UNIVERSITY OF 
 
 ILLINOIS LIBRARY 
 
4W> /// 
 
 FACULTY WORKING 
 PAPER NO. 391 
 
 Sim LIBRARY OF THF 
 
 Optimal Exploitation of a Stock Resource 
 
 Ralph Greenberg 
 Song K. Kim 
 Rene Manes 
 
 College of Commerce and Business Administration 
 Bureau of Economic and Business Research 
 University of Illinois. Urbana-Champaigr. 
 
FACULTY WORKING PAPER NO. 891 
 College of Commerce and Business Administration 
 University of Illinois at Urbana-Champaign 
 August 1982 
 
 Optimal Exploitation of a Stock Resource 
 
 Ralph Greenberg, Assistant Professor 
 Department of Accountancy 
 
 Song K. Kim, Assistant Professor 
 Department of Accountancy 
 
 Rene Manes, Professor 
 Department of Accountancy 
 
Digitized by the Internet Archive 
 
 in 2011 with funding from 
 
 University of Illinois Urbana-Champaign 
 
 http://www.archive.org/details/optimalexploitat891gree 
 
Abstract 
 The paper introduces to the capital budgeting literature the problem 
 of how to select the amount of capital required to exploit a stock resource, 
 Simulation is used to examine the solutions of a discounted cash flow, 
 pretax model of venture profit. The sensitivity of solutions to model 
 parameters is examined with special attention to the counterintuitive 
 result that, for this problem, an increased cost of capital, r, results 
 in higher investment over wide ranges of the value of r. Effects of 
 depreciation and after-tax maximization are also examined as well as the 
 possible impact of capital investment on output demand. 
 
Optimal Exploitation of a Stock Resource 
 
 A problem that has not received adequate attention in the capital 
 budgeting literature is the problem of providing long-lived assets for the 
 development of a stock resource. The mining industry provides many examples 
 of this kind, such as extraction of marble from a quarry, gravel from a 
 pit, oil from a reservoir. A related problem is that of outfitting with 
 special capital assets the firm which has a one-time, fixed-quantity con- 
 tract. An example of the second kind would be the production of a given 
 number of special units in a government contract for which there is no 
 guarantee of renewal. 
 
 In such situations, the entrepreneur must often decide simultaneously 
 whether to engage in the venture and if so, how large the capital equip- 
 ment used to produce the stock resource (or the fixed output) should be. 
 In many capital budgeting models, the size of the capital asset is not 
 a control variable but rather is given. B. Rapp does cite a few examples 
 of approaches in which researchers have treated size of investment as a 
 continuous variable [4] and Weingartner dealt with the combined problem 
 of capital asset variability and indivisibility by his integer programming 
 model [5], Usually however, optimal plant size, if it is not assumed to 
 have already been decided on, is handled by the incremental analysis of 
 larger and larger sizes of plant [2] . 
 
 In this note, the capital budgeting model integrates the decision 
 to invest with the selection of optimal fixed asset size, dealing with 
 assets as continuous or integer valued as each situation requires. For 
 stock resource development, the asset size decision will depend on how 
 
-2- 
 
 much freedom the entrepreneur has in controlling the rate of production 
 and thus the length of life of each particular venture. In the case of 
 mineral extraction, the miner can usually decide, subject to market con- 
 ditions, his rate of production; in the case of fixed quantity contracts, 
 the buyer may impose conditions on delivery dates and eliminate many 
 of the entrepreneur's options regarding the rate of production and 
 thus the necessary size of capital. The capital budgeting decision may 
 be further complicated by the fact that, by increasing the size of the 
 capital equipment utilized in order to achieve higher rate of output, 
 the entrepreneur may affect the demand price for his product. 
 
 We shall first consider the situation in which the entrepreneur is 
 a pricetaker and his decision to van,' output will not affect the price 
 of that output. We assume that the businessman faced with the simultaneous 
 decision of whether to invest or not and if so, how to decide on the optimal 
 level of capital investment will base his decision on net present value 
 maximization. A discounted cash flow model will be presented in its least 
 complicated form and primary reliance made on simulation for solutions 
 and discussions of the model. Two reasons have led to greater dependence 
 on simulation than on analysis: first, even for the most straight-forward 
 models, reduced form solutions quickly become mathematically complex and 
 second, simulation is relatively easy even after simplifying assumptions 
 are dropped to accommodate "real world" intricacies. 
 
