sense and nonsense about depreciation

Sense and Nonsense about DepreciationAuthor(s): John CaksSource: Financial Management, Vol. 10, No. 4 (Autumn, 1981), pp. 80-86Published by: Wiley on behalf of the Financial Management Association InternationalStable URL: http://www.jstor.org/stable/3665222 .

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Sense and Nonsense About Depreciation

John Caks

The author teaches in the College of Business Administration at Louisiana State University. This paper was written while he was a graduate student at the University of Pennsylvania.

Politics and Semantics

In recent years, much controversy has surrounded the treatment of depreciation in calculating corporate profits. For example, consumer advocates have claimed that the public is being cheated when utility rates are not reduced for the "deferred taxes" caused by accelerated depreciation. As these are "taxes that are not paid," presumably consumers should not bear such a fictitious burden in the form of higher utility rates. In general, it is widely believed that allowing accelerated depreciation is a subsidy to businesses, to the extent that claimed depreciation exceeds the actual deterioration of the assets.

As my analysis will prove, any depreciation schedule other than a 100% write-off (i.e., expensing investments in plant and equipment) constitutes a tax on capital. As a consequence, investment in capital goods is discouraged, inefficient technology is employed, and the economy "loses" (possibly sub- stantial amounts of) positive net present value projects.

In view of the attention given to depreciation policy, it is surprising that the true nature of depreciation has not been widely recognized. Although the gist of my analysis has already appeared in scholarly literature

since at least 1963 (see [11] and [12], for example), public debate on further accelerating depreciation still erroneously assumes that accelerated depreciation is a subsidy. It may be only semantics, but in a politicized economy there is a difference between "granting a subsidy" and "ameliorating a penalty." Consider this statement by a distinguished economist and former policy maker:

It [the "10-5-3" plan] would scatter its benefits through industries and among assets in ways that bear little relation to the economy's structural needs. Heavy industry and commercial building would reap big benefits. High technology industries and almost anything on wheels would get little benefit [5, p. 16].

The real issue (as I see it) is whether or not the government should arbitrarily penalize long-term investment, not which industries should be granted "benefits." Indeed, if United States heavy industry (e.g., steel mills) has a relatively low technological content, perhaps it is partially a consequence of government policies that discourage investment in new and technologically more advanced equipment.

The ongoing public discussion of the role of private business in our society is hardly enlightened by such

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CAKS/SENSE AND NONSENSE ABOUT DEPRECIATION

misleading information as:1 Ma Bell paid federal tax of only 9% of 1979 taxable income of $9.14 billion, thanks to investment tax credits and accelerated depreciation.... For 1978, it paid 15% of taxable income [15, p. 1].

It will be shown that, apart from the effect of investment tax credits, the existence of deferred taxes due to accelerated depreciation is evidence of a true effective tax rate above the statutory rate. Interpret- ing this to be "preferential treatment" is adding insult to injury.

I will not address questions such as: Are utilities and other capital intensive industries

undesirable elements in our economy? What should the corporate tax rate be?

But I do maintain that the public debate on these and other questions should be rational and logical. A proper understanding of depreciation is only one step in this direction.

A Simple Analysis In a world without corporate taxation, the value of

a project (or a firm) is

VF = PV(R)- PV(VC)- PV(I) = PV(X)- PV(I) (1)

where R = Revenues in time tl, t2,...; VC = Variable costs, including labor and raw

materials, in time t,, t, ...; I = Expenditures for capital goods such as

equipment; and PV( ) is the present value operator.

Equation (1) applies to evaluating any project and, by the Value Additivity Principle, it also applies (by aggregation) to the value of a firm (see [4] and [16], for example). The use of the present-value operator simplifies the analysis by avoiding the technical details of evaluating risky multi-period investments. Such details may be important in specific practical appli- cations, but they are irrelevant to the issues considered here. For simplicity, assume PV(I) = I; i.e., we examine whether or not an investment in plant and equipment should be made today. It is clear that the analysis is sufficiently general to allow an examination

'Because the investment tax credit was less than 10% of AT&T's 1979 taxable income, the company's "true effective tax rate" was certainly greater than 36%. The long lives of many of its investments, high interest rates in 1979, and the calculations given in Exhibit 1 make it difficult for me to believe that AT&T's "true effective tax rate" in 1979 could have been significantly below the statutory rate of 46%.

of a project in which further investments will be re- quired in the future.

