
12. An interval method of net operating income cash flow capitalization in evaluation of the marine company’s property complex
The marine commercial vessels, real assets and the marine companies’ complexes mastering marine wealth as objects of investment possess number of specific features which can influence the kind of methods used for the investments evaluation and the economic efficiency estimation, in particular, influence recommended kinds of the income approach methods.
Namely, differences of economic properties of marine commercial vessels, the marine companies’ complexes of the assets and their real assets from properties of the cash flows applied in case of present value estimation of on the basis of discount financial functions refer to above mentioned features.
Unlike cash flow which present value usually grows, the vessel value is reduced in process of depreciation, and value of the property complex varies non–uniformly, for example, by step dependence with particular reference to the plan of investment in process of large assets transfer. And it is noticeable for the marine companies, where the value of separate assets of which the property complex consist of is comparable with the value of the company total.
The recommendations for the present value of cash flow determination for estimation of the marine company’s property complex consisted of separate assets which value is comparable with the value of the whole property complex by the income approach are stated below and present value with particular reference to the calendar of investing varies unevenly depending on steady functional properties of separate assets. And within separate stages of investing the present value of cash flows is invariable or varies with constant paces.
Concerning the property of predicted variability of cash flow, if the property complex of the marine company or predictably changeable part of the business for example unidentifiable intangible asset – good will is evaluated it is possible to define, that «stepwise» variability of cash flow with particular reference to the planned schedule of investing as a part of the business plan (T_{0}, T_{1}, T_{2}, ..., T_{N}, NOI_{1}, NOI_{2}, ..., NOI_{N}) is more typical.
For the companies in which structure there are no the separate assets proportional to the value of the whole company total of value and for financial institutions the assumption concerning continuous value capitalization of assets and continuous change of incomes (and expenses), in other words, an assumption about a continuity of the net profit growth is reasonable since the acquisition of any separate asset is an imperceptible step in relation to the value and profitableness of such company.
Just an assumption about growth continuity (it should be underlined: not uniformity of growth but continuity) for the property complex where there is no in its structure assets proportional in value to the whole complex value total connected with rather small non–systematic commercial risks (internal), allows to introduce the evaluation based on income approach in the formal scheme of the discounted cash flow capitalization by the formula (11.1).
The property complex of the marine company, which separate assets values can be proportional to complex value, and accumulation of real assets and change of efficiency according to the investment business plan have a stepwise character is a more characteristic object of value estimation than the company growing in value continuous without reference to any separate planned schedule but only according to interest rate by the discount formula of present value.
By the way, predicted continuity of assets value capitalization by the discount formula of present value linearly or otherwise that is at continuity or at continuous growth of accumulation rates, can also be considered as the basis for use of primary direct capitalization method use with the account predicted rates of profit growth (or the net operating income) in alternative of the discounted cash flow capitalization by the formula (11.1).
Except the marine companies’ complexes of the assets the stepwise variability of cash flow is characteristic for rather small companies, that is for the majority. And stepwise variability can be connected with necessary versatility, in other words, in process of accumulation with the purpose of reinvesting of financial assets in real asset are not used, and current accumulation of financial assets is stored or invested in other activity not of the company’s basic profile if for the investments into a profile activity there are not enough financial assets. The sufficient accumulation of financial assets is required for investing in real asset if a value of a separate asset is proportional to the property complex value.
Thus, the marine company carries out at least two kinds of activity: a profile activity, which is characterized by the greatest efficiency (in particular, according to profit for the investment evaluation), that is the economic basis of the company profile and not a profile activity – storage or any other investing of financial assets in process of their capitalization for investing in real assets the value separate from which is proportional to value of the property complex total.
Not profile investing in the marine company financial assets in process of capitalization levels a little, but does not eliminate stepwise variability of cash flow. It is possible to place, for example, financial assets to a fixed deposit for protection against inflation before investing in real assets for the marine company profile.
It should be noted that from the formal point placing of finances into the deposit most closely corresponds to accumulation of financial assets continuity according to the discount formula of present value just as to continuity of the large company assets capitalization, in the structure of the property complex where there are not the assets proportional in value to a complex.
For elimination of stepwise variability of the marine company cash flow it should be required that efficiency (in particular, of profit from the investment) of not a profile activity was equal to efficiency of profile activity. But it would contradict the general assumption that profile activity is most effective and would put in doubt the marine company profile.
The efficiency of the marine company profile activity is substantially higher than not a profile activity; otherwise the company profile is subject to change. On the other hand, with rather high efficiency of the profile activity it is reasonable to apply a loan that can also be considered as not a profile activity, as a profile activity consists in investing of financial assets in real assets.
The loan usage as well as accumulation of financial assets at the deposit levels a little but does not eliminate stepwise variability of cash flow for the marine company own capital. The equalization of value capitalization rates and efficiency of the marine company’s real assets at the expense of advance investing in assets using the extra financial assets gives to the investor the effect proportional to the cost of borrowed funds.
