8. Examples of estimation of the commercial vessel depreciation

Typical examples of depreciation estimation concerning the marine cargo vessel are considered below:
           A) Estimation of irremovable physical depreciation of commercial vessel by the economic «life time» method (article 8.1);
           B) Estimation of irremovable functional depreciation of a dry–cargo refrigeration vessel (insufficient cargo capacity of vessel, article 8.2);
           C) Estimation of irremovable functional depreciation of a tanker for the crude oil transportation (superfluous displacement of light vessel, article 8.3);
           D) Evaluation of external economic obsolescence of a passenger vessel (article 8.4).

8.1. Estimation of irremovable physical depreciation of commercial vessel by the economic «life time» method

The prediction of structural durability of the commercial vessel or other real asset of the marine company to a certain degree has a conditional character, and obsolescence generally is functional.
           Certainly, physical obsolescence exists, but functional obsolescence proceeds, as a rule, is essentially faster and is the factor inducing ship-owners to sell the commercial vessel in another market (in contrast to the market where the vessel was purchased), that is in the market with other macroeconomic environment and higher values of commercial risks, and the value of the commercial vessel in process of obsolescence decreases during its exhaustion and receipt as an income and profit.
           As for real estate, this feature is not especially noticeable, as the value does not so essentially decreases in the present prices over construction years.
           At the same time there are examples of the marine engineering having age limit, but physically remained in a very good condition: the numerous ships–museums (clipper «Cutty Sark» in Great Britain, «Aurora» cruiser in St.–Petersburg, liner «Queen Mary» in California, etc.), inhabited barges on the Seine river, on channels of Amsterdam, at the coast of the gulfs in the State of Washington, etc.
           Leaving aside the physical safety of such watercrafts, it is necessary to notice, that for the long period they were subjected to some essential functional changes, and, perhaps, today such objects judging by their functional attributes cannot be named without reservations as commercial vessels or the marine engineering or the real assets of the marine companies’ complexes.
           In applied subjects the structural durability of the vessels having an ice-forcing category often is accepted within 25 years. The specified value is connected with the rules of classification surveys which usually become essentially complicated for the owner if the vessel years exceed 25 years.
           In the assumption, that the life time of all infrastructural parts as a components of commercial vessel reproduction cost is identical, irremovable physical depreciation can be predicted recognizing that the operation of the vessel within 25 years is planned at the stage of designing and construction and after write–off the vessel can be sold for scrap value.
           The following recommendations for the approached prediction of structural durability of commercial vessel can be applied:
           – To determine the vessel years and the remained period before expiration of Register Certificate of the vessel seaworthiness;
           – If the sum of vessel years and the term before the expiration of the Certificate of seaworthiness is less than 25 years structural durability of the commercial vessel equal 25 years;
           – If the sum of vessel years and the term before the expiration of the Certificate of seaworthiness is more than 25 years structural durability of the commercial vessel should be equal to the sum of vessel years and the term before the expiration of the Certificate of seaworthiness.
           It is necessary to underline, that the value of life time specified above (25 years) is considered only as a widespread test example. More precisely the life time of marine commercial vessel can be evaluated according to statistical observations and the analysis of regressions or with the account the analysis of economic efficiency (profitability of interest rate) of not a new vessel.
           Irremovable physical depreciation D₂ of the commercial vessel in linear proportion in dependence on age under these assumptions makes at the date of estimation
           D₂ = 100 % × t / 25 – 100 % × Rv / RC ≈ 100 % × t / 25 – (1.0 ÷ 2.0 %),
where t – the vessel years; Rv – the vessel scrap value after write–off; RC – the reproduction cost of the commercial vessel.
           The specific task when estimating the irremovable physical depreciation of the commercial vessel is life time forecasting.
           In some cases the life time can be predicted by the analysis of the statistical regressions characterizing dependence of the vessel value on years.
           With considerable vessel years it is possible to predict the life time on the basis of the sum of the actual age and remaining period of operation, reasoning from the analysis of economic profitability of the vessel having the great years. For example, predicted remaining duration of operation before upon the condition of commercial vessel profitability can be correlated multiple of commercial vessel payback period with the account estimation of commercial risks which are established usually when estimating based on income approach.
           Taking into account the data determined based on comparable sales approach (article 4.4), concerning rates of the vessel value reduction over the years and with the account the received analytical form of the regression dependences of the vessel value or other real asset of the marine company on age the residue from one after subtraction of irremovable internal depreciation (physical and functional) for statistical approximation is determined as:
           (1-D₂)×(1-D₄)=(((1+i)^T-t-1)/((1+i)^T-1))^i/ln(1+i),
           or when using the discounting by the Euler number exponential function:
,
           for small values of the discounting rate, when i ≈ ln(1+i), and eⁱ ≈ 1+i:
           (1-D₂)×(1-D₄)=((1+i)^T-t-1)/((1+i)^T-1),
           when using the discounting by the Euler number exponential function with the account an assumption of small values of the discounting rate:
           (1-D₂)×(1-D₄)=(e^(T-t)×i-1)/(e^T×i-1).
           The estimated residue from one (1-D₂)×(1-D₄) after the subtraction of the irremovable internal depreciation (physical and functional) can be used when the vessel estimating or other real asset of the marine company based on cost approach.
           In proportion of the regression dependences (article 4) the residue from one:
           – For the variant of using the fishing vessel capacity as a unit of comparison is
           (1-D₂)×(1-D₄)=0.504×(1.02^55-t-1)^1.01;
           – For the variant of using the fishing vessel’s main engine power as unit of comparison is
           (1-D₂)×(1-D₄)=1.55×(1.01^50-t-1)^1.005;
           – For the variant of using of the area index equal the product of the cargo water line length of the fishing vessel to the breadth
           (1-D₂)×(1-D₄)=0,417×((1+0.023)^53.5-t-1)^1.01;
           – According to researches of the universal dry–cargo vessels market
           (1-D₂)×(1-D₄)=0.008329×(1.096^50-t-1)^1.047;
           – According to researches of the market of the vessels for transportation of the crude oil and the crude mineral oil
           (1-D₂)×(1-D₄)=0.0086×((1+0.09)^53-t-1)^1.044;
           When using the comparable sales approach concepts for determination of the residue from one after subtraction of the irremovable internal depreciation (physical and functional) it is recommended to consider the following stipulation.
           The offered recommendations by the form are close to the method of «life time» estimating of the irremovable depreciation, applied to depreciation internal – physical and functional, that is, the durability of the commercial vessel or other real asset of the marine company and the degrees of commercial vessel depreciation over years depending on total commercial risks as the discounting rate are determined by the comparable sales approach.
           At the same time, when there are necessary data, the irremovable functional depreciation can be estimated correctly enough, for example, by the method of the income loss capitalization. And irremovable physical depreciation can be estimated by the method of «life time» according to the data about the life time, based on structural and technical survey of the vessel rather than on marketing researches.

