16. Economic models for the support vessel value estimation on the basis of the utility analysis and the factorial indexes prediction
To estimate the operating company’s property complex there is a widespread method based on calculation of market factors which establish the relation of value to one or another economic index: to income, operation costs or profit. And the last specified way formally corresponds to the income approach of value estimation.
In their turn, the market factors should be determined based on comparable sales approach – by the analogues, for example: by the similar enterprises which capitalization is known, and, the data of the financial records are also available.
The specific precondition for an evaluation of the support vessels (tugs, ice breakers, hydrographic, etc.), and also some of the technical fleet vessels and the special purpose vessels is their «inability to generate profit (income)» unlike transport, fishery and the majority of the technical fleet vessels.
For example, the effect of the operation of rescue vessels, tugs, ice breakers etc. is rather difficult to estimate economically in a form of income.
The reasons of possession of vessels of the specified classes are defined by increase of the efficiency of the owner other divisions (or reduction of risks) rather than direct incomes.
Usually the vessels of specified classes belong to the harbors or the shipping companies operate transport or fishing vessels besides these classes with a reason of the ocean resources development and compensating charges for the support vessels maintenance at the expense of incomes, arriving for transport or fishing vessels operation.
For this reason many support vessels of special purpose and also some vessels of technical fleet can be referred to a number of vessels «unable to generate profit (income)».
Apparently, the effect from possession of commercial vessels of the specified types arrives to the owner as economy of expenses for operation of others vessels, for example transport or fishery.
The value of vessels of the vessels of «unable to generate profit (income)» classes is established by the parties when implementing of the property right (and accompanying obligations) by them as purchase and sale, transfer of the right–of–use by the contract of rent, pledge, arrest of property, etc. Thereby the correspondence of economic equivalence of values of these vessels and others, including revenue–generating is defined.
Thus, the value of «unable to generate profit (income)» vessels and the value of those which generate income, is equally objective. Therefore it is required to define formal concepts of value estimation of vessels, non–generating income in an explicit form and, nevertheless, applied, as they enhance the efficiency of other divisions of the owner.
The income can be taken from use of commercial vessel of any class. For example, the tug or the ice breaker can be used for the designated purpose as the vessels which are not bringing the income, but raising efficiency of others vessels, and it can be sold, generating the income this way. For this reason this class of vessels can be referred to a number of «unable to generate profit (income)» to a certain extent conditionally.
To estimate the value of vessels of the specified classes one should adhere to the definition according to which the vessel can be referred to the unable to generate profit (income) property if according to the concept of the prospective highest and the best use the income is not provided.
In the given definition the concept of the «unable to generate profit (income)» vessel is not a synonym of unprofitableness. The unable to generate profit (income) vessel can be quite highly effective, including according to an economic estimation.
For example, the value of the military vessel is maximum when it is issued according to use for to the purpose – for maintenance of defense potential (we do not concern the legal rules of the military technology sale). The income in this case is excluded. At the same time scrapped vessel price is less is less, though the income arrives.
In the considered example vessel disposal for scrap, despite the actual receipt of the income to the owner, cannot be referred to the highest and the best use concept, unlike application for the purpose (in case of absence of the income).
The given statement is based on definition of the highest and the best use, as reasonable and possible operation of commercial vessel which provides the highest present value on the date of estimation.
For the vessels referring to the unable to generate profit (income) property, application of the evaluation method from the point of view of capitalization (that is accumulation) of the predicted net operating income can be interfaced with the methodological difficulties.
The determination of the part of the owner’s income, arriving from other divisions or assets which should be referred into the account of an evaluated unable to generate profit (income) vessel is problematic.
When the value is estimated based on comparable sales approach and based on methods of the transactions, of the capital market and the branch factors the determination of the market factors (or multipliers) – proportional relations between factors of a financial characteristic of the evaluated company and analogues which allow establishing of the dependence between following indexes is required:
– Value MV, on the one hand, and the basic economic indexes, on the another hand – the annual income I (gain), the operation costs C (the annual costs of commercial vessel operation) and net operating income NOI (or profit p) determined as a difference of the basic indicators;
– Value MV of the commercial vessel, on the one hand, and the analogue value, on the another hand, considering, that this dependence is developed by the direct and reverse transformations on the basic indexes for the analogue and the estimated vessel which is specified above.