While estimating the value it is logical to remain within the frameworks of assumption about cash flow stepwise variability which is one of methodological properties of the marine company’s property complex having separate assets proportional in value to the whole property complex for the following reasons:
– Equalization of value capitalization and efficiency rates of real assets as a part of the property complex at the expense of not a profile activity does not lead to an essential change of the results of value estimation of involved resources (loan commitments etc.) is usually proportional in size and is opposite in sign to value change of the property complex;
– Not a profile activity of the marine company does not lead to equalization of value and efficiency of real assets growth in the phase relation, that is instead of stepwise growth of efficiency and value of assets in case of equalization at the expense of involved finances the stepwise changes of the growth rates remain, but they are steady within the intervals between investing in real assets for the profile activity.
Having divided cash flow into stability intervals between investment stages under the planned schedule (T_{0}, T_{1}, T_{2}, ..., T_{N}) updating of assets and change of identification attributes, the present value of cash flow can be determined as a sum of present values for each of the cash flow stability intervals changing at stages of investing under the planned schedule. And cash flow value during each interval of stability can be determined by the method of direct capitalization.
The limited duration of cash flow stability interval is taken into account by introducing of a compensating (reactive) cash flow to the asset cash flow corresponding to the net operating income for the isolated asset as a part of the marine company’s property complex capitalized under the discounting rate as an infinite cash flow for direct capitalization.
The present value of cash flow is evaluated according to planning intervals of the marine company by the formula
, 
(12.1) 
where N – the number of predicted intervals of cash flow stability or stability of rates of accumulation of the cash flow corresponding to a number of investments planning stages and the multiplier (1/i) in front of the sum means in sense of the approximate equality of the investments payback period T_{R}≈1/i, when the efficiency corresponding to the sum of risks and the discounting rate i, and the period of planning T_{N} is determined as:
.
For the investments payback period T_{R}and for the efficiency rate i in case of estimation of the property complex by the interval method and the formula (12.1) there corresponds a planning period of the cash flow of net operating income invariable in value within each interval of stability from T_{n1} to T_{n}, which is the same as the planning period of continuously collecting present value determined by the formula 11.1 and this period is not less than the investments payback period T_{R}, that is .
When using the cash flow capitalization interval method the variable of summation by the formula (12.1) is a number n of cash flow stability interval n, and when estimating the present value of continuously accumulating sum of the discounted cash flow by the formula (11.1), the discrete characteristic of the present time t is the variable.
Unlike the method for present value estimation by determining of continuously accumulating sum of the net operating income discounted cash flow by the formula (11.1), the method for present value determination by capitalization for the intervals of stability (12.1) to estimate the marine company’s property complex considers predicted variability of a cash flow of the net profit as an integral factor of the investment plan (T_{0}, T_{1}, T_{2}, ..., T_{N}).
The interval method of cash flow capitalization is «adhered» to the planned schedule of the investments (T_{0}, T_{1}, T_{2}, ..., T_{N}, NOI_{1}, NOI_{2}, ..., NOI_{N}), that is to the updating of assets and change of identification attributes and the general advantages of present value estimation by interval method, besides the fact that calculations by the formula (12.1) are «most compact», consist in the following:
– The first, the estimation of the present value by the interval formula (12.1) is a dependence on calendar periodicity of investing unlike estimation by the formula (11.1);
– Secondly, the estimation of continuously accumulating sum of the discounted cash flow by the formula (11.1) serves as an approximate numerical calculation, while the estimation of the present value by the interval formula (12.1) is a mathematical solution for the planned schedule of investment set.
