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Dividend
Table 5.9: The similarities between a stock call
al., 1988) UNDEVELOPED RESERVES
Current value of developed reserves
Development cost
Relinquishment requirement
Riskless rate of interest
Net production revenue less depletion
option and undeveloped reserves (source: Paddock et In practice, the key to applying options is in defining the options that are actually
available to management. Trigeorgis (1996) lists a whole range of managerial options
covering research and development and capital intensive industries, as well as oil and
mining. Dixit and Pindyck (1994), the other classic text on real options, describes
several oil applications, including sequencing decisionmaking for opening up oil
fields and a study on building, mothballing and scrapping oil tankers. Since Brennan
and Schwartz’s seminal work, many others have studied petroleum options.
Copeland, Koller and Murrin (1990) for example, describe a case involving an option
to expand production.
Real option theory is best illustrated by an example. The following illustration is
taken from Leslie and Michaels (1997).
Suppose an oil company is trying to value its license in a block. Paying the license
fee is equivalent to acquiring an option. The company now has the right (but not the 115 obligation) to invest in the block (at the exercise price) once the uncertainty over the
value of the developed reserves (the stock price) has been resolved.
Assume that the company has the opportunity to acquire a fiveyear license and that
the block is expected to contain some 50 million barrels of oil. The current price of
oil from the field in which the block is located is $10 per barrel and the cost of
developing the field (in present value terms) is $600 million. Using static NPV
calculations the NPV will be $500 million  $600 million=$100 million.
The NPV is negative so the company would be unlikely to proceed. The NPV
valuation ignores the fact that decisions can be made about the uncertainty, which in
this case is twofold; in the real world there is uncertainty about the quantity of oil in
the block and about its price. It is, however, possible to make reasonable estimates of
the quantity of oil by analysing historical data in geologically similar areas and there
is also some historical data on the variability of oil prices.
Assume that these two sources of uncertainty between them result in a 30% standard
deviation around the growth rate of the operating cash inflows. Assume also that
holding the option obliges the company to incur the annual fixed costs of keeping the
reserve active, say $15 million. This represents a dividendlike payout of 3% (15/500) of the value of the asset.
Using the Black and Scholes formula for valuing a real option
δ ROV=Se  t * {(N(d1)}  Xert * {(N(d2))
where, d1={1n(S/X)+(rδ+σ2/2)t}/σ * √t, d2= d1σ * √t, S=presented value of expected
cash flows, X=present value of fixed costs, δ=the value lost over the duraction of the
option, r=risk free interest rate, σ=uncertainty of expected cas...
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This document was uploaded on 03/30/2014.
 Summer '14
 The Land

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