 Model 1 
 
 A businessman owns a quarry containing an estimated stock of Y units 
 of gravel. The price of a single unit of gravel is p. Exploitation of 
 
-3- 
 
 the quarry requires a shovel which produces y units per period; production 
 per period can be increased proportionally by the purchase of additional 
 shovels. The initial cost of acquiring one shovel is CC and its operating 
 cost per period is VC per shovel. Finally, if the venture is undertaken, 
 fixed costs per period, FC, are incurred. Letting X be the decision vari- 
 able (i.e., the number of shovels to be purchased), the net present value 
 of the venture is 
 
 N N N 
 
 rr = x • p • y z x • vc z fc z cc • x 
 
 n=l (1 + r) n n=l (1 + r) n n=l (1 + r) n 
 where r is the discount rate and N is the life of the project. 
 
 Assuming that the project meets the firm's hurdle rate for the cost 
 of capital, i.e., II is positive for some values of X (or N since alterna- 
 tive solutions can be obtained in terms of optimal N), the optimal number 
 of shovels may be selected. One approach to solving this problem is 
 to take the first derivative of equation (1) with respect to X (or N) 
 and set it equal to zero and solve for X (or N) . The second derivative 
 test can be performed to check that the point is the maximum. From the 
 point of view of maximization of a function, if a function is strictly 
 concave over the interval (a, b), there is a single unique global maxi- 
 mum that may be either in the interval or at one of the end points. See 
 Appendix for the first and second order conditions for equation (la) below. 
 
 At this point, a numerical example is provided to illustrate the 
 capital budgeting decision. 
 
 Let 
 
 Y = a total stock of 1,000,000 units of gravel 
 y = 50,000 units of gravel per shovel/per period 
 p = $5 sales price per unit of gravel 
 
-u- 
 
 CC = $400,000 per shovel 
 
 VC = S 20,000 per shovel/per period 
 
 FC = $ 80,000 per period 
 
 r = 10% cost of capital per period 
 
 Note that N, the life of venture, varies as a function of X, i.e., M = Y/yX. 
 
 For the above parameter values, equation (1) becomes 
 
 . .-20/X 
 
 H = (230.000X - 80,000) [- K -^ 11 ] - 400,000X 
 
 Equation (la) takes its the maximum value when X equals 3.112 and the 
 corresponding life of the venture is 6.426 periods. If we assume shovels 
 (units of capital, X) to be integer values, for X rounded to 3 the net 
 present value of II is $1,668,690. If X is rounded to 4, the net 
 present value of E is $1,584,260. Therefore, due to the convexity of 
 equation (la) , the optimal number of shovels is 3 for the numerical 
 example. 
 
 Figure 1 graphs profit and shows that the advantages of increasing 
 discounted total net revenue and decreasing discounted total fixed costs 
 on the one hand must be balanced against the disadvantages of purchasing 
 more shovels. Grant, et al. on page 203 [3] have a good example of a 
 comparable situation. They show that when installing an oil pipeline 
 the firm must consider the tradeoff between the immediate capital expen- 
 diture on larger pipe versus the increased annual expenditure incurred 
 to run a pumping station. Economists would point out that profit is 
 maximized when X is acquired so as to make the value of the discounted 
 net revenue less the discounted savings in fixed costs due to an incre- 
 mental shovel equal to the cost of one shovel. The poinc A on Figure 1 
 ($800,000) can be thought of as a consol value, i.e., the present value 
 of the fixed ccsts in perpetuity which would be incurred if the property 
 
-5- 
 
 were held but the project was never started. Mining companies which 
 hold properties for future development incur such costs in the form of 
 required land taxes and other annual fees. 
 
 Note that model (la) assumes that the lives of the capital assets 
 and the project are coterminous, i.e., that capital assets are committed 
 to the project with no allowance for salvage value. The assumption 
 of zero salvage value is reasonable for many investments in stock resource 
 development such as soil removal for open pit mining or intangible cost 
 
 of oil well drilling. If, however, some percentage of COX, (aCCX) is expec- 
 
 -20 /X 
 
 ted to be recovered at the end of project life, a term aCOX (1 + r) 
 
 would have to be added to IT. It should be pointed out that, depending 
 on the values of N, salvage values may change. The observation that 
 salvage value can be a function of N has its parallel in the use of a 
 bail-out factor in payback period analysis. We should also point out 
 that variable costs (VC) have been made a function of the number of 
 shovels rather than a function of output as is perhaps more commonly done. 
 The same costs result, if we assume that once a shovel is acquired it is 
 operated at capacity throughout the life of the project. If inflation is 
 anticipated for p, VC and/or FC, the model can be expanded to take it into 
 account. 
 
