Abstract
The purpose of this article is to apply a risk-adjusted required
rate of return to evaluate supply chain capitol investments. As part of
the design methodology, a computer simulation provides expected cash
flows resulting from alternative supply chain investments. These cash
flows are discounted at a risk-adjusted required rate of return. The
analysis represents a process to measure the risk inherent in supply
chain investments. The logistics and supply chain literature has not
addressed this problem of the risk inherent in a specific supply chain
project. A corporate-wide hurdle rate applied to usually conservative
supply chain investments may result in less than adequate investments in
supply chain infrastructure.
Prior studies have determined risk-adjusted required rate of return
for the entire firm, an enterprise's entire supply chain network,
but not an individual project within the supply chain. This study
calculates a required rate of return for a specific supply chain
investment project using a discrete simulation model rather than the
more common mathematical model. Individual supply chain investment
projects may have less risk or possibly more risk than reflected by a
corporate hurdle rate or a supply chain hurdle rate. Using a standard
required rate of return could result in too little or too much
investment in supply chain facilities.
In this study, when the risk-adjusted rate was employed to discount
expected cash flows, only two of eleven alternatives evaluated were
acceptable investments. The best investment with the highest return was
a 12 percent increase in ship loading rate combined with a 33 percent
increase in rail unloading capacity. It provided a benefit-cost ratio of
1.25.
The limited availability of publicly traded firms that invest in
supply chain projects represents a constraint, limiting the accuracy of
estimating the market risk factor. Nevertheless, the practical
implication is that, when making supply chain infrastructure investment
decisions, it is advisable to adjust risk factors in evaluating such
capital investments. This approach is preferable to using a
corporate-wide hurdle rate, typically too high for such conservative
investments. A firm-wide hurdle rate might result in under investment in
supply chain facilities.
**********
Strategic logistics decisions normally consider infrastructure
investment, including supply chain capacity levels and design
configuration (Novack et al. 1992). Logistics and supply chain managers
should identify and estimate the costs, revenues, and risks associated
with related investments. These elements remain difficult to quantify
with any degree of certainty. The competition for an organization's
funds demands that the "value added" by investment projects to
the enterprise be carefully measured (Speh and Novack 1995).
Some organizations evaluate all projects against an entity-wide
target rate of return. However, many capital projects in the supply
chain are relatively less risky, as they involve costs savings that are
measurable and rather certain, but may generate less than spectacular
rates of return. An adjustment to the target return based on the
riskiness of the project might prove indispensable. Investments in
logistics assets with the same risk command the same required rate of
return (Pringle and Harris 1987). Consequently, lower target rates of
return should be reasonable for less risky supply chain projects.
This article describes a simulation model of an intermodal transfer
and bulk commodity blending facility and the financial analysis of
potential changes to the actual plant capacity and design configuration.
The model estimated cash flows (measured as annual cost savings) due to
an increase in capacity. The cash flows are adjusted for the same volume
and scheduling performance. The risk-adjusted required rate of return
from several possible capital investment projects in logistics
infrastructure was computed based on the business risk of proxy firms
that normally undertake these same types of investments in supply chain
assets. Benefit-cost ratios were then calculated to determine which
projects exceeded the required rate of return for the risk levels of
these investments.
RELATED LITERATURE ON SUPPLY CHAIN MODELING AND RISK
The current research literature increasingly recognizes the
importance of supply chain risks (Cavinato 2004; Spekman and Davis 2004;
Ritchie and Brindley 2007; Kish 2007; Krishnan and Shulman 2007). The
importance of global competition and technological change, with firms
searching for sources of competitive advantage, has increased the
importance of risk analysis in supply chains (Christopher and Lee 2004;
Zsidisin et al. 2004; Cavinato 2005; Tang 2006; Tomlin 2006; Bogataj and
Bogataj 2007; Craighead et al. 2007; Golda and Philippi 2007). Mintzberg
and Waters (1985), Paulsson (2004), and Kleindorfer and Wassenhove
(2003) viewed the analysis of the risk associated with supply chain
decisions as strategic.
Quantitative Models and Supply Chain Design
Much of the published research in the area of supply chain network
design relates to mathematical programming models. Examples include
Arntzen et al. (1995) and Camm et al. (1997), who employed integer
programming models to address supply network design issues. More
recently, Cochran and Marquez-Uribe (2005) employed an integer
programming model to evaluate alternative investments in supply chain
capacity.