           Test questions          

1. Proportion of commercial vessel physical and functional obsolescence rates.
            2. Recommendations for the approximate prediction of not a new vessel structural durability.
            3. Forms of proportional dependences in estimation of irremovable depreciation on vessel years.
            4. Recommendations concerning the use of estimation methods of depreciation commercial vessel of various forms

 

8.2. Estimation of irremovable functional depreciation of a dry–cargo refrigeration vessel (insufficient cargo capacity of vessel)

The service loading of a cargo vessel is most fully characterized by deadweight DW (difference of vessel total cargo displacement DW = D – DP and empty displacement or the sum of weight variables composed: cargo, fuel, supply, crew with luggage, etc.).
           As a rules the specification deadweight to the displacement ratio for the vessel estimated in the given example, making about 0.424 (the relation of deadweight 530 tonne to total cargo displacement 1250.7 tonne, that is DW / D) is much less than specification deadweight operating ratio to the displacement for dry–cargo refrigeration vessels which makes about 0.529 (Tab. 8).

Table 8
The data of dry–cargo refrigeration vessels – analogues of estimated one

The names of analogues (construction shipyard)	Total cargo displacement D, t	Deadweight DW, t		Proportion DW/D
«Capella» (Kanassashi Shipbuilding Co., Japan)	2357	1351.5	0.573
«Luchezarny» (Khabarovsk, Russia)	1202	531.5	0.442
«Captain Voloshin» (Nikolayev, Ukraine)	10107	5263	0.556
«Talniki» (Szczecin, Poland)	9203	5009	0.544
The average value of the factor DW/D			0.529

