the open sources, since its market information, that is publicly available. The risk-free rates for the certain years, as well as the information about currency changes were taken from the central bank of Russia.

Lukoil Company	Year
Proxies	2010	2013	2014	2015
Value of Debt (mln rubles)	338 520	351 324	756 118	859 713
Risk-free rate	8.40%	7.40%	12.00%	11.40%
Value of equity (mln rubles)	719241	1208830	815902	1058749
Year Volatility of the company	23.51%	22.28%	38.57%	41.65%

Table 3.3.1. The proxy values for Lukoil company

It can be seen, that the difference between pre-crisis and crisis years is quite significant. Firstly, the value of debt had been raised in 2014 more than twice, comparing to 2013. This had happened due to the fact, that huge amount of Lukoils debt were issued in the form of Eurobonds, so when the dollar strengthen almost double time against rubble in 2014, the value of debt corresponded to it. The risk free rate was also increasing, since the Russian economy suffered a lot from the crisis of 2014, and long term rates on the Russian federal bonds, had increased almost for 50%. Due to all this factors, the yearly volatility of the company also rise a lot, being almost twice as much in 2015 as it were in 2013. It also should be mentioned that, the difference between the years in the same category (pre-crisis and crisis), does not differs much, however, the difference between this two categories is huge. So, it can be said that, this environment is a perfect field for model testing, since here are both situations: similar looking years, and highly different, so any gained results can be analyzed in deferent circumstances, but at the same time, can be compared in the similar situations. Now, according to the algorithm of model implementation the parameters of the model should be estimated by solving the problem of minimization the sum of residuals. By doing this, the following results were gained:

Lukoil Company	Year
Estimated Parameters	2010	2013	2014	2015
Value of business (mln rubles)	986169.07	1485544	1530210.75	1862044
Volatility of business	24%	25%	43%	44%
Rate of recovery	91%	91%	93%	90%
Effective Tax Rate	25%	25%	25%	25%
Risk free rate	8.40%	7.40%	12.00%	11.40%
Coupon (mln rubles)	28953.11	27381.3	109708.8942	117669.7
Required return on debt	8.55%	7.79%	14.51%	13.69%
Fraction of uncovered currency debt	85.3%	92%	83.2%	83.1%
Price of hedging as a fraction of coupon	5.3%	4.53%	23.5%	15.3%

Table 3.3.2. Estimated parameters for the Lukoil company

So, here it can be seen that the same patterns as for the proxy values appears in the estimated parameters. First thing, that should be mentioned, is that through the years the value of unlevered firm is constantly rising, which can be considered as a proof that Lukoil is quite successful company. The growth continues even in the crisis years, so it can be assumed that the company is managed in a proper way. However, the volatility of unlevered business grew significantly in the crisis years. Again, here can be seen a pattern, that the situation with volatility is quite similar in both groups of years, which partly proves the assumption about constant volatility of unlevered firm. So, already can be defined, that some of the assumptions of the model holds, but with huge changes in the circumstances, the values are also significantly changes. The recovery rate, however, stays the same for all years, despite the crisis, so the conclusion might appear, that recovery rate does not depend on the external market situation, and this thought is quite logical, since recovery rate is mostly characteristic of the company and its possibility to cover possible bankruptcy costs. The effective tax rate also stays the same trough all the years, which also is understandable, since tax rate depends on the tax codes of the countries, where the company is paying taxes, but not on the market conditions. The coupon that Lukoil is paying for the debt is rising with the crisis years and this has several possible explanations. Firstly, the falling market and prices of oil made Lukoil more risky company for investment, as well as its risen volatility. The other reason is again the ruble falling, since most of the Lukoils obligations were in currency, the amount of rubles paid for the interest had risen. The same situation is with return on debt, since it is a representation of coupon. What is more, it can be seen that the price of “hedging” for Lukoil, as a value of a currency risk rose significantly. This happened because higher volatility, and lower currency profits, so in 2014 and 2015 the cost of debt had become significantly higher for the Lukoil. Now, when all parameters are estimated, the optimal leverage structure of the firm can be defined for different years.