In alternative quantitative approaches to this issue, Levy (1995)
captured risk issues related to different supply network designs in a
simulation model. Swaminathan et al. (1998) also applied simulation
modeling risk-benefit analysis to re-engineered supply chains. Agrell et
al. (2004) applied game theory to evaluate a multi-stage supply chain.
Quantitative Models and Risk Analysis
There is some literature about the investment decision making in
supply chain networks under conditions of risk and uncertainty.
Huchzermeier and Cohen (1996) applied a multi-period stochastic
programming to evaluating design risks in a global supply chain network.
Lee and Tang (1998) developed a stochastic inventory model to examine
network tradeoffs under conditions of uncertainty. Applequist et al.
(2000) presented a metric for evaluating supply chain design projects
where significant elements of risk and uncertainty are present.
Alonso-Ayuso et al. (2003) and Goh et al. (2007) applied stochastic
models to analyze supply chain uncertainties in multi-stage networks.
Ojala and Hallikas (2006) investigated how firms with supply chains make
investment decisions and the risks associated with those investments.
There have also been multi-criteria decision-making models applied to
supply chain risks analysis, such as studies by Nagurney and Matsypura
(2005).
Research Contribution
This study is concerned with the strategic planning function of
network configuration that deals with manufacturing facilities and
distribution centers. It does not address other supply management issues
such as product or customer assignment. Spearman (2007) suggested that
risk in manufacturing supply chains results from the failure to operate
them under conditions different from those for which they were
originally designed. The research reported herein focuses on this
concern by evaluating an existing logistics facility that is an integral
part of a larger supply chain.
Our research offers two contributions to the evaluation of supply
chain risk. It incorporates a risk premium in the discount rate, rather
than trying to adjust the cash flows themselves. This latter approach is
more common. Secondly, the risk analysis is applied to a specific node
that is part of a much larger supply chain network.
Prior studies have determined risk-adjusted required rate of return
for the entire firm, an enterprise's entire supply chain network
(Applequist 2000), but not an individual project within the supply
chain. This study calculates a required rate of return for a specific
supply chain investment project using a discrete simulation model rather
than the more common mathematical model. Individual supply chain
investment projects may have less risk or possibly more risk than
reflected by a corporate hurdle rate or a supply chain hurdle rate.
Using a standard required rate of return could result in too little or
too much investment in supply chain facilities.
Incorporating risk into the decision of whether to add capacity or
not to an actual facility that is part of a much larger supply chain,
the model estimates cash flows resulting from proposed capacity changes.
The study then determines whether the resulting returns provide enough
payback to justify the project under the estimated risk.
Methodological Issues
Queuing theory provides numerous models for describing a
waiting-line situation, such as an intermodal facility that is
integrated into a supply chain. In terms of a queuing model, ship
arrivals at the facility are selected for service according to a
priority procedure, usually first-come, first-served. If the service
center is occupied, the arriving ship joins a queue, possibly with
others already waiting. If the service center is empty, the arriving
ship receives service immediately. After the service is performed, the
ship leaves the port system.
If an analytical model can be developed to determine the optimal
ship-loading rate, rail unloading, and quantity of storage, the
mathematics of optimization could be used to obtain a solution. If not,
simulation analysis can be employed to obtain a solution (Gross and
Harris 1998). The research literature suggests that simulation
techniques are preferable to mathematical approaches for the analysis of
supply chain facilities. These experiments, or simulations, permit
inferences to be drawn about proposed systems without building them;
they can also study actual operating systems that are costly to conduct
real-world experiments on--such as supply chain facilities--without
disturbing them.
More than forty-five years ago, Steer and Page (1961) rejected
mathematical optimization models for the analysis and planning of port
facilities, finding that a mathematical formulation could not adequately
incorporate the heterogeneity of ships calling at the port, the nature
of their arrivals, or the service operation performed on each vessel
while in port. Simulation is the best method for the analysis of such
supply chain infrastructure because of its relative efficiency in
describing the complex interrelationships involved with the operation of
bulk commodity facilities. In another early study of capacity for marine
terminals in terms of unloading rail cars, inventory capacity, and
ship-loading rates, Culbert and Leighton (1968) advocated computer
simulation to model the primary factors involved in the study of these
facilities: (1) the variability of arrival pattern in land- and
sea-based carriers; (2) the payload capacity of the carriers; (3) the
cost of idleness of the carriers; (4) the fixed and variable costs of
providing the facility; and (5) the level of annual throughput.
