1 Introduction
Currently, Discounted Cash Flow method is the most popular valuation instrument. However, questions still arise whether the discounter cash flow is the best tool which presents a more accurate valuation. Critics have argued that the DCF model neglected the management’s ability to adjust the business strategies according to the market situation. They claim that the real option valuation incorporates the management abilities into the valuation process. For example, the oil price fluctuates frequently and it is feasible to expand the oil excretion when the price is high and cease the excretion when the price is too low. These can increase the project value by exercising the “option to expand” when the oil price is high. Furthermore, it helps to eliminate the negative cash flow in the DCF model by exercising the “option to abandon”. Thus the asset value calculated by Real Option model is higher than the DCF model. Which method is more preferable? In this paper, I will evaluate the DCF model and Real Option valuation through examining some of the limitations of both models.
1.1 Discounted Cash Flow Model
The discounted cash flow is an approach to value an asset or a project by using the concept of “time value of money”, the future cash flows are estimated and discounted back to present value, the discount rate is the cost of capital incorporated with the risk of the project. In other words, the discount rate is the investors’ required return given a certain level of risk, the more risky the project is, the higher the require return and hence the lower the present value.
discounted rate is calculated by the CAPM or the weighed average cost of capital, it depends on whether the project is fully financed by equity or both equity and debts. If the project is fully financed by equity, the required return is Re which calculated by capital asset pricing model.
Re = Rf + Beta * (Rm – Rf)
Where:
Re: required return of equity holder
Rf: risk free rate
Rm: expected market return
beta: sensitivity of the asset returns to market returns or the systemetic risk. The higher the sensitivity of the asset return to the market return, the higher the Beta.
CAPM assumes that all investors have rational expectations; have same expectations about security returns in any time period where; investors can borrow as much as they want at the risk free rate, the risk free borrowing is equal to the risk free lending; return of asset is normally distributed; there is no arbitrage opportunities.
One limitation of CAPM is the estimation of Beta; it represents the risk which is undiversifiable. It is actually esitmated by the least squares regression between the stock and market return. In other words, Beta is equal to the convariance of stock’s return with market return based on historical records. So beta itself has some error. Besdies, Levy (1978) shows that the systematic risk is not the only risk paid by the investors when the investors can only hold a limited noumber of different stocks. As such, we can not overlook the unsystemetic risk in the CAPM. In addition, Fama and French (1996) demonstrated that the size of company and the book to market ratio should also be taken into account when calculating the require return of the investors. In sum, opportunity for improvement exists in the current CAPM. Additional shortcomings of DCF model will be discussed later.
If the project is financed by both equity and debt, then the required return of the investor is the weighted average of Re and the required return of debtor denoted by Rd
WACC = E/V * Re + D/V * Rd * (1 – T )
Where
WACC: Weighed average cost of capital
E/V: ratio of equity to total value
D/V: ratio of debt to total value
Rd: require return of debtor
T: Tax rate
It is rational to use weighed average cost of capital when projects are financed by both equity and debt but more problems occur: There is tax benefit when using the debt finance, but the increase of debt can cause agency problem and can increase the default risk of the company when WACC equation is not taken into account.
In conclusion, although the DCF model still remains as the most popular valuation tool for finance analysts, there appears to be some problems associated in the estimation of discount rate.
