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Does taxation alter exploration?
Does taxation alter exploration? The effect of uncertainty and risk
H.F. Campbell and R.K. Lindner
The effect of resource rent taxation on mineral exploration is a controversial issue on which very little research has been carried out. Simple numerical examples are used in this paper to demonstrate that a ‘pure’ resource rent tax, or Brown Tax, can reduce the extent of exploration of a ‘promising’ deposit by a risk averse explorer, but encourage exploration of ‘unpromising’ deposits. This counter-intuitive result is explained in terms of the effect of the tax and of exploration on the costs of risk and uncertainty. Keywords: Mineral exploration; Taxation; Uncertainty H.F. Campbell is Professor of Economics at the University of Tasmania, Hobart, Tasmania 7000; R.K. Lindner is Professor of Agriculture, School of Agriculture, University of Western Australia, Nedlands, WA 6009, Australia.
0301-4207/87/040265-l
Some considerable attention has been given in the pages of this journal and others to the question of the effects of various forms of mineral taxation. Much of the attention has been focused on the effect of taxation on extraction decisions and several techniques of analysis have been developed. Less attention has been devoted to the effect of taxation on mineral exploration, despite the fact that this is a major concern of industry and government when tax proposals are being considered. If we wish to predict the effect of mineral taxation on exploration we need an economic model of the firm’s decision to explore. In this paper we outline a simple model of exploration and use it to assess the effect of a type of resource rent tax - the Brown Tax - on the amount of exploration undertaken by a firm. The basic thrust of the paper is that firms explore in order to obtain information which reduces the costs of uncertainty and risk. Taxation has the effect of altering those costs and hence changing the value to the firm of information obtained from exploration. In this way taxation may affect the firm’s incentive to explore. Before we introduce taxation, however, we need to understand the role of exploration in reducing the costs of uncertainty and risk. Why do firms explore for minerals? The obvious answer is to find them, but a significant proportion of exploration takes place after the initial discovery. Such exploration is aimed at ascertaining the size and quality of the prospect in question as a basis for assessing economic viability, and at working out how best to extract the mineral or energy resource if it seems to be profitable to do so. A case in point is exploration for oil: the seismic work is directed at locating a structure which may or may not contain oil; exploration drilling is undertaken to determine whether there is likely to be enough oil in the structure to be worth producing; and development drilling is aimed at bringing the reservoir to commercial production. In this paper we are concerned exclusively with the role of exploration in ascertaining those characteristics of the prospect which influence economic viability. In order to concentrate upon this aspect we assume
4$03.00 @ 1987 Butterworth
& Co (Publishers)
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1. 2.
‘See H.F. Campbell and R.K. Lindner, ‘A model of mineral exploration and taxation’, The Economic Journal, Vol 95, 1985, pp 146-160.
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that a prospect has already been located and that some preliminary information about it is available; and that there is only one way of extracting a deposit so that once the prospect is believed to be economically viable there is no advantage in undertaking the additional exploration which is usually associated with development.
If there were only one way of extracting a deposit, firms would most probably still explore before mining it because of the risk and uncertainty involved in development. Before extraction can take place significant development costs must be incurred and sums of money spent which may not be recovered if the deposit fails to live up to expectations. The purpose of the type of exploration we are concerned with is to reduce the cost of risk and uncertainty associated with development. Of course exploration itself involves some risk and considerable cost. In deciding upon its exploration programme for a prospect the firm weighs the reduced cost of risk and uncertainty associated with development against the cost of exploration. Within the mineral industry opinions about the economic wisdom of particular exploration or development decisions may vary. This is because different firms have different degrees of access to the critical factors which are involved in the exploration and development processes. The most important differences are: differences in the amount of information initially available; differences in levels of expertise in interpreting information; differences in access to exploration and development technology; and differences in access to factor markets, with the capital market being perhaps the most significant. These differences mean that different companies will have different initial views about the potential value of a mineral prospect; they will explore differently and interpret results differently; and they will incur different costs of risk as well as costs of exploration itself. To simplify our discussion we will assume that all firms in the mineral industry share the same initial information about a prospect; that they share the same views about the exploration process; that they have the same attitude to risk; and that they have the same exploration and development costs and returns. In the paper we develop some simple numerical examples which illustrate the benefits and costs of mineral exploration. To further clarify the issues involved, we assume in these hypothetical examples that the processes of exploration and of development (ie extraction) are carried out by separate firms. In other words, we have in mind a scenario where an exploration firm acquires (at a price) the right to explore a prospect, and after exploration on-sells the prospect to a development firm at a price which depends on the actual exploration results. A possible problem with such an arrangement is the incentive for the exploration firm to misrepresent the results of exploration at the time of sale to the development firm. This problem may explain why in practice exploration and development are often carried out by the same firm. In our analysis we assume that misrepresentation of exploration results is not possible. We use the technique of analysis developed to address a problem of interest to policy makers: what effect does resource rent taxation have on mineral exploration? This is a problem which we have addressed elsewherei in a different way.
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Does taxation Table 1. Hypothetical finding oil.
Prior probability
prior
probability
of
State of nature Oil (+ $20 million)
No oil (- $20 million)
0.6
0.4
Table 2. Likelihood of receiving under perfect information.
message
Message
State of nature Oil (+ $20 million)
No oil (- $20 million)
WET DRY
1 0
0 1
alter exploration?
Cost of uncertainty Our example starts at the point at which the initial survey associated with the discovery has been completed. We will assume that on the basis of that survey a view has been formed that the prospect could be worth either $20 million or -$20 million.2 For example, suppose the prospect is a structure which may or may not contain oil. If the company decides to develop; it incurs costs of $20 million. If there is little or no oil in the structure, a loss of $20 million is incurred. If the structure contains oil worth $40 million then the $20 million initial investment is recovered and an additional $20 million is earned. Since the development and production process involves time, we can think of these figures as being net present value (NPV) estimates made prior to the exploration process with which we are concerned. In addition to NPV estimates the company’s staff will have formed an opinion as to the probability of each of the outcomes. We refer to these as prior probabilities since they reflect the state of knowledge prior to exploration. We will assume that these beliefs are shared by the industry as a whole. In summary, we suppose the set of prior beliefs is as shown in Table 1. The exploration process can be assumed to yield one of two messages: either that there is oil, which we will refer to as WET; or that there is no oil, or DRY. If exploration yielded perfect information, the likelihoods of receiving each of these messages are as indicated in Table 2. For the moment suppose that exploration is costless and that the firm which is making the development decision is indifferent to risk. What is the value of exploration which yields perfect information? If the firm receives perfect information before deciding whether or not to develop the prospect, it will develop the deposit if it contains oil, and abandon if it does not. Using the prior probabilities we can calculate the expected net present value (ENPV) of the deposit as a 60% chance of $20 million (if the deposit is developed) plus a 40% chance of zero (if the deposit is abandoned). Thus the ENPV would be $12 million if perfect information were to be available. If no further information beyond the prior beliefs is available the firm will have to base its decision on the prior beliefs alone. Without exploration, development is perceived to involve a 60% change of $20 million plus a 40% chance of -$20 million, giving an ENPV of $4 million. For a risk neutral firm, this prospect is superior to that of not developing (ENPV = 0). The difference between the ENPV of development given perfect informaton and the ENPV of development without exploration is the expected value of exploration yielding perfect information to a firm which is indifferent to risk. Alternatively, the $8 million difference between the two ENPVs can be thought of as the cost of the uncertainty which would be eliminated by perfectly informative exploration.
Cost of risk
*Of course in practice, a range of possible returns would be possible a priori. However, to make the example more realistic in this way would greatly complicate the arithmetic needed to solve it.