Firstly, yield spreads associated with the choice of leverage should be analyzed:

Graph 3.3.1. Yield spreads on debt as a function of leverage

As it can be seen from the graph, the debt was really “cheap” for Lukoil in 2010, that's why, the model suggests for Lukoil in 2010 to take more debt, in order to benefit from the tax shields.

From the point of view from the overall firms value, the situation is the following:



Graph 3.3.2. Total firm value as a function of leverage

So, it seems that because of low required rate on return on debt for Lukoil in 2010, the model assumes that the leverage number should be increased. This can be explained with the fact, the the model mostly includes only two risks: the risk of default, and currency risk. However, the company suffers from other possible risks, that are not fully included in the model. But still, as it will be seen further, the model is quite accurate in terms of identifying leverage structure under certain circumstances. From the point of view of numbers, the situation for Lukoil in 2010 is described in the following table:

Values	Lukoil 2010	Optimal Value	Change
Leverage	32%	62%	96%
Debt	338520	699051.75	107%
Coupon	28953.11	63523.97	119%
Requared return on debt	8.55%	9.09%	6%
Yield spreads	0.15%	0.69%	350%
Total Firm Value	1071050.1	1127502.83	5%
V-Bankruptcy	194967.04	427763.40	119%
V-Bancruptcy/ Total Firm Value	18%	38%	108%

Table 3.3.3 The optimal leverage rate for Lukoil 2010

Here it is shown that increasing level of leverage would increase the total company value. However, Huge amount of risk appears, but the value that can be added with this choice of leverage is only 5% from the total value of the Lukoil, so it might be rational managerial decision not to increase the leverage, because outcomes just do not cover the risks, since, as it was mentioned already, the model is limited by its assumptions. Moreover, in this table there is a new parameter of the firm introduced: fraction of Vb to the firms value. This can be an interpretation of a risk of the firm, because the higher percentage of the firms bankruptcy triggering value is from the value of firm, the more probability the firm has to become bankrupt. Of course, due to the complicated nature of the option-like nature of firms equity, this fraction cannot be easily interpreted, it still can serve as a certain indicator of the firms bankruptcy risk.

The situation for the 2013 year is really common to those of 2010. The yield spreads are:

Graph 3.3.3. Yield spreads on debt as a function of leverage

So, the same as in 2013, the “cheap” debt is leading to the recommendation, made by the model to take more debt in order to have more tax benefits. The situation with the value of the firm, is also really alike to 2010:



Graph 3.3.4. Total firm value as a function of leverage

The reasons, for the same recommendations as were made in 2010 is the same, since the market situation and economic conditions are nearly the same. Even, the overall company value grew almost for a 40%, the amount of recommended leverage didn't change much. This situation partly proves the assumption, that leverage value does not depend on value of business. Moreover, it proves that, if the market situation doesn't change significantly, the model gives the same results, which partly proves the assumption of time-independence of the optimal leverage structure. In the following table numerical solution for 2013 is presented:

Values	Lukoil 2013	Optimal Value	Change
Leverage	22%	58%	161%
Debt	351324	971827	177%
Coupon	27381.309	79377	190%
Requared return on debt	7.79%	8.17%	5%
Yield spreads	0.36%	0.74%	103%
Total Firm Value	1578401.5	1675564	6%
V-Bankruptcy	280008.54	572077	104%
V-Bancruptcy/ Total Firm Value	18%	34%	92%

Table 3.3.4 The optimal leverage rate for Lukoil 2013

The same as for 2010, significant increase in leverage, and so in the risk of the firm will lead to the slight increase of the total firms value. So, again the difference in the model solution and a real situation most likely can be explained from the point of view of managerial decisions. It is recommended to the Lukoil, to increase its leverage ratio, because the ability to take cheap debt ( because the really low default risk of the company) will pay -off greatly through tax benefits. The most important thing here, is that the results partly proves that the assumptions of time-independence of the optimal leverage structure for the same company, under alike conditions. The next step is to analyze crisis years, and the differences between results for different situations for the same company.