1.2 Real Option Valuation
A real option is the right, but not the obligation, to undertake some business decision. For example, the opportunties to ceason the business operation and expand the production are real options. The use of binomial tree is the main feature of the Real Option Valuation, it assumes the market price follows a geometric Brownian motion. Copeland, Weston and Shastri (2005) suggested 7 classifications of option: 1) abandonment options which the holder is able to abandon the asset by selling or cease the operation; 2) contraction options which allow the holder to “contract” the amount of asset; 3) expansion options mean the holder is able to expansion the amount of production when the selling price is high; 4) deferral options enable the holder to defer the project; 5)extension options is exercised when the holder want to extend the asset’s life; 6) compounds options can be exercised when the holder want to get another option; 7) rainbow options are used when there are multiple sources of uncertainly. There are 4 approaches of option pricing: Black-Scholes formula, replicating-portfolio approach, expectation pricing, and risk neutral valuation. The Black-Scholes formula is only applicable to the European style option. Risk neutral valuation is the most convenient way to evaluate the project embedded with American option. In actual fact, the option valuation is still using the concept developed in the DCF model, but present in the binomial tree. For example, in the risk neutral valuation, we use the risk neutral probability to calculate the expected cash flow and discounted with the risk free rate to get the present value of project. This is actually applying the DCF concepts. So, does the small conceptual difference of DCF and Real Option Valuation generate very large difference in the values of a project?
2 Comparisons of Real Option Valuation and Discounted Cash Flow Valuation
In this section, I will present the valuation of oil project by using the discounted cash flow model and the real option valuation; in both cases, I adopted the risk-neutral method developed by Merton (1973), Black and Scholes (1973): utilize the risk- neutral probabilities to calculate the expected cash flow and discounted with the risk free rate. As the effect of change in expected cash flow and the require return exactly cancels each other out, the answer is the same as by using the real world probabilities to estimate the expected cash flow and discounted with the risk adjusted cost of capital. In the risk neutral valuation, it assumes the investors are risk neutral and don’t require higher return for riskier investment, hence the appropriate discount rate is just the risk free rate. By applying risk neutral into both DCF and Real Option Valuation, I can clearly show that the major different between the DCF method and Real Option method is the ignorance of management abilities in the DCF method.
2.1 Example 1
A company discovers 5 million gallons of oil under the sea; assume it is going to excrete 1 million gallons per year and the free cash flow in year 0 is equal to zero, hence this is a 5 years project. There is 52% chance for the oil price to go up by 17% and 48% to go down by 10% per year (the real world probabilities are irrelevant). The risk free rate is 6%, the variable cost is $40 per gallon and the fixed cost is 10 million per year, the price of oil is $60 at year 0 (Assume the company can abandon the project in any year with no cost.) Table 1 shows the market price of oil. The free cash flow received by the firm is presented in table 2
Firstly, let’s calculate the risk neutral probability (P*) which will be used in the DCF model and Real Option Valuation.
u: the upward movement of oil price= 1.17
d: the downward movement of oil price = 0.9
r: the risk free rate = 0.06
t?lt;/em>: the number of year per step = 1
Thus, P* = (1.061836547 – 0.9) / (1.17 – 0.9) = 0.5994
(1- P*) = 0.4006
Remark: P* is the risk neutral probability for the oil price to increase by 17%, thus (1-P*) is the risk neutral probability for the oil price to decrease by 10%
Discount Cash Flow
Table 3 shows the value of the oil project in each year by using the idea of discounted cash flow method. Traditionally, when using the DCF method, we have one expected cash flow in each period and discount with a single rate of return. In this example, I have adopted the risk neutral probabilities instead of the real world probabilities, so the payoffs are discounted with the risk free rate at each node. For example, on the top of period 4, the project is valued at 127.8916 Million, it is estimated by calculating the expected payoff using risk neutral probability and discount with risk free rate, then plus the cash flow received at the node in period 4:
Value on the top node of Period 4:
(0.5994 * 81.54688 + 0.4006 * 51.18991)/1.06 + 62.43323
= 127.8916
Repeat the above process and we finally reach $90.94599 Millions in period 0 which is the present value of the project as shown in table 3.
Real Option Valuation
Table 4 estimates the value of project in each year by using the Real Option Valuation, the calculation is the same as the DCF but it considers the option to abandon, when the project value is negative, instead of taking the loss, the manager simply abandon the project and received zero payoffs. So the last 2 nodes of period 5 are both 0 instead of -3.94178 and -14.57. One may asks in period 2 of table 2, there is a negative cash flow of -1.4, why don’t we abandon the project at that node? Since there is positive gain to continue the project, the third node of period 2 have a value of 15.4371 which is the present discounted value of all the future expected cash inflow. The value of the project is 91.63416 Millions by using the Real Option valuation.