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Of course, firms are generally not indifferent to risk. As most firms are averse to risk, it imposes a significant cost. One of the benefits of exploration is the reduction of that cost. Risk aversion is associated with diminishing marginal utility of income or wealth. To introduce risk aversion into our analysis we need to assume that the firm acts to maximize a utility function which exhibits this characteristic. We choose the function
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U = 1 - exp[-b(NPV
+ W,)]
where b = 0.02, a constant value which, given our numerical indicates strong risk aversion NPV = the net present value of the deposit (in $million) W, = the initial level of wealth (in $million)
example,
Since this particular utility function displays constant absolute risk aversion the cost of risk is independent of the initial level of wealth, which in our simulations we set at $100 million. It will be evident that the utility function can be used either to calculate the utility resulting from a given NPV of a mineral deposit (as in U = f(NPV)), or to calculate the certain NPV of a mineral deposit which would be necessary to secure a given level of utility (as in NPV = g(U)). Suppose that there is a risky prospect such as the 60% chance of $20 million and the 40% chance of -$20 million which the developer faces in the absence of information from exploration. The expected utility to be obtained from such a prospect is: E(U)
= 0.6 f(20) + 0.4 f(-20)] = 0.8648
The certainty equivalent value of the prospect (the sum of money the firm would be willing to pay for the prospect) is given by:
which
AECU) = g[O.8648]
CEV =
= $O.O5m The cost of development risk is measured as the difference between the ENPV of the prospect, which is the amount a risk neutral firm would value it at, and the certainty equivalent value estimated from the utility function. The calculation of the cost of risk is illustrated in Figure 1. In the case of our example of a firm deciding to develop the mineral prospect without first obtaining information from exploration, the CEV of a 60% chance of $20 million and a 40% chance of -$20 million is $0.05 million. Since the ENPV of this prospect is $4.00 million, the cost of development risk is $3.95 million. If perfect information were obtained through exploration there would be no development risk. Development would take place only if the message WET was received, and if that message was received the NPV of the project would be known with certainty to be $20 million. Thus, the value of perfect information in reducing development risk is the avoided cost of development risk, or $3.95 million. In the example used to this point, we have identified two possible benefits of exploration that yields perfect information. One is a reduction in the cost of uncertainty from $8 million to zero, and the other is a reduction in the cost of development risk from $3.95 million to zero. The sum of these two benefits is the value of perfect information to our hypothetical risk averse firm in reducing the costs of uncertainty and development risk. There is one further cost which also needs to be considered. From the point of view of the exploring firm, there is a risk associated with exploring which will not be incurred if no exploration takes place. According to the firm’s a priori beliefs there is a 60% chance that the message WET will be generated by exploration, and a 40% chance of
268
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Does taxation alter exploration? U = f INPV)
l l
l l
I
I
III ’ I I l l I
I
II’
Figure 1.
Calculating
the
cost
of
risk.a A = W, - $20 million; i3 = W, + $20 million; C = W, + ENPV = W, + $4 million; D = W, + CfV = W, + $0.05 million; C-D = cost of risk = $3.95 million.
A
I
i
I l l I I l I
II
I I
II1 II if;
1
I
I I I I ) :
! ! !
1
I
I
W, D C
I I
6
$
the message being DRY. For perfectly informative exploration, this is equivalent to a 60% chance of learning with certainty that the deposit is worth $20 million (ie that it can be sold to a mineral developer for $20 million) and a 40% chance of learning that it is worthless. The ENPV of this risky prospect is $12 million while the CEV of a 60% chance of $20 million and a 40% chance of zero is $11.02 million. This means that the cost of exploration risk is $0.98 million.
The value of perfect information
for different deposits
We have been considering mineral exploration which is assumed to yield perfect information about a mineral prospect which would still be developed even if exploration were not possible. Such deposits will be referred to in this paper as ‘initially promising’. Conversely, deposits which would not be developed if exploration were not possible will be termed ‘initially unpromising’. To illustrate how this second type of deposit differs from initially promising deposits, we take as an example a case which is identical to that outlined above except that the potential loss which would be incurred given the ‘no oil’ state is $25 million rather than $20 million. For this second example, the ENPV of immediate development is $2 million, and the cost of development risk $5 million. In the absence of exploration this deposit has a certainty equivalent value of -$3 million and will not be undertaken. For both types of deposit, once perfect information is obtained the correct decision will be made: to develop the prospect if there is
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‘Indeed, as will be shown below, exploration yielding less than perfect information is likely to increase rather than reduce development risk for initially unpromising deposits.
sufficient oil or to abandon it if there is not. Hence perfect information always eliminates the cost of uncertainty. Similarly, if the ultimate decision is to develop, there will be no development risk since the value of the deposit is known with certainty. Thus, the value of perfect information about an initially promising deposit also includes the elimination of the cost of the development risk that would otherwise be faced. By definition, initially unpromising deposits would not be developed if exploration was impossible, so there is no such development risk to eliminate for these types of deposit.3 The fact that exploration is an inherently risky business in the sense that a priori the outcome is uncertain also reduces the value of information by the cost of this exploration risk in both cases. Table 3 summarizes the numerical results for our hypothetical examples. The value of perfect information in reducing the cost of uncertainty is the difference between the value of the prospect to a risk neutral firm when perfect information is available, and its value when no extra information is available. It can be seen from the first column of Table 3 that it equals $8 million and $12 million for the initially promising and initially unpromising deposit examples respectively. The value of perfect information in reducing development risk is the difference between the cost of development risk under perfect information (which is zero since there is no risk under perfect information) and the cost of risk (if any) of the optimal act when no further information is available prior to mining. From the second column in Table 3, it can be seen that the value of perfect information in eliminating development risk equals $3.95 million for the promising deposit case, and is zero for the unpromising deposit case because, in the absence of exploration, there is no development risk to be eliminated. Of course the decision to explore involves some risk, and the cost of this risk in both cases equals $0.98 million (see column 3 of Table 3). It can be seen from the last column of Table 3 that the total value of exploration yielding perfect information is $10.97 million for the promising deposit, and $11.02 million for the unpromising deposit. This estimate of the value of exploration can be obtained in a simpler way as a cross check. If no information is available prior to making the decision to develop then, according to the table of prior beliefs, the developer is facing a 60% chance of an NPV of $20 million and a 40% chance of an NPV of either -$20 million or -$25 million depending on the type of deposit involved. The corresponding CEVs of developing these two prospects are $0.05 million and -$3 million respectively. If no further information could be obtained, only the former (ie initially promising) deposit would be developed, so the ‘value’ of the initially
Table 3. Value of exploration yielding perfect information (values in $ million).
Type of deposit
Information base for decision
Initially promising
No exploration With exploration
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cost of
cost of
development risk
exploration risk
8 0
3.95 0
a
3.95
-0.98
12 0
0 0
0 -0.98
Exploration benefit
12
0
-0.98
RESOURCES
EVPI
0 0.98
No exploration With exploration
Exploration benefit Initially unpromising
cost of uncertainty
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10.97
11.02
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Does taxation Table 4. Likelihood of receiving under imperfect information.
message
Message
State of nature Oil
No oil
WET DRY
0.8 0.2
0.3 0.7
alter exploration?
unpromising deposit would be zero. If, on the other hand, the developer knows that perfect information will be available before the decision to develop or abandon the prospect has to be made, then the a priori risky prospect changes to a 60% chance of $20 million and 40% chance of zero for both the promising and unpromising deposits. We have already seen that the CEV of this prospect is $11.02 million. The difference between the initial CEV estimate with no exploration and the CEV estimate taking account of exploration is the total contribution made by exploration. This difference equals $10.97 million (= $11.02 million $0.05 million) for the initially promising deposit, and equals $11.02 million for the initially unpromising deposit. It can be seen then that the value of the deposit ex ante to an explorer comprises its ‘without exploration’ value (of either $0.05 million or zero), plus the expected value of information from exploration (equal to either $10.97 million or $11.02 million).