As it was described previously, the 2014 is really different from 2013 in terms of economical and market situation for the Russian companies. 2014 is a first crisis year for Russia, as well as for Lukoil. The currency risk risen, and the oil prices fell down, so there is a significant change in the Lukoils performance and model results. The yield function for Lukoil in 2014 is following:

Graph 3.3.5. Yield spreads on debt as a function of leverage

In this graph, it is clear that the debt is not so “cheap” as it used to be in 2010 and 2013. This had happened due to the fact that the overall risk of the company had risen, as well as the currency risks associated with debt. Also, the yield curve become more sharply, since the function parameters had changed, due to changed economic environment. The total value of the firm function also differs a lot from the situation in 2010 and 2013:

Graph 3.3.6. Total firm value as a function of leverage

So, the shape of the firms value curve had changed, and now optimal leverage structure predicted by the model, and the actual Lukoil capital structure are the same. This happened due to the fact that the reprising of the Lukoil debt, which was nominated in rubbles, but had to be paid in currency. Moreover, the overall company risk had rise, so the optimal capital structure predicted by the model was reduced. So, all in all, that situation represented the case, when the theoretical solution of a problem was completely approved on practice, so it can be said that most of the assumptions that were made in the process of model development seems to be holding for Lukoil in 2014. The numerical representation is:

Values	Lukoil 2014	Optimal Value	Change
Leverage	46%	45%	-2%
Debt	756118	745006.4532	-1%
Coupon	109708.8942	106533.1371	-3%
Requared return on debt	14.51%	14.30%	-1%
Yield spreads	2.53%	2.32%	-8%
Total Firm Value	1648212.982	1655569.896	0%
V-Bankruptcy	385277.5179	374124.8413	-3%
V-Bancruptcy/ Total Firm Value	23%	23%	-3%

Table 3.3.5 The optimal leverage rate for Lukoil 2014

So, from this table it can be defined that the optimal leverage structure recommend by the model is really close to the capital structure that really was in Lukoil in 2015. However, this results are quite different from those in 2013. This can be explained by heavily changed economic conditions. The goal of analysis pre-crisis years and crises years was achieved, since gained solution corresponds to common sense, because when the crisis appears, the model recommends significantly lower leverage level than before the crisis, due to increase in risks. Finally, in order to complete study about the Lukoil Company, another crisis year should be analyzed, in order to prove the previously made assumption, that the optimal leverage structure is time - independent, under the same circumstances for crisis situations.

The situation in 2015 for Lukoil didn't change much, however, it should be stated that in 2015 risk of the company is less than in 2014. It can be explained firstly, with the lower risk free rate for this year, and secondly, with the lower price of obligatory hedging, since the volatility of the currency had become lower. So, the yields for the year 2015 are:



Graph 3.3.7. Yield spreads on debt as a function of leverage

It can be seen that yield spreads are nearly the same as for 2014 year, but the curve is slightly less sharp. This curve is still really different from the curves of pre-crisis years, which can explain the differences in the suggested capital structure. The value of the firm curve, is also looking the same as one for the year 2014, and quite differs from the pre-crisis years.

Graph 3.3.8. Total firm value as a function of leverage

So, as it can be seen on the graph, the same amount of leverage is recommended as it were in 2014. This can be explained by the nature of the proxies and estimated parameters, since they are the same for the crisis years. The numerical representation will be:

Values	Lukoil 2015	Optimal Value	Change
Leverage	43%	45%	5%
Debt	859713	903748.4	5%
Coupon	117669.7	125022.5	6%
Requared return on debt	13.69%	13.83%	1%
Yield spreads	2.34%	2.48%	6%
Total Firm Value	2007509	2008330	0%
V-Bankruptcy	421566.3	447908.7	6%
V-Bancruptcy/ Total Firm Value	21%	22%	6%

Table 3.3.6 The optimal leverage rate for Lukoil 2015

However, the optimal level of leverage is the same as a year before - 45%. And it should be stated, that Lukoil company suits this optimal level quite well.

