ELEMENTS OF THE TAX ENVIRONMENT OF R & D

19

firm as a whole, then, the B-index must be at least 1, and a higher tax rate is never preferred to a lower one.

The marginal effect of additional deductions or sp cial allowances also depends on the corporate tax rate. It was calculated above that if the corporate tax rate is 50 per cent, a 100 per cent write-off of R & D costs plus a 25 per cent special allowance will result in a B-index of .75. If the corporate tax rate were 25 per cent, the same write-off, special-allowance combination would result in a B-index of .92. In this case the marginal effect of the special allowance on the B-index decreases as the corporate tax rate falls.

Tax credits can also result in a B-index that is less than 1. If a tax credit equal to 10 per cent of R & D expenditures is allowed in addition to a 100 per cent write-off and if the corporate tax rate is 50 per cent, the B-index is (1-t−.10)/(1−t), or .80. Again, the B-index is a decreasing function of the tax rate. If the corporate tax rate were 40 per cent, for example, the B-index would be 89. If, however, the amount of R & D expenditures that may be deducted is reduced by the amount of the credit (the credit is taxable), then the B-index takes on a value of (1−t)(1 − .10)/(1 −t), or .90 regardless of the corporate tax rate. The lowering of the corporate tax rate reduces the marginal effect of a tax credit on the B-index then, provided that the credit itself is not taxable. If the credit is taxable (deductions allowed are reduced by the amount of the credit), its marginal effect on the B-index will be independent of the corporate tax rate.

Both special allowances and credits that are based on increases in R & D spending over some base year also have the effect of reducing the Bindex. The magnitude of this effect depends on how one views the R & D decision. Strain3 assumes, in effect, that base year spending is zero and then calculates the after-tax cost of R & D for the first year in which positive spending occurs. If the allowance is fraction w of the increase in nominal R & D spending over the base period (which in this example is the previous year) and if there is a 100 per cent write-off but no other credit or allowance, the B-index will be (1−(1+w)Q/(1−t). If w is 50 per cent the B-index is (1-(1150)(50) (1 50), or 50. The problem with this type of calculation is that it overstates the impact of this type of incentive. In this example, if nominal R&D spending remains constant or decreases the next year, there is no additional deduction at all and the B-index is 1. The problem, then, is to find what is the incentive provided by this once-for-all tax saving that will maintain a given annual level of R & D spending over time.

In order to obtain a more general measure of the impact of this type of incentive on the B-index, we assume and will continue to assume that the firm

William J. Strain, “Tax and Other Incentives to Reduce R & D Costs," in Current Develupmeius in Measuring Business Income for Tax Purposes, Corporate Management Tax Conference 1981 (Toronto: Canadian Tax Foundation, 1982), 227-54, ₪ 251.

is choosing an annual level of R & D spending that is profitable to maintain over time. Thus, real annual R & D expenditures are maintained at a level such that the benefit-cost ratio on the last dollar spent annually equals the Bindex. The B-index, in turn, is calculated on the assumption that R & D expenditures will be maintained at a constant level in real terms over time. Under these circumstances, allowances or credits based on increases in nominal R & D spending over the previous period will have two effects on the B-index. First, given constant real R & D spending and inflation at an annual rate of p, nominal R & D spending will rise at a rate of p per period and the firm will be entitled to a deduction of wp annually. In the absence of other incentive measures and assuming a 100 per cent write-off of R & D expenditures, the B-index is (1−(1+wp)t)/(1−t). If w is 50 per cent and p is 10 per cent, then the B-index is (1−(1+.05)(.50) )/(1−.50), or .95. Second, there will be a one-time tax saving of wt for each dollar added to the annual level of R & D spending that the firm decides to maintain. This tax-saving would produce an annual income of r(1−t)wt if invested elsewhere. This is simply the value in annual terms of the once-for-all tax saving associated with an increase of one dollar in the firm's real annual R & D budget. If the rate of interest is 15 per cent, the tax saving involved is (.15)(1.50)(.50)(.50), or $.019 per dollar added to the annual R & D budget. When both effects of this incentive are included in the calculation, the B-index takes on a value of

[1−(1+w(p+r(1−t) )t))/(1−t),

which is .91. This implies that it will be profitable to maintain real annual R & D spending at a level such that the benefit-cost ratio on the marginal dollar spent each year is .91.

Favourable tax treatment of royalties resulting from past R & D projects can also reduce the B-index. The advantage of R & D in this case stems from the fact that R & D expenses may be deducted from aggregate taxable income, which is taxed at a higher rate than royalty income. Thus, if ordinary income is taxed at rate to and royalty income at a lower rate to and if ordinary income amounts to a fraction, u, of the total, the firm's average tax rate is

The after-tax cost of R & D is $1(1-T). If the R & D results in nothing but royalties, the firm's B-index is

(1-T)/(1~tr) = 1-tr-u(to-tr)/(1-tr) < 1.