 Sensitivity Analysis 
 
 Obviously solutions depend on the particular values of the 
 model's parameters. Most of the effects of parameter changes on optimal 
 capital investment are predictable, at least directionally. Higher values 
 of Y, p, and FC for example lead to higher values of X. Where the cost 
 of capital, r, is concerned though, the effects are contrary to usual 
 
Discounted Net Revenue 
 
 
 77(000s) 
 
 X = 1 
 
 877 
 
 2 
 
 1535 
 
 3 
 
 1669 
 
 4 
 
 1584 
 
 5 
 
 1391 
 
 6 
 
 1138 
 
 7 
 
 847 
 
 8 
 
 531 
 
 1 2 3 4 5 6 7 8X9 
 
 Exhibit #1 
 
 REVENUES, COSTS AND PROFIT (it) 
 
 FOR VARIOUS x 
 
 (Y= 1,000,000 and r=10%) 
 
8400r 
 7600 
 6800 
 6000 
 
 9 5200 
 
 o 
 
 ■*-< 
 *-> 
 
 %wmm 
 
 o 4400 
 
 b 
 
 8 3600- 
 
 & 
 
 2800- 
 
 2000- 
 
 1200- 
 
 400- 
 
 2 4 6 8 10 12 14 
 
 Exhibit #2 
 
 x 
 
 PROFIT,^, FOR VARIOUS VALUES OF r & x 
 
 (Y= 3,000,000) 
 
-8- 
 
 capital budgeting results and somewhat couterintuitive. In order to 
 increase the present value of net revenue and to diminish the present 
 value of fixed cost outlays over time by shortening N, there are inducements 
 to increase X, even when r is increasing. Figure 2 shows that for the 
 same model [with Y = 3,000,000], optimal units of X increase as the cost 
 of capital increases. Whereas the marginal efficiency of capital and 
 the firm's investment opportunity schedule (Ackley [1], p. 473) are 
 generally conceded to be downward sloping to the right (refer to line 
 A3, in Figure 3), the firm's optimal demand for capital and for funding 
 the development of a stock resource increases up to some level of 
 higher interest rates and then gradually recedes, as in line CD. For 
 example, if we examine optimal investment levels for model la allowing 
 the cost of capital to vary from percent to 50 percent and select for 
 each interest rate the profit maximizing non-integer number of shovels, 
 we see that investment in capital, line CD, increases as r increases 
 from percent to 28 percent, the point of maximum investment, after 
 which it gradually decreases (profit itself becomes negative at 49%). 
 As the ratio of fixed costs, FC, to capital cost CC, increases, so does 
 the demand for capital, i.e., line CD moves directionally to C'D'. 
 
 Effect of Depreciation 
 
 Far from exhausting the subject, this note is intended primarily to 
 open up a new direction for capital budgeting research. Two more points 
 however will be made. The first relates to depreciation and its effect 
 on taxes . 
 
if'To 
 
 =S> INVESTMENT 
 31,455,000- 
 
 3.0 4.0 
 
 X* = 3.64 
 
 Exhibit #3 
 
 COMPARISON OF TRADITIONAL 
 
 INVESTMENT OPPORTUNITY CURVE (AB) 
 
 TO OPTIMAL INVESTMENT IN CAPITAL 
 
 TO DEVELOP A STOCK RESOURCE (CD) 
 
 (Y = 1,000,000) 
 
-10- 
 
 If we examine net present value after taxes, H', equation (1) 
 becomes : 
 
 N 1 
 n 1 = (1 - t)(II + CC • X) + (t • depreciation) ( Z — = — ) - CC • X 
 
 n=l (l=r) n 
 for t equal to the tax rate. 
 
 If we maintain the assumption that all assets are committed to the 
 venture at hand, and that no salvage will be recovered, then CC • X must 
 be charged off completely (as mentioned above not unrealistic for develop- 
 ment cost such as intangible well drilling, mineshafts and excavation 
 
 CCX Y 
 
 costs). Therefore depreciation per period is — —. Since N = =— , 
 
 N 9 Xy 
 
 CCX" 'V 
 straightline depreciation in terms of X only is — - — ^ where y/Y is 
 
 a constant. 
 
