Corresponding author: Artem V. Klauz ( uni.klauz@gmail.com ) Academic editor: Yury Korovin
© 2021 Artem V. Klauz, Igor E. Frolov, Vladimir V. Kharitonov, Aleksandra A. Shaeva.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Klauz AV, Frolov IE, Kharitonov VV, Shaeva AA (2021) Methodology for calculating the criteria of economic efficiency of investments in nuclear icebreakers. Nuclear Energy and Technology 7(4): 333339. https://doi.org/10.3897/nucet.7.78501

An economic and analytical model for evaluating the criteria of efficiency (profitability) of investments in the projects of innovative nuclear icebreakers of the Northern Sea Route is suggested. The model is based on the new analytical representation of the methodology for forecasting the investment project efficiency that is widely used in international practice. The mathematical expression for the net discounted income provides convenient formulas for calculating several investment efficiency criteria for nuclear icebreakers: internal rate of return, minimum annual revenues from icebreaker convoys, discounted payback period, and the volume of delivered cargo. The paper gives estimates of the criteria for the efficiency of investments in “Leader” class icebreakers that depend on the discount rate of cash flows, capital, and operating costs. It is shown that at high capital costs, typical for construction of “Leader” class nuclear icebreakers, the minimum required revenue of an icebreaker, representing a financial burden for ships transporting cargo along the NSR, rapidly increases with the growth of discount rate and the reduction of investment payback period. This means that the profitability of such icebreakers is only possible at low discount rates of 2–3% per year, which is an extremely lowinterest credit. Even with low interest and impressive technical characteristics of the icebreaker (high speed of navigation, large number of ships in the caravan and their maximum capacity) the payback period would exceed 25 years.
Northern Sea Route (NSR), nuclear icebreakers, capital and operating costs, revenues, investment efficiency criteria, ship escort tariffs
In the 21^{st} century interest is growing in the development of the Arctic zone by the state of Russian Federation (
According to the data in the above table, relative fraction of the FSUE Atomflot earnings from new products (business areas) of the Rosatom SAEC amounts to slightly more than 4% of the total earnings from new products but, however, it does have a growth tendency. At the same time the planned volume of cargo traffic along the NSR was again overachieved in в 2020: 479 vessels with total tonnage of more than 32.4 million tons were escorted by nuclear icebreakers. Earnings of the FSUR Atomflot and earnings of the Rosatom SAEC from this business will be further bolstered by the recently adopted amendment of the Merchant Marine Code (
In accordance with given documents the FSUE Atomflot would conduct construction at the “Baltiysky Zavod” JSC of five new generation nuclear icebreakers from the “Project 22220” equipped with coupled innovative RITM200 nuclear reactors generating propulsive power of the icebreaker (propeller power) reaching 60 MW (Table
Cost of icebreaker amounts to 37–52 billion rubles. Construction of three nuclear icebreakers of Leader type under Project 10510 equipped with a pair of innovative RITM400 nuclear reactors generating 120MW(th) icebreaker propulsive power (See Table
Commercial use of the Arctic presupposes that Arctic cargo transport along the NSR must be competitive against cargo transport across South Seas circumventing Eurasia. The costs of icebreaker escort are the additional financial burden in the conduct of cargo transport operations (
The purpose of the present study is the development of the economic analysis model for evaluating microeconomic criteria of efficiency (profitability) of investments in the projects of nuclear icebreakers for the NSR on the basis of the methodology previously developed at the NRNU MEPhI (
Summary information about new products of the Rosatom SAEC for the period of 2015–2020
Indicators  2015  2016  2017  2018  2019  2020 

Rosatom SAEC, earnings (total), billion rubles  821.2  878.1  967.4  1033.9  1151.9  1207.2 
Earnings from new products, billion rubles  125  147.4  170.9  196.7  227.9  261.6 
Fraction of new products in the Rosatom SAEC earnings, %  15.2  16.8  17.7  19.0  19.8  21.7 
Portfolio of orders of new products for 10 ahead, billion rubles  583.5  1018.8  814.1  1082.6  1169.1  1602.1 
FSUE Atomflot, earnings (total), billion rubles  6.073  6.364  6.622  6.806  9.476  н.д. 