The value of imperfect information from exploration In practice, exploration yields less than perfect information, so we do not expect it to eliminate the costs of uncertainty and development risk. This means that the potential cost savings we have estimated are upper bounds to the actual value of exploration. When we consider the value of imperfect information, we will be comparing the value of a prospect when the development decision will be based on imperfect information from exploration with its value when no such information is available. Relative to the values in the previous section, this comparison will yield lower estimates of the savings in costs of uncertainty and development risk resulting from exploration, and hence the estimate of the value of exploration will be lower. To introduce the imperfect nature of the information obtained in practice from exploration, we assume the set of likelihoods set out in Table 4 so that there is some probability of receiving a misleading message. For example, it can be seen from Table 4 that we assume there is a 20% chance of exploration telling us that there is no oil (DRY) when in fact the prospect is economically viable, and that there is a 30% chance of the converse possibility. A firm will decide to explore only if it intends to act on the information obtained. In our simple model, in which we assume there is no possibility of obtaining further information beyond the WET or DRY message, the firm will decide to develop if it receives the WET message and to abandon the prospect if it receives the DRY message. For the moment, we restrict our discussion to the case of an initially promising deposit. The exploration and development process can be put in the form of a decision tree, as illustrated in Figure 2. The probabilities reported in Figure 2 are a priori probabilities of the various events. For example, the a priori probability of the message WET is:
P(W/SO) P(S0)
+ P(W/SN)
P(SN)
The probabilities of the message WET conditional on the states of nature oil (SO), and no oil (SN), are given by the likelihoods in Table 4, while the a priori probabilities of the states of nature are determined by the firm’s prior beliefs. It will be recalled from Table 3 that the value of the promising mineral prospect to the risk averse firm was $0.05 million in the absence of exploration. This means that the decision, in the
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Does taxation alter exploration? Decision
Do not explore
Exolore
/\ DRY (0.4)
WET (0.6)
Figure 2. Decision tree for exploration decision.
I\
+20 (0.48)
Develop
Abandon
Develop
-20 (0.12)
/ \
+20 (0.6)
(Op40,
-20 (0.4)
absence of exploration, will be to develop as indicated in the righthand side of Figure 2. It can be seen from Figure 2 that there is no development risk if the mesage DRY is obtained because in that event the deposit will be abandoned. If message WET is obtained the firm will decide to develop but it will not be certain that the project is going to be profitable. The probability of getting the message WET and making a $20 million profit is 0.48 while the probability of receiving the message DRY and making a $20 million loss is 0.12. The posterior probabilities of oil and no oil given that the message WET has been received are expressed as P(SOIW) and P(SN/VV) respectively. According to the basic axioms of probability, as illustrated in Figure 3, we can write: P(w/S0)P(S0)
= P(SOIw)P(w)
and P(W/SW)P(SIV)
= P(SN/W)P(w)
These expressions allow us to work out the posterior probabilities and no oil, given that the message WET has been received, as: P(SOIW) A
Figure 3.
= P(wIso)P(so)IP(w) E
The event .space.a
aP(O/W) = AEGDIABD; P(W) ABCD; P(W/O) = AEGDIAEFD; AEFDIABCD.
272
of oil
= ABDl P(0) =
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and
P(SNIW)
= P( W/SN)P(SN)lP(
W)
These probabilities can be calculated from the prior probabilities (Table 1) and the likelihoods (Table 4). They are 0.8 and 0.2 respectively. Thus if the decision is to develop it will be after the message WET has been received and the risky prospect will consist of an 80% chance of $20 million and a 20% chance of -$20 million. The expected net present value of this prospect is $12 million and its certainty equivalent value to a developer is $9.04 million. Note then that the cost of development risk, if the prospect is developed, is $2.96 million. A priori there is only a 60% chance of receiving the message WET, which is a precondition for development, so a priori the expected cost of development risk is $1.78 million. We have just seen that if an exploration company were contemplating exploring the initially promising prospect and then selling it to a risk averse mining company it could expect to receive $9.04 million if the exploration results were favourable, and nothing if the results were unfavourable. These figures represent the market value of the prospect conditional on the exploration results received. Of course the exploration company cannot know the results of exploration in advance and so the decision to explore involves some risk. A priori there is a 60% chance that the prospect can be sold for $9.04 million to a mineral development company but a 40% chance that it will have to be abandoned after exploration. The expected value of the prospect to the exploration company a priori is $5.42 million, but the certainty equivalent value of this risky prospect is $5.22 million. The difference between the expected value and the certainty equivalent value is, as usual, a measure of the cost of risk. In this case it is the cost of exploration risk, which is equal to $0.20 million. So far in this section we have considered the costs of two kinds of risk _ exploration risk and development risk - which will be incurred in the exploration and development process. As noted previously, exploration also reduces the cost of uncertainty. However, even though exploration is to be undertaken, in practice it is still possible that the wrong decision will be made with respect to development because information obtained through exploration is less than perfect. Table 4 tells us that if the message WET is received there is a 20% chance of the deposit having an ENPV of -$20 million, and if the message DRY is received there is a 30% chance of the deposit having an ENPV of $20 million. Since the decision will be to develop if the message WET is received and to abandon the prospect if the message DRY is received, the expected opportunity losses associated with the messages WET and DRY are $4 million and $6 million respectively. Since the a priori probabilities of the messages WET and DRY are 0.6 and 0.4 respectively, the expected opportunity loss as a result of the wrong decision being made is $4.80 million. This represents the residual cost of uncertainty given that exploration is undertaken. We can see from Table 5 that in our example a firm considering exploring an initially promising prospect would anticipate lowering the cost of uncertainty and development risk, as compared with not exploring, by $5.37 million. The cost of exploration risk incurred in doing so would be $0.20 million, so that the net reduction in cost of risk and uncertainty would be anticipated to be $5.18 million. This is the
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Does taxation
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cost Type of deposit
Information base for decision
Initially promising
No exploration With exploration Exploration benefit
Initially unpromising
No exploration With exploration Exploration benefit
cost of uncertainty
of development risk
8.0 4.8
3.95
1.78
3.2
2.17
12.0 5.4
0.0 2.28
6.6
~2.28
cost of exploration risk
Value of exploration information
0.0 5.17 -0.20
5.17
0.0 0.13 -0.13
4.19
value of exploration which must be compared with the actual exploration costs - costs of drilling etc - when the decision as to whether or not to explore is being made. For the alternative case of an initially unpromising deposit, there are important differences which are illustrated by the values in the second part of Table 5. Because the prospect would not be developed in the absence of further information, the initial cost of uncertainty is $12 million (equal to the 0.6 probability that the deposit contains oil worth $20 million). With exploration, this cost of uncertainty is reduced to $5.4 million, so the reduction in the expected opportunity loss of the development decision equals $6.6 million. This greater value of exploration in reducing the cost of uncertainty relative to the case of the promising deposit derives from the fact that the prior decision differs between the cases. An even more important difference between the two cases is the effect of exploration on the cost of development risk. As already explained, for an initially unpromising deposit, there is no development risk if exploration cannot be undertaken. On the other hand, if exploration is possible, and if a WET message is the outcome, then the optimal decision is to develop the deposit with a consequent risk of losing $25 million if in fact there is no oil. The cost of this development risk conditional on a WET exploration result in $3.81 million, so ex ante the expected cost of development risk equals $2.28 million. Hence in this case exploration increases the cost of development risk rather than reducing it as in the case of an initially promising deposit. Finally, although the principles governing the cost of exploration risk are the same in both cases, the actual value of $0.13 million in this latter case is somewhat less than in the first case developed above. Perhaps surprisingly, the various differences between the two cases cancel out to some extent, so the actual value of exploration for the unpromising deposit case of $4.19 million does not differ from the value of $5.17 million for the alternative case by as much as might be expected a priori.
The effect of a Brown Tax on the value of information from exploration We have chosen the Brown Tax to illustrate the possible consequences of resource rent taxes generally on levels of exploration. This tax is extremely simple in the sense that it operates symmetrically on both profits and/or losses. Put differently, it reduces all of the firm’s revenues, and all of the firm’s expenses by the same proportion (equal to the rate of tax). In particular, all costs including both exploration and
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4H. Leland, ‘Optimal risk sharing and the leasing of natural resources with application to oil and gas and the OCS’, Quarter/y Journal of Economics, Vol 92, 1978, pp 413-438. 5For a minority of cases on the borderline between unpromising and promising deposits, the effect of a Brown Tax on the cost of uncertainty is more complicated than described in this paper. As such cases are a minority, they are ignored here in the interests of expositional clarity. A separate paper explaining these marginal cases is available from the authors.
