A Real Options Approach to Ship Investment Appraisal

Review

A real options approach to ship investment appraisal

Floriano C. M. Pires 1, Luiz Felipe Assis 1 and Mauro Rezende Fiho 2*

1Ocean Engineering Department, Rio de Janeiro Federal University, Brazil. 2Production Engineering Department, Gama Filho University, Brazil.

Accepted 5 March, 2012

Initially, this paper presents a methodology for analysis of investment in a tanker ship, based on Monte Carlo simulation of auto-correlated series of time-charter rates and prices of new building and second hand ships. Subsequently, a real options analysis is introduced, considering the possibility of project abandonment. The method is employed for evaluation of the investment in a suezmax tanker. The results indicate that the investment analysis outcome is significantly sensitive to the consideration of the managerial flexibility to project abandonment. Finally, the paper discusses the effect of the decision maker’s risk attitude on the abandonment option value.

Key words: Shipping investment appraisal, real options, risk attitude.

INTRODUCTION

The shipping sector is peculiar in terms of the investment options in response to future events in the uncertain rationale and investor behavior. The cyclical nature of the environment of shipping markets. Some other authors market, its extreme volatility and the international have also dealt with ROA in ship investment decision character of the operations are the main factors that making (Bendall and Stent, 2005; Dikos (2008). confer unique characteristics to the sector. The rationale The present paper presents a methodology for ship behind the investment decision varies according to the investment analysis, considering the abandonment different shipping sectors, as well as the types of players. option. A typical tanker ship investment decision problem For example, decision criteria and available information is analyzed on the basis of Monte Carlo simulation of the vary between a container operator and a bulk carrier future behavior of time-charter and second hand prices. shipowner. An oil company willing to implement a The contribution of this work is two-fold: it proposes a logistical strategy and an asset player would also have simple and practical approach and discusses the effect of different approaches to investment decision making. The the tanker investor’s risk aversion on the abandonment nature of the ship investment problem has been studied option value. This significant effect was not considered by many authors, such as Klausner (1970), Haralambides before in the literature. (1993) and Thanopoulu (2002). Initially, an alternative Monte Carlo approach to Real options analysis (ROA) is nowadays largely investment analysis in oil tankers is presented. Next, the applied for evaluating investment decisions under method is adapted to incorporate the option to abandon. uncertainty. Particularly, in the shipping sector, ROA has Finally, the article raises and discusses the issue of the been increasingly applied. Gonçalves (1993) has impact of decision maker’s risk aversion on the option pioneered the application of real options approach in value. shipping economics. More recently, ROA has been recognized as a suitable methodology for shipping investment analysis. ANALYSIS OF INVESTMENT IN OIL TANKERS Bendall (2002) presents an overview on ROA applicability and a discussion on the relevant managerial The present study considers the case of an oil company that runs both owned and chartered ships. The parcel of

the demand for maritime transport that the oil companies *Corresponding author. E-mail: [email protected]. engaged in the international market fulfill with owned

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Table 1. Daily operational costs. present a complex autocorrelation pattern. Therefore, the pairwise estimation of correlation coefficients would H&M insurance 3.49 not lead to a satisfactory modeling. The behavior of the P&I insurance 0.72 average annual time charter rates is better described Maintenance & Repair 2.49 through an autocorrelated time series model. The same Store/Supplies/Spares 1.48 argument applies to the ship price series. Administration 0.94 Thus, an alternative approach will be proposed, based Total Operational Costs 9.12 on the simulation of autocorrelated series of time charter rates, new building and second-hand ship prices. In order to estimate a model for the average annual rates of 1-year time charter contracts, data obtained from Clarkson (2011) during the period between 01/1981 and 60 12/2010 will be used. Corrected 50 Since the period is long, it will be necessary to correct Observed the values and take the inflation rate of the American 40 dollar into consideration. The consumer price index will

30 be used (U.S. Department of Labor, 2011). The same procedure was used to new building and second hand 20 series. Figure 1 shows the 1-year time charter series