The similar concepts can be applied for the evaluations of the marine company isolated real assets for which one of the basic indexes – the income or operation costs is known, and the second of these indexes is unknown or depends on the first one.
To determine the financial characteristic and market factors in case of value estimation of the marine company’s property complex the corrected forms of the accounting records are usually used (the official forms # 1, 2, that are balance and profit and loss statements).
However as the financial records usually are not kept in full in full usually concerning each isolated asset, even such as a marine commercial vessel, which by the set of economic properties almost corresponds to the property complex of the marine company the alternative approach for evaluation of factors is required, for example, based on an estimation of factors depending on macroeconomic indexes, such as risks which can be determined as an estimation of the discounting rate.
The estimation of market factors dependences on total commercial risks gives the chance to use factors not only for evaluation of the property complex for which records are kept, but also for separate assets, such assets which owing to those or other reasons cannot be estimated based on income approach with the net operating income, and it is possible to estimate only operation costs or only the annual income (gain).
And if for commercial vessel it is quite possible correct estimation of the net operating income the market factor is the capitalization rate R or, with rather great life time of the commercial vessel, the discounting rate i, which in this case includes the rate of the property tax η_{MV} and the rate of insurance coverage η_{INS} in the general structure of the components of the sum.
The productive operation of the commercial vessel can bring the profit p and the net operating income NOI, as a difference of the annual income I and operation costs Ñ, only if there are sufficient working assets OC for the advance payment of the operation costs Ñ before receiving of the income I.
When the vessel is estimated by the income approach or the comparable sales approach on the basis of the market factors calculated depending on indexes of commercial risks, it is required to account the correcting adjustment for working assets OC should be made to the result.
The definition of annual income R _{I}=(I-OC×i)/MV_{I} and operation costs R_{C}=C/MV_{C} factors for the commercial vessel is of interest on the basis of commercial risks estimation i.
Considering, that net operating income NOI is proportional to the investments, correlated with the sum of the value MV and the present value of investments into replenishment of working assets OC, that is (MV+OC×i/R), the rate of the net operating income capitalization can be defined by transformation of the formula (11.4), as:
R=NOI/(MV+OC×i/R), |
(16.1) |
or, in case of value estimation based on income approach and the method of the net operating income capitalization with the account the adjustment to the vessel value (or other real asset of marine company) for the replenishment of working assets:
MV=(I-C)/R-OC×i/R, |
(16.2) |
and the capitalization rate of net operating income R as it is noted above (article 11), is calculated depending on the discounting rate i by the well–known formula R=i+f_{m}.
Test questions
1. Market factors method of value estimation of the acting company’s property complex.
2. Commercial reasons of the «unable to generate profit (income)» support vessels use.
3. The reasonable ground to classify a commercial vessel as the «unable to generate profit (income)» property.
4. Ways of market factors determination.
5. Vessel value estimation based on income approach by the method of the net operating income capitalization as the estimation based on comparable sales approach by the market factor (the formula derivation).
6. Adjustment to the vessel value estimated based on income approach and by the account of need of the working assets replenishment.
16.1. Vessel value estimation based on use of operation costs index account
If possession of a commercial vessel is connected only with expenses and, nevertheless, is reasonable and efficient by other reasons, for example in view of increase of efficiency of other divisions of the proprietor, the vessel value can be estimated using the below–mentioned formal scheme.
The net operating income NOI should be commensurate with the vessel annual «consumption cost» Ñ_{U}, to be more exact, with expenses for annual consumption.
Consumption costs of the commercial vessel or other real asset of the marine company’s property complex Ñ_{U} correspond to the sum of annual operation costs C and the annual deductions for the property tax η_{MV}×MV_{C}, for the insurance coverage η_{INS}×MV_{C } and for the compensation of real assets depreciation f_{m}×MV_{C} and are equal
Ñ_{U}=C+f_{m}×MV_{C}+η_{MV}×MV_{C}+η_{INS}×MV_{C}. |
(16.3) |
The index «c» means, that value MV_{C} of the vessel (or other real asset of the marine company) is calculated according to operation costs Ñ, which are rational for the investor as they raise the value or the efficiency of the property complex.
The consumption costs Ñ_{U} are equal to minimum income I_{MIN}, when vessel operation (or other asset) is not connected with losses, that is, provided that the profit and losses are equal to zero, and the net operating income NOI with the account the residual life time of commercial vessel (Ò – t) and the macroeconomic index of total risks i in case of estimation of the factor of fund of compensation f_{m} (Chapter 13, table. 13) corresponds to deductions for compensation of real asset depreciation f_{m}×MV_{C} in the sum with the property tax η_{MV}×MV_{C} and insurance coverage η_{INS}×MV_{C}.