To sum up, it could be said that the crisis years for Lukoil changed everything in terms of effective leverage. From tone point of view, the company became riskier, which is not really greal for its stakeholders. On the other hand, crisis years allowed it to achieve optimal level of leverage in terms of the proposed model. It is important that the model gives the same values, for the similar years. It can lead to the conclusion that the assumption of the time independency of the optimal leverage structure and overall model parameters can be considered as true, but only if the economic situation does not change significantly. As a managerial application, it can be stated, that the analysis of the Lukoil's capital structure defined that according to the proposed model, Lukoil's management had made right decisions in terms of capital structure, gaining all possible tax benefits, with the reasonable amount of default risk. However, it should be taken into account, that model itself has tendency to over valuate debt and its benefits, since the risks that are taken into account seems to be not the all risks that are associated with the firm. Still, the results shown are quite valuable for Lukoil, as well as for scientific community, since they show the theoretical behavior of the model, as well as its possibility to evaluate the risk value.

After gaining this results, it is needed to analyze, how the model performs on a basis of other similar company, that fulfill the model assumptions, in order to gain more variable testing results.

3.3.2 Case of Rosneft company

Firstly, as it was described in the proposed algorithm it is needed to estimate the proxy values for every year. The information about the company was taken from the same sources as for Lukoil company. The proxies are following:

Rosneft Company	Year
Proxies	2010	2013	2014	2015
Value of Debt (mln rubles)	641 519	2 076 000	2 240 000	2 822 000
Risk-free rate	8.40%	7.40%	12.00%	11.4%
Value of equity (mln rubles)	1593213	304668.7	128374.8	250411.7
Year Volatility of the company	30.99%	20.83%	30.21%	28.01%

Table 3.3.7. The proxy values for Rosneft company

From this table, it can be defined that Rosneft in many cases is quite similar to Lukoil. However, the most interesting difference, and, basically a reason, why this company was also taken for an estimation is the fact that even in the pre-crisis years the company seemed to be more riskier than Lukoil. So, in order to gain better understanding about the model performance, there were taken two similar companies, but with quite different amount of risk. What is also interesting about the proxies of the rosneft, is that unlike the Lukoils debt, the debt of Rosneft had been risen not only in crisis years, but in the pre-crisis also. Of course, when the crisis appears, the value of Rosneft's debt risen even more, for the same reasons as for Lukoil - the fall of the oil prices, and the rubble currency. The risk free rate is the same for both companies, since it was proxied by the Russian federal long term bonds rates. So now, the same algorithm as was used for the Lukoil will be implemented, so the parameters will be estimated.

Rosneft Company	Year
Estimated Parameters	2010	2013	2014	2015
Value of business	2131675	2754908	2610899	3051294
Volatility of business	33%	36%	81%	65%
Rate of recovery	30%	37%	29%	21%
Effective Tax Rate	20%	20%	28%	26%
Risk free rate	8.40%	7.40%	12.00%	11.4%
Coupon	54765.06	323249	1512577	920269.2
Requared return on debt	8.54%	15.57%	67.53%	33%
Fraction of uncovered currency debt	83.20%	79.90%	83.50%	94%
Price of hedging as a fraction of coupon	5.20%	4.30%	23.55%	18.70%