First, consider the case of a firm whose "income" is taxed at rate TC and that does not invest in plant and equipment or other fixed assets. Clearly investors value the firm on the basis of its after-tax cash flows.

VF = [PV(R) - PV(VC)] (1 - TC) = PV(X) (1 - TC). (2)

Equation (2) illustrates an interesting point: the government is beneficial owner of (TC) * 100% of such firms.

Equation (2) also shows that corporate taxation has only one possible effect on the investment behavior of firms that do not invest in capital goods: It can only affect the amount invested but not the kind of investment.2 That is, the owners of firms are affected by corporate taxation only with respect to their alternative choice of consumption. If the after-tax return is sufficient to induce them to forgo consumption, their decision regarding which projects to choose (including the choice of appropriate technology and level of labor input) is identical to the no-tax decision. The condition that the marginal rates of substitution among inputs equal their relative prices is identically deduced from either the no-tax case (1) or the tax case (2). This is obvious because

VI = VF (1 - TC) (3)

and because we assume that the owners seek to maxi- mize their wealth.

It is straightforward to extend the analysis to the case of capital goods investment by specifying

VI = VF° (1 - TC) = [PV(R) - PV(VC) - I] (1 - TC). (4)

Equation (4) represents the case when investment in capital goods is expensed. Again we have the situation where the government is beneficial owner of (TC) 100% of the firm and the owners of the firm make the same technological decisions (given a level of investment) as they would in the no-tax case. However, Equation (4) does not apply to United States practice, in which investment in plant and equipment must be amortized over some arbitrary period for purposes of claiming a "depreciation" deduction. Under such circumstances, the net present value of a project is

'It should be noted that assuming no investment in capital assets is not equivalent to assuming no investment; e.g., purchases of raw materials, advertising, etc., can be expensed.

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FINANCIAL MANAGEMENT/AUTUMN 1981

VF = PV(R - VC). (1 - TC)- I + .* TC I (5)

where ( is the present value of the depreciation deductions per dollar of investment.

As a brief digression, let us consider a recent proposal for stimulating investment:

Appealing in its economic logic, but too novel and costly to attract widespread support as yet, is a plan for full write-offs of the discounted value of lifetime depreciation allowance in the first year of an asset's life [5, p. 16]. (Emphasis added.)

In other words, it is proposed that the amount 4 * I be allowed as a deduction during the first year, with no further depreciation deductions allowed. But it is obvious from Equation (5) that such a proposal would have absolutely no effect. It makes no difference whether a person receives $1.00 next year or $0.909 today if the interest rate is 10%. Businessmen or businesswomen are so easily fooled! In fact, their analyses - as well as the analyses taught in elemen- tary finance texts - are essentially equivalent to Equation (5). The only difference is that in the "real world" it is difficult to determine the proper discount rates for estimating present values. There may also be some controversy as to how to correctly calculate the present value of a project. For example, some analysts may not recognize that the proper discount rate for the depreciation stream is the risk-free interest rate (see [6]).

Comparison of Equation (5) with Equation (4) makes it clear that capital goods are taxed at an implicit rate of

VI - VF =TC(I - ) (6) I

That is, Equation (6) represents the rate of an implicit government tax on capital expenditures. (See Exhibit 1 for numerical examples showing the magnitude of this tax.) One consequence of this implicit tax on capital is that firms will not choose the most efficient technology (from the standpoint of a no-tax world). There is a clear bias in favor of

1. Using raw materials instead of purchasing technologically more efficient machines; and

2. Substituting labor for capital. Equation (5) also reveals as nonsense the claim that

(through accelerated depreciation) firms can have effective tax rates that are below the statutory rate. The effective tax rate of a project or firm that employs no capital assets is (TC) * 100%, because this is the portion of the value of the project that will be taken by

Exhibit 1. Implicit Tax on Capital*

After-tax Asset Interest Rate Life .02 .04 .06

2 .003 .006 .009 4 .009 .017 .025 6 .015 .028 .041 8 .020 .039 .056

10 .026 .049 .070 15 .040 .073 .102 20 .052 .095 .130

*Assuming "sum-of-years" depreciation method and TC = .46.

the government. For projects with capital investments, the effective tax rate (T*) is given by

VF - - -T,or

T* = TC [1 +( )(1 - (4)] > TC. PV(X) - I

In other words, firms which seem to have "effective tax rates below the statutory rate" because of accelerated depreciation actually have true effective tax rates above the statutory rate. Needless to say, T* is even higher if the firm does not use accelerated depreciation for its tax accounting.