The advantages of present value estimation by the interval method formula (12.1) can be illustrated by comparative example for the following initial data:
– Investment project of the marine company is planned for T=10 years with the discounting rate estimated by the sum of commercial risks i=10 %;
– According to the plan, the net operating income for the initial investments is 1000 thousand US dollars annually;
– Sequence of assets acquisition, in particular commercial vessels, corresponds to accumulation for initial investments with the account risks and efficiency of the marine company, and the growth of the net operating income is discrete;
– At the expense of self–financing and accumulation in 3.5 years it is planned to buy a new vessel, and the net operating income will increase in the prices on the settlement day up to 1400 thousand US dollars annually, and in 7.5 years at the expense of the next acquisition the net operating income will increase up to 2000 thousand US dollars annually;
– The reversion planned in appraisal in 10 years can be determined by capitalization of the net operating income in the prices on the day of settlement, as:
thousand US dollar;
– For the estimation of the continuously accumulating sum of the discounted cash flow (11.1) it is required to pass from planning of discrete cash flow of the net operating income for the investment intervals to planning for years, that is an approximate transformation of the initial data, tab. 12;
Table 12
The planning of the net operating income discrete
cash flow (thousand US dollar) for the years
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 


1000 
1000 
1000 
1400 
1400 
1400 
1400 
2000 
2000 
2000 
– By the formula of the sum of continuously accumulating discounted cash flow of the net operating income (11.1) in case of planning till the time of reversion receipt T=T_{N} the present value which by the income approach relates to the value of the marine company’s property complex, is equal MV=(1+0.10)^{1/2}×(1000/(1+0.10)^{1}+1000/(1+0.10)^{2}+1000/(1+0.10)^{3}+1400/(1+0.10)^{4}+1400/(1+0.10)^{5}+1400/(1+0.10)^{6}+1400/(1+0.10)^{7}+2000/(1+0.10)^{8} +2000/(1+0.10)^{9} +2000/(1+0.10)^{10} )+2000×(1+0.10)^{10} =15684
thousand US dollar;
– With particular reference to the marine company investment schedule for three intervals of planning: from T_{0}=0 to T_{1}=3.5 years NOI_{1}=1000 thousand US dollars a year, from T_{1}=3.5 year to T_{2} = 7.5 year NOI_{2}=1400 thousand US dollars a year, from T_{2}=7.5 year to T_{3} =T_{N}= 10 year NOI_{3}=2000 thousand US dollars a year, the present value according to the formula (12.1) is determined, as:
,
that is a mathematical solution for the given example, suitable for substitution of the data of the planned investment schedule ((T_{0}, T_{1}, T_{2}, T_{3}, NOI_{1}, NOI_{2}, NOI_{3}), and the value of the marine company estimated by the income approach is equal
thousand US dollars.
The comparison of two methods of the income approach for the considered example of estimation of the cash flow of the marine company net operating income when the value relates to the schedule of investing, shows that the evaluation by the interval formula (12.1) is «more compact» by the number of actions than the estimation of the continuously accumulating over the years value of the net operating income cash flow by the formula (11.1). Besides, the formula (12.1) is a mathematical solution for set calendar periodicity of the investments unlike value estimation by the formula (11.1).
The error of the net operating income cash flow value estimation by the formula (11.1) in the considered example is equal 15801 – 15684 = 117 thousand US dollars (0.7 %), and it should be noted that with increase of stages number N planned by the schedule of investments ((T_{0}, T_{1}, T_{2}, ..., T_{N}, NOI_{1}, NOI_{2}, ..., NOI_{N}), the error of the continuously accumulating over the years value of the net operating income cash flow grows, and, for example, for more than three steps of investing in the marine company assets made within 10 years (if the sum of commercial risks is equal about 10 %) the error can be from 3 to 5 % and more.
The cause of error of calculations of the capitalized cash flow continuously accruing over the years by the formula (11.1) is the required initial data replacement and transition from planning of the investment stages to the planning over years, that can be viewed as a rather close approximation for the companies of certain types, for example: for the financial and the stocks share companies, the wholesale and retail companies for without number the marine companies among them concern.
The recommended interval form (12.1) of the methods of the present value estimation of marine company’s property complex by capitalization of the discounted present values of cash flow estimation which corresponds to the planned investment schedule has advantages from the point of application as indexes of the isolated property complex are connected technologically and by the economic strategy.
This way of cash flow present value estimation from the methodological point is suitable for introducing the continuity of investments assumptions in the conditions of self–financing unlike the formula (11.1) which describes accumulation in the financial markets more precisely than in real sector.
It should be taken into account that the cash flow value NOI_{n} for each interval of the net operating income stability from T_{n1} to T_{n} characterizes the assets efficiency accumulation of the marine company during the previous intervals of planning.
The cash flow for investing is a source of the future investments and the result of the previous that is the accumulation of the marine company assets means the accumulation of their ability to generate cash flow NOI. And the rates of assets accumulation correspond to the total sum of commercial risks i.
In case of self–financing of the marine company’s property complex the cash flow during each interval of stability depends on cash flow accumulation for the previous intervals invested in real assets and is equal
, 
(12.2) 
that is . 
(12.3) 
. 
(12.4) 
. 
(12.5) 
(12.6) 
Test questions
1. Properties of the marine company’s complex of assets on the basis of the valuation of the complex value parity and the separate real assets (a relation of the total value and the value of a part).
2. Predicted continuity of assets accumulation and change of the marine company efficiency index as the reason to use the method of direct capitalization when estimating based on income approach.
3. Continuity of cash flow accumulation in case of self–financing of the marine company’s property complex (the formula derivation).
4. Duration of the planned schedule stages corresponding to intervals of financial assets accumulation for investing in the real assets of the marine company, determined on condition of cash flow continuity (the formula derivation).
5. Interval method of capitalization with the account continuity of the cash flow accumulation influencing the stages of the planned investment schedule duration.
6. Calculation of own risks of the innovative strategy in marine industrial activity (the formula derivation).
7. Characteristic tasks of the marine company’s property complex evaluation with the account the property of cash flow accumulation continuity in case of self–financing..