 Thus Equation (2) becomes 
 
 2 N 
 
 n 1 = u-t)Ci + cc x) + [ tCC ' x y ] • [ z — ^— ] - cc • x 
 
 Y n-l (l+r) n 
 
 and equation (la) becomes 
 
 -20/X 
 n ' = [(l-t)(230,000X - 80,000) + t20,000X 2 ][ - " (1+r) ] - 400,000X 
 
 In all of the cases we have examined the combined effect of taxes and 
 the quadratic tax shield is to push the profit function down and to the 
 right as in Figure 4 and to increase investment in X, again a counter- 
 intuitive result. 
 
 Effect of Investment on Firms Demand 
 
 Finally, we consider the case where the level of output can affect the 
 price of output. Now in order to make an optimal capital budgeting decision, 
 the firm must have an estimate of demand. Demand functions are usually 
 
$ 
 
 PRETAX OPTIMAL x« --' / )( 
 
 AFTER TAX OPTIMAL x'* ' 
 
 Exhibit #4 
 
 EFFECT OF TAXES AND 
 
 STRAIGHT LINE DEPRECIATION 
 
 ON PROFIT AND OPTIMAL CAPITAL 
 
-12- 
 
 expressed in terms of output per period such as P = a - b-yX or 
 
 P = a - b'X (since y has been defined as output per period per unit of X) 
 
 As an example, assume that the demand function is 
 
 P = 6.5 - (-rrjr)yX or P = 6.5 - 0.5X then (equation la) can be 
 
 restated as 
 
 N N 
 
 II" = (50000X)(6.5 - 0.5X) E = — - 20000X E 
 
 n=l (l+r) n n=l (l+r) n 
 
 N 1 
 - FC I 400000X 
 
 n=l (l+r) n 
 The integer solution to equation (3a) is 2 shovels, and the resulting net 
 present value is $1,843,163. Recall that, for the case of a fixed price 
 of S5 (i.e., equation la), the optimal number of shovels and net present 
 value are 3 and $1,668,690 respectively. Based on the given demand 
 function, the firm can increase the net present value by lowering its 
 periodic production to 100,000 units (as opposed to 150,000 per period) 
 thereby extending the life of venture and increasing the unit price. 
 Extension of the life of a venture may not affect the optimal number of 
 shovels when the discount rate is very low. For example, the optimal 
 value of X is 2 for both equations (la) and (3a) when the discount rate 
 is 3% per period. 
 
 Conclusion 
 
 This note considers a problem in capital budgeting which has been 
 largely neglected, namely the simultaneous decision to invest and to 
 select the optimal amount of capital asset investment when a stock resource 
 is to be developed. The relevance of this model is to extractive in- 
 dustries and especially to energy development is suggested. How the cost 
 
-13- 
 
 of capital affects optimal size of plant is shown as are the effects of 
 depreciation on this particular capital budgeting situation. Finally, 
 the note considers the possibility that the investment decision will 
 impact on output demand and price. 
 
-14- 
 
 Ref erences 
 
 [1] Ackley, G. Macroeconcmic Theory , New York, The MacMillan Co., 1961. 
 [2] Bierman, H. Jr. and Dyckman, T. R. Managerial Cost Accounting , 
 
 New York, MacMillan Publishing Co, 1976 (Chapter 15). 
 [3] Grant, E., Ireson, W. G. and Leavenworth, R. Principles of Engineering 
 
 Economy , 6th Edition, New York, The Ronald Press Comp- ny, 1976. 
 [4] Rapp, B. Models For Optimal Investment and Maintenance Decisions , 
 
 New York, John Wiley and Sons, 1974, p. 1-12. 
 [5] Weingartner, H. M. Mathematical, Programming and the Analysis of 
 
 Capital Budgeting Problems , Englewood Cliffs, Prentice Kail, 1963. 
 
 M/3/232 
 
-15- 
 
 Appendix 
 
 This appendix shows the first- and second-order conditions for 
 
 equation (la) . It also shows that the net present value function is 
 
 strictly concave for X _> 1 . This is done by showing that the second 
 
 derivative is negative for all X >_ 1 . Differentiating with respect to 
 
 X we get the following first-order conditions (000' s omitted) . 
 
