Pulling Rabbits out of Hats in the Oil Business-and Elsewhere

CFA Institute

Pulling Rabbits out of Hats in the Oil Business-and ElsewhereAuthor(s): Robert Ferguson and Philip PopkinSource: Financial Analysts Journal, Vol. 38, No. 2 (Mar. - Apr., 1982), pp. 24-27Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4478529 .

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by Robert Ferguson and Philip Popkin

Pulling Rabbits DOte!o Hats in the Dii Business -and Elsewhere

The prices recently offered for Conoco and Marathon Oil clearly astounded many market observers. Where did these figures-10, 20, 30 per cent over prevailing market values-come from? Had the managements of Dome Petroleum, Mobil, Du Pont et al. deserted their calculators for magic wands? Were they pulling the numbers out of their hats?

Are companies acting irrationally when they pay seemingly excessive prices to acquire other companies? Not necessarily. When tax deductions such as depreciation can be increased, it is sometimes possible to gain at the government's expense. Perhaps this is what has been happening in the oil industry.

S OMETIMES one oil company buys another in order to obtain its reserves. If the only

L assets of the company being purchased are its reserves, then the market price of the company ought to equal the market value of its reserves. If this were not the case, the company could make a riskless profit by either incorporating or unincorporating reserves.

Why, then, are some companies willing to pay well above the market price of another company's securities in order to obtain its reserves? As it turns out, there is a reason.

The Hats Uno, Inc. is a particularly simple company; Table I shows its balance sheet. It owns $1,000,000 in Treasury bills and some lousy acreage having a market value of one dollar. Needless to say, the market value of Uno's stock is $1,000,001.1

Suddenly, however, the world finds out that Uno's little acre contains oil. A careful analysis of Uno's reserves results in the schedule shown in Table II. Since the net present value of the proj-

ect is $1,509,385, Uno's market price jumps im- mediately to $2,509,385. Table III shows Uno's new balance sheet.2

The stockholders are happy because their wealth has increased 150.9 per cent.3 All is as it should be.

Dos, Inc. is another particularly simple company; Table IV shows its balance sheet. Dos owns $3,000,000 in Treasury bills. Its stock sells for $3,000,000.

Dos has very clever management, however. They realize that if they buy in Uno's stock for a total price of $2,509,385, Dos' depreciation will be higher than Uno's. Uno based its depreciation on its investment of $1,000,000-the amount necessary to implement the project. Dos would base its depreciation on the $2,509,385 it would pay for Uno.

A careful analysis by Dos results in the schedule shown in Table V. Dos' revenue and operating costs will be the same as Uno's, since the project is the same. The discount rate will also be the same, for the same reason. The net present value of the transaction is $378,760.

If Dos accomplished this transaction as planned, its market value would jump by $378,760-an immediate return of 15.1 per cent on its investment of $2,509,385. Dos' new market value would be $3,378,760. Its stockholders would be happy, and so would its management.

1. Footnotes appear at end of article.

Robert Ferguson is Vice President in charge of quantitative research at College Retirement Equities Fund. He is also an Associate Editor of this journal. Philip Popkin is a Security Analyst at College Retirement Equities Fund. The idea for this paper zvas his; any complaints should be sent to him.

FINANCIAL ANALYSTS JOURNAL / MARCH-APRIL 1982 C 24



All would be as it should be. Or would it?

The Rabbit If it pays Dos to buy Uno at a price of $2,509,385, it must also pay Dos to buy Uno at a higher price. Net present values do not change discontinuous- ly as the investment increases. A higher investment will reduce Dos' net present value, but a small increase will still leave a net present value greater than zero. Furthermore, as Dos' con- templated investment increases, so does its depreciation; this will tend to offset the decline in computed net present value.

What if Dos considers paying $3,000,000 for Uno? At this price, Dos' analysis will result in the

Table I Uno, Inc. Balance Sheet

T-Bills 1,000,000 Acreage 1 Equity 1,000,001

schedule shown in Table VI. Dos' market value will now increase by only $11,261-but it will still increase. Dos improves its own position even if it pays almost a 20 per cent premium over the market price for Uno's stock.