The vessel estimated in a considered example is subject to irremovable functional depreciation which lies in insufficient cargo capacity for received cargo and supply, in other words, in insufficient deadweight with the given displacement, or in superfluous of displacement of the empty vessel with the given deadweight.
           In other words, at the same value of deadweight DW = 530 tonne, as the deadweight of the vessel estimated in the example, the total cargo displacement of the comparable dry–cargo refrigeration vessel can make 1002 tonne, that is   530 tonne / 0.529 = 1002 tonnes.
           The unit of comparison in the given example is deadweight DW. The comparable vessel has identical deadweight with an estimated vessel.
           Total cargo displacement D of the comparable dry–cargo refrigeration vessel can at the same deadweight as of evaluated vessel be roughly 20 % less than the total cargo displacement of the evaluated refrigeration vessel which makes 1250.7 tonne, that is
           (1250.7 – 1002.0)/1250.7=0.199 .
           Displacement empty DP of the refrigeration vessel comparable to the estimated vessel by deadweight will make (1002 – 530) = 472 tonnes.
           Displacement empty of the estimated refrigeration vessel equals 720.7 tonnes. It is more on the size of (720.7 – 472.0) = 248.7 tonne than the displacement empty of the comparable vessel, that is the comparable refrigeration vessel can have the displacement empty less 34.5 % than the estimated vessel: 248.7 / 720.7×100 % = 34.5 %.
           With the same deadweight DW as of estimated vessel, and the same operational velocity V_s of the comparable transport refrigeration vessel which total cargo displacement is less 20 % than total cargo displacement of the estimated vessel, the main engine power and the fuel expense can be roughly on 14 % less than for the estimated vessel.
           The proportion of the main engines powers Ne of comparable and estimated vessels assumed with identical velocity roughly corresponds to the proportion of their total cargo displacement in degree ²/3 (the exponent ½ is sometimes used that more closely corresponds to the low–speed commercial vessels), that is
           100 %×(1 – (1002/1250,7) ) = 13,7 % ≈ 14 %.
           Thus, the comparable dry–cargo refrigeration vessel having the same values of the deadweight DW and operational speed V_s , as well as an estimated vessel, could have roughly on 20 % less the total cargo displacement D, 34.5 % less the displacement empty DP and 14 % less the main engine power Ne.
           The general value of the irremovable functional depreciationD₄ estimated in the example of the cargo vessel in relative magnitude is estimated with the account expert values of shares which reflect the degree of influence of various discrepancies for irremovable functional depreciation:
           D₄ = 20 % × ¹/3 + 34,5 % × ¹/3 + 14 % × ¹/3 ≈ 22,6 %.
           As a survey explanation it should be noted, that the listed drawbacks of the commercial vessel, apparently, are connected with the fact that the estimated refrigeration vessel was designed on the basis of the fishing vessel project with the account technological continuity of construction and by the majority of characteristics coincides with the fishing vessel (Middle size fishing freezing trawler) of the Russian project # 502 M. In this case the structural and functional characteristics optimal for fishing vessel can be irrational for the cargo vessel.

Test questions

1. Estimation of an inefficiency element on the basis of deadweight specification to displacement ratio for commercial vessel.
            2. Inefficiency proportion of the vessel propulsion device (superfluous of the main engine power and the fuel expense) in the relation to superfluous of commercial vessel displacement. 

8.3. Estimation of irremovable functional depreciation of a tanker for the crude oil transportation (superfluous displacement of light vessel)

The operating ratio of the deadweight DW to displacement D, that is the relation of deadweight 4999 tonne to total cargo displacement 8550 tonne the series tanker «Kaliningradneft» (constructed at the ship–building yard «Rauma Repola» in Finland of the Soviet project according to rules of the USSR Register), making D/DW = 0.585 for the estimated vessel, is much less than the deadweight specification to the displacement ratio of the comparable vessel of foreign construction.
           The tanker «George Frojer» for mineral oil crude cargo, constructed at the ship–building yard in port Chung–Mu (Republic of Korea) is considered as a comparable vessel. The relation of comparable vessel deadweight 4999 tonne to total cargo displacement 6750 tonne is equal D / DW = 0.740.
           The project of the comparable vessel was developed according to the requirements of Norwegian Bureau Veritas DNV.
           Estimated and comparable vessels have the close architectural–structural class, an identical class of the Register, including similar ice category, and identical class of the power–plants.
           The estimated vessel is subject to irremovable functional depreciation which lies in insufficient cargo capacity for received cargo and supply, in other words, in insufficient deadweight DW at given displacement D, or in superfluous weight of empty vessel DP at given deadweight DW (that is in superfluous displacement empty).
           The attribute of comparability attribute in the given example is deadweight DW. The comparable vessel has identical deadweight with the estimated vessel.
           At the same magnitude of deadweight DW = 4999 tonne as of the estimated tanker for mineral oil crude cargo, the total cargo displacement of the comparable tanker which was projected for other rules, can make 6750 tonnes.
           Total cargo displacement of the comparable vessel DP with the same deadweight as of the estimated vessel roughly 21 % less than the total cargo displacement of the estimated vessel, that is (8550 – 6750)/8550 = 0.21 .
           The displacement empty DP of the tanker for mineral oil crude cargo comparable to the estimated vessel for deadweight makes (6750 – 4999) = 1751 tonnes.
           The displacement empty of the estimated tanker is equal (8550 – 4999) = 3551 tonnes. It is greater by 1800 tonne, that is (3551 – 1751) = 1800 tonne than the displacement empty of the comparable tanker, that is the comparable vessel has the displacement empty 50.7 % less than the estimated vessel 1800 / 3551 × 100 % = 50.7 % .
           With the same deadweight DW and the same operational velocity V_s as of the estimated tanker for mineral oil crude cargo, for the comparable vessel which total cargo displacement D is 21 % less than the total cargo displacement of the estimated vessel, the main engine power Ne and the fuel expense can be roughly 15 % less than of the estimated tanker for mineral oil crude cargo.
           The proportions of the main engines powers of comparable and estimated vessels with assumed identical speed roughly corresponds to the proportion of the total cargo displacement in degree 2/3, that is
           100 % × (1 – (6750/8550)^2/3) = 14.6 % ≈ 15 %.
           Thus, the tanker for transportation of the mineral oil, having the same values of the deadweight DW including mainly cargo and supply, and operational speed V_s, as well as a comparable vessel, could have total cargo displacement D roughly 21 % less, displacement empty DP 50.7 % less and main engine power Ne 15 % less than of comparable vessel.
           The listed drawbacks of the tanker for transportation of mineral oil apparently are connected with defects of applied rules of designing.
           The relative magnitude of irremovable functional depreciation of the evaluated tanker for transportation of the mineral oil with the account values of share scales which reflect the degree of influence of various discrepancies for irremovable functional depreciation, is evaluated expertly as:
           D₄ = 21 % × ¹/3 + 50,7 % × ¹/3 + 15.0 % × ¹/3 = 28.9 %.

