# Natural resource options

Natural resource companies provide cash flows from their reserves. Even they can have cash flow from their undeveloped reserves by developing them. For example, If price of oil resource raises, oil companies would be able to have a good position to develop their undeveloped reserves by using call options. However, most this kind of such investment for developing the resource causes an initial expense for the companies. This payoff is similar to a call option. This expense calls as development cost. Stern J. and Chew D. (2003)(P.96) states that The cost of development as X, and the estimated value of resource as V, the potential payoffs on a natural resource option can be written as follow:

=V-X If V bigger that X, or

=0 If V equal to X

### Real-option valuation

### Why many oil companies use Real-option valuation

Most of Oil companies prefer to use Real-option valuation (ROV) in order to decide better options for company so that it can be often seen that they usually take into account to it as complimentary to techniques such as discounted cash flow (DCF) to assess their investments. ROV provides more parameter details which give efficiency to take future actions.

This approach has been supported with example of Texaco;

In the mid-1990s, the executive management of Texaco was split over what to do with a significant lease-holding in a developing country. The lease included several existing oil discoveries and many other substantial undeveloped discoveries.Part of the management team want to sell the asset, while others on the team want to carry on with it. The company management used ROV to decide which option will give benefit to the company. Result from the ROV was that the asset was far less valuable that suggested by DCF. Texaco believed that ROV helped its executives reach a better understanding of its holding. It is clear that ROV help to see investment opportunities.

Real-option analysis bases on the theory of financial options. This option gives the owner the right to buy or sell a specific asset at a fixed price and at before ending date of option. When the buyer prefers to exercise his right, this calls exercise price. The option is partitioned into two parts; call options and put options. A call options often uses in natural reserve area.

### Call option

A call option provides holder to buy a specific asset at fix price at any time prior before ending date of option. This option is known as the strike or the exercise prise in the stock market. The problem is that it is very hard to find the opportunity for cost of capital as risk of an option is very fluctuated. Furthermore, regarding this option if the value of the asset is lower than exercise price, option is not used. However, if the value of the asset bigger than exercise price option is used. The real option is determined to find the value of the future option. In the past there was the only one way to value call option that was buying and selling options until Black-Scholes Formula stared to use for valuing options.

### Black-Scholes (B/S) Formula

Fischer Black, Myron Scholes and Robert Merton created the famous formula of Black-Scholes. It calls European call option as well. They generated that it was likely to value the worth of option by constricting a copy of portfolio, which contains a numeral of shares in the underlying asset and a numeral of risk free. Black-Scholes Formula indicates the interest of the investment opportunity.

The full Black-Scholes Formula for call options can be written as below:

C0 = S0e-6TN(d1) - Ke- rTN(d2)

ln(S/X) + (r+ q 2/2)T q √T

d2= d1- q √T

N(D1)= D1 N(D2)=D2

V= Value of assets

S/q = Current value of the asset

X/K = Strike/exercise price of the option

r = Risk-free interest rate

y = Dividend rate

t = Time to expiration of the option

Using real option state where N(d) is the probability that a random draw from a standard normal distribution (where the mean is zero and q is one) will be less than d. "e" is the base for the natural logarithm (e = 2.718...) and "ln" is the natural logarithm.

The process of valuing options with the Black-Scholes model involves the following steps:

- Step 1 Used the inputs for the five variables listed above to estimate d1 and d2,
- Step 2 Used d1 and d3 to estimate the cumulative normal distribution functions N(d1) and N(d2),
- Step 3 Estimate the present value of exercise price ,
- Step 4 Estimate the value of the call with the Black-Scholes formula.

### Assumptions;

These formulas illustrate that real options give a way of valuing project in term of future advantage and can be used to assess value of real option. The formulas provide information for ongoing projects whether companies abandon the projects or continue with it. They show their investment benefit so that it can be said that this formulas are suitable to answer the above mention the interest of investment opportunity question.

Your rich uncle has left you a one third interest in an offshore oil property with estimated reserves of 50 million barrels.

The present value of the development cost is $12/bbl, and the development lag (the time between when development begins until the wells begin producing) is two years.Your uncle's partners have an option of up to twenty years to develop the resource, and the marginal value per barrel is at present $12.

Once developed, net production revenue each year will be 5 per cent of the value of the reserves. The riskless rate of interest is 8 per cent and the variance in the ln (natural logarithm) of oil prices is 0.03.

### Interpretation:

The project of the investment opportunity in the stock market is that a twenty year of this project worth 544.22 ( current value for the asset) and exercise price is ( -600) as that it indicates that the project has a negative static of NPV -55.78 : (-600)+544.22=- -55.78 it can be seen that 2 year time might not be enough to be available for sale. The cost of delay would create lost of manufacture revenue

Regarding Black-Scholes model which was mentioned above; current price 50 million is changed, this oil reserve is still a good investment as current price increase with call value from $50 million to $97.08 million. This situation indicates there is lack loss in the company. Moreover, the product can be exercised during 20 years. The investment opportunity could have worth about $ 97millions

Today. Moreover, If more time is given for a project more likely present event could influence current price option. Therefore, If the time increase this situation gives positive effect on the option and negative effect on present value of exercise price. As it can be seen above project that time to expiration on option is quite long.( 20 years) Therefore, Call value increases as the unpredictability of stock increase and cost of developing reserve decrease in a long period time.

### Conculation

- (2003). The Revolution in Coporate Finance. In S. J. D., The Revolution in Coporate Finance (4th ed) (p. 92). Blackwell.
- Finance, T. P. (2000). In R. A. Brealey, The Principles of Corporate Finance (7 Edition) (pp. 601-608).
- REAL OPTIONS APPROACHES IN VENTURE CAPITAL FINANCE . (n.d.). Retrieved 11 12, 2009, from http://www.realoptions.dk/PDF/essay3.pdf