When the investor is typically motivated, that is, when investing in a vessel (or other real asset of marine company) for the purpose of maximisation of the property complex value and with account of the annuity OC×i, which present value at the time of the net operating income calculation corresponds to the needs for the replenishment of the working assets OC, the expenses equal to cost of consumption Ñ_{U}, mast make profit p (or the equivalent good if the profit is not provided), proportional to the cost of vessel consumption Ñ_{U}×i, that is
Substituting of the formula (16.3) in the formula (16.4), it is possible to define
p-OC×i= (C+f_{m}×MV_{C}+ η_{MV}×MV_{C}+η_{INS}×MV_{C})×i |
(16.5) |
Taking into account, that cost of vessel MV_{C} and profit p (or the equivalent good if the profit is not provided) are connected by the formula
, |
(16.6) |
then, substituting the formula (16.6) in the formula (16.5), it is possible to define
, |
(16.7) |
or MV_{C}= Ñ / RÑ, |
(16.8) |
where RÑ– the factor of operation costs Ñ, that is proportionality factor between the asset value and the operation costs, estimated with the account residual life time (Ò – t) and a macroeconomic index of risks i.
The factor RÑ of operation costs Ñ is equal
R_{C}=1 - f_{m}- η_{MV }- η_{INS}=1 - i / ((1+i)^{T-t}-1) -η_{MV }- η_{INS}, |
(16.9) |
or on the basis of discounting by The Euler number exponential function
R_{C}=1 - i/(e^{i×(T-t)}-1) - η_{MV }- η_{INS}.
And the factor RÑ of the operation costs Ñ is estimated not on the basis of the marine company financial records indexes, as all for the isolated asset, even for a vessel, the financial records are not kept in full, but taking into account the formula (16.9) of the macroeconomic indexes of risks i and characteristics: age t, life time T and residual life time (Ò – t).
Leaving along the analysis of reasonable operation costs for the investor, when determining the value by the formula (16.8) it is supposed, that operation costs Ñ are reasonable by their utility that is the methodological precondition for value MV_{C} estimation of commercial vessel (or other real asset).
If the income I is not provided in vessel operation, it is supposed, that other good are equivalent to advantages of the income receipt according to the assumption of reasonable operation costs Ñ.
For value estimation on the basis of operation costs C analysis or the annual income I, that is in each of variants only one of the specified components of the net operating income, issued the second index, which is not used directly is supposed, to depend on the first one, and both indexes, and also their difference – net operating income NOI – are proportional to the intensity of commercial vessel operation.
The basic economic indexes are methodologically interconnected, that means that: the value MV, the operation costs Ñ, the annual income I and the net operating income NOI depend on intensity of commercial vessel productive operation.
The vessel value estimation based on income approach also can be problematic at some circumstances when the income, the profit and the net operating income depend on intensity of commercial vessel operation, and in supposed cases it is inconvenient to determine unequivocally only depending on vessel characteristics.
The approach of value vessel estimation, based on the application of annual income index I is presented below.
Test questions
1. Concept of the vessel annual «consumption cost» and its structure in the sum of operation costs and deductions for compensation of real asset depreciation.
2. Conformity of commercial vessel’s consumption cost break–even.
3. Typical motivation of the investor, the concept of operation costs utility.
4. Definition of operation costs factor according to risks (the formula derivation).
5. Difficulties in case of determination of the net operating income for certain classes of vessels.
16.2. Application of the annual income index for vessel value estimation
The possibility of value estimation MV of the commercial vessel (or other real asset of marine company) depending on the annual income I, besides the fact that it is methodologically valuable is rather important when solving certain applied tasks, for example such task as evaluation MV when the commercial vessel is used within the limited resources, particularly, in case of fishery operation within the amount of fishing quotas of the ocean biological resources when the annual income is limited.