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development costs are effectively subsidized by government at the rate of the Brown Tax. This symmetry in the impact of a Brown Tax is theoretically appealing because it is less likely to distort production decisions. For other types of resource rent tax where losses are not subsidized so explicitly, much the same effect could be achieved by allowing any taxes due on profitable mining ventures to be offset in full by losses on other mining projects in which the present value of revenues fall short of the present values of exploration plus development costs. A Brown Tax also is of interest because it is sometimes claimed to be neutral, in the sense that decisions about how best to extract a deposit are supposedly independent of the rate of tax. It is now generally recognized that this property does not hold if the miner’s aversion to risk is such that the cost of development risk is a non-proportional function of the rate of tax. For instance, Leland4 has shown that one of the main effects of such a tax is to spread the cost of development risk between the firm and the government, so long as the cost of development risk is a non-linear function of the tax rate. He concluded that the choice of an optimal tax rate should be influenced by this risk spreading capacity of a resource rent tax. We have shown above how the value of information from exploration can be decomposed into three separate components, namely the reduction in the cost of uncertainty, a change in the cost of development risk, and an increase in the cost of exploration risk. To understand how a Brown Tax affects the value of information from exploration, we will demonstrate how such a tax impacts on each of these three component parts. The effect of a Brown Tax on the cost of uncertainty is quite straightforward in most cases. To illustrate, consider the numerically simple case where a Brown Tax is levied at the rate of 50 cents in the dollar on a promising deposit. In this case, the opportunity loss of proceeding to develop the field in circumstances where ‘no oil’ is present will be $10 million (ie 50% of the $20 million opportunity loss in the no tax case). Thus the prior cost of uncertainty given no exploration is the ex ante expected value of this opportunity loss. This value is derived by multiplying the conditional opportunity loss by the prior probability of there being ‘no oil’ (equals 0.4), which is equal to $4 million (ie 50% of $8 million). For most cases of initially unpromising deposits, the situation with respect to the cost uncertainty is the exact opposite of that described above.5 The optimal decision given no possibility of further exploration is to not develop the deposit, the relevant opportunity loss is the potentially forgone profits from development for the oil state of nature. This reduces from $20 million with no tax to $10 million with a 50% tax rate. As the prior probability of the oil state is 0.6, the corresponding costs of uncertainty are $12 million and $6 million respectively, which are considerably larger than for the promising deposit case. For both cases though, note that if a firm were neutral in its attitude to risk, then a Brown Tax would have no effect on the level of exploratory activity undertaken by the firm. This is because both the value of exploratory information (equal to the reduction in cost of uncertainty due to exploration), and the cost of exploration itself will be reduced by the same proportion (ie the rate of the Brown Tax). Hence, the level of exploration at which expected marginal benefit of
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exploration equals the marginal cost of exploration will not be altered by the imposition of a Brown Tax. The key to understanding why a Brown Tax is likely to affect exploration levels despite the neutrality of its impact on the cost of uncertainty, is an appreciation of the non-linear relationship between the tax and the cost of development risk, and (of less import in our example) the cost of exploration risk. For instance, from Table 6 it can be seen that where no exploration of a promising deposit is possible, the imposition of a 50% tax rate reduces the cost of development risk to the firm from a figure of $3.95 million to only $0.98 million. On the one hand, such a cost reduction makes a promising deposit an even more attractive development prospect than it would be in the absence of the tax. This can be seen in Table 6, where the certainty equivalent of developing a promising deposit without exploration increases from $0.05 million to $1.02 million. On the other hand, exploration of promising deposits subject to a Brown Tax becomes less attractive as the tax rate increases because the potential for exploration to reduce the cost of development risk diminishes more than proportionately. For the hypothetical example depicted in Table 7, the reduction in the cost of development risk attributable to exploration is only $0.57 million when the tax rate is 50%, as compared to reduction of $2.17 million when there is no tax. For an unpromising deposit, exploration still increases the cost of development risk when a Brown Tax is imposed, but the extent to which the impact of exploration on this type of cost is diminished by the tax is very similar to the promising deposit case. As can be seen from Table 7, the actual figures for the hypothetical example are an increase in the cost of development risk of $0.53 million with tax as compared to an increase of $2.82 million without the tax. For both types of deposit, the tax also induces a more than proportionate reduction in the cost of risk incurred by exploring. However, as can be seen from Table 7, this effect is swamped in our example by the other two effects described above. Given a 50% Brown Tax, the actual increase in the cost of exploration risk for the two examples of a promising and unpromising deposit was $0.07 million and $0.05 million respectively. It is clear from Table 7 that the aggregate effect of a Brown Tax on the value of information from exploration is dominated by the impact on the cost of development risk. For promising deposits, its reduction in value of exploratory information is more than proportionate to the tax rate, while the reverse is true for unpromising deposits. The consequences of these effects are best illustrated by the assumption in Table 7 that the cost of exploration equals $5.0 million. Given this assumption, exploration of the promising deposit example yields a positive net benefit without the tax (ie $0.17 million), but a negative net benefit given a 50% Brown Tax (ie -$0.40 million). For the unpromising
Table 6. The non-neutrality (values in $ million).
of a Brown Tax on the decision to develop without exploration
Tax rate = 50%
Tax rate = 0% %VPV = expected net present value of development, %DVR = cost of development risk and ‘CEV = certainty equivalent of development.
276
Type of deposit
ENPV=
CDW
CEV”
ENPV
CDVR
CEV
Initially promising Initially unpromising
4 2
3.95 4.99
0.05 -2.99
2 1
0.98 1.24
1.02 -0.24
RESOURCES
POLICY December
1987
Does taxation Table 7. Effect of Brown Tax on net value of exploration brackets).
alter exploration?
(values in $million - no tax case in
cost of Type of deposit
Information base for decision
Initially promising
No exploration With exploration
Exploration benefit
cost of uncertainty
risk
4.0 (8.0) 2.4 (4.8)
0.98 (3.95) 0.41 (1.78)
1.6
0.57 (2.17)
(3.2)
exploration risk 0.0 (0.0) 0.07 (0.20) -0.07 (-0.20)
Less exploration cost
No exploration With exploration Exploration
benefit
Less exploration cost Net benefit
2.10 (5.17) 2.50 (5.0) -0.40 (+0.17)
Net benefit Initially unpromising
Value of exploration information
6.0 (12.0) 2.7 (5.4) 3.3 (6.6)
0.0
0.0
(0.0)
(0.0)
0.53 (2.28) ~0.53 (-2.28)
0.05 (0.13) -0.05 (-0.13)
2.72 (4.19) 2.50 (5.0) +0.22 (~0.81)
deposit example, exploration should not proceed if there is no tax (net benefit = -$O.Sl million), but would be beneficial to the extent of $0.22 million with the tax. To sum up, any decision to proceed to develop (extract) a mineral deposit involves both a cost of uncertainty and a cost of development risk. The potential value of exploration derives from the expected reduction in these two costs consequent on making the extraction decision with better information about the size of the mineral deposit. For so-called promising deposits, a Brown Tax induces a proportionate reduction in the cost of uncertainty, but a more than proportionate reduction in the cost of development risk. Hence the decisions of a risk neutral explorer should be independent of the Brown Tax, as both the expected value of information from exploration, and the cost of actually exploring, will be reduced in proportion to the rate of tax. For the risk averse explorer of a promising deposit, the Brown Tax reduces the expected value of information from exploration by a greater proportion than the rate of tax because the aforementioned effect on the cost of development risk is only partially offset by reduced exploration risk. Consequently, the amount of prior exploration of promising deposits is likely to be reduced if a Brown Tax is introduced. Conversely, the reduction in the expected value of information from exploration is less than proportionate to the rate of tax for unpromising deposits. As a result, there is likely to be more exploration of unpromising deposits with a Brown Tax than without. The result that a Brown Tax will inhibit exploration of promising deposits has intuitive appeal. The contrary result that the same tax encourages exploration of unpromising deposits is not so intuitively obvious. However, the explanation is perfectly straightforward, and hinges on two aspects of the cost of development risk noted above. One is the fact that exploration reduces the cost of development risk for promising deposits, but increases it for unpromising deposits. The other
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Does taxation alter exploration?
is the fact that a Brown Tax results in a more than proportionate decrease in the cost of development risk borne by the firm.
