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The risk adjustment of required rate of return for supply chain infrastructure investments.


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.


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.


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


[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)]


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.


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 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.


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.


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.


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).


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.


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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(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 Mr. LeBlanc is professor of business administration, Campbell School of Business, Berry College; e-mail
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
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Author:Moon, Gisung; Leblanc, Louis A.
Publication:Transportation Journal
Date:Jan 1, 2008
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