US$ thousands/day US$ 10 observed in U$S and corrected to US$ (December, 2010). 0 This analysis will require the estimation of the residual

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 value of 15-year-old ships, which will be calculated based

on the value of a 5-year-old ship, through an exponential Figure 1. Suezmax Tanker 1 year time charter rate (1981 to 2010). decay function. In order to model the series of time charter rates, and new building and second hand prices, three models were compared: mean reversion, exponential smoothing and ships depends on the risk management strategy. ARIMA. Table 2 shows the respective square errors. The The problem is to decide if a ship should or should not errors have been estimated for a validation set formed by be bought to substitute an equivalent chartered ship. It is the last 24 observations (the first 336 have been used for supposed that the decision of operating a ship with these estimation). specific characteristics has already been taken. The ship The mean reversion model, which best fitted to data, under analysis will be a typical suezmax, with 150,000 has been adopted. Its mathematical expression is the dwt, which will be incorporated to the fleet either through following: purchase or chartering. There is a significant uncertainty associated with __ -2η∆η∆η∆ t -tη∆ -t η∆ 1 - e running costs. Nevertheless, ship prices and time charter Xt = X t-1 e + X(1 - e ) +σ 2ηηη rates exhibit much higher volatility. Therefore, the latter 1442443 are the uncertainties that dominate the decision problem. N(0,1) In the following discussion, the running costs will be considered as deterministic. The running costs, considered constant within the period of analysis, have Where: η – speed of reversion, X - average of the been estimated with reference to Drewry (2011), and are period, ∆t – time interval (in this case 1). indicated in Table 1. The most frequently employed method for investment In order to determine the value of η, a nonlinear analysis under uncertainty is Monte Carlo simulation programming model for square error minimization was (Klausner, 1970; Hertz, 1983). The models depend on employed. This way, the average speed of reversion was the probability distribution of the random variables, which determined for each series: should capture all relevant sources of uncertainty. In the -5 present case, the random variables will be the residual Time charter (TC) ηTC = 0.11781 x 10 -5 value and the 1-year time charter rates, between the New building (NB) ηNB = 128.981 x 10 -5 years 1 and 15. Second hand (SH) ηSH = 12.4726 x 10 In the conventional models, the correlation coefficients are introduced as inputs, when there are correlated The simulation of the series will be based on the variables. generation of pseudo-random series for the white noise The problem here is that the time charter rates series processes in the expressions:

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Table 2. Alternative models of time series – square error.

Square error Variable Time Charter New Building Second Hand Mean reversion 131.48 201.74 346.19 Exponential smoothing 804.07 901.78 1,098.52 ARIMA 381.59 (1, 2, 1) 452.28 (2, 2, 1) 504.64 (1, 0, 1)

Table 3. Observed correlation coefficients. period, it will be necessary to ensure that the correlation pattern is compatible with the observed. For that, the New Second Variable Time Charter Cholesky Decomposition Method has been used Building Hand (Scheuer, 1962). Figure 2 shows a subset of the time- Time Charter 1 charter annual cost series minus the running costs, in New Building 0.09769 1 order to illustrate the behavior of the sample.

Second Hand 0.76729 0.83289 1 In the conventional discounted cash flow approach, a risk-adjusted discount rate should be taken to net present value (NPV) calculation. The risk-adjusted rate is the sum of the risk-free interest rate, used to discount for the time value of money (pure discount) and a discount risk 14 premium, used to compensate for the risk associated with 12 the project (Trigeorgis, 1996; Dragot ă and Dragot ă, 2009). This rate, which can be determined by the capital 10 asset pricing model (CAPM), depends on parameters that 8 may be difficult to determine. However, when the probability distribution of NPV is derived from Monte 6 Carlo simulation of future cashflow, the risk-free rate 4 should be used, as discussed for example, in the seminal work of Trigeorgis (1996). In the following analysis, the