278
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1987
H.F. Campbell and R.K. Lindner
The effect of resource rent taxation on mineral exploration is a controversial issue on which very little research has been carried out. Simple numerical examples are used in this paper to demonstrate that a ‘pure’ resource rent tax, or Brown Tax, can reduce the extent of exploration of a ‘promising’ deposit by a risk averse explorer, but encourage exploration of ‘unpromising’ deposits. This counter-intuitive result is explained in terms of the effect of the tax and of exploration on the costs of risk and uncertainty. Keywords: Mineral exploration; Taxation; Uncertainty H.F. Campbell is Professor of Economics at the University of Tasmania, Hobart, Tasmania 7000; R.K. Lindner is Professor of Agriculture, School of Agriculture, University of Western Australia, Nedlands, WA 6009, Australia.
0301-4207/87/040265-l
Some considerable attention has been given in the pages of this journal and others to the question of the effects of various forms of mineral taxation. Much of the attention has been focused on the effect of taxation on extraction decisions and several techniques of analysis have been developed. Less attention has been devoted to the effect of taxation on mineral exploration, despite the fact that this is a major concern of industry and government when tax proposals are being considered. If we wish to predict the effect of mineral taxation on exploration we need an economic model of the firm’s decision to explore. In this paper we outline a simple model of exploration and use it to assess the effect of a type of resource rent tax - the Brown Tax - on the amount of exploration undertaken by a firm. The basic thrust of the paper is that firms explore in order to obtain information which reduces the costs of uncertainty and risk. Taxation has the effect of altering those costs and hence changing the value to the firm of information obtained from exploration. In this way taxation may affect the firm’s incentive to explore. Before we introduce taxation, however, we need to understand the role of exploration in reducing the costs of uncertainty and risk. Why do firms explore for minerals? The obvious answer is to find them, but a significant proportion of exploration takes place after the initial discovery. Such exploration is aimed at ascertaining the size and quality of the prospect in question as a basis for assessing economic viability, and at working out how best to extract the mineral or energy resource if it seems to be profitable to do so. A case in point is exploration for oil: the seismic work is directed at locating a structure which may or may not contain oil; exploration drilling is undertaken to determine whether there is likely to be enough oil in the structure to be worth producing; and development drilling is aimed at bringing the reservoir to commercial production. In this paper we are concerned exclusively with the role of exploration in ascertaining those characteristics of the prospect which influence economic viability. In order to concentrate upon this aspect we assume
4$03.00 @ 1987 Butterworth
& Co (Publishers)
Ltd
265
Does taxation
alter exploration?
1. 2.
‘See H.F. Campbell and R.K. Lindner, ‘A model of mineral exploration and taxation’, The Economic Journal, Vol 95, 1985, pp 146-160.
266
that a prospect has already been located and that some preliminary information about it is available; and that there is only one way of extracting a deposit so that once the prospect is believed to be economically viable there is no advantage in undertaking the additional exploration which is usually associated with development.
If there were only one way of extracting a deposit, firms would most probably still explore before mining it because of the risk and uncertainty involved in development. Before extraction can take place significant development costs must be incurred and sums of money spent which may not be recovered if the deposit fails to live up to expectations. The purpose of the type of exploration we are concerned with is to reduce the cost of risk and uncertainty associated with development. Of course exploration itself involves some risk and considerable cost. In deciding upon its exploration programme for a prospect the firm weighs the reduced cost of risk and uncertainty associated with development against the cost of exploration. Within the mineral industry opinions about the economic wisdom of particular exploration or development decisions may vary. This is because different firms have different degrees of access to the critical factors which are involved in the exploration and development processes. The most important differences are: differences in the amount of information initially available; differences in levels of expertise in interpreting information; differences in access to exploration and development technology; and differences in access to factor markets, with the capital market being perhaps the most significant. These differences mean that different companies will have different initial views about the potential value of a mineral prospect; they will explore differently and interpret results differently; and they will incur different costs of risk as well as costs of exploration itself. To simplify our discussion we will assume that all firms in the mineral industry share the same initial information about a prospect; that they share the same views about the exploration process; that they have the same attitude to risk; and that they have the same exploration and development costs and returns. In the paper we develop some simple numerical examples which illustrate the benefits and costs of mineral exploration. To further clarify the issues involved, we assume in these hypothetical examples that the processes of exploration and of development (ie extraction) are carried out by separate firms. In other words, we have in mind a scenario where an exploration firm acquires (at a price) the right to explore a prospect, and after exploration on-sells the prospect to a development firm at a price which depends on the actual exploration results. A possible problem with such an arrangement is the incentive for the exploration firm to misrepresent the results of exploration at the time of sale to the development firm. This problem may explain why in practice exploration and development are often carried out by the same firm. In our analysis we assume that misrepresentation of exploration results is not possible. We use the technique of analysis developed to address a problem of interest to policy makers: what effect does resource rent taxation have on mineral exploration? This is a problem which we have addressed elsewherei in a different way.
RESOURCES
POLICY December
1987
Does taxation Table 1. Hypothetical finding oil.
Prior probability
prior
probability
of
State of nature Oil (+ $20 million)
No oil (- $20 million)
0.6
0.4
Table 2. Likelihood of receiving under perfect information.
message
Message
State of nature Oil (+ $20 million)
No oil (- $20 million)
WET DRY
1 0
0 1
alter exploration?
Cost of uncertainty Our example starts at the point at which the initial survey associated with the discovery has been completed. We will assume that on the basis of that survey a view has been formed that the prospect could be worth either $20 million or -$20 million.2 For example, suppose the prospect is a structure which may or may not contain oil. If the company decides to develop; it incurs costs of $20 million. If there is little or no oil in the structure, a loss of $20 million is incurred. If the structure contains oil worth $40 million then the $20 million initial investment is recovered and an additional $20 million is earned. Since the development and production process involves time, we can think of these figures as being net present value (NPV) estimates made prior to the exploration process with which we are concerned. In addition to NPV estimates the company’s staff will have formed an opinion as to the probability of each of the outcomes. We refer to these as prior probabilities since they reflect the state of knowledge prior to exploration. We will assume that these beliefs are shared by the industry as a whole. In summary, we suppose the set of prior beliefs is as shown in Table 1. The exploration process can be assumed to yield one of two messages: either that there is oil, which we will refer to as WET; or that there is no oil, or DRY. If exploration yielded perfect information, the likelihoods of receiving each of these messages are as indicated in Table 2. For the moment suppose that exploration is costless and that the firm which is making the development decision is indifferent to risk. What is the value of exploration which yields perfect information? If the firm receives perfect information before deciding whether or not to develop the prospect, it will develop the deposit if it contains oil, and abandon if it does not. Using the prior probabilities we can calculate the expected net present value (ENPV) of the deposit as a 60% chance of $20 million (if the deposit is developed) plus a 40% chance of zero (if the deposit is abandoned). Thus the ENPV would be $12 million if perfect information were to be available. If no further information beyond the prior beliefs is available the firm will have to base its decision on the prior beliefs alone. Without exploration, development is perceived to involve a 60% change of $20 million plus a 40% chance of -$20 million, giving an ENPV of $4 million. For a risk neutral firm, this prospect is superior to that of not developing (ENPV = 0). The difference between the ENPV of development given perfect informaton and the ENPV of development without exploration is the expected value of exploration yielding perfect information to a firm which is indifferent to risk. Alternatively, the $8 million difference between the two ENPVs can be thought of as the cost of the uncertainty which would be eliminated by perfectly informative exploration.
Cost of risk
*Of course in practice, a range of possible returns would be possible a priori. However, to make the example more realistic in this way would greatly complicate the arithmetic needed to solve it.
RESOURCES
POLICY
December
Of course, firms are generally not indifferent to risk. As most firms are averse to risk, it imposes a significant cost. One of the benefits of exploration is the reduction of that cost. Risk aversion is associated with diminishing marginal utility of income or wealth. To introduce risk aversion into our analysis we need to assume that the firm acts to maximize a utility function which exhibits this characteristic. We choose the function
1987
267
Does taxation
alter exploration?
