Leasing, taxes, and the cost of capital

Journal

of Public

Economics

44 (1991)

173-197.

North-Holland

and the

Leasing,

cost

of capital*

J.S.S. Edwards Faculty of Economics and Politics and St John’s College, University of Cambridge, Cambridge CB3 9DD, UK

C.P. Mayer City University Business School, The Barbican Centre, London ECZY 8HB, UK Received January

1984, revised version

received July 1990

A model of firm financial and investment behaviour when there is a possibility of tax exhaustion is used to analyse the incentives for firms to act as lessees or lessors and the determination of the equilibrium rental rate in the leasing market. A number of results emerge which are relevant for public policy. It is shown that: (i) leasing may diminish aggregate investment by comparison with the situation when it does not occur; (ii) rents are likely to be earned on leasing activities; and (iii) a purely tax-induced positive relationship exists between aggregate investment and corporate profits.

1. Introduction A feature of many corporate tax systems that has become of increasing practical importance in the last decade is the asymmetrical treatment of taxable profits and taxable losses. If in a particular year the value of tax allowances claimed by a firm exceeds the value of its profits that are subject to tax, then the firm is unable to receive a rebate in respect of the taxable loss. Instead the firm is required either to carry the taxable loss back and set it against previous profits if available, or, failing that, to carry the loss forward and deduct it from subsequent profits. In many cases both provisions are restricted: in the United Kingdom, for example, while losses can be carried forward indefinitely, they can only be carried back for up to three years. In the United States losses can be carried forward for a maximum of fifteen years. In neither case can losses be carried forward with interest, and *This work is part of the Institute for Fiscal Studies project on Fiscal Policy in the Corporate Sector, supported by the Economic and Social Research Council and the Esmee Fairbairn Charitable Trust. We thank these organisations for their financial support. We are also grateful to Steve Satchel1 and two anonymous referees for their helpful comments on earlier versions of this paper, and especially to Michael Keen for his considerable contribution to it. 0047-2727/91/$03.50

0

1991-Elsevier

Science Publishers

B.V. (North-Holland)

174

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

this is the general feature of the tax system that causes the effective tax rate on taxable profits and losses to differ. Tax losses have become an increasingly important characteristic of many countries’ corporate tax systems. In the United Kingdom the 1982 Green Paper on Corporation Tax [HMSO (1982)] estimated that accumulated tax losses stood at g30,OOO million, and that during the latter half of the 1970s only about 40 percent of all companies paid mainstream corporation tax in any one year. Devereux (1987) estimates that in 1982 about 35 percent of all U.K. non-oil industrial and commercial companies had tax losses. Even after the 1984 reform, and assuming no behavioural response, the estimate for 1988 is around 11 percent. In the United States, Cordes and Sheffrin (1983) observed that the average effective tax advantage to debt finance falls well short of the full corporate tax rate as a consequence of the inability of many firms to claim all available interest deductions. Auerbach and Poterba (1987) report that nearly 15 percent of their sample of U.S. non-financial corporations had tax-loss carryforwards in 1984. Shoven and Tachibanaki (1988) estimate that in 1983 55 percent of Japanese corporations did not pay any corporate taxes because of losses. One of the consequences of widespread tax losses has been the rapid growth of leasing as a means of financing investment: for example, the proportion of manufacturing investment in plant, machinery and vehicles in the United Kingdom financed by leasing rose from 6 percent in 1975 to 21 percent in 1981 [Bank of England (1982)]. There is a large literature in the finance journals on how firms should decide whether or not to lease [see, for example, Bower (1973), Myers, Dill and Bautista (1976), Franks and Hodges (1978, 1987) and Brealey and Young (1980)], and it is widely recognised that differences in the tax payment position of firms are an important, though not always sufficient, condition for both lessee and lessor to gain from leasing [see Brealey and Myers (198 1) and Myers, Dill and Bautista (1976)]. While a number of authors have considered the effects of tax exhaustion on the firm’s investment and financing decisions [Auerbach (1983, 1986), Cooper and Franks (1983) Cordes and Sheffrin (1981, 1983), De Angelo and Masulis (1980), Edwards and Keen (1985), Green and Talmor (1985, 1986), Majd and Meyers (1985), and Mayer (1986)], there has not yet been an integration of leasing into the literature on taxation and the cost of capital which follows the work of King (1974, 1975) and Stiglitz (1973). The purpose of this paper is to provide just such an integration. In this paper a model of firm financial and investment behaviour when there is a possibility of tax exhaustion is presented in order to analyse both the incentives for particular firms to act as lessees and lessors, and the determination of the equilibrium rental rate in the leasing market. The model permits a precise description of how asymmetries in the treatment of taxable profits and losses establish cross-company variations in the cost of capital for