From Equations (5) and (6), we can separate the tax effects of depreciation into two parts:

1. The government imposes a tax of TC * I on a capital expenditure; and

2. The government gives the firm a bond-like financial asset which reduces its future tax payments; the present value of this "quasi bond" is $ * TC * I.

Since 4) < 1.0, the net effect of this process is to tax investment expenditures. By accelerating depreciation schedules, $ increases and the net tax diminishes, but it never becomes a subsidy. In contrast, consider the following argument:

The role of growth in our analysis may raise questions. For example, since the present value of future depreciation deductions for a particular asset is independent of the rate of growth of the firm's capital acquisitions, how can accelerated methods for tax purposes discriminate in favor of growing firms? The answer turns on interest-free loans. A firm that uses accelerated depreciation can be thought of as receiv- ing loans from the Treasury in the early years of an asset's life equal to the tax rate times the amount by which its deductions exceed those under straight-line. These loans are repaid, without interest, in the later years of the asset's life when the deductions under

(7)

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accelerated methods are smaller than those with straight-line. The advantage of growth is simply that the firm continuously receives a larger volume of loans than it is repaying [10, p. 575].

The error, of course, lies in the authors' failure to recognize that the "interest-free loan" is only a partial reduction of the tax on the capital expenditure. There is no inherent tax "discrimination" in favor of firms with large capital expenditure programs. Quite the

contrary! Such faulty analyses might be amusing if it were not for the fact that policy makers sometimes take them seriously.

Yet another implication of Equation (5) is that the economy "loses" positive net present value projects because of the tax on capital. No firm would rationally accept a project if it were taxed at a rate ex- ceeding 100%. Hence T* < 1 implies that projects will be accepted only if

PV(X)>I+ I(1-P)TC = 1--'TC) (1 - TC) 1 - TC (8)

For example, with TC = .46 and q = 0.8, it is

necessary for the present value of the "benefits" of an investment I to exceed (1.215) I. Assuming labor and other variable cost inputs are not perfect substitutes for plant and equipment, it is obvious that many worthwhile projects will be rejected. This not only lowers the wealth of the owners, but it may also reduce the present value of the taxes the government collects. Of course, the loss of taxes on forgone projects is offset (at least partially) by the increased taxes on accepted projects. Exhibit 2 presents numerical values of this depreciation-induced hurdle factor (i.e., minimum acceptable PV(X)/I).

Offsetting "Subsidies"

As the analysis given above clearly shows, any depreciation policy (other than full write-offs of investment) constitutes a tax on capital. This really is obvious. But the depreciation penalty is only one part of the economic environment that firms face. Whether the net effect of all government policies is to discourage investment is a complicated question that will not be answered here, but it may be useful to examine two "subsidies" which may offset the depreciation penalty.

Most prominent is the investment tax credit: firms may claim as a tax credit 10% of their new investment in plant and equipment with lives of seven years or longer, and lesser amounts for equipment with lives of three to seven years. The tax credit necessary to com-

Exhibit 2. Hurdle Factors

After-tax Asset Interest Rate Life .02 .04 .06

2 1.01 1.01 1.02 4 1.02 1.03 1.05 6 1.03 1.05 1.08 8 1.04 1.07 1.10

10 1.05 1.09 1.13 15 1.07 1.14 1.19 20 1.10 1.18 1.24

pletely offset the depreciation penalty is given by Equation (6) and Exhibit 1. For moderate interest rates, it appears that the existing investment tax credit does in fact provide adequate relief.

Nonetheless, I maintain that it does make a difference in a politicized economy whether the investment tax credit is correctly recognized to be a "rebate of a tax on investment expenditures" or whether it is erroneously considered to be a "free lunch" given to business at the expense of "the people." Further- more, examination of Exhibit 1 shows that there is a net subsidy or penalty on new investment that is determined solely by the estimated life of the asset instead of by some more rational criterion. Indeed, the implicit tax on equipment with lives of less than three years is not ameliorated at all, because the investment tax credit does not apply.