Compare the result of DCF and Real Option Valuation
The present value estimated by Real Option Valuation is 91.63416 millions when the present value calculated by DCF is 90.94599. The difference is 0.76%. One may argue that the small difference is not convincing for analysts to switch to the Real Option Valuation, also there is some cost to abandon the project in reality, as a result traditional DCF should be used. However in my example, I assume there is only option to abandon. There is also option to expand the oil excretion, when the price of oil raise, manager can increase the amount of oil and thus increase the cash flow. Besides, if the project length is longer, the Real Option value is much higher than the DCF value because it will have more negative cash flow to be eliminated. In addition, the larger the fluctuation of the oil price, the higher the option value:
2.2 Example 2
Consider the following example, the oil price is either increase by 17% or decrease by 15% and keep any other assumptions constant as the above example. The market price of oil, free cash flow, DCF and Real Option Valuation are shown in table 5, 6, 7 and 8 respectively.
The risk neutral probability becomes:
P* = (1.061836547 – 0.85) / (1.17 – 0.85) = 0.662
(1- P*) = 0.338
In this case, the value generated by the Real Option valuation is 92.61111 when by the DCF method is 90.94782. The difference is now 1.83%, compared to the 0.76% in the first example. To sum up, the DCF model ignores the option value which is crucial to the accurate valuation. We should adopt the Real Option Valuation especially when the price fluctuates strongly or the project length is long.
In the above examples, I did not use the traditional DCF model which includes the risk adjusted cost of capital because my aim is to show that the difference of the 2 valuation methods is the unawareness of the options in DCF method.
As I mentioned before hand, the Real Option Valuation is structurally based on the DCF model. In fact, a more appropriate name for the Real Option Valuation of a project should be “Discounted Cash Flow Valuation incorporated with Option”.
3 Shortcomings of DCF and Option Valuation
One limitation of DCF model is the lack of knowledge in management abilities. Berger, Ofek and Swary (1996) compared the market value of stocks and the value estimated by DCF model for 7102 firms from 1984 to 1990. Evidence revealed that the DCF valuation undervalues the stock and the difference is due to the ignorance of option value. The real option valuation can solve this problem but as Real Option Valuation is similar to DCF model except the incorporation of management abilities, they share similar shortcomings. For example the risk in each period is different when constant discount rate is used in both methods. Besides, the cash flows are the only expected values, so inaccuracies are unavoidable.
Conclusion
Increasingly, researchers have showed that DCF model undervalued the market values of stock, land and natural resources like oil. In today’s world, computers provide us with the most current information from the internet. In my opinion, management abilities add more value to the asset today when compared to the past because market information is more readily distributed. Subsequently DCF model is less accurate when compared to the Real Option Valuation nowadays. Managers should take up the Real Option Valuation instead of the DCF model especially when the length of option is long and the fluctuation of price is large. The DCF model doesn’t take the option value into account when the Real Option Method does; this is actually the only conceptual difference between the 2 models. As a result, it can be said that they share similar shortcomings.
References
Berger, P., Ofek, E. and Swary, I. 1996. Investor Valuation of the Abandonment Option. Journalof Financial Economics 42: 257-281
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Copeland, T.E., J.F. Weston and K. Shastri, 2005. Financial Theory and Corporate Policy, Pearson Addison Wesley, USA.
Fama, E. F. and K. R. French: The CAPM is Wanted, Dead or Alive. The Journal of Finance, vol. 51, n”aƒn5, 1996, pp. 1947-1957.
Levy, H.: Equilibrium in an Imperfect Market: a Constraint on the Number of Securities in the Portfolio. American Economic Review, vol. 68, n”aƒn4, 1978, pp. 643-658.
Merton, R.: Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science, Spring 1973, pp. 141-183.