Of course Uno, one would hope, will have the ability to do the same analysis that Dos does. Realizing that a price slightly in excess of $3,000,000 is a break-even proposition for the purchaser, both Uno and Dos will haggle about

Table III Uno, Inc. Balance Sheet After Discovery of Oil

T-Bills 1,000,000 Acreage 1,509,385 Equity 2,509,385

Table IV Dos, Inc. Balance Sheet

T-Bills 3,000,000 Equity 3,000,000

the price to be paid. It will be somewhere be- tween $2,509,385 (Uno's market price) and about $3,000,000 (the purchaser's break-even price). A price in excess of current market value is to be expected.4

The Magic in Mergers The appendix sets forth the argument in algebraic terms. Basically, however, the project will be worth more to Dos than to Uno as long as Dos can charge more depreciation than Uno. Greater depreciation will result in greater cash flows from the project, since revenues and costs will remain the same while taxes decrease. Since the appropriate discount rate is specific to the project, the present value of the project's cash flows will be directly related to the level of depreciation: The greater the depreciation, the greater the project's present value.

As long as the cost of the project to Uno is less than the project's present value, implementing

Table II Uno, Inc. Cash Flow Analysis

Operating Pretax Net Discounted Year Revenues Costs Depreciation' Profit Profit2 Cash Flow3 Cash Flow4

0 $ 0 $ 0 $ 0 $ 0 $ 0 -$1,000,000 -$1,000,000 1 1,000,000 100,000 100,000 800,000 400,000 500,000 434,783 2 1,000,000 100,000 100,000 800,000 400,000 500,000 378,072 3 1,000,000 100,000 100,000 800,000 400,000 500,000 328,758 4 1,000,000 100,000 100,000 800,000 400,000 500,000 285,877 5 1,000,000 100,000 100,000 800,000 400,000 500,000 248,588 6 1,000,000 100,000 100,000 800,000 400,000 500,000 216,164 7 1,000,000 100,000 100,000 800,000 400,000 500,000 187,969 8 1,000,000 100,000 100,000 800,000 400,000 500,000 163,451 9 1,000,000 100,000 100,000 800,000 400,000 500,000 142,131

10 1,000,000 100,000 100,000 800,000 400,000 500,000 123,592

$1,509,385

Required capital investment: $1,000,000 Net present value : $1,509,385. Project's present value : $2,509,385

1. Based on straight-line depreciation of $1,000,000 over 10 years. 2. A 50 per cent tax rate is assumed. 3. The cash flow of -$1,000,000 in year zero is the required capital investment. This is presumed to be obtained by selling the T-bills. The

foregone interest must have a present value of -$1,000,000 no matter the interest rate (because this is the market value of the T-bills, by assumption).

4. The appropriate discount rate for this project is assumed to be 15.0 per cent.

FINANCIAL ANALYSTS JOURNAL I MARCH-APRIL 1982 U 25



Table V Dos, Inc. Cash Flow Analysis

Operating Pretax Net Discounted Year Revenues Costs Depreciation' Profit Profit2 Cash Flow3 Cash Flow4

0 $ 0 $ 0 $ 0 $ 0 $ 0 -$2,509,385 -$2,509,385 1 1,000,000 100,000 250,939 649,061 324,530 575,469 500,408 2 1,000,000 100,000 250,939 649,061 324,530 575,469 435,137 3 1,000,000 100,000 250,939 649,061 324,530 575,469 378,380 4 1,000,000 100,000 250,939 649,061 324,530 575,469 329,026 5 1,000,000 100,000 250,939 649,061 324,530 575,469 286,110 6 1,000,000 100,000 250,939 649,061 324,530 575,469 248,791 7 1,000,000 100,000 250,939 649,061 324,530 575,469 216,340 8 1,000,000 100,000 250,939 649,061 324,530 575,469 188,122 9 1,000,000 100,000 250,939 649,061 324,530 575,469 163,584

10 1,000,000 100,000 250,939 649,061 324,530 575,469 142,247

$ 378,760

Required capital investment: $2,509,385 Net present value : $ 378,760 Project's present value : $2,888,145

1. Based on straight-line depreciation of $2,509,385 over 10 years. 2. A 50 per cent tax rate is assumed. 3. The cash flow of -$2,509,385 in year zero is the required capital investment. 4. The appropriate discount rate for this project is assumed to be 15.0 per cent.

Table VI Dos, Inc. Cash Flow Analysis After Purchase of Uno

Operating Pretax Net Discounted Year Revenues Costs Depreciation' Profit Profit2 Cash Flow3 Cash Flow'

0 $ 0 $ 0 $ 0 $ 0 $ 0 -$3,000,000 -$3,000,000 1 1,000,000 100,000 300,000 600,000 300,000 600,000 521,739 2 1,000,000 100,000 300,000 600,000 300,000 600,000 453,686 3 1,000,000 100,000 300,000 600,000 300,000 600,000 394,510 4 1,000,000 100,000 300,000 600,000 300,000 600,000 343,052 5 1,000,000 100,000 300,000 600,000 300,000 600,000 298,306 6 1,000,000 100,000 300,000 600,000 300,000 600,000 259,397 7 1,000,000 100,000 300,000 600,000 300,000 600,000 225,562 8 1,000,000 100,000 300,000 600,000 300,000 600,000 196,141 9 1,000,000 100,000 300,000 600,000 300,000 600,000 170,557