Fraction of new products in the FSUE Atomflot earnings, %  4.9  4.3  3.9  3.5  4.2  н.д. 
Total tonnage of vessels convoyed along the NSR, million tons(number of vessels, units)  2.043 (195)  5.29 (400)  7.2 (492)  12.7 (331)  31.5 (510)  33.0 (497) 
Characteristic  Project 22220, “Arktika” type icebreaker  Project 10510, “Leader” type icebreaker 

Principal region of operations  Western part of Arctica – yearround, Eastern region – summerautumn  All Arctica regions, yearround 
Length, m  173  209 
Width, m  34  47 
Water draft, m  10,5  13 
Propeller power, MW  60  120 
Speed on icefree water, knots  22  20 
Icebreaking capability (ice thickness penetrable at a speed of 1.5–2 knots), meters  2.9  4.3 
Crew complement, persons  53  60 
Capital investment, billion rubles  37–52*  127 
Operating costs, million rubles/day  3–4*  4–5* 
Nuclear propulsion plant  RITM200  RITM400 
Thermal power, MW  2×175  2×315 
Duty factor (reactor design SOW requirement)  0.65  0.65 
Uninterrupted operation time, hours  26 000  26 000 
Required reactor core power generating capacity, TW·hour  4.5–7.0  6.0 
Fuel enrichment, %**  17.5–19.7  17.5–19.7 
Fuel burnup, MW·day/kg (g ^{235}U/MW·day)  77 (2.3)  77* (2.3)* 
Time period between fuel reloading, years  4.5–7  6–10 
Preset lifespan, years  40  40 
Construction period, years  6*  8* 
The main microeconomic criterion of efficiency of the investment project characterizing its profitability is the net present value NPV, i.e., essentially, the net discounted income accumulated during the period of the project’s lifecycle including building and operation of the icebreaker reduced to a certain time moment Т_{с} (
$NPV=\sum _{t=1}^{{T}_{\mathrm{c}}}\frac{{K}_{t}}{(1+r{)}^{t{T}_{\mathrm{c}}}}+\sum _{t={T}_{\mathrm{c}}+1}^{{T}_{\mathrm{c}}+{T}_{\mathrm{o}}}\frac{{R}_{t}{Y}_{t}}{(1+r{)}^{t{T}_{\mathrm{c}}}}=K{\phi}_{\mathrm{c}}+\frac{RY}{r}{\phi}_{o},K=\sum _{t=1}^{{T}_{\mathrm{c}}}{K}_{t}$ (1)
where K are the net capital costs (rubles) aggregated over the whole period of icebreaker operation Т_{с}, years; R_{t} and R are the operating and the yearly average (over the whole period of operation) revenues, RUB/year; Y_{t} and Y are the current and the yearly average operating costs, RUB/yeaг. Dimensionless reduction factors φ_{с} and φ_{o} take into account the period of construction Т_{с} and the period of operation Т_{o} of the icebreaker, respectively, and are described by the formulas derived from the definition of the weighted average value:
${\phi}_{\mathrm{c}}=\frac{1}{K}\sum _{t=1}^{{T}_{\mathrm{c}}}\frac{{K}_{t}}{(1+r{)}^{t{T}_{\mathrm{c}}}}\approx \frac{(1+r{)}^{{T}_{\mathrm{c}}1}}{r{T}_{\mathrm{c}}}$ (2)
${\phi}_{o}=\frac{r}{RY}\sum _{t={T}_{\mathrm{c}}+1}^{{T}_{\mathrm{c}}+{T}_{o}}\frac{{R}_{t}{Y}_{t}}{(1+r{)}^{t{T}_{\mathrm{c}}}}\approx 1(1+r{)}^{{T}_{o}}$ (3)
Right sides of expressions (2) and (3) correspond to the base case scenario with constant annual costs and revenues. Reduction factors correspond to the tying of the moment of reduction of cashflows to the beginning of operation of the icebreaker and indicate the difference between the real project from the “ideal” one for which φ_{с} = φ_{o} = 1. For instance, for 8year period of construction of the icebreaker, 40year operation and discount rate equal to 5%/year the reduction factors calculated from expressions (2) and (3) are equal to φ_{с} = 1.19 and φ_{o} = 0.86.