Test questions

1. Definition of cargo vessel functional analogue for estimation of depreciation (analogy attribute under according to the main characteristic – deadweight).
            2. Factors of functional inefficiency of the cargo vessel.

8.4. Evaluation of external economic obsolescence of a passenger vessel

The external obsolescence (economical) is defined as decrease of commercial vessel functional suitability owing to the environment influence that is the irremovable factor for the ship-owner. The external obsolescence (economical) can be conditioned by a number of the causes, for example the general decline of marine transport activity.
           The passenger vessel, which external economic obsolescence determination is being processed in the given example, is substantially subjected to external obsolescence (economical) in view of a decline in the activity of passengers transportation both at coasting internal lines and at cruising foreign lines that can be characterized as follows.
           The analysis of intensity of passenger marine traffic in the Far East of Russia during the period from 1993 to 1996 years is made for the estimation of external obsolescence (economical).
           During the certain period (from 1993 to 1996), that is previous time before the vessel estimation is made, the number of passengers transportation coasting trips in the Far East of Russia was reduced 2.7 times (from 86 to 32 annually).
           For the same period the number of passengers transported annually at coasting trips was reduced 4.57 times (from 34300 to 7500 annually).
           The reduction of passenger traffic capacity at coasting lines has considerably exceeded the reduction of trips number. Hence, it is characteristic that passenger vessels loading at coasting lines is incomplete.
           According to the specified indicators in 1996 in comparison with 1993 the reduction of commercial vessels filling by passengers at coasting lines can be determined as
           100 % × (1.0 – 2.7 / 4.57) = 40 %.
           During the considered years (from 1993 to 1996), that is previous time before the vessel evaluation is made, the number of foreign passengers trips practically was not reduced (in 1993 were carried out 66 foreign trips, in 1996 – 65 trips).
           For the same period the number of passengers transported annually at coasting trips was reduced approximately by 60 % (from 26200 to 10000 annually).
           As the number of foreign trips was not reduced the reduction of passenger traffic capacity for this period approximately corresponds to the reduction of passenger vessels filling in foreign cruising trips.
           Reduction of passenger vessels filling in foreign cruising trips from 1993 to 1996 has made – 40 %.
           It is supposed, that the external obsolescence (economical) for vessel is insignificant till 1993 for the period from the construction (1990) as the considered environment crisis phenomena and the decline in passenger transport activity are most clearly shown after 1993.
           The reduction of passenger vessels filling in coasting and foreign trips characterizes the reduction of the demand for sea passenger transportations and external obsolescence (economical) for similar vessels which makes from 40 to 60 %.
           Conclusion: the external obsolescence (economical) of the passenger vessel is approximately equal D₅≈ 50 %. The estimated value of the external obsolescence (economical) concerns the difference of reproduction cost and irremovable internal depreciation total (the physical and functional).

Test questions

1. Estimation of external economic obsolescence on the basis of correlation of passenger traffic capacity changes and vessels number in operation changes.
            2. Prediction of external economic obsolescence in case of vessels operation on several lines in coasting and foreign trips.