When estimating value MV_{I} the annual income index I is used and it is supposed, that operation costs C and the annual income I are interdependent. The index «I» means, that value MV_{I} is estimated on the basis of the annual income I and the factor of the annual income account. As the profit, as shown ahead, can be correlated (16.5) with the operation costs:
p= (C+f_{m}×MV_{I}+ η_{MV}×MV_{I}+η_{INS}×MV_{I}+OC)×i,
so
further
. |
(16.11) |
The value MV_{I} can be determined after substituting the formula (16.11) in the formula (16.8), that is
,
or after transformation:
, |
(16.12) |
further
, |
(16.13) |
where RI– the factor of the annual income I equal:
, |
(16.14) |
or on the basis of discounting by The Euler number exponential function , that is
. |
(16.15) |
Just as the factor of operation costs R_{Ñ}(evaluated by the formula 16.9), the factor of annual income R_{I} is determined on the basis of the analysis of a macroeconomic index of risks i rather than by the financial reporting of the marine enterprise on the basis of factors, as there is a task to estimate the isolated asset.
The recommendations of the given chapter (Chapter 16) have the direct relation to the process of solving the applied expert tasks to estimate the vessel value or other real asset of marine company:
– By the formulas (16.8, 16.9) if for an estimated asset the records are kept only for operation costs, but there are no doubts about the efficiency of operation, as, for example, for support vessels in the structure of the shipping companies;
– By the formulas (16.13, 16.14) if there are limitations in the subject preconditions – servitudes concerning the intensity of asset operation, for example, the limitations of ocean biological resources development or others, and the servitude can be estimated as limitation of the annual income, keeping in mind, that operation costs depending on the annual income are also become limited;
– By any formulas specified ahead if methodologically is difficult to estimate the net operating income NOI index, and only one of two indexes – the annual income I or operation costs C is subject to determination, and besides if concerning the estimated asset the financial records are not fully kept.
The geometrical analogy to explain the formulas (16.8, 16.9, 16.13 and 16.14) is shown on the scheme (fig. 16).
Fig. 16. The geometrical analogy (a) of economic indexes parities: the annual income I, the operation costs C, the investments (cost MV, MV_{I} and MV_{C}), the factors R_{C}=1-f_{m}-η_{MV}-η_{INS} and R_{I}=1+i , with the account variations of factors (b) and ratio of the annual income I to operation costs C (c)
With rather large durability of the commercial vessel (or other asset of the marine company), that is, if to neglect the factor of fund of compensation of the value depreciation, the capitalization rate of net operating income R can be estimated as the discounting rate i.
Taking into account that R=i, the value can be estimated by the income approach as MV = NOI/i. On the scheme of the geometrical analogy (fig. 16, a) the corner ICC – tangent – the relation of leg of the triangle NOI = I–C to a leg of the triangle i of rectangular triangle ICC corresponds to value MV.
At the same time the corner ICC is equal to cornersI0(1+i) and C01. Thus, tangents of all listed corners correspond to value MV.
If, that is more exact, the legs of triangle of rectangular triangles adjoining to corners ICC, I0(1+i) and C01, which tangents correspond to the value, to define by the formulas 16.9 and 16.14 as factors R_{I} and R_{C} of the annual income and operation costs (fig. 16, b) the geometrical analogy serves as value estimation by the formulas 16.8 and 16.13.
Thus factors R_{I} and R_{C} of the annual income and the operation costs are defined as macroeconomic indexes with the account the total risks estimated as the discounting rate i rather then according the results of the financial records which usually are not kept in full concerning the isolated assets.
The geometrical analogy where the value corresponds with the tangent of the corresponding corner at the scheme, also shows, the influence of efficiency of the ocean resources on the vessel value (or other asset of the marine company), and it is taken into account when formulating the economic optimality criteria in marine industrial activity.
As a whole it is clear, that the vessel value essentially depends on the intensity of the cargo traffic, the vessel is used for which development, or on the productivity of marine fishery ground etc.
The superfluous marine wealth (economic advantages) or the lack of resources transform the diagram of geometrical analogy (fig. 16, c), that leads to a change of corners of the diagram (ICC, I0(1+i) and C01) and corresponding value estimations (MV, MV_{I} and MV_{C}), which parity is used to define the economic criteria of the ocean resources contribution to the vessel value (or other asset of the marine company, see Chapter 26).
The results obtained by the formulas 16.8, 16.9, 16.13 and 16.14 should be considered as approximate and directly connected with the assumptions used in a substantiation of specified formulas.
Test questions
1. Assumption of conforming the annual income and operation costs conformity with the intensity of productive operation of the commercial vessel which is characterized by the net operating income.
2. Determination of the annual income factor according to risks (the formula derivation).