Estimated future cash flows and the appropriate discount rate are
key ingredients in a capital budgeting decision. Estimating the future
cash flows is a complicated process given the uncertainties involved.
Applequist et al. (2000) established a risk-adjusted discount rate for a
supply chain network model, but not for a specific facility. The
analysis reported herein uses a simulation model to incorporate various
plausible capacity scenarios in estimating future cash flows. A
simulation model can be equally powerful and more flexible in estimating
future cash flows and used in conjunction with the appropriate
risk-adjusted discount rate to ensure the correct level of investment in
specific supply chain capacities.
AN APPROPRIATE DISCOUNT RATE FOR SUPPLY CHAIN PROJECTS
It appears that risky projects are less desirable than sate ones,
other things being equal. Consequently, financial managers require a
higher rate of return on risky investments. Modern finance theories in
capital budgeting suggest that a project should be undertaken if its net
present value (NPV) is positive. To calculate the NPV of a project,
financial managers must understand the risk characteristics of the
project itself, as the discount rate appropriate for the project risk
should be employed, rather than a company-wide hurdle rate. In
estimating the required rate of return on a project, companies often use
the rate of return required by security holders. While a positive
relationship between risk and return seems intuitive, there is still no
consensus on what type of project risk is relevant and/or how to measure
it.
While debatable, the capital asset pricing model (CAPM) has gained
popularity among practitioners. For example, Graham and Harvey (2001)
found in a survey of financial practice that 74 percent of firms always,
or almost always, used the CAPM to estimate the cost of capital. This
analysis utilizes the CAPM to estimate the cost of capital for a supply
chain investment project.
The CAPM is widely used to estimate the return that equity
investors require. The model stipulates the positive relation between
the expected return and risk in an equation commonly known as the
security market line (SML):
[R.sub.i] = [R.sub.f] + [[beta].sub.i] ([R.sub.m] -[ R.sub.f]
The expected return on equity of firm i ([R.sub.i]) is equal to the
risk-free rate ([R.sub.f]) plus a risk premium, which is proportional to
its beta ([[beta].sub.i]) and the market risk premium ([R.sub.m] -
[R.sub.f]). Beta measures the firm's market risk that cannot be
diversified away, and therefore must be borne by a firm's
investors, who in turn demand to be compensated accordingly for assuming
risk. This model can be employed in capital budgeting to estimate the
cost of capital for a project.
Implementing the model, however, brings a few challenges. First,
the parameters in the SML equation must be estimated. There are no true
risk-free assets, but Treasury securities are essentially free of
default risk. As common equity is a long-term claim, Brigham and
Ehrhardt (2005) suggest that the yield on a Treasury bond be used to
estimate the risk-free rate. A thirty-year Treasury bond as of September
30, 2005 yields 4.42 percent, according to Yahoo Finance. On the basis
of historical data, the long-term Treasury bonds have yielded 5.02
percent (geometric average) over the period 1928 to 2004.
The market risk premium ([R.sub.m] - [R.sub.f], or the market
expected return--risk-free rate) then needs to be estimated. As Welch
(2000) noted, however, there is no universally accepted model for the
risk premium estimation. Depending on the models or indices used, the
estimates can vary. We estimate the market risk premium on a historical
or forward-looking basis. Using the S&P 500 index as a proxy for the
U.S. stock market, the geometric average return over the 1928-2004 time
frame is 9.86 percent. With the risk-free rate of 5.02 percent on
Treasury bonds, the risk premium is then 4.84 percent on the basis of
historical data.
As an alternative to historical risk premium, a forward-looking
risk premium can be inferred by applying a dividend discount model to
current level of the index:
Expected rate of return = [R.sub.m] = [D.sub.1]/[P.sub.0] + g =
[D.sub.0](l + g)/[P.sub.0] + g
where:
[D.sub.1] is the expected dividend on the Standard &
Poor's (S&P) 500 index;
[P.sub.0] is the current level of the index; and g is the expected
growth rate of dividend.