Table 3.3.8 Estimated parameters for the Rosneft company

From the table it can be defined that, even thought the proxy values were quite the same for the Rosneft and Lukoil companies, the parameters of their models differs a lot, despite effective tax rates, and price of hedging. The similarities can be explained by the fact that both companies operate in the same markets, so they pay alike taxes, and gain similar currency profits. However, the volatility of business of the Rosneft is higher than volatility of the Lukoil Company, which can be explained by the different business models that are implemented in the companies. Moreover, unlike the Lukoil company, who was continuously growing - in terms of unlevered firm value - even when the crisis appears, the Rosneft had decrease in value of business in the first crisis year. This, most likely, was caused by the higher volatility of Rosneft business. Nevertheless, in the second crisis year, Rosneft business value was risen, and not only fully recovered from the losses, but gained some additional value compared to the pre-crisis years. As well as the situation with loss in value in 2013, the situation of huge addition to the value of business can also be explained by the higher overall volatility of the firm, since higher volatility means not only higher possible losses, but also the higher gains. This reflects the overall market rule: more risk is taken - higher possible profits can be gained. What is more, it is necessary to state that improving the unlevered value of capital is the common for every existing firm. If the firm does not improve its business value, it means that it doesn't creates any value, or, even working with losses of assets. This kind of situation can occur only for short period of time, since if this pattern continues to long, firm is becoming bankrupt, since its operations does not create any value. In terms of the proposed model, if firm has constantly reducing value of unlevered business, it reaches the value that triggers bankruptcy, and firm declares default. All in all, the difference between this two companies were analyzed, so now the differences im model implementation should be analyzed.

For the year 2010 the yields on debt for the Rosneft are following:

Graph 3.3.9 Yield spreads on debt as a function of leverage

This graph is really similar to the yield spreads for Lukoil company in 2010. This happened, since the values for both companies are really similar in this year. However, the debt is even “cheaper” for Rosneft, than it was for Lukoil at the same time period, since Rosneft have better rate of recovery. So, like it was described in the last paragraph of the previous chapter, this leads to the higher optimal leverage level defined by a model for the company. The situation with the firms value is also similar to the situation taken place for Lukoil at 2010.

Graph 3.3.10 Total firm value as a function of leverage

The situation here is really similar to the lukoil company for the same time period, with the difference mainly caused by other recovery rate. The numerical solution to this problem can be described as

Values	RosNeft 2010	Optimal Value	Change
Leverage	28%	61%	114%
Debt	641519	1424486	122%
Coupon	54765.06	140210.9	156%
Requared return on debt	8.54%	9.84%	15%
Yeild spreads	0.14%	1.44%	955%
Total Firm Value	2254521	2335223	4%
V-Bankruptcy	318293.3	814902.7	156%
V-Bancruptcy/ Total Firm Value	14%	35%	147%

Table 3.3.9 The optimal leverage rate for Rosneft 2010

As it can be seen from this table, the theoretical optimal leverage structure is the same as it is recommended to the Lukoil in 2010. This can be explained by the fact that the companies perform in a really similar way, in 2010. Nevertheless, the interesting difference here between Rosneft and Lukoil case in 2010 is that even increasing the leverage for more significant amount (114% for Rosneft versus 96% for Lukoil), the gains of this operations in terms of total firm value are less, then those for the Lukoil case (4% against 6%), so most likely, the reasons why the model here is over valuating debt are the same as for Lukoil. The model just does not take into account some risks, except currency risk and default risk. The similar situation holds only for the year 2010, while for other years it differs a lot in terms of model implementation in Lukoil and Rosneft case, so now the following years should be analyzed in order to gain better understanding of the model performance.

For the year 2013 the situation for Rosneft had changed significantly, unlike in Lukoil case. For example, the yield curve is moved to the following form:

Graph 3.3.11 Yield spreads on debt as a function of leverage

Here, the cost of debt curve is similar to those of the Lukoil for the same time period. However, it seems that the managers of the Rosneft decided to take significantly more debt, compared to the 2010 year. Basically, it is shown that in 2013, according to the model the company is over levered, and has more risk that it should have been taken In terms of possible total value of the firm, with the probability of the default the situation is following:

Graph 3.3.12 Total firm value as a function of leverage

So, again, the theoretical leverage structure that should be in the Rosneft company, according to the model is nearly 50%, having the same amount as the Lukoil in the same time period. But, unlike the Lukoil, Rosneft seems to be over levered even in the pre-crisis years, when the Lukoil had too low leverage according to the model.