 . .-20/X 
 n = (230X-80) [- " u r; ] -400X 
 
 ATI 1 fH ^" 2 °/ X 
 
 ~ = 230 [ l " U r; ] - (230X-80) 
 
 dA r 
 
 [■i (l+r)" 20/X (^) ln(l+r)] - 400 
 X~ 
 
 the second-order condition is 
 
 ^ o™ r 1 m^" 20 ^ 2 ^ i / 1A m 
 — — r = -230 [- (1+r) (— ) ln(l+r) J 
 
 dX r X~ 
 
 460 ... v-20/X n ,^,,2.20, 460 ... ,-20/X . .... 
 - — =- (1+r) [ln(l+r)J (— =■) + — x (1+r) ln(l+r) 
 
 X rX~ 
 
 , 160 ... ,-20/X n ... ,,2,20, 320 ... ,-20/X , . 
 + — 2 ( 1+r ) [ln(l+r)] (— y) r (1+r) ln(l+r) 
 
 rX X rX 
 
 920 ... ,-20/X M ... ..2 , 320 ... ,-20/X . ... ,,2 
 = x (1+r) [ln(l+r)] + — t (1+r) [ln(l+r)j 
 
 rX rX 
 
 . 220 (1+r) -20/X ln(1+r) __ Q 
 rX 
 
 The second-order condition is always negative for X >_ 1 . The first term 
 
 is obviously negative. By examining the second and the third term we 
 
 can see the sum of the two are also negative. 
 
-16- 
 
 3 9 3°0 
 That is, since X > 1, -=~ > — =7 
 
 rX rX 
 
 and since < r < 1, < ln(l+r) < 1 
 
 ln(l+r) > [ln(l+r)] 2 
 
 . . 320 , ,-20/X . .... ^ 320 ... ,-20/X M ..^ ,.2 
 therefore — - (1+r) ln(l+r) > — - (1+r) [ln(l+r)] 
 
 rX rx 4 
 
 Since the left-side term is negative and the right-side term is positive, 
 the sum of the two are negative. Therefore the function is concave. 
 This result can also be derived if the assumption of continuous 
 discounting is made. For this case equation (la) can be rewritten as: 
 
 n = (230X-80) - [1 - exp (-20r/X)] - 400X (4a) 
 
 Taking the first derivative equation 4a we get 
 
 ||» i2£ [i- exp(-20r/X)] - 230 ^ 8Q [ (2 exp (-20r/X) ] - 400 = 
 
 X 
 
 The second-order conditions of equation 4a are 
 
 £-f = -^ [exp (-20r/X)] (20) - -^ [20 exp (-20r/X) ] C^ 1 ) 
 dX" X z A x Z 
 
 + -^f [20 exp (-20r/X) ] = 
 X 
 
 Simplifying we get 
 
 -(9 20rX-3 20r+320X) (rj [exp (-20r/X)]) = 
 
 X 4 
 
 Notice that =-r [exp (-20r/X)] > 0. 
 
 X"* 
 And since < r < 1 and X >_ 1 , then -320r < 320X. 
 
 Thus the second-order condition is negative for all X >_ 1 and all r. 
 
 Q.E.D 
 
Table 1 
 Discounted Costs and Net Present Value When Y = 1,000,000 
 
 
 Discounted 
 
 Cost of 
 
 Total 
 
 Net Present 
 
 X 
 
 Fixed Cost 
 681,088 
 
 Fixed Cost 
 400,000 
 
 Costs 
 1,081,088 
 
 Value 
 
 1 
 
 877,034 
 
 2 
 
 491,568 
 
 800,000 
 
 1,291,568 
 
 1,534,935 
 
 3 
 
 375.920 
 
 1,200,000 
 
 1,575,920 
 
 1,668,690 
 
 4 
 
 303,264 
 
 1,600,000 
 
 1,903,264 
 
 1,584,260 
 
 5 
 
 253,592 
 
 2,000,000 
 
 2,253,592 
 
 1,391.756 
 
 6 
 
 217,144 
 
 2,400,000 
 
 2,617,144 
 
 1,138,331 
 
 7 
 
 190,536 
 
 2,800,000 
 
 2,990,536 
 
 847,298 
 
 S 
 
 168,896 
 
 3,200,000 
 
 3,368,896 
 
 531,453 
 
 9 
 
 152,064 
 
 3,600,000 
 
 3,752,064 
 
 198,388 
 
 10 
 
 138,840 
 
 4,000,000 
 
 4,138,840 
 
 -147,107 
 
Table 2 
 Net Present Value When Y = 3,000,000 
 
 8% 
 
 10" 
 
 X 4- /o 
 
 20? 
 
