A Simple Model
for Estimating Newbuilding Costs
Thanks
are due to Harry Benford, Ian L. Buxton, Charles R. Cushing, Kevin Moak, and an
anonymous referee, for helpful comments and suggestions. The author retains responsibility for errors
or shortcomings.
Abstract
This paper presents a simple model for estimating newbuilding
costs. Regression equations are
estimated on a large dataset of recent 20032007 shipyard deliveries reported
in Lloyd's Shipping Economist. The equations developed in this paper can be
used in a wide variety of economic analyses involving new ship construction and
operating costs. The models presented here capture the most modern design and
construction techniques, and most uptodate cost information, compared to
those previously described in the literature.
Key
words: newbuilding costs; pooled data; modern ship designs; regression analysis.
Introduction
The
established methodology for estimating ship construction and operating costs is
largely based on 1960s design and construction data. Given design dimensions, cargo capacity is
determined along with the required amount of steel. The earlier approaches assume steel constructions and are less applicable to
some of the more exotic modern materials such as aluminum or composites. They also assume a displacement hull, which
is increasingly less valid for newer, higherspeed ships (Baird, 2004; Becker,
Burgess and Henstra, 2004). The amount
of steel in turn determines the material and labor costs.
The
basic approach remains valid, but must be updated in light of modern
construction and design techniques which were never captured in the original
data. Contemporary ship designs, for
example, are routinely optimized by computer with finite element methods to
balance minimum fabrication cost and maximum cargo capacity requiring a boxier,
more rectangular hull, with minimum drag and maximum fuel economy requiring a
more streamlined design. The need for a
revised cost estimation methodology becomes increasingly critical as
environmental imperatives make waterborne transport the mode of choice
(Mulligan and Lombardo, 2006).
Literature Review
The
accepted method for estimating ship construction and operating costs is due to
Harry Benford, a professor of naval architecture and marine engineering at the
Benford
also estimated relationships between steel weight and labor requirements. This enabled him to estimate separate
equations for materials and labor costs to build a cargo ship. Again, both technical design parameters and
economic factors have changed so dramatically in the intervening forty years
that, at the very least, Benford's equations need to be reestimated with more
modern data.
Benford
published his regression studies in two research monographs (Benford, 1961;
1965) and a refereed article (Benford, 1967).
Little or no work has been done in this field since then (except Benford,
1991a; 1991b) and his articles, though outdated, remain definitive. Benford's estimates and approach continue to
be highlighted in contemporary textbooks (e.g., Hunt and Butman, 1995), due in
part to the broad applicability of his approach.
[Table 1 about here.]
Data
Data
on newbuilding costs are from Lloyd's
Shipping Economist, published from market reports in each monthly issue,
for various types and standard ship sizes.
For dry bulk carriers, newbuilding prices are given for handysize
(45,000 dwt), handymax (51,000 dwt), Panamax (72,000 dwt), and Capesize
(170,000 dwt) ships. Tanker newbuilding
prices are listed for handymax (clean) (45,000 dwt), Panamax (72,000 dwt),
Aframax (110,000 dwt), Suezmax (160,000 dwt), and very large crude carriers
(VLCCs) (300,000 dwt). Newbuilding costs
are listed for 140,000 m^{3 }liquid natural gas (LNG) tankers up to
December 2004 and for 150,000 m^{3} LNG tankers afterwards. Newbuilding costs are reported for 8,000 m^{3},
24,000 m^{3}, 52,000 m^{3}, and 72,000 m^{3} liquid
petroleum gas (LPG) tankers. In December
2004, the largest class of LPG tankers, for which data were reported, increased
to 78,000 m^{3}. For container
carriers, newbuilding prices are given for 1,000 teu, 2,500 teu, 4,000 teu, and
7,000 teu capacities. Starting in May
2005, the largest class of containership in the dataset was increased to 8,000
teu. Newbuilding costs are also given
for general cargo carriers of 10,000 dwt and 20,000 dwt. Although some data are available for RoRo and
reefer ships, newbuilding costs were not given for these types. Ship sizes by type are summarized in Table
1. To allow for adjustments for
inflation, the producer price index (PPI) for heavy industry was taken from the
Federal Reserve Bank of
Methodology
The dataset includes
only two monthly observations for each size and type of ship: newbuilding cost,
which is an average of all newbuilding costs of all ships of that type and
approximate size delivered in that month, and the standard size category,
characterized by deadweight tonnage.
Because the data are reported for particular months, cost indices can be
used to reflect supply (producer price index) and demand (consumer price index)
determinants. The consumer price index
was never found to contribute significant explanatory power. This may result from collinearity with the
producer price index, or from temporal demand instabilities which, as Dikos
(2004) showed, could occur in competitive markets. Although the dataset is unfortunately
parsimonious, the number of datapoints included is much greater than Benford
(1961, 1965, 1967) was able to include in his otherwise much richer datasets. It is hoped that the larger dataset will
allow for more reliable estimates.
With two basic
explanatory variables, deadweight tonnage and producer price index, and one
thousand observations, it was simple to include second and third order terms in
the explanatory variables to explore the possibility of nonlinear
relationships of the kind successfully estimated by Ådland and Koekebakker
(2004, 2007) for secondhand bulk carriers.
As newbuilding costs were reported in current dollars, i.e. not adjusted
for inflation, one approach could have been to adjust for inflation by a price
index before estimation. However, with a
view toward the final user who would need to predict newbuilding costs in
currentyear rather than baseyear dollars, the price indices were included in
the basic specification.
The general
specification was modeled as a firstorder function of the PPI and a
thirdorder function of deadweight tonnage:
Newbuilt Cost = a(PPI) + b(dwt) +
c(dwt)^{2} + d(dwt)^{3}
Four dummy variables
were added to this basic specification to distinguish among observations for
five different type ships as described above.
Statistically insignificant coefficients were then deleted from the
model to arrive at a final specification.
Results
The
first approach is to pool the dataset including all dissimilar ship types. Estimation of a single model including all
ship types allows available degrees of freedom afforded by the large dataset to
be used to the fullest advantage. Each type is distinguished in the dataset by
dummy variables for each type: dry bulk carriers, containerships, tankers,
liquid petroleum gas tankers, and liquid natural gas tankers. General cargo ships are also included in the
dataset and are distinguished from other types by the absence of a dummy set to
one for that type. Omitting the dummy