U = 1 - exp[-b(NPV
+ W,)]
where b = 0.02, a constant value which, given our numerical indicates strong risk aversion NPV = the net present value of the deposit (in $million) W, = the initial level of wealth (in $million)
example,
Since this particular utility function displays constant absolute risk aversion the cost of risk is independent of the initial level of wealth, which in our simulations we set at $100 million. It will be evident that the utility function can be used either to calculate the utility resulting from a given NPV of a mineral deposit (as in U = f(NPV)), or to calculate the certain NPV of a mineral deposit which would be necessary to secure a given level of utility (as in NPV = g(U)). Suppose that there is a risky prospect such as the 60% chance of $20 million and the 40% chance of -$20 million which the developer faces in the absence of information from exploration. The expected utility to be obtained from such a prospect is: E(U)
= 0.6 f(20) + 0.4 f(-20)] = 0.8648
The certainty equivalent value of the prospect (the sum of money the firm would be willing to pay for the prospect) is given by:
which
AECU) = g[O.8648]
CEV =
= $O.O5m The cost of development risk is measured as the difference between the ENPV of the prospect, which is the amount a risk neutral firm would value it at, and the certainty equivalent value estimated from the utility function. The calculation of the cost of risk is illustrated in Figure 1. In the case of our example of a firm deciding to develop the mineral prospect without first obtaining information from exploration, the CEV of a 60% chance of $20 million and a 40% chance of -$20 million is $0.05 million. Since the ENPV of this prospect is $4.00 million, the cost of development risk is $3.95 million. If perfect information were obtained through exploration there would be no development risk. Development would take place only if the message WET was received, and if that message was received the NPV of the project would be known with certainty to be $20 million. Thus, the value of perfect information in reducing development risk is the avoided cost of development risk, or $3.95 million. In the example used to this point, we have identified two possible benefits of exploration that yields perfect information. One is a reduction in the cost of uncertainty from $8 million to zero, and the other is a reduction in the cost of development risk from $3.95 million to zero. The sum of these two benefits is the value of perfect information to our hypothetical risk averse firm in reducing the costs of uncertainty and development risk. There is one further cost which also needs to be considered. From the point of view of the exploring firm, there is a risk associated with exploring which will not be incurred if no exploration takes place. According to the firm’s a priori beliefs there is a 60% chance that the message WET will be generated by exploration, and a 40% chance of
268
RESOURCES
POLICY
December
1987
Does taxation alter exploration? U = f INPV)
l l
l l
I
I
III ’ I I l l I
I
II’
Figure 1.
Calculating
the
cost
of
risk.a A = W, - $20 million; i3 = W, + $20 million; C = W, + ENPV = W, + $4 million; D = W, + CfV = W, + $0.05 million; C-D = cost of risk = $3.95 million.
A
I
i
I l l I I l I
II
I I
II1 II if;
1
I
I I I I ) :
! ! !
1
I
I
W, D C
I I
6
$
the message being DRY. For perfectly informative exploration, this is equivalent to a 60% chance of learning with certainty that the deposit is worth $20 million (ie that it can be sold to a mineral developer for $20 million) and a 40% chance of learning that it is worthless. The ENPV of this risky prospect is $12 million while the CEV of a 60% chance of $20 million and a 40% chance of zero is $11.02 million. This means that the cost of exploration risk is $0.98 million.
The value of perfect information
for different deposits
We have been considering mineral exploration which is assumed to yield perfect information about a mineral prospect which would still be developed even if exploration were not possible. Such deposits will be referred to in this paper as ‘initially promising’. Conversely, deposits which would not be developed if exploration were not possible will be termed ‘initially unpromising’. To illustrate how this second type of deposit differs from initially promising deposits, we take as an example a case which is identical to that outlined above except that the potential loss which would be incurred given the ‘no oil’ state is $25 million rather than $20 million. For this second example, the ENPV of immediate development is $2 million, and the cost of development risk $5 million. In the absence of exploration this deposit has a certainty equivalent value of -$3 million and will not be undertaken. For both types of deposit, once perfect information is obtained the correct decision will be made: to develop the prospect if there is
RESOURCES
POLICY December 1987
269
Does taxation
alter exploration?
‘Indeed, as will be shown below, exploration yielding less than perfect information is likely to increase rather than reduce development risk for initially unpromising deposits.
sufficient oil or to abandon it if there is not. Hence perfect information always eliminates the cost of uncertainty. Similarly, if the ultimate decision is to develop, there will be no development risk since the value of the deposit is known with certainty. Thus, the value of perfect information about an initially promising deposit also includes the elimination of the cost of the development risk that would otherwise be faced. By definition, initially unpromising deposits would not be developed if exploration was impossible, so there is no such development risk to eliminate for these types of deposit.3 The fact that exploration is an inherently risky business in the sense that a priori the outcome is uncertain also reduces the value of information by the cost of this exploration risk in both cases. Table 3 summarizes the numerical results for our hypothetical examples. The value of perfect information in reducing the cost of uncertainty is the difference between the value of the prospect to a risk neutral firm when perfect information is available, and its value when no extra information is available. It can be seen from the first column of Table 3 that it equals $8 million and $12 million for the initially promising and initially unpromising deposit examples respectively. The value of perfect information in reducing development risk is the difference between the cost of development risk under perfect information (which is zero since there is no risk under perfect information) and the cost of risk (if any) of the optimal act when no further information is available prior to mining. From the second column in Table 3, it can be seen that the value of perfect information in eliminating development risk equals $3.95 million for the promising deposit case, and is zero for the unpromising deposit case because, in the absence of exploration, there is no development risk to be eliminated. Of course the decision to explore involves some risk, and the cost of this risk in both cases equals $0.98 million (see column 3 of Table 3). It can be seen from the last column of Table 3 that the total value of exploration yielding perfect information is $10.97 million for the promising deposit, and $11.02 million for the unpromising deposit. This estimate of the value of exploration can be obtained in a simpler way as a cross check. If no information is available prior to making the decision to develop then, according to the table of prior beliefs, the developer is facing a 60% chance of an NPV of $20 million and a 40% chance of an NPV of either -$20 million or -$25 million depending on the type of deposit involved. The corresponding CEVs of developing these two prospects are $0.05 million and -$3 million respectively. If no further information could be obtained, only the former (ie initially promising) deposit would be developed, so the ‘value’ of the initially
Table 3. Value of exploration yielding perfect information (values in $ million).
Type of deposit
Information base for decision
Initially promising
No exploration With exploration
270
cost of
cost of
development risk
exploration risk
8 0
3.95 0
a
3.95
-0.98
12 0
0 0
0 -0.98
Exploration benefit
12
0
-0.98
RESOURCES
EVPI
0 0.98
No exploration With exploration
Exploration benefit Initially unpromising
cost of uncertainty
POLICY
December
10.97
11.02
1987
Does taxation Table 4. Likelihood of receiving under imperfect information.
message
Message
State of nature Oil
No oil
WET DRY
0.8 0.2
0.3 0.7
alter exploration?
unpromising deposit would be zero. If, on the other hand, the developer knows that perfect information will be available before the decision to develop or abandon the prospect has to be made, then the a priori risky prospect changes to a 60% chance of $20 million and 40% chance of zero for both the promising and unpromising deposits. We have already seen that the CEV of this prospect is $11.02 million. The difference between the initial CEV estimate with no exploration and the CEV estimate taking account of exploration is the total contribution made by exploration. This difference equals $10.97 million (= $11.02 million $0.05 million) for the initially promising deposit, and equals $11.02 million for the initially unpromising deposit. It can be seen then that the value of the deposit ex ante to an explorer comprises its ‘without exploration’ value (of either $0.05 million or zero), plus the expected value of information from exploration (equal to either $10.97 million or $11.02 million).