10 1,000,000 100,000 300,000 600,000 300,000 600,000 148,311

$ 11,261

Required capital investment: $3,000,000 Net present value : $ 11,261 Project's present value : $3,011,261

1. Based on straight-line depreciation of $3,000,000 over 10 years. 2. A 50 per cent tax rate is assumed. 3. The cash flow of -$3,000,000 in year zero is the required capital investment. 4. The appropriate discount rate for this project is assumed to be 15.0 per cent.

the project will increase Uno's market price. Bas- ing depreciation on Uno's market price, rather than on the cost of the project, will increase depreciation, hence the project's cash flows (as Dos finds out). Since Uno's market price is the present value corresponding to the smaller depreciation charge, the present value corresponding to the increased depreciation charge

will exceed Uno's market price. If Dos buys Uno at this higher present value,

and charges still higher depreciation as a result, the project's present value will exceed Dos' purchase price. Thus Dos will experience an increase in its market price even if it buys Uno's stocks at a price exceeding Uno's market price. It clearly pays Dos to make the purchase. U

FINANCIAL ANALYSTS JOURNAL / MARCH-APRIL 1982 O 26



Appendix

Define:

7ri the project's operating profit, before depreciation, in period i.

Dji the depreciation charged by company j in period i.

Cj the cost of the project to company j. T the tax rate. Vj the present value of the project to com-

pany j, excluding Cj. R the project's discount rate.

Company 1 computes V1 as follows:

X [-(irDlif-D)T] V,= E ,R. (1)

i=l (1 + R)'

Note that:

wi - Dli = pretax profit.

Rearranging the terms in Equation (1) results in:

V, = (1 - T) E X + T E .1i (2) i=1 (1 + R) =1(1 + R)'

Company 1 chooses to do the project only if:

V, > C, - (3)

Assume this is true. Remember that D1i reflects C1, not V1. Since V1> C1, depreciation based on V1 will exceed D1i.

Suppose that Company 2 pays C2 for Com- pany 1. Then:

V2 = (1 - T) r , 4+T (4)

Here, D2i reflects C2, not C1. If C2 exceeds C1, then D2i will exceed D1i and Equations (2) and (4) show that V2 will exceed V1:

V2-V1 = T E (D2,- D1i) i=1 (1 + R)' (5)

Company 2 will not take on the project by buy- ing it at C2 from Company 1 unless:

V2 > C2 . (6)

Rearranging Equation (5), we have:

V2 = V1 + T E (D2(7DR), ='(1 + R)' (7

V2-C2 = (V1-C1) + T E (1-DR) (8) i=1 (1 + R)' (8

Suppose C2 equals V1, the market price of Com- pany 1. Then the first term on the right of Equa- tion (8) is zero. Then V2 exceeds C2 if D2i exceeds D1i. But in this case, D2i is based on V1 and D1i is based on C1, and V1 exceeds C1. Thus D2i exceeds D1i and V2 exceeds C2. It pays for Company 2 to buy Company 1 at its market value.

Since V2 exceeds C2 when C2 equals V1, V2 also will exceed C2 when C2 is greater than V1 (but not too much greater). This follows because D2i changes smoothly as C2 changes. As C2 increases from V1 in Equation (8), the first term on the right begins at zero and becomes increasingly negative. The second term begins at some positive number and increases, but more slowly than the first term declines. Thus V2 - C2 begins at some positive number and declines. For a while it will remain positive as C2 increases. Thus there is some price greater than the market price of Company 1 at which it still pays Company 2 to buy Company 1 out.

Footnotes

1. If you do not agree with this, return to GO. 2. Clearly this balance sheet was provided by an

economist, not an accountant. We leave it to the reader to impugn the profession of his choice.

3. Management is happy, too. It has a bigger empire to run, and the new budget includes a generous allowance for interior decorating.

4. The example assumes that investors set a market price for Uno's stock equal to the project's present value computed using Uno's depreciation. Some investors may understand Dos' opportunity. To the extent this is so, Uno's stock will sell for a higher price. Because of lack of understanding on the part of some investors, market and other frictions, and other real world imperfections, it is unreasonable to expect Uno's price to be as high as Dos' break- even price.

FINANCIAL ANALYSTS JOURNAL / MARCH-APRIL 1982 rO 27



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Pulling Rabbits out of Hats in the Oil Business-and Elsewhere