for one category is a standard and necessary practice to avoid a noninvertible,
exactlysingular matrix which would make it impossible to estimate regression
coefficients. The other variables in
each observation are the newbuilding cost in current dollars, the producer
price index, and the deadweight volume for each ship, and its square and cubic
power.
With
1,000 observations and ten estimated coefficients (an intercept, coefficients
on four ship type dummies, and coefficients on the producer price indexPPI,
dwt, dwt^{2}, and dwt^{3}), the estimate's degrees of freedom
were 990. An alternative approach would
have been to suppress the intercept to reflect the fact that the ship estimate
model R: this is shipbuilding cost and not ship model should pass through the
origin so that a ship of zero size should cost zero dollars. This approach was dropped because the dummy
variables estimate independent, nonzero, intercepts for each ship type anyway.
[Table 2 about here.]
The
pooled regression is reported in Table 2.
Tstatistics are significant for all variables in this
specification. The coefficient of PPI is
positive and significant. More explicitly, the coefficient value of 2.6 implies
an average increase in newbuilding cost of 2.6 million dollars for every one
percent increase in the PPI. However
obvious this finding may seem, it lends credence to the estimate. The firstorder coefficient on deadweight
volume indicates that the larger a ship’s tonnage, the more it will cost, which
again is a fairly intuitive finding. On
average, and across all types of ships, every increase in 1,000 tons deadweight
results in an increase of 1.8 million dollars in newbuilding cost. The secondorder coefficient of tonnage is
negative and significant, indicating that scale economies are present, but the
thirdorder term is positive and significant, indicating scale economies are
not unlimited.
[Figure
1 about here.]
Equations
for forecasting newbuilding costs based on this estimate are presented below
for liquid natural gas carriers (LNG), liquified petroleum gas carriers (LPG),
general cargo carriers (GC), container carriers (C), tankers (T), and dry bulk
carriers (B), listed in order of decreasing cost:
C_{LNG}
=  253.012 + 2.60(PPI) + 1.8053(dwt)  0.01009(dwt)^{2} +
0.0000189(dwt)^{3}
C_{LPG}
=  341.082 + 2.60(PPI) + 1.8053(dwt)  0.01009(dwt)^{2} +
0.0000189(dwt)^{3}
C_{GC}
=  380.078 + 2.60(PPI) + 1.8053(dwt)  0.01009(dwt)^{2} + 0.0000189(dwt)^{3}
C_{C} =  401.727 + 2.60(PPI) + 1.8053(dwt) 
0.01009(dwt)^{2} + 0.0000189(dwt)^{3}
C_{T} = 
411.551+ 2.60(PPI) + 1.8053(dwt)  0.01009(dwt)^{2} + 0.0000189(dwt)^{3}
C_{B} = 
418.202 + 2.60(PPI) + 1.8053(dwt)  0.01009(dwt)^{2} + 0.0000189(dwt)^{3}
The
dummy variable coefficients are also all significant and serve to distinguish
the different types of ship, which have systematically different costs. LNG tankers are dramatically more expensive
than other types of ships. Bulk
carriers, tankers, and containerships cost less. Containership cost is not much less than
general cargo carriers, though the small difference is statistically
significant. LNG tankers are the most
expensive ship type; dry bulk carriers the cheapest to build, followed by
ordinary tankers. Assuming a fixed PPI =
149.3 (May 2007), newbuilding costs vary with deadweight tonnage as illustrated
in Figure 1.
Next,
we set the ship type dummy variables aside and estimate separate regression models
for each type of ship. The dummy
variable approach allows for estimates with more degrees of freedom while
estimating independent intercepts, slopes, and algebraic specifications, for
each type of ship. Estimating separate
regressions makes the slope coefficients independent as well as the
intercepts. Separate regression models
are reported in Table 3.
[Table 3 about here.]
Interestingly,
intercepts are always large and negative, particularly considering that they
are dimensioned in millions of dollars. Newbuilding
cost always rises directly with size and the price index. Higherorder terms in deadweight tonnage were
only significant for dry bulk carriers.
Thus, all the other independent estimates yield linear models.
C_{LNG}
=  885.127 + 5.56(PPI) + 5.3368(dwt)
C_{LPG}
=  385.921 + 2.86(PPI) + 2.1444(dwt)
C_{GC}
=  34.903 + 0.304(PPI) + 0.6740(dwt)
C_{C}
=  219.933 + 1.56(PPI) + 0.5961(dwt)
C_{T}
=  480.899 + 3.530(PPI) + 0.2611(dwt)
C_{B} = 
291.147 + 1.689(PPI) + 2.8526(dwt)  0.03165(dwt)^{2} + 0.00011(dwt)^{3}
[Figure
2 about here.]
These
relationships are graphed in Figure 2.
One implausibility of the thirdorder, nonlinear cost function for dry
bulk carriers is that cost declines between about 70,000 and 120,000 tons,
suggesting that a linear specification may be preferable.
An Illustration
Given
the equations presented above, it will help to illustrate how they might be
used by practitioners and shipping analysts.
A firm contemplating a building programme needs to have some idea at the
preliminary stage of what magnitude of newbuilding costs they may be confronted,
before they can employ more sophisticated forms of analysis such as Bendall and
Stent's (2005) real option valuation model.
Posit
the potential construction of an 8,000 teu, 170,000 ton containership, with
contract date of mid 2010 and delivery scheduled for late 2011.The contract
date determines the number of years of compounding for the price index. Assuming an inflation rate of three percent,
compounded for three years, and starting with the May 2007 PPI of 149.3, the
PPI is multiplied by (1.03)^{3} = 1.0927. This gives 163.1 for the projected 2010
PPI. Together with the desired
deadweight tonnage, these parameters are plugged into the newbuilding cost
equations, first using the pooled estimate equation from Table 2:
C_{C} =  401.727 + 2.60(163.1) + 1.8053(170)
 0.01009(170)^{2} + 0.0000189(170)^{3}
=
130.90 million USD in 2010
Alternatively, using the unpooled estimate from Table 3, a simpler, linear
specification yields:
C_{C} =  219.933 + 1.56(163.1) +
0.5961(170)
=
136.37 million USD in 2010
Though the two equations
accord fairly closely, they can be interpreted as a probable range in which newbuilding
costs will likely fall, given contract time, design size, and assumptions about
inflation. These estimates depend on
projected future PPIs for heavy industry, reflecting both shipyard cost and the
level of demand faced by shipyards.
Consequently, estimates from these equations can be performed for a
variety of projected levels of PPI inflation.
These estimates are presented in Table 4 for several different
hypothesized inflation rates.
[Table 4 about here.]
Conclusion
This
paper presents new models for estimating newbuilding costs, based on recent
20032007 data. This dataset reflects
contemporary ship design and construction practices, and recent cost
trends. The models can be used as a
basis for economic analysis whenever newbuilding ship cost is considered as an
alternative. Though not making an abrupt
break with accepted practice, the cost equations presented above offer various
advantages for shipping economists and strategic planners. Estimating newbuilding costs with these
models captures recent practical experience and cost trends facing the industry
in the past few years.
References
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Mulligan, RF and
Table 1 Standard Ship Sizes Included in the Dataset 