The value of imperfect information from exploration In practice, exploration yields less than perfect information, so we do not expect it to eliminate the costs of uncertainty and development risk. This means that the potential cost savings we have estimated are upper bounds to the actual value of exploration. When we consider the value of imperfect information, we will be comparing the value of a prospect when the development decision will be based on imperfect information from exploration with its value when no such information is available. Relative to the values in the previous section, this comparison will yield lower estimates of the savings in costs of uncertainty and development risk resulting from exploration, and hence the estimate of the value of exploration will be lower. To introduce the imperfect nature of the information obtained in practice from exploration, we assume the set of likelihoods set out in Table 4 so that there is some probability of receiving a misleading message. For example, it can be seen from Table 4 that we assume there is a 20% chance of exploration telling us that there is no oil (DRY) when in fact the prospect is economically viable, and that there is a 30% chance of the converse possibility. A firm will decide to explore only if it intends to act on the information obtained. In our simple model, in which we assume there is no possibility of obtaining further information beyond the WET or DRY message, the firm will decide to develop if it receives the WET message and to abandon the prospect if it receives the DRY message. For the moment, we restrict our discussion to the case of an initially promising deposit. The exploration and development process can be put in the form of a decision tree, as illustrated in Figure 2. The probabilities reported in Figure 2 are a priori probabilities of the various events. For example, the a priori probability of the message WET is:
P(W/SO) P(S0)
+ P(W/SN)
P(SN)
The probabilities of the message WET conditional on the states of nature oil (SO), and no oil (SN), are given by the likelihoods in Table 4, while the a priori probabilities of the states of nature are determined by the firm’s prior beliefs. It will be recalled from Table 3 that the value of the promising mineral prospect to the risk averse firm was $0.05 million in the absence of exploration. This means that the decision, in the
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December
1987
271
Does taxation alter exploration? Decision
Do not explore
Exolore
/\ DRY (0.4)
WET (0.6)
Figure 2. Decision tree for exploration decision.
I\
+20 (0.48)
Develop
Abandon
Develop
-20 (0.12)
/ \
+20 (0.6)
(Op40,
-20 (0.4)
absence of exploration, will be to develop as indicated in the righthand side of Figure 2. It can be seen from Figure 2 that there is no development risk if the mesage DRY is obtained because in that event the deposit will be abandoned. If message WET is obtained the firm will decide to develop but it will not be certain that the project is going to be profitable. The probability of getting the message WET and making a $20 million profit is 0.48 while the probability of receiving the message DRY and making a $20 million loss is 0.12. The posterior probabilities of oil and no oil given that the message WET has been received are expressed as P(SOIW) and P(SN/VV) respectively. According to the basic axioms of probability, as illustrated in Figure 3, we can write: P(w/S0)P(S0)
= P(SOIw)P(w)
and P(W/SW)P(SIV)
= P(SN/W)P(w)
These expressions allow us to work out the posterior probabilities and no oil, given that the message WET has been received, as: P(SOIW) A
Figure 3.
= P(wIso)P(so)IP(w) E
The event .space.a
aP(O/W) = AEGDIABD; P(W) ABCD; P(W/O) = AEGDIAEFD; AEFDIABCD.
272
of oil
= ABDl P(0) =
RESOURCES
POLICY December
1987
Does taxation
alter exploration?
and
P(SNIW)
= P( W/SN)P(SN)lP(
W)
These probabilities can be calculated from the prior probabilities (Table 1) and the likelihoods (Table 4). They are 0.8 and 0.2 respectively. Thus if the decision is to develop it will be after the message WET has been received and the risky prospect will consist of an 80% chance of $20 million and a 20% chance of -$20 million. The expected net present value of this prospect is $12 million and its certainty equivalent value to a developer is $9.04 million. Note then that the cost of development risk, if the prospect is developed, is $2.96 million. A priori there is only a 60% chance of receiving the message WET, which is a precondition for development, so a priori the expected cost of development risk is $1.78 million. We have just seen that if an exploration company were contemplating exploring the initially promising prospect and then selling it to a risk averse mining company it could expect to receive $9.04 million if the exploration results were favourable, and nothing if the results were unfavourable. These figures represent the market value of the prospect conditional on the exploration results received. Of course the exploration company cannot know the results of exploration in advance and so the decision to explore involves some risk. A priori there is a 60% chance that the prospect can be sold for $9.04 million to a mineral development company but a 40% chance that it will have to be abandoned after exploration. The expected value of the prospect to the exploration company a priori is $5.42 million, but the certainty equivalent value of this risky prospect is $5.22 million. The difference between the expected value and the certainty equivalent value is, as usual, a measure of the cost of risk. In this case it is the cost of exploration risk, which is equal to $0.20 million. So far in this section we have considered the costs of two kinds of risk _ exploration risk and development risk - which will be incurred in the exploration and development process. As noted previously, exploration also reduces the cost of uncertainty. However, even though exploration is to be undertaken, in practice it is still possible that the wrong decision will be made with respect to development because information obtained through exploration is less than perfect. Table 4 tells us that if the message WET is received there is a 20% chance of the deposit having an ENPV of -$20 million, and if the message DRY is received there is a 30% chance of the deposit having an ENPV of $20 million. Since the decision will be to develop if the message WET is received and to abandon the prospect if the message DRY is received, the expected opportunity losses associated with the messages WET and DRY are $4 million and $6 million respectively. Since the a priori probabilities of the messages WET and DRY are 0.6 and 0.4 respectively, the expected opportunity loss as a result of the wrong decision being made is $4.80 million. This represents the residual cost of uncertainty given that exploration is undertaken. We can see from Table 5 that in our example a firm considering exploring an initially promising prospect would anticipate lowering the cost of uncertainty and development risk, as compared with not exploring, by $5.37 million. The cost of exploration risk incurred in doing so would be $0.20 million, so that the net reduction in cost of risk and uncertainty would be anticipated to be $5.18 million. This is the
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1987
273
Does taxation
alter exploration? Table 5. Value of exploration yielding imperfect information (values in $ million).
cost Type of deposit
Information base for decision
Initially promising
No exploration With exploration Exploration benefit
Initially unpromising
No exploration With exploration Exploration benefit
cost of uncertainty
of development risk
8.0 4.8
3.95
1.78
3.2
2.17
12.0 5.4
0.0 2.28
6.6
~2.28
cost of exploration risk
Value of exploration information
0.0 5.17 -0.20
5.17
0.0 0.13 -0.13
4.19
value of exploration which must be compared with the actual exploration costs - costs of drilling etc - when the decision as to whether or not to explore is being made. For the alternative case of an initially unpromising deposit, there are important differences which are illustrated by the values in the second part of Table 5. Because the prospect would not be developed in the absence of further information, the initial cost of uncertainty is $12 million (equal to the 0.6 probability that the deposit contains oil worth $20 million). With exploration, this cost of uncertainty is reduced to $5.4 million, so the reduction in the expected opportunity loss of the development decision equals $6.6 million. This greater value of exploration in reducing the cost of uncertainty relative to the case of the promising deposit derives from the fact that the prior decision differs between the cases. An even more important difference between the two cases is the effect of exploration on the cost of development risk. As already explained, for an initially unpromising deposit, there is no development risk if exploration cannot be undertaken. On the other hand, if exploration is possible, and if a WET message is the outcome, then the optimal decision is to develop the deposit with a consequent risk of losing $25 million if in fact there is no oil. The cost of this development risk conditional on a WET exploration result in $3.81 million, so ex ante the expected cost of development risk equals $2.28 million. Hence in this case exploration increases the cost of development risk rather than reducing it as in the case of an initially promising deposit. Finally, although the principles governing the cost of exploration risk are the same in both cases, the actual value of $0.13 million in this latter case is somewhat less than in the first case developed above. Perhaps surprisingly, the various differences between the two cases cancel out to some extent, so the actual value of exploration for the unpromising deposit case of $4.19 million does not differ from the value of $5.17 million for the alternative case by as much as might be expected a priori.
The effect of a Brown Tax on the value of information from exploration We have chosen the Brown Tax to illustrate the possible consequences of resource rent taxes generally on levels of exploration. This tax is extremely simple in the sense that it operates symmetrically on both profits and/or losses. Put differently, it reduces all of the firm’s revenues, and all of the firm’s expenses by the same proportion (equal to the rate of tax). In particular, all costs including both exploration and
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4H. Leland, ‘Optimal risk sharing and the leasing of natural resources with application to oil and gas and the OCS’, Quarter/y Journal of Economics, Vol 92, 1978, pp 413-438. 5For a minority of cases on the borderline between unpromising and promising deposits, the effect of a Brown Tax on the cost of uncertainty is more complicated than described in this paper. As such cases are a minority, they are ignored here in the interests of expositional clarity. A separate paper explaining these marginal cases is available from the authors.