With the growth rate estimated with historical data for the period
from 1960 to 2004, the expected return on S&P 500 is computed:
[R.sub.m] = 19.407(1 + 0.0532) / 1211.92 + 0.0532 = 0.0701 = 7.01%
Given the current long-term Treasury bond yield of 4.42 percent,
the forward-looking risk premium is only 2.59 percent, which seems low.
Finally, the analysis estimates the beta of the port facility
project. Since we cannot directly observe the market prices or returns
on the port facilities, we rely on surrogate firms who make similar
investments in port facilities. Using Value Line and S&P's Net
Advantage stock surveys, we identified twelve companies for Table 1 in
the marine transportation and storage industry that appear to possess
similar types of assets as port transfer facilities (excluding one
company that went public in 2002). These firms include Sunoco Logistics
Partners (pipelines, terminals, and storage), Alexander & Baldwin
(shipping and terminals), Kinder Morgan EN (pipelines and bulk
terminals), Martin Midstream (marine transportation terminals), SEACOR
Holdings (inland bulk barge and logistics support), and Valero L.P.
(pipelines, terminals, and storage).
The analysis then determines the weighted average beta of these
firms, weighted by their market capitalization. As shown in Table 1, the
weighted average of beta is 0.588 (while a simple arithmetic average of
beta is 0.540). As a benchmark, we also use the beta of the maritime
industry. According to Value Line, there are twenty-eight firms in the
broader maritime industry with an average beta of 0.67.
These betas are equity betas that represent not only business risk,
but also financial risk that arises when a firm takes on debt. As a firm
increases its leverage by borrowing more, the leverage causes extra risk
for equity investors, reflected in higher equity beta. In fact, Hamada
(1969) proposed the following equation to show the effect of leverage on
equity beta:
[beta] = [[beta].sub.u] [1 + (1 - T) (D/S)]
where:
T is the marginal tax rate;
[[beta].sub.u] is un-leveraged beta measuring only the business
risk of a firm;
D is the market value of debt; and
S is the market value of equity.
Therefore, an increase in financial leverage (D/S) results in
additional risk to the firm's business risk. By rearranging the
equation, we can un-leverage the equity beta to remove any effects from
financial leverage on the beta.
[[beta].sub.u] = [beta] / [1 + (1 - T) (D/S)]
In evaluating the port facility investment project (as part of the
supply chain infrastructure), it seems sensible to focus on the business
risk because it is likely that a local government, or quasi-governmental
agency, will invest in this type of project. Obviously, a local or state
government is not subject to federal income taxes. Therefore, its debt
financing would not have the same effect on the equity beta as described
in the Hamada equation above. For this reason, we will use un-leveraged
beta to estimate the risk-adjusted discount rate. To employ the Hamada
equation, we used 62 percent debt-to-equity ratio that the firms in this
industry have on average.
Table 2 shows the risk-adjusted discount rates for various input
values. The discount rate is lowest at 5.42 percent when forward-looking
market risk premium and Treasury bond rate are used with the
un-leveraged proxy beta of 0.39. The forward-looking market risk premium
of 2.59 percent is too low to apply to a long-term project. The
historical risk premium of 4.84 percent is more conservative and it is
more likely a better estimate for the port facility project. For this
reason, we show the lower discount rate only for a reference.
THE PORT ELEVATOR AS TRANSPORTATION AND MANUFACTURING FACILITY
A grain elevator at a port serves two supply chain functions.
First, as a transportation facility, it is an intermodal facility that
transfers commodities from land-based modes of transport (motor carriers
and/or rail) to marine mode of transport (ocean-going ships). In
addition to the transfer between modes, the elevator provides an
inventory or storage function between land and sea because of the
scheduling problems, i.e., sufficient grain to meet the demand
represented by a ship does not arrive when the ship arrives and vice
versa. (Refer to Figure 1 for depiction of the various components of the
port facility.) The storage capacity ameliorates this scheduling
difficulty at the port between modes.
At the same time, the port grain elevating facility provides a
manufacturing or transformation function. Each ship arriving at port
represents a demand for a specific amount (usually tonnage) of a certain
quality of product; for example, 65,000 tons of #2 grade winter wheat.