Values	RosNeft 2013	Optimal Value	Change
Leverage	87%	46%	-47%
Debt	2076000	1348282	-35%
Coupon	323249.4	120602.5	-63%
Requared return on debt	15.57%	8.94%	-43%
Yeild spreads	15.57%	1.51%	-90%
Total Firm Value	2384917	2931047	23%
V-Bankruptcy	1853560	691552.5	-63%
V-Bancruptcy/ Total Firm Value	78%	24%	-70%

Table 3.3.10. The optimal leverage rate for Rosneft 2013

Here, it can be seen, that according to the model, company has more risks, that it should take. The value of asset that triggers bankruptcy is almost 80% from the total value of the firm, which, with considered fact that the company has quite volatile business, seems to be to much risk to take. So here, the model suggest to reduce the value of leverage, and unlike all previous suggestions that will lead to slight increase in the firms value (around 5%), in this case the reduction of the risk taken by the company improves the value of the firm significantly for 23%. So, after the analisis it can be stated, that Rosneft case is not really corresponding to the models assumptions, since the predicted value of leverage is significantly less then observed one. From the other point of view, every management decision have some hidden partners, that cannot be seen from the external view of the company, and it might happened that Rosneft managers had some plan to use this high leverage in order to make more profits. However, the crisis appears in the next years, and it can be assumed, that high leverage policy, excepted by Rosneft was not the best path to take for the company development.

For the first crisis year, the situation for yield curve for the debt of the Rosneft company was following:

Graph 3.3.13 Yield spreads on debt as a function of leverage

In the first crisis year, the cost of debt for the Rosneft had been rose significantly. This is a result of a higher risks, associated with the company, due to high currency risks, and high risk of default. High leverage value in the pre-crisis years led to the debt reprising, and really high risks of the company, so the reared rate of return on debt become numerously high. This also can be explained with the fact that in 2014 the business value of the company fell, respectively to the pre-crisis years, and it was previously discussed, how dangerous this situation can be for the company. In order to make some conclusions it seems reasonable to compare it to the values in 2015.

The yield spreads for Rosneft in 2015 are following:

Graph 3.3.14 Yield spreads on debt as a function of leverage

The main difference here is that the debt become slightly “cheaper” for Rosneft in 2015. This can be explained by the facts, that firstly, the currency risk is less valuable in this year. Secondly, as it was described previously, the firm had increased its value of business, compared not only to previous year, but even for the pre-crisis years. However, the firm is still quite over levered, from the point of view of proposed model.

The differences for the crisis years in terms of value of the company are following:

Graph 3.3.15 Total firm value as a function of leverage

And for the year 2015 there is a slightly different situation:

Graph 3.3.16 Total firm value as a function of leverage

From the analysis of this graphs, it can be seen, that for 2015 the situation in terms of risks is slightly better, then in 2014, the reasons for that are the same as the reasons for difference in the yield curves. The numerical differences are following:

Values	RosNeft 2014	Optimal Value	Change
Leverage	95%	55%	-42%
Debt	2240000	1556203	-31%
Coupon	1512577	486520.5	-68%
Requared return on debt	67.53%	31.26%	-54%
Yeild spreads	55.55%	19.28%	-65%
Total Firm Value	2359937	2829460	20%
V-Bankruptcy	1867223	600592.4	-68%
V-Bancruptcy/ Total Firm Value	79%	21%	-73%

Table 3.3.11 The optimal leverage rate for Rosneft 2014

And for the 2015:

Values	RosNeft 2013	Optimal Value	Change
Leverage	87%	46%	-47%
Debt	2076000	1348282	-35%
Coupon	323249.4	120602.5	-63%
Requared return on debt	15.57%	8.94%	-43%
Yeild spreads	15.57%	1.51%	-90%
Total Firm Value	2384917	2931047	23%
V-Bankruptcy	1853560	691552.5	-63%
V-Bancruptcy/ Total Firm Value	78%	24%	-70%