Somewhat more controversial is the question of whether debt financing provides a subsidy to business. For simplicity, let us assume a "flat" after-tax term structure, and confine our analysis to par bonds. The price (P) of a par bond with face value (I) is8

N rI(l - TP) I t=l (2 + =i) t = I (lI+ i)t (I + i)N

(9)

where r = coupon rate; i = after-tax interest rate; and

TP = tax rate of the marginal bond investor. It directly follows that r = i/(l - TP) in the case of

par bonds. Now let us consider the net present value (A) to the

firm of selling a bond:

N rI(1-TC) I t = ( + i)t ( + i)N

AI[( + i)-1 TC-TP (l+i)N 1-TP (10)

'See Caks [2] for a justification of Equation (9).

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If TC > TP, firms could increase their market value by issuing as much debt as possible and using the proceeds to pay dividends, to repurchase their own shares, or to purchase shares of other firms. Thus Miller [8] argues that the supply of new bonds will exceed demand until the before-tax interest rate is bid up to r = i/(l - TC) and TC = TP in equilibrium. Then there would be no debt subsidy (A = 0) and, hence, debt financing cannot be used by the firm to offset the depreciation-induced tax on capital, as is sometimes suggested in the literature (see [13] and [1], for example).

Miller's conclusion that TC = TP has not gone un- challenged. DeAngelo and Masulis [3] offer theoreti- cal objections. Furthermore, empirical estimates of TP vary widely; McCulloch's [7] estimate that TP is between 20% and 30% is perhaps the most extreme in its deviation from TP = TC. In view of the controversy on the debt subsidy issue, it may be worthwhile to repeat the analysis given earlier (ignoring investment tax credits) under the assumption that TP < TC. We will also assume that capital investments are 100% debt financed with "bullet loans" and that the firm's borrowing is constrained by its investments in real assets.4 Under these circumstances,

VF = PV(X) (1 - TC)- I + TC I + A. (11)

Using the (unlevered firm) no-tax case VF from Equation (1) and the unbiased case VF from Equation (4), we obtain the following results:

The tax on capital with 100% debt financing is

vI - vL a VI = TC(l - )- A (6')

Similarly, the effective tax rate (T*) is given by

- 1 - T*, or

T*=TC [1+ ,-( _1. (7') T*= TC [l + p %(X)-I PV(X)-I (7')

As investments will be made only if T* 1, this implies that projects will be accepted only if

PV(X) > I ( ) - TC) (8') 1 - TC I - - TC

4Assuming "bullet loans" overstates the magnitude of the debt subsidy (if it exists) because lenders do not typically lend 100% of the asset's value and usually require periodic partial repayment of the loan to offset the declining value of the collateral. If borrowing is not constrained by the firm's investments in real assets, then it makes no sense to introduce financing into an analysis of the investment decision.

Exhibit 3 shows numerical examples of the "hurdle factors" for TP = .20 and TP = .40.

Some Loose Ends

"Economic Depreciation" I have argued that the only depreciation scheme

that does not penalize investment in capital goods is 100% expensing. This is obvious from Equation (5), because neutrality requires c = 1.0, and presumably the sum of depreciation deductions equals the cost of the asset. If we relax the second requirement, other patterns of "depreciation" are acceptable, provided that their present value equals the cost of the asset. This would mean allowing firms to charge off as "depreciation" more than they paid for the asset.

Another alternative to 100% write-offs is to allow the firm to deduct "economic depreciation," where this represents the change in pre-tax market value of the project (see [9] and [12]). Such a policy, though, might be irrelevant to "depreciation" of assets per se, because an asset would be eligible for varying amounts of "economic depreciation" depending on how profitably it is used. As a practical matter, it would be difficult to obtain an impartial and accurate estimate of "economic depreciation."

Some authors use the term "economic depreciation" to refer to the decline in market value of (for example) a machine as it deteriorates physically. This sort of "economic depreciation," however, is an implicit tax on capital.

Lost Tax Revenues

One of the major concerns with proposals to further accelerate depreciation schedules is the loss of tax revenues. To put this into proper perspective, recall that the tax effects of depreciation can be broken into two parts:

1. The government imposes a tax of TC * I on a capital expenditure; and

2. The government gives the firm a bond-like financial asset which reduces its future tax payments; the present value of this asset is 4 * TC * I.

As half of this process involves "selling" a government "quasi bond," an obvious solution to the "reduced tax revenues" problem is simply to sell more bonds. Possibly the increase in future taxes [through increased investment; see Equation (8)] will "pay" for these additional bonds. If not, then tax rates or government spending will need to be adjusted.