Time charter Time costs annual 2 discount rate I = 6% would be applied. This figure 0 corresponds to a risk-free interest rate estimated for the Brazilian economic environment. Nevertheless, in order 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 to assess the sensitivity of the result to the discount rate,

Figure 2. Simulation of the time charter annual costs minus the the following analysis will be performed considering three running costs - million US$. different rates: 4, 6 and 8%. For each element of the sample, formed by the set of simulated series, the NPV is calculated through:

15 TC TC e−ηTC TC (1 e −η TC ) 1 RV t= t− 1 ⋅ +⋅− +ε t NPV= (TC −× C ) + − NB ∑∑∑ K opk 15 0 k=== 1 (1+ i) (1 + i) NB= NB ⋅ e−ηNB +⋅− NB (1 e −η NB ) +ω t t− 1 t Where: TC = Time charter annual costs, C = Annual k op fixed costs, i = Discount rate, RV = Residual, NB 0 = New −ηSH −η SH SHt= SH t− 1 ⋅ e +⋅− SH (1 e ) +υ t building price value. Table 4 presents the descriptive statistics of the NPV samples resulting from the Monte Carlo simulation, for Where: TC t = time-charter rate in year t, NB t = price of the new building in year t, SH = price of the 5-year-old-tank the three levels of discount rate. The main results, for t supporting investment decision are the expected value of in year t, TC, NB,SH = mean values of the series, εt, ωt, υt NPV and the risk, which can be measured by the = white noise (N(0,1)), ηTC , ηNB , ηSH = reversion speeds. probability of NPV resulting negative (p[NPV<0]). The TC, NB e SH series presented the correlation Figure 3 shows the normal distribution fitted to the coefficients indicated in Table 3, in the sample of 360 sample data. The results show the extremely significant observations, between 01/1981 and 12/2010. impact of the risk-free discount rate on the investment To simulate the series for the 15-years useful life decision.

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Table 4. NPV distribution resulting from the simulation – exercise of the action under pre-established conditions. million US$. When the holder buys an asset we call it call option , and when he/she sells it we call it put option. The pre- Statistics Fit Data established price is called exercise price or strike price. Mean 0.0688 0.0691 An option that may be only exercised at its expiration Median 0.0707 0.0691 date ( maturity date ) is called European option, while an Std. Deviation 0.0218 0.021 option that may be exercised at any time before the Skewness -0.4625 0 expiration date (at the life of the option) is called Kurtosis 3.1858 3 American option. A call-option is in-the-money for the holder if the current market value of the underlying asset is above the exercise price of the option, while a put option is in-the- money if the current market value of the underlying stock 0.6 is below the exercise price. Otherwise, the option will not

0.5 Year 0 be exercised. Year During the useful life of the project, the real options 0.4 analysis incorporates the flexibility associated to strategic

Year 10 decisions to the evaluation of investments made through Year 15 0.3 the discounted cash flow method, from an analogy with

Probability financial options.

0.2 Probab i l ity The origin of the term "real options" can be attributed to Myers (1977), who first identified the fact that many 0.1 corporate real assets can be viewed as call options. It 0 was the beginning of a new approach to the investment

77 93

0.00 analysis, based on the analogy between an option and 0. 2.31 4.62 5.39 6.16 6. 7.70 8.46 9.23 1.54 3.08 3.85