Table 3.3.12 The optimal leverage rate for Rosneft 2015

In both cases, the Rosneft considered to be over levered and bearing too many risks. The model predicts, that lowering the leverage value to the fraction of approximately 50% will allow to increase the company's overall firms value for nearly 20%. It is necessary to state, that optimal leverage value for Rosneft in the crisis years is quite similar to the optimal leverage value of Lukoil at the same dates. To sum up, the overall model predictions are very similar fro the Lukoil and Rosneft for the same time periods. However, unlike Lukoil Company, Rosneft didn't reach the optimal capital structure predicted by the model, and consider to be over levered, especially in the crisis years. The other interesting outcome is that, while the under - levered firms can gain only small amounts of additional firm value by taking more debt, however, the companies with over-levered structure, gaining significantly more value, by reducing the risks. Finally, it can be stated, that the assumptions of time-independence of most of the model parameters holds, if the situation on market does not change significantly.

The final part of the model testing, is to test on t6he company, that is from the one point of view, similar to the Lukoil and Rosneft business, but at the same time will be able to keep the same amount of leverage for pre-crisis and crisis years. This approach is necessary in order to understand, how the model performs for the companies, that are staying in the relatively same situation even in the crisis, that effects the other analyzed companies, since previously it was found out that the model offer the similar solutions for the alike market situations. So, by testing the model on such a company, the following questions can be answered: if the assumption of time-independence of the model parameters holds in certain circumstances, and if the model over or under valuating the level of leverage in the companies. To fulfill this goal the company Novatek was chosen.

3.3.3 Case of Novatek company

The Novatek case in this work is used as a litmus test, in order to understand the performance of the model from the point of view of over or under valuating the leverage fraction, under the same circumstances. So, unlike the previous companies, the Novatek case will be analyzed as a whole, without single year situation description. So, as well as for the previous cases, the first step of model implementation algorithm should be used and the proxies for the Nivatek Company should be described. As well as in the previous cases, the data was gained from the reports of the company and open sources, like bank of Russia, and market information. The proxies for the Novatek are:

Novatek Company	Year
Proxies	2010	2013	2014	2015
Value of Debt (mln rubles)	72199	165621	245679	350645
Risk-free rate	8.40%	7.43%	11.98%	11.35%
Value of equity (mln rubles)	440936.71	916397.01	930434.1	1422223.7
Year Volatility of the company	30.99%	24.17%	38.91%	54.10%

Table 3.3.13. The proxy values for Novatek company

It can be already seen, that there is no huge “jump” in the values, like it were in the previous cases in the first crisis year. The growth of the values seems to be less sharply, and the assumption can be made, that all the values have similar fractions to each other in all years, and it can be illustrated better, after implementation the following steps of model's algorithm, and defining the estimated parameters:

Novatek Company	Year
Estimated Parameters	2010	2013	2014	2015
Value of business	502349.41	1053474	1130465.713	1713342
Volatility of business	32.58%	25.39%	41.03%	57.57%
Rate of recovery	87.50%	87.78%	87.00%	87.90%
Effective Tax Rate	18.14%	19.82%	27.00%	24.51%
Risk free rate	8.40%	7.43%	11.98%	11.35%
Coupon	6343.0314	12718.4	35199.90441	48766.71
Requared return on debt	8.79%	7.68%	14.33%	13.91%

Table 3.3.14. Estimated parameters for the Novatek company

So, as it can be seen, the values are not growing as rapidly as in the previous cases, and, the most importantly, the “jump” in volatility for the 2014 year is not so huge as it were for the Lukoil and Rosneft cases. Also, the value of business of the company is constantly growing, demonstrating the “normal” case of the company performance. Required return on debt demonstrates the same trends as were found in the cases of the Lukoil and Rosneft, with increasing in the 2013, and after this slightly falling for 2015, however, the difference between this values is not as significant as it were for the previous companies. So, all in all it should be mentioned that the Novatek company is similar to the other estimated cases in terms of parameters changes and overall patterns. Now, the performance of the company thought the years should be analyzed, to show difference in model approach. So, the yields for the different years are presented in the following graph.