The following three auxiliary but, nevertheless, popular and important in the analysis criteria of competitiveness stem out from the mathematical definition of the NPV: internal rate of return IRR, reduced (minimal) revenues of the icebreaker LR (Levelized Revenue) and the discounted payback period Θ counted from the beginning moment of the icebreaker operation. The IRR value serves as the upper limit of the discount rate (profitability of the project r < IRR) and, correspondingly, of the interest rate for the attracted financial resources (loans) and is determined from the condition NPV (r = IRR) = 0 by the following expressions:
IRR×φ_{с}(r = IRR)/φ_{o}(r = IRR) = IRR_{0}; IRR_{0} = (R – Y)/K. (4)
Here, IRR_{0} (1/year or %/year) is the internal rate of return for the “ideal” project (with φ_{с} = φ_{o} = 1) equal to the ratio of the yearly average revenues to the capital costs, where IRR<IRR_{0}. For example, for IRR_{0} = 12.8%/year, Т_{с} = 8 years and Т_{o} = 40 years we obtain IRR = 9%/year. The higher is the IRR value the more sustainable is the project and the wider are the possibilities to look and find the required loan offers on the market. As follows from (4), internal rate of return is the higher the larger is the yearly average revenues R – Y and the smaller are the capital costs K.
The minimal possible yearly average revenues of the icebreaker LR (RUB/year) for which the project does not cause losses and NPV = 0 is determined from (1) in the following form:
LR = AK + Y; A = rφ_{с}/φ_{o}, (5)
where A is the effective norm of depreciation of capital costs, A > r. The value AK + Y is called the reduced yearly costs consisting of the capital AK and the operating Y components. Correspondingly, the value of the minimal yearly average revenues from the icebreaker is equal to the present value. With such revenues the costs associated with the icebreaker are compensated by the end of its lifecycle, i.e., after Т_{o} ≈ 40 years after the beginning of its operation.
If the lender requires the return of investments after Θ < Т_{o} years after the beginning of operation of the icebreaker, then the value of revenues during the time period Θ must exceed the value (5) in accordance with Formula (
$L{R}_{\Theta}=\left\{\begin{array}{cc}{A}_{\theta}K+Y,& {T}_{c}\le t\le {T}_{c}+\Theta ;\\ Y,& t{T}_{c}+\Theta .\end{array}\right)$ (6)
Here the effective norm of depreciation of capital costs during the period Θ of return of investments A_{Θ} = rφ_{с}/φ_{Θ}, where φ_{Θ} = φ_{o} (Θ) = 1 – (1 + r)^{–Θ}, exceeds the value А in (5) because φ_{Θ} < φ_{o} with all remaining conditions being equal. For instance, for Θ = 15 years, r = 5%/year, Т_{с} = 8 years and Т_{o} = 40 years we obtain φ_{Θ} = 0,519 and A_{Θ} = 11.5%/year > A = 6.9%/year, i.e., the capital component of the present value is increased by almost two times. After settling accounts with the lender (t > T_{c} + Θ) the icebreaker is operated without generating profit, with earnings equal to the operating costs, which is required by the definition of LR corresponding to NPV = 0. It follows from the comparison of espressions (4) and (5) that for achieving profitability of the project internal rate of return IRR_{0} must exceed the depreciation rate A.
Discounted payback period of investments in the icebreaker is determined in the general case by the sequential calculation of NPV as a function of time of implementation of the project. From the right side of (1) with reduction factors (2) and (3) we obtain the analytical expression for estimating the payback period Θ (after the beginning of operation of the icebreaker) as follows:
Θ = –ln (1 – rφ_{с}/IRR_{0})/ln(1 + r). (7)
For instance, with IRR_{0} = 15%/year the payback period for the icebreaker Θ will amount to 10 years when the discount rate does not exceed 5%/year. It is clear that the conditions of profitability of the project require low discount rates and, correspondingly, lowinterest credits.