The impact of the ability to deduct R & D expenditures whenever income is available, through the use of carryforward losses and the like, cannot readily be illustrated with the B-index or any other summary index. In special cases where the distribution of income over time is known, such calculations can be made. They are not helpful, however, in making the type of general comparisons between countries that are required here.

ELEMENTS OF THE TAX ENVIRONMENT OF R & D

The Economic Implications of International Differences in the B-Index

21

The B-index provides a summary measure of international differences in the tax treatment of R & D. As established above, the lower the B-index the lower the benefit-cost ratio at which an R & D project will increase the overall profitability of the firm that undertakes it. Other things being equal, the amount of R & D that will be conducted by a nation's corporate residents varies inversely with its B-index. Since the tax measures that reduce the B-index generally apply only to R & D conducted within the country concerned, as a country's B-index falls, the amount of R & D conducted within that country will increase.

Suppose that country A allows the deduction of current R & D expenses and requires that the capital component be depreciated on a straight-line basis over five years. If 20 per cent of R & D expenditures are of a capital nature and we discount at 15 per cent, the present value of the depreciation charges on the capital component of the R & D is $.09. If the corporate tax rate is 50 per cent, the B-index for country A, BA, is (1-.89(.50) )/.50, or 1.11. Country B maintains a 50 per cent tax rate, a 100 per cent write-off of R & D expenditures and a 20 per cent tax credit that does not reduce the deduction that would otherwise be available. The B-index for country B, B. is (1-.50-20)/.50, or .60.

The implications of the difference between the respective B-indexes of countries A and B are illustrated in Figure 2.1. The R & D opportunities available to residents of countries A and B are summarized by the MBC or marginal benefit-cost ratio schedule. This is simply the benefit-cost ratio on each additional dollar spent annually on R & D in either country. If the R & D opportunities available to the residents of either country are the same, then the same MBC schedule can be used to determine annual R & D spending in each country. Residents of country A will find it profitable to move along the MBC schedule until their annual R & D spending is $OSA. At this point the benefitcost ratio on the last dollar spent (annually) is 1.11, which is also the B-index for coumry A. R & D spending in excess of OSA per period would reduce the overall profitability of the corporate residents of A. Residents of country B will find it profitable to move along the MBC schedule until their annual R & D spending is OS At this point the benefit-cost ratio on the last dollar spent each year will be 60. Annual R & D spending in excess of OS would decrease the overall profitability of the corporate residents of country B.

In a no-tax world, residents of both A and B would spend $OS, annually on R & D. At that level of spending the benefit-cost ratio on the marginal dollar spent each year would be. This, of course, is the minimum benefit-cost ratio that R & D can have and still contribute to profitability in a no-tax world. By way of comparison with a no-tax world then, residents of country A will be

Figure 2.1 The Impact of International Differences in B-Indexes

spending too little" annually on R & D they will not be undertaking R&D projects they would undertake if there were no taxes, credits, or allowances. Residents of country B, on the other hand, will be undertaking projects they would have rejected in a no-tax world—they will be undertaking some R & D ($SpSB per year) not because of the income it produces but because of the taxes they will save on other income. While country B spends more each year on R & D than A, neither country is spending the "correct" amount. When compared with the level of R & D spending that would prevail in a notax world, residents of A are forgoing surplus in the amount of $LA annually, while residents of B are forgoing surplus in the amount of $L ̧ annually.

The above discussion has assumed that, while R & D opportunities are similar in A and B, they are specific to each country. An alternative assumption is that the MBC schedule represents the world-wide distribution of R & D opportunities, and that these opportunities can be exploited from within either A or B. In this case, SASB of these opportunities could only be exploited by residents of B. While OSA could profitably be conducted within A, the tax burden would be higher by $.255 per dollar spent than in B. For this reason, all R&D will be located in B.

In the case just examined, annual R & D spending, all of which takes place in B, will be greater by $S,SB per year than in a no-tax world. Some projects will be undertaken because they reduce the overall tax liability of the firm that

23

Present value of

R & D related benefits

+ present value of

R & D related Costs and thigeab va alafoob grubnoge idda

pufen am to SA dari Spoganjana Q1 SBS 2013
Annual R & D spending

Figure 2.2 The Impact of Differences in B-Indexes
When Social and Private Benefits of R & D Differ

undertakes them rather than because of the value of the new technology they expect to develop. The resulting deadweight loss, all of which is borne by residents of B, is given by triangle Lin Figure 2.1.

Most commentators follow Arrow in asserting that there is a positive externality associated with R & D. That is, R & D confers benefits on individuals for which the latter are not obliged to pay. Put another way, it is costly for inventors to keep others from copying their inventions ("free riding"). To the extent that R & D results in benefits to society in excess of those received by the R & D performer, the social benefit-cost ratio of a given R & D project will call the private benefit-dost ratio. Thus there will be a marginal social benefit-cut schedule (MSBC schedule), which lies above the MBC schedule employed in Figure 2.1. The relationship between the two schedules is illustrated in Figure 2.2. The vertical distance between the two schedules represents, for each successive dollar of R & D, the benefits that accrue to someone other than the performer of the R & D.