Gender

Voyage duration is a key variable for simulating a realistic cash flow, as it decides the number of voyages possible, fuel cost and when vessels are fixed on the next voyage. Variables affecting voyage duration in addition to distance are time spent in port, port congestion, operating speed and sea margin. In the following section, we will describe how the different variables are incorporated.

4.2.4.1 Time spent in Port

On a voyage, vessels need to both load and discharge cargo. The length of this operation varies between ports, as some ports are more modern and efficient than others. Different type of vessels will also affect time spent at port. Data used are gathered from Clarkson and are observed averages for Capesize vessels on the routes. The figures are presented in table 4.8. (Clarkson, 2012)

4.2.4.2 Port congestion

As a vessel arrives at its designated port, the time the vessel spends waiting for anchorage is an important factor to determine the duration of a trip. Congestion in bulk load ports is an increasing problem as the average waiting time has increased in recent years (DNV, 2013).

Data provided by Klaveness Chartering and Ådland shows that congestion differs quite heavily from day to day, therefore weekly averages is believed to give a better idea of actual congestion in a period. Gathering a complete dataset for all relevant ports proved to be difficult. On some ports we do not have any data, while on others the data do not cover the whole relevant period.

On ports where there is no data, the congestion is assumed to be equal to a port nearby. Table 4.8 highlights sources on congestion for each route. On ports where we missed data on certain periods, the congestion is assumed to randomly vary within a given interval based on observed

values. In addition, since congestion only has been a problem since 2006, the maximum congestion was reduced for the period 2003 to 2005.

Table 4.8: Distance and time spent at port for different routes

Route Laden

* Congestion has not been a problem in Rotterdam, and it is assumed to be equal to zero

4.2.4.3 Operating speed

Operating speed influences the time spent at sea, the fuel consumption and thus the fuel cost.

Each vessel has a designed operating speed, but this may not be the speed they operate at. There have been several studies on how shipowners can maximize their cash flow by operating at an optimal speed. Ådland (2013) suggest that Capesize vessels constantly slow steam, regardless of the theory on optimal speed choice. In the following, this level of operating speed is assumed to be 11.5 knots, and will be referred to as the charterparty speed. The model incorporates operating speed based on Baltic standard speed, optimal speed and charterparty speed, to emphasize how the cash flows and hedging efficiency are affected. Below we give a thorough description of the theory around optimal speed choice.

4.2.4.3.1 Optimal speed

Over the years there has been different studies looking at how to find the optimal operating speed. Strandenes (1981) looked at potential cost cutting from slow steaming for large tankers compared to smaller sizes and bulk carriers. Next, Ronen (1982) formulated a theoretical framework for speed optimization in subject to different operational modes. Assman (2012) tested the theoretical linear relationship between the log-speed and the logarithmic of the freight/fuel price ratio for the dry bulk and VLCC¹⁶ market. These studies show that the relationship between vessel speed (V) and the daily fuel consumption (F) can be expressed as

F = α ∗ 𝑉 In the range Vmin < V < Vmax ( 28 )

Where  α  and  β  are  vessel-specific constants that vary depending on whether a vessel is sailing laden or ballast. The speed (V) is set to vary within a minimum and maximum range. Vessels have to maintain a minimum speed for safe steering and are not able to travel at speeds above designed maximum. Maximum operating speed varies between the three vessels, but the minimum speed is assumed to be constant at 6 knots. For simplicity, the fact that charter-parties may lay restriction on the operating speed has been ignored.

As the relationship between speed and fuel consumption is in place, the next task a shipowner has to overcome is how to optimize his income, supposing that the vessel is chartered on a voyage charter. For the purpose of illustration we ignore the time spent in port and add this to the model later on. As port costs do not depend on the chosen vessel speed we can simplify the daily spot earnings  of  the  vessel  (π)  as

𝜋 = ^∗

∗

− 𝑃 ∗ 𝐹 = ^∗

∗

− 𝑃 ∗ 𝛼 ∗ 𝑉 ( 29 )

where R is the spot freight rate obtained on a voyage charter party ($/tonne), W is the cargo size (in tonnes), Pb is the price of bunkers ($/tonne) and the total trip distance is D (nautical miles).

By deriving the profit with respect to speed and set the equation equal to zero we get the optimal with theory about equilibrium in the shipping sector presented earlier. When rates are low, one way to increase spot rates is by reducing the supply of vessels. When shipowners adjusts the operating speed, this will have an impact on total supply and the prices for their services.

Exhibit 4.2: Optimal laden speed

The exhibit shows the theoretical optimal speed for the Baltic standard Capesize vessel on the C2 route (Rotterdam – Tubarao – Rotterdam) from 1/1/2003 to 12/31/2012

Exhibit 4.2 shows that prior to mid-2011 the ratio between bunker prices and freight rates was such that there was not optimal to slow steam. It is important to have in mind that this is a static

6.00

found, the vessel is set to operate at that level throughout the leg, regardless on the development in bunker prices or spot rates. The speed is updated twice for each voyage, one for the ballast leg and one for the laden leg.

4.2.4.4 Sea Margin

Time spent at sea is not only determined by the operating speed, but is also affected by weather and other delays. To account for such delays it is added a 5 percent sea margin. The sea margin influences the operating speed, and is set to reduce the operating speed by 5%. (Ådland &

Strandenes, 2004)