Grade level has quality characteristics of minimum moisture level,
minimum protein content, and maximum foreign matter. Grain arriving by
land is stored in the various silos and interstices (space between the
round silos) according to the grade level and its attributes. As the
ship is loaded, the grain elevating facility in its manufacturing
function optimizes and mixes a commodity at the least cost that meets
the constraints of moisture, protein, and foreign matter in the desired
quantity.
SIMULATION MODEL OF AN INTERMODAL TRANSFER AND BLENDING FACILITY
Simulation experiments were conducted using a model of a blending
facility situated on the Texas seacoast. The facility is owned and
operated by a government agency that is part of a county jurisdiction
(i.e., a port authority enabled by the State of Texas). This intermodal
system receives and unloads bulk commodities (i.e., wheat, corn, and
other grains) by rail, temporarily holds the merchandise in storage,
mixes product to grade, and then ships the product by ocean-going
carriers. Twelve combinations of transfer plant capacity (i.e., loading,
unloading, and storage) were analyzed. The criterion variable was the
average cost per ton to transfer and store bulk commodities.
During the simulated operation of the transfer and blending plant,
several uncontrollable factors affected the cost. These factors include
(1) the volume at which the system operates; (2) the coordination
between different modes of transportation; (3) the scheduling of
successive ships arriving at the port, which determines queue time; and
(4) the lot sizes designated for each vessel.
Any of the aforementioned variables can significantly affect the
cost of plant operation, regardless of capacity. In order to carefully
examine the effect on cost resulting from changes in plant capacity,
evaluation of such modifications should be conducted at the same level
of volume and scheduling performance (i.e., queue times).
Simulation Logic and Output
The computer simulation model of the transfer and blending facility
consists of several sub models. The most important of these are the
loading and unloading sub models. Figure 2 depicts the operating logic
of the simulation model.
The simulation program was written to evaluate the ability of the
transfer and blending plant to handle the forecasted volume of 550,000
tons per month. The parameter values of ship inter-arrival times and
cargo sizes were formulated so as to schedule the forecasted level of
bulk commodity for the blending plant system during the simulation
experiments. The statistical distributions describing vessel
inter-arrival times, cargo sizes, and ship types (exponential, normal,
and discrete probability, respectively) in the simulation model were
selected on the basis of goodness of fit testing (chi-square technique)
against observed operating data from the port. These data included the
actual times between ship arrivals, load sizes in tons, as well as the
distribution of ship types (i.e., bulk carriers versus tankers) arriving
at the blending plant.
In the last segment of the Monte Carlo sequence of the ship
sub-model, each ship is randomly identified as either a bulker or a
tanker, based on a two-interval cumulative distribution frequency,
giving 75 percent bulkers and 25 percent tankers. (1) In addition, the
larger a vessel, the faster it should load by design. The program logic
of the ship sub-model identifies the type of vessel and then tests the
size of respective vessels, which were of three size categories. The
larger the ship, regardless of type, the faster it would load.
[FIGURE 1 OMITTED]
Ship waiting times are a function of the scheduling performance
between successive ship arrivals achieved by terminal operators (i.e.,
better scheduling results in less carrier waiting and less inventory). A
good schedule would have an incoming ship arriving at the blending
facility just when the preceding vessel had finished loading in
just-in-time fashion.
Other pertinent statistics provided about the one-month simulations
include plant volume and average inventory. Work-in-process for each
simulation is influenced by the coordination of ship and rail carriers,
as well as the scheduling of successive ocean-going carriers. Monthly
plant volume is affected by a particular simulation' s sample of
randomly generated ship inter-arrival times, its sample of lot sizes,
and its sample of carrier types (i.e., bulk carriers versus tankers)
that affect loading rates and queue times.
[FIGURE 2 OMITTED]
Tactical Planning
Simulations of the selected length (each simulation with a
different sample of vessel arrivals, lot sizes, and ship types) are
repeated for a particular combination of plant capacity. One-month plant
simulations were selected as the appropriate length of computer
execution, as they were the least costly and had the same sample
variance as the longer simulations of two months and three months. The
pilot results indicated that a one-month simulation of the blending
facility approached steady state or equilibrium conditions. The
simulations were started with queues empty and facilities idle, but with
one million bushels of inventory. This mitigated the initial bias or
transient condition and allowed for a rapid achievement of steady state
operation.