Dry Bulk Carrier 
Handysize 
45,000 dwt 

Handymax 
51,000 dwt 

Panamax 
72,000 dwt 

Capesize 
170,000 dwt 
Tanker 
Handymax (clean) 
45,000 dwt 

Panamax 
72,000 dwt 

Aframax 
110,000 dwt 

Suezmax 
160,000 dwt 

VLCC 
300,000 dwt 
LNG Tanker 
140,000 m^{3} 
49,500 dwt 

150,000 m^{3} 
53,000 dwt 
LPG Tanker 
8,000 m^{3} 
2,800 dwt 

24,000 m^{3} 
8,500 dwt 

52,000 m^{3} 
18,000 dwt 

72,000 m^{3} 
25,000 dwt 

78,000 m^{3} 
27,500 dwt 
Container Carrier 
1,000 teu 
45,000 dwt 

2,500 teu 
51,000 dwt 

4,000 teu 
72,000 dwt 

7,000 teu 
150,000 dwt 

8,000 teu 
170,000 dwt 
General Cargo 
10,000 dwt 
10,000 dwt 

20,000 dwt 
20,000 dwt 
Source: Lloyd's Shipping
Economist, various 20032008 issues. 
Table 2 Newbuilding Cost Model I: Ship Type Distinguished by Dummy Variables 