9.99

14.30

0,00 0 ,77 1,54 2,31 3,08 3 ,85 4 ,62 5,39 6,16 6 ,93 7 ,70 8,46 9,23 9 ,99

1 0,68 11 ,29 11 ,99 12,76 1 3,53 14 ,30 15 ,07 the managerial flexibility for strategic decision making in 11.99 2.76 11.29 15.07 10.68 3.53 15.84 Time charter annual costs an investment project. A company with an irreversible investment opportunity Figure 3. Evolution of the distribution of time-charter annual costs. has the option to defer the investment (option to delay). It has the right, but not the obligation, to buy a product (the project) in the future for the exercise price (initial investment). When the company invests, it exercises the In the previous analysis, like it is normally done in option and pays an opportunity cost equal to the value conventional discounted cash flow (DCF) method, it was invested. supposed that, once the investment is made, the tanker The exercise of the option (investment) is irreversible, will operate in the same conditions during the whole but the company has always the possibility to delay the useful life. Actually, this hypothesis does not represent investment, until the market conditions become more the reality. The analysis can be improved by the advantageous, and more information about the project introduction of the abandonment option. That is, by and the factors that influence it could be obtained, in considering a new model, in which the project could be order to reduce the uncertainties. reevaluated in certain intervals, and, in case of poor A capital investment project can be seen as a set of performance, abandoned by selling the ship for the real options. Among which we can mention the options to market price. defer, abandon, or interrupt the project; cancel new stages of the investment; and alter the production scale (expand, contract, shut down temporarily, restart), the ANALYSIS OF INVESTMENT IN OIL TANKERS WITH uses (entry and exit) and the growth options (Trigeorgis, ABANDONMENT OPTION 1996). The real options analysis is complementary to the net In the financial market, an option is the right, but not the present value, including the flexibility value, or the options obligation, of the holder to perform a certain action, at a value, in the calculation of the NPV: pre-agreed price, on a given date. The agent who TOTAL FINAL NPV = PROJECT’S NPV + OPTION’S “launches” the option has the obligation to buy or sell the VALUE object of the option (bonds, commodities, stocks or similar products), under the conditions established, if it is Thus, a project with negative net present value may be the buyer’s wish (Dixit and Pindyck, 1994). viable, if the managerial flexibility is considered, such as The launcher receives a premium as soon as the option the possibility to defer, expand or abandon the project is sold, since he/she has taken the risk of assuring the after the implementation.

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The real option analysis has already been proposed by NormalNormal (8.0632;24.316) ( 8,0632;24,316) many authors as a solution for decision problems in shipping. Two works in particular should be mentioned. 0.018 Gonçalves (1993) proposed a real options approach for 0.016 investment decisions and ship chartering strategy 0.014 Input planning. The hypotheses of the work are too restrictive, 0.012 Normal but the mathematical model proposed brings an interesting and pioneering approach. Bendall (2002) 0.01 presents a discussion on the applicability of the real 0.008 options in ship investment analysis. 0.006 In the previous section, the investment in a crude oil 0.004 tanker was analyzed under the hypothesis, implicit in the conventional DCF method, that, once the investment is 0.002 made, the tanker will operate during the whole useful life 0

20 40 60 80 period. -80 -60 -40 -20 40 40 0 20 20 60 80

100 -10 0 -20 -20

-60 -60 -40 100 - -80 -80

This analysis can be clearly improved, as a way to

bring the model closer to reality. It is important to Figure 4. NPV distribution resulting from the simulation – million consider that in case of unfavorable market conditions or US$. negative expectations, the investor has the option to abandon the project by selling the tanker, as a way to reduce or avoid greater losses. In the sequence, the model will be modified to consider NormalNormal(0,069072;0,021014) (0.069072;0.021014) the value of this option. The new model will be based on 0.250,25 the hypothesis that the investor will reevaluate the project th th every five years (that is, in the 5 and 10 years), 0.200,2 Input deciding between continuing with the project and selling Normal 0.150,15 the tanker. This model is able to identify the principal effect of the managerial flexibility and the value of the 0.100,1 information acquired throughout the project. Probability Probability To simulate the decision to abandon or continue with Probability 0.050,05 the project in year 5, a sample of NB, TC and SH series th th 00 is generated for the period between the 5 and 15 years 4 1 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14

with the information available in year 5 for each 0. -0,06 -0,04 -0,02 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 -0.04 -0.04 -0.02 -0.02 observation of the sample that was initially generated for -0.06 Interest rate Interest rate the series between the years 0 and 15. The expected value E(NPV 5) is calculated for each simulation scenario Figure 5. IRR distribution resulting from the simulation. for the period between years 0 and 15, from samples resulting from cash flow simulation for the period between years 5 and 15. To simulate the abandonment or abandonment option. continuation decision-making process, it is necessary to know the minimum value accepted by the decision maker, which will be called NPV base . RISK ATTITUDE AND REAL OPTION VALUE If E(NPV 5)