EXPERIMENTAL DESIGN - RANDOMIZED FACTORIAL FRAMEWORK
The average costs resulting from the simulation model of the
blending plant can be employed as completely random sample observations
in an experimental design framework. A factorial type design was
selected to evaluate the response to a change in the capacity factors of
the transfer/blending plant operation.
Rail car unloading capacity was evaluated at three levels, whereas
the other factors were analyzed at two levels. Table 3 illustrates the
completely randomized factorial style design, which was employed to
measure the effect of capacity factors on the cost criterion. In Table
3, the cost (in dollars per ton) in each cell represents the treatment
mean for fifteen simulation runs for each of the twelve combinations of
capacity.
In the completely randomized design, each of the 180 computer
simulations was conducted at a different level of operating volume and
scheduling performance. Further, the values for volume and queue times
are not known until after each simulation is completed.
The criterion variable in this capacity analysis is a linear
function of the selected covariates, namely operating volume and queue
time. An increase in volume would be associated with lower plant costs,
whereas an increase in vessel queue times would be correlated with
higher costs. The cost (2) for each month-long simulation is adjusted
for the same volume and schedule performance by estimated covariate
values (Johnson 1998; Lattin et al. 2003).
APPLYING THE RISK-ADJUSTED DISCOUNT RATE TO SUPPLY CHAIN
INVESTMENTS
Through simulation of the intermodal transfer facility, the model
estimated the cash flows that would result from the possible changes to
that facility's capacity design. The average total cost per ton for
the various combinations of plant capacity is shown in Table 3. Each
cell in that diagram represents the mean response for fifteen
simulations, adjusted for volume and scheduling performance. Each
simulation represents a one-month operation of the port transfer and
blending system.
The average total cost per ton of bulk commodity moved through the
supply chain facility is $0.808 for the initial or current equipment
combination. Although twelve different combinations of plant equipment
were evaluated by the model, only those combinations with less than
$0.808 average total cost per ton (i.e., less cost than cell #1 or
initial facility) were considered in the financial analysis. The present
or initial facility had the low ship-loading rate, three million bushels
of storage as well as three rail unloaders.
Table 4 lists the costs and returns for the combinations of
infrastructure with lower average total cost than the initial facility
(i.e., cells #7, #8, and #9 of Table 3). The net annual cash flows were
calculated by determining the difference in average total costs between
combinations of capacity and then multiplying these net savings by the
expected annual tonnage, approximately six million tons.
The NPV and benefit/cost (B/C) ratios from the cost savings are
calculated by discounting the differential cash flows from each
equipment (capacity) alternative simulated by the computer model. The
analysis used the more conservative historical and therefore higher
discount rates of 6.89 and 7.14 percent, using the un-leveraged proxy
and industry betas, respectively (see Table 2).
It is assumed that annual savings would grow at 2.5 percent
annually, the average inflation rate over the most recent ten-year
period based on the Consumer Price Index. In Table 4, if the internal
rate of return (IRR) of a project is greater than the project discount
rate, the project should be accepted. For each cell, the NPV and B/C
ratios are reported. Upper values are based on a discount rate based on
proxy beta (6.89 percent), while lower values are computed with a
discount rate with industry beta (7.14 percent).
The financial analysis indicates that a 12 percent increase in ship
loading rate coupled with a 33 percent addition to rail un-loading would
yield the highest benefit-cost ratio (i.e., 1.248). This represents a
$1.25 return on each $1.00 invested. Increasing the ship loading rate by
12 percent provided the second best (and only other acceptable)
investment, with a B/C ratio of 1.107.
SUMMARY AND CONCLUSIONS
The incorporation of risk in capital expenditures is essential to
evaluate alternatives and capacity strategies under conditions of
uncertainty in supply chains. Rather than relying on subjective
probability distributions of estimated cash flows expected to result
from a project, The CAPM provides a mechanism to measure directly the
systematic risk of a project, which then leads to an appropriate
discount rate for the project.
This analysis estimated the cash flows produced by various
potential combinations of improvements to supply chain infrastructure
and discounted these cash flows on a risk-adjusted basis. Based on
risk-adjusted benefit-cost ratios and other capital budgeting
techniques, projects can be accepted (or rejected), as well as rank
ordered if capital is scarce. The financial manager can select discount
rates that are more conservative to match the organization's
tolerance for risk.