Pooled Data 
Coefficient 
Std Error 
tstatistic 
Probability 
Intercept 
380.07788 
15.2686 
24.8927 
0.00000 
LNG 
127.06628 
2.4552 
51.7540 
0.00000 
LPG 
38.99597 
1.3126 
29.7087 
0.00000 
Containership 
21.64896 
2.1654 
9.9976 
0.00000 
Tanker 
31.47307 
2.3069 
13.6428 
0.00000 
Dry Bulk Carrier 
38.12387 
2.1339 
17.8657 
0.00000 
PPI 
2.60120 
0.1056 
24.6404 
0.00000 
DWT 
1.80527 
0.0760 
23.7634 
0.00000 
DWT^{2} 
0.01009 
0.0006 
18.1144 
0.00000 
DWT^{3} 
0.0000189 
0.0000 
16.6142 
0.00000 
No Obs 
1000 

Adj R^{2} 
0.9311032 
Table 3 Newbuilt Cost
Models, Various Type Ships, Independent Estimates 

1. LNG Tanker 
Coefficient 
Std Error 
tstatistic 
Probability 
Intercept 
885.12736 
33.26143 
26.61122 
0.00000 
PPI 
5.56042 
0.43918 
12.66095 
0.00000 
DWT 
5.33685 
0.81423 
6.55445 
0.00000 
No Obs 
50 

Adj R^{2} 
0.96846 





2. LPG Tanker 
Coefficient 
Std Error 
tstatistic 
Probability 
Intercept 
385.92095 
14.87953 
25.93637 
0.00000 
PPI 
2.86128 
0.10340 
27.67195 
0.00000 
DWT 
2.14442 
0.03649 
58.76587 
0.00000 
No Obs 
200 

Adj R^{2} 
0.95593 





3. General Cargo 
Coefficient 
Std Error 
tstatistic 
Probability 
Intercept 
34.90298 
8.08377 
4.31766 
0.00004 
PPI 
0.30392 
0.05603 
5.42459 
0.00000 
DWT 
0.67400 
0.03589 
18.78102 
0.00000 
No Obs 
100 

Adj R^{2} 
0.79339 





4. Container Carrier 
Coefficient 
Std Error 
tstatistic 
Probability 
Intercept 
219.93267 
32.31667 
6.80555 
0.00000 
PPI 
1.56284 
0.22469 
6.95559 
0.00000 
DWT 
0.59606 
0.01586 
37.59086 
0.00000 
No Obs 
200 

Adj R^{2} 
0.88182 





5. Tanker 
Coefficient 
Std Error 
tstatistic 
Probability 
Intercept 
480.89908 
20.66656 
23.26943 
0.00000 
PPI 
3.52981 
0.14347 
24.60287 
0.00000 
DWT 
0.26107 
0.00510 
51.14381 
0.00000 
No Obs 
250 

Adj R^{2} 
0.92820 





6. Dry Bulk Carrier 
Coefficient 
Std Error 
tstatistic 
Probability 
Intercept 
291.14668 
30.84261 
9.43976 
0.00000 
PPI 
1.68883 
0.09013 
18.73703 
0.00000 
DWT 
2.85256 
1.14969 
2.48116 
0.01394 
DWT^{2} 
0.03165 
0.01413 
2.24080 
0.02617 
DWT^{3} 
0.00011 
0.00005 
2.22859 
0.02698 
No Obs 
200 

Adj R^{2} 
0.92121 
Table 4 Projected Newbuilt
Cost for Hypothetical 170,000 dwt Container Carrier,
Contract Date 2010 

Projected Inflation rate 
Projected 2010 PPI 
Pooled Estimate (Table 2) 
Unpooled Estimate (Table 3) 
3% 
163.1 
130.90 
136.37 
4% 
167.9 
143.38 
143.86 
5% 
172.8 
156.10 
151.51 
6% 
177.8 
169.07 
159.30 
Notes: 1. PPI is projected
n years into the future assuming a particular annual PPI inflation rate i by the formula PPI_{t+n }= PPI_{t}(1+i)^{n}. The inflation rate must be represented as a
decimal fraction, i.e., 3% = .03. 2. Estimated cost
is given in millions of current year (2010) unadjusted U.S. dollars. 