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development costs are effectively subsidized by government at the rate of the Brown Tax. This symmetry in the impact of a Brown Tax is theoretically appealing because it is less likely to distort production decisions. For other types of resource rent tax where losses are not subsidized so explicitly, much the same effect could be achieved by allowing any taxes due on profitable mining ventures to be offset in full by losses on other mining projects in which the present value of revenues fall short of the present values of exploration plus development costs. A Brown Tax also is of interest because it is sometimes claimed to be neutral, in the sense that decisions about how best to extract a deposit are supposedly independent of the rate of tax. It is now generally recognized that this property does not hold if the miner’s aversion to risk is such that the cost of development risk is a non-proportional function of the rate of tax. For instance, Leland4 has shown that one of the main effects of such a tax is to spread the cost of development risk between the firm and the government, so long as the cost of development risk is a non-linear function of the tax rate. He concluded that the choice of an optimal tax rate should be influenced by this risk spreading capacity of a resource rent tax. We have shown above how the value of information from exploration can be decomposed into three separate components, namely the reduction in the cost of uncertainty, a change in the cost of development risk, and an increase in the cost of exploration risk. To understand how a Brown Tax affects the value of information from exploration, we will demonstrate how such a tax impacts on each of these three component parts. The effect of a Brown Tax on the cost of uncertainty is quite straightforward in most cases. To illustrate, consider the numerically simple case where a Brown Tax is levied at the rate of 50 cents in the dollar on a promising deposit. In this case, the opportunity loss of proceeding to develop the field in circumstances where ‘no oil’ is present will be $10 million (ie 50% of the $20 million opportunity loss in the no tax case). Thus the prior cost of uncertainty given no exploration is the ex ante expected value of this opportunity loss. This value is derived by multiplying the conditional opportunity loss by the prior probability of there being ‘no oil’ (equals 0.4), which is equal to $4 million (ie 50% of $8 million). For most cases of initially unpromising deposits, the situation with respect to the cost uncertainty is the exact opposite of that described above.5 The optimal decision given no possibility of further exploration is to not develop the deposit, the relevant opportunity loss is the potentially forgone profits from development for the oil state of nature. This reduces from $20 million with no tax to $10 million with a 50% tax rate. As the prior probability of the oil state is 0.6, the corresponding costs of uncertainty are $12 million and $6 million respectively, which are considerably larger than for the promising deposit case. For both cases though, note that if a firm were neutral in its attitude to risk, then a Brown Tax would have no effect on the level of exploratory activity undertaken by the firm. This is because both the value of exploratory information (equal to the reduction in cost of uncertainty due to exploration), and the cost of exploration itself will be reduced by the same proportion (ie the rate of the Brown Tax). Hence, the level of exploration at which expected marginal benefit of
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exploration equals the marginal cost of exploration will not be altered by the imposition of a Brown Tax. The key to understanding why a Brown Tax is likely to affect exploration levels despite the neutrality of its impact on the cost of uncertainty, is an appreciation of the non-linear relationship between the tax and the cost of development risk, and (of less import in our example) the cost of exploration risk. For instance, from Table 6 it can be seen that where no exploration of a promising deposit is possible, the imposition of a 50% tax rate reduces the cost of development risk to the firm from a figure of $3.95 million to only $0.98 million. On the one hand, such a cost reduction makes a promising deposit an even more attractive development prospect than it would be in the absence of the tax. This can be seen in Table 6, where the certainty equivalent of developing a promising deposit without exploration increases from $0.05 million to $1.02 million. On the other hand, exploration of promising deposits subject to a Brown Tax becomes less attractive as the tax rate increases because the potential for exploration to reduce the cost of development risk diminishes more than proportionately. For the hypothetical example depicted in Table 7, the reduction in the cost of development risk attributable to exploration is only $0.57 million when the tax rate is 50%, as compared to reduction of $2.17 million when there is no tax. For an unpromising deposit, exploration still increases the cost of development risk when a Brown Tax is imposed, but the extent to which the impact of exploration on this type of cost is diminished by the tax is very similar to the promising deposit case. As can be seen from Table 7, the actual figures for the hypothetical example are an increase in the cost of development risk of $0.53 million with tax as compared to an increase of $2.82 million without the tax. For both types of deposit, the tax also induces a more than proportionate reduction in the cost of risk incurred by exploring. However, as can be seen from Table 7, this effect is swamped in our example by the other two effects described above. Given a 50% Brown Tax, the actual increase in the cost of exploration risk for the two examples of a promising and unpromising deposit was $0.07 million and $0.05 million respectively. It is clear from Table 7 that the aggregate effect of a Brown Tax on the value of information from exploration is dominated by the impact on the cost of development risk. For promising deposits, its reduction in value of exploratory information is more than proportionate to the tax rate, while the reverse is true for unpromising deposits. The consequences of these effects are best illustrated by the assumption in Table 7 that the cost of exploration equals $5.0 million. Given this assumption, exploration of the promising deposit example yields a positive net benefit without the tax (ie $0.17 million), but a negative net benefit given a 50% Brown Tax (ie -$0.40 million). For the unpromising
Table 6. The non-neutrality (values in $ million).
of a Brown Tax on the decision to develop without exploration
Tax rate = 50%
Tax rate = 0% %VPV = expected net present value of development, %DVR = cost of development risk and ‘CEV = certainty equivalent of development.
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Type of deposit
ENPV=
CDW
CEV”
ENPV
CDVR
CEV
Initially promising Initially unpromising
4 2
3.95 4.99
0.05 -2.99
2 1
0.98 1.24
1.02 -0.24
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(values in $million - no tax case in
cost of Type of deposit
Information base for decision
Initially promising
No exploration With exploration
Exploration benefit
cost of uncertainty
risk
4.0 (8.0) 2.4 (4.8)
0.98 (3.95) 0.41 (1.78)
1.6
0.57 (2.17)
(3.2)
exploration risk 0.0 (0.0) 0.07 (0.20) -0.07 (-0.20)
Less exploration cost
No exploration With exploration Exploration
benefit
Less exploration cost Net benefit
2.10 (5.17) 2.50 (5.0) -0.40 (+0.17)
Net benefit Initially unpromising
Value of exploration information
6.0 (12.0) 2.7 (5.4) 3.3 (6.6)
0.0
0.0
(0.0)
(0.0)
0.53 (2.28) ~0.53 (-2.28)
0.05 (0.13) -0.05 (-0.13)
2.72 (4.19) 2.50 (5.0) +0.22 (~0.81)
deposit example, exploration should not proceed if there is no tax (net benefit = -$O.Sl million), but would be beneficial to the extent of $0.22 million with the tax. To sum up, any decision to proceed to develop (extract) a mineral deposit involves both a cost of uncertainty and a cost of development risk. The potential value of exploration derives from the expected reduction in these two costs consequent on making the extraction decision with better information about the size of the mineral deposit. For so-called promising deposits, a Brown Tax induces a proportionate reduction in the cost of uncertainty, but a more than proportionate reduction in the cost of development risk. Hence the decisions of a risk neutral explorer should be independent of the Brown Tax, as both the expected value of information from exploration, and the cost of actually exploring, will be reduced in proportion to the rate of tax. For the risk averse explorer of a promising deposit, the Brown Tax reduces the expected value of information from exploration by a greater proportion than the rate of tax because the aforementioned effect on the cost of development risk is only partially offset by reduced exploration risk. Consequently, the amount of prior exploration of promising deposits is likely to be reduced if a Brown Tax is introduced. Conversely, the reduction in the expected value of information from exploration is less than proportionate to the rate of tax for unpromising deposits. As a result, there is likely to be more exploration of unpromising deposits with a Brown Tax than without. The result that a Brown Tax will inhibit exploration of promising deposits has intuitive appeal. The contrary result that the same tax encourages exploration of unpromising deposits is not so intuitively obvious. However, the explanation is perfectly straightforward, and hinges on two aspects of the cost of development risk noted above. One is the fact that exploration reduces the cost of development risk for promising deposits, but increases it for unpromising deposits. The other
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is the fact that a Brown Tax results in a more than proportionate decrease in the cost of development risk borne by the firm.
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