Evaluation of a Stochastic Freight Rate Model for Valuating Shipping Companies

Jesper Feldthaus

Student thesis: Master thesis


The valuation of companies in volatile markets is problematic using the discounted cash flow model, because the forecasting of revenues often relies on the analysts’ guestimation of a revenue growth rate. In the thesis “The Valuation of Shipping Companies – A Stochastic Freight Rate Valuation Model” by A. D. Rasmussen a one-factor stochastic process for forecasting freight rates is developed, that in conjunction with a company’s portfolio of ships will generate possible revenues for the DCF model. By applying a Monte-Carlo simulation to this process it is possible to obtain a share price distribution instead of the best, base and worst case scenarios otherwise used. In his thesis Rasmussen only tests the model on a single shipping company and ends up with a fairly good result. The purpose of this thesis is to evaluate whether or not the model developed by Rasmussen is generally applicable in the valuation of shipping firms regardless of their firm-specific characteristics. This is done by applying the model to five different shipping companies with different financial structures and fleet portfolios. The thesis starts out by explaining the components of the mean reverting stochastic process that drives the simulation of the freight rate indices; then moves on to describe the state of the shipping industry using Porters Five Forces framework, before applying real world data to the model and examining the results. The model simulates 8 freight rate indices in total. 4 in the dry-bulk market and 4 in the wet-bulk market. The markets are assumed to be uncorrelated. The valuation of the five companies is done retrospectively, with a valuation date in mid 2009. This is in part done to back-test the models estimated revenues with the actual reported revenues for the companies in the period. The model performance is evaluated based on its ability to generate precise share price estimates and accurate revenues, though the precision of the share price has been given the most weight in the final assessment. To measure precision and compare it between companies the relative standard deviation has been used. In assessing the accuracy and precision of the results for each company it was found that the accuracy of the revenue estimation to a large extent depended on the accuracy of the analyst’s expectations for the development in the fleet portfolio; effectively moving the analyst guesstimation of a revenue growth rate to a guesstimation on fleet development. This is however considered to be a simpler task to accurately estimate due to the fact that most companies do have fairly good estimates of their future fleet development listed in their annual reports. The model was found to be applicable to all five companies, though the quality of the results produced varied greatly from company to company. A range of sensitivity analysis has been conducted on the size of the fleet portfolio and the amount of debt carried. A linear relationship between revenue and fleet size was found, confirming the expectations from the model results. Furthermore the amount of debt carried by the companies, and consequently their WACC was found to have a profound impact on the models ability to generate precise share price estimates. In conclusion the accuracy of the revenue estimates is considered to be dubious – at best. And that the fairly precise result obtained by Rasmussen had as much to do with the financial structure of the company he was valuating as the stochastic generation of freight rates. It could not be concluded that the results produced by the model provided better results for an analyst compared to that of a classic DCF model. The information contained in the analysis and estimation of the share price distribution is however very interesting for other fields, such as risk management.

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
Publication date2013
Number of pages135