Actually, the issue of lost tax revenues is an irrele-

84




Exhibit 3. Hurdle Factors (100% Debt Financing)

TP = .40

20

Asset Life

15 :

TP = .20

.80

Minimum Acceptable PV(X) / I

vant one. Superficially, it may seem legitimate to ask, "Can we afford these subsidies to business?" The real issue, however, is whether or not to tax investment expenditures. If such a tax is not desirable, then eliminating it cannot be undesirable.

The two-part representation of the tax effects of depreciation points out the true adverse effect of infla-

tion. Business is not hurt by rising replacement costs per se but rather by the decline in market value of the · * TC * I "quasi bond" as interest rates rise. If, for example, the market price of a particular machine did not rise with the general price level, the firm would still be adversely affected by inflation, replacement costs notwithstanding.

1.15

1.10

1.05

1.00

.95

.90

.85

85




Conclusion

Whether government policy has a net favorable, neutral, or unfavorable effect on private investment is a difficult question. It does seem clear to me that current depreciation schemes do discourage long-term capital investments. Whether this is in the form of smaller net incentives or larger net penalties can only be determined in a more comprehensive analysis than attempted here. In any case, I hope that future public discussion of depreciation and related issues will be more logical than in the past.

References 1. R. W. Broadway and W. Bruce, "Depreciation and

Interest Deductions and the Effect of the Corporation Income Tax on Investment," Journal of Public Eco- nomics (February 1979), pp. 93-105.

2. J. Caks, "Corporate Debt Decisions: A New Analytical Framework," Journal of Finance (December 1978), pp. 1297-1315.

3. H. DeAngelo and R. W. Masulis, "Optimal Capital Structure Under Corporate and Personal Taxation," Journal of Financial Economics (March 1980), pp. 3-29.

4. C. W. Haley and L.D. Schall, The Theory of Financial Decisions, New York, McGraw-Hill Book Co., 1979.

5. W. W. Heller, "The Tax Cut Battle Lines," The Wall

Street Journal (August 6, 1980), p. 16. 6. H. Levy and F. D. Arditti, "Valuation, Leverage, and

the Cost of Capital in the Case of Depreciable Assets," Journal of Finance (June 1973), pp. 687-693.

7. J. H. McCulloch, "The Tax-Adjusted Yield Curve," Journal of Finance (June 1975), pp. 811-836.

8. M. H. Miller, "Debt and Taxes," Journal of Finance (May 1977), pp. 261-275.

9. P. A. Samuelson, "Tax Deductibility of Economic Depreciation to Insure Invariant Valuations," Journal of Political Economy (December 1964), pp. 604-606.

10. J. B. Shoven and J. I. Bulow, "Inflation Accounting and Nonfinancial Corporate Profits: Physical Assets," Washington, Brookings Papers on Economic Activity (1975), pp. 557-598.

11. V. Smith, "Tax Depreciation Policy and Investment

Theory," International Economic Review (January 1963), pp. 80-91.

12. J. E. Stiglitz, "The Corporation Tax," Journal of Public Economics (April-May 1976), pp. 303-311.

13. J. E. Stiglitz, "Taxation, Corporate Financial Policy, and the Cost of Capital," Journal of Public Economics

(February 1973), pp. 1-34. 14. "The Attack on Bell's Billions," Business Week (April

17, 1978), pp. 137-138. 15. Wall Street Journal (March 12, 1980), p. 1. 16. J. B. Williams, The Theory of Investment Value, Cam-

bridge, Harvard University Press, 1938.

EASTERN FINANCE ASSOCIA TION CALL FOR PAPERS

The Eastern Finance Association will hold its eighteenth annual meeting in Jacksonville, Florida, April 22-24, 1982, where the headquarters hotel will be the Sheraton at St. Johns Place. Research papers covering numerous aspects of finance will be presented and discussed. All academicians, business professionals, and government specialists with an interest in finance are cordially invited to at- tend. Please send a two-page, single-spaced abstract of your paper, or indicate your interest either in organizing a panel discussion or in serving as a chairperson/discussant. Send your proposal to par- ticipate before October 31, 1981, to

Philip L. Cooley Vice President-EFA Program College of Business Administration University of South Carolina Columbia, SC 29208.

Information on local arrangements such as lodging and travel can be obtained from Charles W. Young, College of Business Administration, University of North Florida, Jacksonville, Florida 32216.

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sense and nonsense about depreciation

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