Graph 3.3.17. Yield spreads on debt as a function of leverage for 2010-2015

In this graph can be seen that through the years the cost of debt changes, however the leverage structure in observed in the company, as well as the optimal capital structure predicted by the model stays nearly the same. This situation is caused by the fact, which basically, the Novatek is not suffering from the crisis as strong as the other analyzed companies. The shape of the curve also changes trough the years, since more costly - or risky in other words - the debt becomes, faster the yield spreads grow with the value of leverage. However, it does not affect the company's optimal and observed optimal capital structure, since the internal risk of the firm is following the market trend perfectly. This means, that Novatek, unlike Lukoil or Rosneft is not creating additional risk by itself, with the over levered capital structure, like for example Rosneft. The performance of the model in terms in overall company value as a function of leverage is presented on the following graph.

Graph 3.3.18. Total firm value as a function of leverage for 2010 - 2015

The graph represent the situation of model implementation, where the crisis influence both calculated and observed capital structure of the firm in quite a minor way. The approximate optimal leverage value is nearly 40- 45 %, and the observed one is around 20% for all the years. However, the overall increase in riskiness can seen on this graphs. Through the years, with the appearance of the crisis, the “sharper” fall of the company's value appears at the huge leverage values. This fact is understandable, since, in more risky environment the company operates, the more risky it is to have huge leverage values, as it was shown on the Rosneft example. Moreover, it can be said that most of the time-independence assumptions cal be called realistic, since it was shown, that if the company doesn't change a lot with the market changes, the calculated values of optimal capital structure are quite the same for all the years, regardless of crisis, and it is true also for the observed values. Finally, it can be concluded, that in all the years the model over valuates the real value of the capital structure, which can be explained by the model limitations in the risk valuation.

3.4 Analysis of the results and the managerial implications

Application of the proposed model showed some difference in the calculated level of leverage and observed one. For the most of cases, the calculated level of leverage exceeds the observed level of leverage. This debt value overvaluation was already mentioned in this type of models by the previous researches [Taxeira, 2007]. This can be explained by the fact, that the proposed model, mostly concentrates on the value of default risk. However, this is not only type of risk that company suffers from. In the model modification, proposed in this thesis, the currency risk of the debt was also taken into account. Nevertheless, the value of risks is still under valuated by the model, since firstly, the proposed method of the valuing currency risk, assumes that the currency returns volatility will remain relatively constant through time, but as it was shown by the implementing of the model, this situation is not really happening, especially, when the crisis appears in the country, where the company operates. So, the first recommendation of the further model development will be, the modification of the proposed model due to more reliable analysis of the debt reprising due to the currency risk change. The other reason for debt value overvaluation is a really specific debt approach in the theoretical model. The assumption here is that the debt of the company can be presented with the perpetual coupons debt, so the bankruptcy will be associated with the inability of the firm to pay required coupons. However, this assumption might not be hold in some practical situation, so the second theoretical recommendation is to develop a model in a way that will be similar to the Leland and Toft model (1996), since as it was mentioned before, due to limited recourses of the Master thesis recourses, I have made a decision to base the work on the model that was more suitable for the practical implementation. Nevertheless, the algorithm developed in the current work and modifications that were made for the theoretical model, can be called universal for the implementation of the models based on the “option like” approach to the company's equity, so the further research, based on this thesis might be - the described algorithm implementation to the other theoretical models.

From the other point of view, the model implementation was quite successful for some cases - like Lukoil Company in 2014- 2105 years, since the calculated capital structure corresponded perfectly to the observed results. Moreover, the analysis shows, that in the stable environment most of the model assumptions holds, and the parameters that were assumed to be time-independent are time independent under certain circumstances. In addition to that, the model testing on the real data showed that most of the gained results are the same as were expected, and model does not provide any “unordinary” or non logical solutions. So, it seems that after several modifications the model might become quite powerful tool in identifying optimal leverage structures for the different companies.

The theoretical contribution of this thesis can be described as, firstly this thesis one of the rare examples of the implementation of the models based on the “option-like” nature of equity to the real companies situation. Even thought, certain limitation of the model was found, it could be stated that the implementation of the model showed quite reasonable results, and the model itself seems to be quite applicable to the real business situations. Another important theoretical...