 : 
 
 2024214. 
 
 ,16 
 
 1456482.77 
 
 1095073. 
 
 ,59 
 
 848607.39 
 
 349986.69 
 
 2 
 
 4430635. 
 
 ,34 
 
 3477957.67 
 
 2782227. 
 
 50 
 
 2260969.91 
 
 1091995.83 
 
 3 
 
 5796651. 
 
 ,94 
 
 4789069.92 
 
 3993273. 
 
 ,87 
 
 3356360.61 
 
 1770443.64 
 
 4 
 
 6558289, 
 
 ,15 
 
 5589962.10 
 
 4789106. 
 
 ,78 
 
 4121126.17 
 
 2327397.02 
 
 5 
 
 6970713. 
 
 ,02 
 
 6063603.48 
 
 5290650, 
 
 ,25 
 
 4627980.42 
 
 2749961.90 
 
 h 
 
 7168113, 
 
 ,17 
 
 6323105.82 
 
 5587937, 
 
 ,24 
 
 4945289.94 
 
 3050213.71 
 
 7 
 
 7224924, 
 
 ,95 
 
 6436916.82 
 
 5740773. 
 
 ,71 
 
 5123398.77 
 
 3246883.66 
 
 8 
 
 7185156, 
 
 .55 
 
 6447794.32 
 
 5788723, 
 
 ,60 
 
 5197695.80 
 
 3358063.40 
 
 iJ 
 
 7076324 
 
 .77 
 
 6383513.48 
 
 5758513, 
 
 ,86 
 
 5193078.24 
 
 3399143.39 
 
 10 
 
 6916460 
 
 .00 
 
 6262792.85 
 
 5668678, 
 
 .75 
 
 5127324.26 
 
 3382632.46 
 
 11 
 
 6717847 
 
 .06 
 
 6698664.69 
 
 5532406, 
 
 .92 
 
 5013368.12 
 
 3318537.53 
 
 12 
 
 6489139 
 
 .95 
 
 5900462.90 
 
 5359308 
 
 .54 
 
 4860800.22 
 
 3214840.53 
 
 13 
 
 6236584 
 
 .58 
 
 5675039.06 
 
 5156537 
 
 .28 
 
 4676860.58 
 
 3077927.23 
 
 14 
 
 5964837 
 
 .40 
 
 5427531.65 
 
 4929520 
 
 .56 
 
 4467106.21 
 
 2912936.95 
 
 15 
 
 5677405 
 
 .91 
 
 5161867.45 
 
 4682446 
 
 .55 
 
 4235867.30 
 
 2724045.49 
 

 Table 3 
 
 
 
 Optimal Investment 
 
 
 Interest Rate 
 
 
 Optimal X 
 
 2 
 
 
 2.329 
 
 4 
 
 
 2.588 
 
 6 
 
 
 2.794 
 
 8 
 
 
 2.969 
 
 10 
 
 
 3.112 
 
 12 
 
 
 3.233 
 
 14 
 
 
 3.334 
 
 16 
 
 
 3.417 
 
 18 
 
 
 3.485 
 
 20 
 
 
 3.540 
 
 22 
 
 
 3.581 
 
 24 
 
 
 3.611 
 
 26 
 
 
 3.629 
 
 28 
 
 
 3.637 
 
 30 
 
 
 3.634 
 
 32 
 
 
 3.620 
 
 34 
 
 
 3.596 
 
 36 
 
 
 3.561 
 
 38 
 
 
 3.514 
 
 40 
 
 
 3.455 
 
 42 
 
 
 3.384 
 
 44 
 
 
 3.297 
 
 46 
 
 
 3.193 
 
 48 
 
 
 3.068 
 
 50 
 
 
 2.917 
 
HECKMAN 
 
 BINDERY INC. 
 
 JUN95 
 
 - „, v N.MANCHESTER, 
 lound-To-IWr |ND1ANA 46962