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Table 5. IRR distribution resulting from the simulation. does not consider important elements related to the managerial flexibility present in many investment Statistics Fit Data projects. The present work has proposed a Monte Carlo Mean 0.062 0.062 approach, taking the option to abandon into Median 0.062 0.066 consideration. The case of a tanker with a useful life of 15 Std. Deviation 0.035 0.035 years was analyzed, with an option to abandon in years 5 Variance 0.001 0.001 and 10. Skewness 0 -0.501 The consideration of the abandonment option can Kurtosis 3 3.443 significantly affect the indicators that support investment decision making. In fact, projects that would be rejected by the conventional approach can become viable, if the managerial flexibility is taken into consideration. Particularly, in the case of investment in oil tankers, the Year5 Year 10 conventional discounted cash flow analysis is demonstrated not to be able to provide useful elements for practical decision making. Finally, the analysis evidenced the effect of the decision maker’s risk attitude on the value of option to abandon.

REFERENCES

Bendall H (2002). Valuing Maritime Investments Using Real Options

Figure 6. Simulation of the decision of abandonment in year 5 and Analysis - in the Handbook of Maritime Economics and Business. LLP, London. year 10 – structure of the sample. Bendall H, Stent AF (2005). Ship Investment under Uncertainty: Valuing a Real Option on the Maximum of Several Strategies. Marit. Econ. Log., 7: 19-35. Clarkson - Shipping Intelligence Network (2011). Clarksons Research Studies, United Kingdom. (www.clarksons.net). NPV x Option Value Dikos G (2008). Real options econometrics for aggregate tanker 9.00 investment decisions. Int. J. Ocean Syst. Manag., 1(1): 31-44. 8.50 Dixit RK, Pindyck RS (1994). Investment under Uncertainty. New Jersey: Princeton University Press. 8.00 Dragot ă V, Dragot ă M (2009). Models and Indicators for Risk Valuation 7.50 of Direct Investments. Econom. Comput. Econom. Cybern. Stud. 7.00 Res., 43(3): 69-76. Drewry (2011). Investments in Ships, Drewry Shipping Consultants. 6.50 England. (www.drewry.co.uk). 6.00 Gonçalves FO (1993). Freight Futures and Chartering: A Contingent 5.50 Claims Analysis Approach Applied to Optimal Operational and Investment Decisions in Bulk Shipping. In Current Issues in Maritime Optio n value (US million)5.00 Economics. Kluwer Academic Publishers. Option value (US$ million) Option value million) (US$ 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Haralambides H (1993). Sensitivity Analysis of Risk in Shipping NPVbase (US million) Finance. In Current Issues in Maritime Economics – Kluwer Academic Publishers. Figure 7. Value of the abandonment option in the years 5 or 10 and Hertz DB, Thomas H (1983). Risk Analysis. J. Wiley and Sons. attitude towards risk. Klausner RF (1970). The Evaluation of Risk in Marine Capital Investment. Mar. Technol., Oct. Myers S (1977). Determinants of Capital Borrowing. J. Financ. Econ., 5: 147-175. Scheuer E, Stolle D (1962). On the Generation of Random Normal. The results indicate how significant is the effect of the Vectors-Technometr., 4: 268-281. investor’s risk attitude in the option value. Also, the Thanopoulu H (2002). Investing in Ships: An Essay on Constraints, Risk impact of the risk-free discount rate on the option value is and Attitudes. In The Handbook of Maritime Economics and Business evidenced. – LLP – London. Trigeorgis L (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation – The MIT Press, Cambridge, MA. U.S. Department of Labor (2008): www.bls.gov/bls/inflation.htm. CONCLUSION

The real options analysis has been used as an alternative to the traditional discounted cash flow approach, which