To demonstrate a CAPM model capable of evaluating expenditures on
supply chain facility in this example, the value for beta should reflect
the systematic risk associated with firms in the bulk commodity handling
industries. Firm can be identified that normally undertake similar
infrastructure investments. These enterprises would have systematic risk
characteristics similar to transfer and blending facilities, and the
average beta for those firms can be used as a surrogate for deriving a
particular organization's required rate of return for a logistics
capital project.
The limited availability of publicly traded firms that invest in
supply chain projects represents a constraint, limiting the accuracy of
estimating the market risk factor. Nevertheless, the practical
implication is that, when making supply chain infrastructure investment
decisions, it is advisable to adjust risk factors in evaluating such
capital investments. This approach is preferable to using a
corporate-wide hurdle rate, typically too high for such conservative
investments. A firm-wide hurdle rate might result in under-investment in
supply chain facilities.
A general or corporate-wide hurdle rate approach often fails to
accommodate different risk profiles for different projects. As
demonstrated in this analysis, port facility projects may be less risky
than other investments evaluated at the hurdle rate. If evaluated at the
hurdle rate, the projects might not be feasible, resulting in
under-investment. It is crucial that a discount rate for a project is
appropriate for the true risk of the project.
The risk-adjusted required rate is not foreign to the weighted
average cost of capital. In fact, it is part of the weighted average
cost of capital. In this case, however, we un-leveraged the estimated
beta such that it focuses only on the business risk. As argued herein,
typical ownership of these projects is by local or state governments,
and thus there are no tax shields from debt. Then, it follows that added
debt would have no impact on the cost of capital.
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ENDNOTES
(1) These frequencies were estimated by management of the port
authority. The ship loading rate is determined by its type and size,
tanker load being significantly slower than the bulk cargo vessels as
the former is designed for liquid product rather than for a dry
commodity.
(2) All economic cost estimates were calculated and validated with
the assistance of port authority's economists, accountants, and
engineers. This included waiting costs for both ships and rail cars
(i.e., demurrage), elevator fixed and variable costs, including labor
and utilities, as well as all construction cost estimates.
Mr. Moon is assistant professor of accounting and finance, Campbell
School of Business, Berry College, Mount Berry, Georgia 301449; e-mail
gmoon@berry.edu. Mr. LeBlanc is professor of business administration,
Campbell School of Business, Berry College; e-mail lleblanc@berry.edu.
Table 1. Equity Beta and Un-Leveraged Beta
Number of Equity Un-leveraged
Firms [beta] [beta]
Proxy Firms 12 0.59 0.39
Maritime Industry 28 0.67 0.44
Table 2. Discount Rates with Inputs
Market Risk T-Bond
Premium Rate
Historical 4.84% 5.02%
Forward-Looking 2.59% 4.42%
Risk-Adjusted Discount Rate
Un-leveraged Leveraged
Proxy Industry Proxy Industry
[beta] [beta] [beta] [beta]
Historical 6.89% 7.14/ 7.88% 8.26%
Forward-Looking 5.42% 5.56% 5.95% 6.16%
Table 3. Adjusted Treatment Means in Dollars per Ton to Transship
Bulk Product
Storage Low Ship Loading Rate
3 Rail 4 Rail 5 Rail
3 Million $0.808 (1) $0.827 (2) $0.821 (3)
4 Million $0.861 (4) $0.856 (5) $0.851 (6)
Storage High Ship Loading Rate
3 Rail 4 Rail 5 Rail
3 Million $0.791 (7) $0.785 (8) $0.796 (9)
4 Million $0.819 (10) $0.815 (11) $0.825 (12)
Table 4. Financial Analysis of Capacity Expansion Projects in
Supply Chain
Capacity Expected
Adjustment Cell Investment Life IRR
12 % Increase #7 $1,500,000 25 Years 7.91%
Ship Loading
12% Increase #8 $1,800,000 25 Years 9.20%
Ship Loading
33% Increase
Rail Unloading
12% Increase #9 $2,100,000 25 Years 1.85%
Ship Loading
66% Increase
Rail Unloading
Capacity B/C
Adjustment NPV Ratio
12 % Increase $160,035 1.107
Ship Loading $118,673 1.079
12% Increase $445,930 1.248
Ship Loading $389,970 1.217
33% Increase
Rail Unloading
12% Increase -$928,210 0.558
Ship Loading -$957,407 0.544
66% Increase
Rail Unloading