Thus, using expressions (1) – (7) it is possible to analytically estimate the main profitability criteria for icebreaker projects. Requirements imposed on key factors influencing profitability of icebreaker projects (high positive values of NPV and the internal rate of return IRR, minimal earnings LR and payback period Θ) are the following: reduction of capital and operating costs and duration of icebreaker construction, as well as facilitation of access to cheap borrowing (low discount rate).
In accordance with (Resolution of the Government 2020) K = 127 BRUB (BRUB = 1×10^{9} rubles) are allocated from the budget for the eightyear cycle of icebreaker building (Т_{с} = 8 years),it must be noted that Leadertype icebreakers are the most expensive civilian vessels in Russia. Yearly average capital costs are accepted here at the level of K_{t} = K/T_{с} ≈ 15.9 BRUB/year. Capital costs increase, as a rule, with increased duration of icebreaker building. For the sake of argument let us assume K = 15,9T_{C}. There is no publicly available reference to icebreaker operating costs in the references. Estimations of daily nuclear icebreaker rent equal to 3–5 MRUB/day (MRUB = 1×10^{6} rubles) are provided in (Mu Aril’d 2020). Annual operating costs for Leadertype icebreakers amount to 2.9 BRUB/year (≈ 7.94 MRUB/day) and are presented in (
If the discounted payback period Θ (years) in (7) is assumed to be preset, then it is possible to determine the dependence of the minimal permissible internal rate of return IRR_{0} on the values of Θ and the discount rate (Fig. 2а), and to estimate using the determined IRR_{0} value from Formula (4) the dependence of the minimal permissible yearly average revenues R = IRR_{0}K + Y on Θ and r (Fig.
Minimal required annual revenues for Leadertype icebreakers depending on the duration of construction Т_{с} = 4–10 years, capital costs K = 64–159 Billion RUB, discount rate r = 1–11%/year and the investment return period Θ = 40 years (а) and 15 years (b) with yearly average capital costs K/Т_{с} = 15.9 Billion RUB/year and operating costs Y = 1.5 Billion RUB/year. Calculation performed using Formulas (5) and (6). 1 – T_{c} = 4 years, K = 64 Billion RUB; 2 – T_{c} = 7 years, K = 111 64 Billion RUB; 3 – T_{c} = 10 years, K = 64 Billion RUB.
Dependence of internal rate of return IRR_{0} (а) and annual revenues R (b) for the icebreaker as function of discounted payback period Θ and discount rate r for K = 127 Billion RUB, Y = 1.5 Billion RUB /year Т_{с} = 8 years, Т_{o} = 40 years and NPV = 0. Calculation performed using Formulas (7) and (4). 1 – Θ = 10 years; 2 – Θ = 15 years; 3 – Θ = 20 years; 4 – Θ = 40 years.
Annual revenues of the icebreaker depend on the mass of transported cargo and tariffs for icebreaker supported pilotage of vessels. Leadertype icebreakers will be capable to pass through ice with thickness over four meters forming navigable channel with width up to 50 meters, which allows escorting vessels with high carrying capacity and cargo mass up to 175 kilotons or container vessels with carrying capacity up to 14 TEU (TEU – Twentyfoot Equivalent Unit – standard measurement unit of carrying capacity of container vessels based on the volume of 20ft container with load of about 14.5 tons which can be transported using different means of transportation) or tankers with liquefied natural gas with capacity in excess of 100 kilotons.
Leadertype icebreaker is capable of escorting vessels through 2meterthick ice with the above cargo carrying capacity and ice reinforcement class no less than Arc7 at a speed of up to 12 knots (1 knot = 1.852 km/hour). Maximum speed of vessels during summerautumn navigation period (from July 1 until November 30) can reach up to 17–19 knots. However, during winterspring period (from December 1 until June 30) the speed may be reduced to six knots or less. The number of vessels in the caravan and its speed are affected by the consolidation of ice measured by: 0 corresponds to icefree water, 10 – compact ice. Consolidation of ice characterizes the degree of coverage of water surface with ice (from 0 to 100%). The higher is the ice consolidation, the smaller is the number of vessels in the caravan. Normally, caravan consists of no more than 10 vessels.
The volume of cargo transported along the NSR affects the duration of operation during calendar year. According to some estimations each icebreaker is on the average used during 9.5 months a year (289 days). With duty factor for RITM400 reactor equal to 65% (Duty factor in Table
Tariffs for escorting vessels by icebreakers are applied depending on the carrying capacity and the ice reinforcement class of the vessel, distance along which the vessel is escorted, period of navigation and the section of the NSR waterway (
Forecasting revenues of the icebreaker from escorting vessels along the NSR is a multiparameter problem requiring large volume of specific information not available in references. For performing analytical estimations of revenues of the icebreaker we will apply optimistic set of data presented in Table
Correspondingly, for average speed of pilotage equal to 14 and 8 knots, number of vessels in the caravan equal to 10 and 5, average tariffs equal to 265 RUB/register ton and 665 RUB/register ton for icebreaker supported escort of vessels of Arc6 – Arc9 ice reinforcement class with gross cargo carrying capacity of 100 register ton the annual revenues of the icebreaker will amount to 10.3 BRUB/year assuming that the vessels are loaded to full capacity during both forward and return voyages along the NSR. It is of great interest is that earnings during the most difficult winterspring period are practically the same as those for the summerautumn period despite significant difference between the numbers of trips (seven and five, respectively). This is related to higher tariffs and longer duration of this navigation period.
Comparing the estimated earnings in Table
Estimation of performance characteristics of Leadertype icebreaker for one calendar year of operation on the NSR
Period of navigation  Summerautumn (July 1 – November 30), 153 days  Winterspring (December 1 – June 30), 212 days 

Number of days of icebreaker operation  133  182 
Average speed of escort, knots  14  8 
Travelling time (one way) *, days  9  16 
Number of twoway voyages (round trips) during one year  7  5 
Number of vessels in the caravan  10  5 
Average gross cargo carrying capacity of the vessel**, register ton  100 000  100 000 
Volume of cargo transported during one year (round trips) ***, million register ton/year.  14  5 
Average tariff for icebreaker supported pilotage of vessels, RUB/register ton  265  665 
Annual revenues, BRUB/year  3,7  3,3 
Aggregate annual revenues, BRUB/year  7 
Economic analysis model is suggested for estimation of microeconomic efficiency criteria (profitability) for investments in the projects of innovative nuclear icebreakers for the Northern Sea Route. The model is based on the analytical representation of the methodology for forecasting efficiency of investment projects widely used in the international practices. Easy to use formulas for calculating such icebreaker investment efficiency criteria as the net present value, minimal annual revenues from escorting vessels and discounted icebreaker payback period are derived from the mathematical expression for discounted net income.
It is demonstrated that for high capital costs typical for building of the Leadertype nuclear icebreakers, the minimal permissible revenues for the icebreaker, which represent the financial burden for escorted vessels transporting cargo along the NSR, rapidly increases with growing discount rates and decrease of the investment payback period. This means that profitability of icebreakers is possible for low discount rates equal to 2–3%/year which is an extremely cheap credit. Even for such lowcost credit and exceptional performance of the icebreaker (high vessel transport speed, large number of vessels in the convoy and their cargo loading capacity) the payback period would exceed 25 years.
Continued research implies that the increase of complexity in presented economic analysis model aimed at the more accurate accounting for the risks of increased icebreaker payback period due to the development, inflation in Russian economy including those due to the increased volatility of the Russian currency, as well as due to the overrun of time needed to build serial sea vessels caused, in particular, by the increase of Russian ruble exchange rate volatility, as well as by the overrun of schedules of production of serial vessels for the NSR caused by the low pace of production and technological restructuring of Russian shipbuilding industry.