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

175

assets owned by firms in the absence of leasing, and so give rise to incentives for leasing activity. The substantial variations in the cost of capital for assets owned by firms which can result from the possibility of tax exhaustion create large benefits to trade in taxable capacity through leasing, and the scale and nature of a particular firm’s leasing activities are seen to reflect the relationship between demands for the use of capital assets by, and costs of capital for assets owned by, the firm and the market as a whole. The emergence of leasing as an important source of investment finance has raise several policy questions. First, it is generally presumed that by permitting trade in taxable capacity leasing encourages capital investment. Since the extent to which tax minimisation schemes are tolerated is at least to a degree at the discretion of governments, the observation in this paper that leasing may diminish aggregate investment by comparison with a situation where there is no leasing suggests that such discretion should be used with care. Secondly, the rents associated with leasing activities have been used in the past to justify the imposition of special taxes [see Edwards and Mayer (1983) for discussion of this issue in the context of the 1981 windfall tax on U.K. banks’ profits]. In contrast with other discussions [see Miller and Upton (1976)] this paper provides a theoretical justification for the existence of such rents and suggests the need for empirical analysis to identify their magnitude. Finally, the paper shows that there is a positive relationship between aggregate investment and corporate profits which is purely tax-induced, and so existing corporate tax systems which involve asymmetric treatment of taxable profits and losses may exacerbate fluctuations of aggregate investment over the cycle because of this relationship. Section 2 of the paper describes a model of firms facing a corporate tax system that requires taxable losses to be carried forward without interest but permits firms to trade taxable capacity via the leasing market. Section 3 analyses the effects of the asymmetric treatment of taxable profits and losses on firms’ costs of capital for assets they own, and the relationship of these costs of capital to the lease rental rate. It also analyses the equilibrium properties of the leasing market and the effects of tax exhaustion and leasing on investment. The results of the paper are summarised in section 4. 2. A model of firm behaviour under possible tax exhaustion In this section we develop a model of firm financial and investment behaviour with possible tax exhaustion and leasing. This model will be used in the following section as the basis of our analysis of equilibrium in the leasing market and the effects of leasing on investment. The model we develop involves a number of simplifying assumptions that permit us to focus clearly on the implications of tax exhaustion and leasing for the cost of capital and investment.

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

176

The firm is assumed to behave competitively in a perfect capital market and to maximise the value of shareholders’ equity in a discrete time framework. Investors in the firm are assumed to be a homogeneous group facing proportional tax rates of m on personal income and z on accrued capital gains and losses.’ It is assumed that the personal tax system discriminates in favour of retained profits and against new share issues as sources of equity finance: under a classical form of corporation tax system this requires that m>z,

while under

(14 an imputation

system the required

relationship

is

m>z+s(l-z),

(lb)

where s is the rate of imputation [we abstract here from the possibility that the firm may be unable to claim a full imputation deduction; see Edwards and Keen (1985), Keen and Schiantarelli (1988) and Mayer (1986)]. Given our assumption of discrimination by the personal tax system against new equity as a source of finance, we assume, for simplicity, that firms cannot issue new equity. Investors in the firm are risk-neutral, and both corporate and personal investors can borrow and lend at a safe rate of interest, r. We assume that there is no bankruptcy, as the issues that we wish to analyse do not depend on the possibility of bankruptcy, and the difficulties of modelling bankruptcy in a multi-period framework would greatly complicate the paper. Since the stochastic process for profits described below is not in general a random walk, there is no presumption that bankruptcy will occur in finite time. In any event since ownership of the leased assets resides with the lessor, a lease contract is equivalent to a secured loan thereby permitting the transfer of leased assets at minimum cost in the event of bankruptcy. The firm’s gross profits from production at the start of period t depend on the capital stock which it uses in production at the start of period t, K,, and a random variable, E,, which is uncertain prior to the start of period t and has a density function, conditional on information available in period t - 1, f(&J, over the range (c,,E;). Gross profits from production at the start of period t, 7cf, are therefore written as x,= n,(K,, EJ, and it is assumed that TC,is concave in K, and increasing in E,. The capital stock used by the firm in any period may be either owned by the firm or leased from other firms: Kt denotes that part of the capital stock used in production at the start of period t which is leased. Kk is positive for a lessee firm and negative for a ‘Note that asymmetry being analysed.

of tax treatment

of gains and losses in the personal

tax system

is not

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

177

lessor firm. A one-period installation or removal lag for the capital stock is assumed, so that the firm’s own net purchases of capital goods at the start of period t, I,, and its net additions to its leased capital stock, I:, affect the capital stock used by the firm at the start of period t+ 1. The capital stock is assumed to depreciate at the rate 6 per period. These assumptions mean that the evolution over time of the capital stock used and leased by the firm can be described in the following two equations:

K r+1=(1-d)K,+i,+Z:,

(2)

K,L,, =(1-~5)K;+Zk.

(3)

A firm that uses leased assets at the start of period t has to make lease rental payments at the rate R, per unit of leased assets at the beginning of that period, while a firm that leases out assets receives lease rental payments at that rate. At the start of period t firms may either make interest payments at the rate of interest I on the stock of bonds outstanding at the start of period t-l, B,_1, or received interest payments at the same rate on debt they held at the start of the previous period in the case where B,_1 is negative. At the beginning of period t the firm’s gross profit from production is realised, and the firm makes a dividend payment, denoted D,, to its shareholders. The firm’s dividend payment is related to the other components of its sources and uses of funds identity as follows:

D,=711(K,,~t)-ZIt-RR,K~+B,-(1+r)B,_,-IT;,

(4)

where 7; denotes corporation tax paid at the start of period t. In what follows we assume, for simplicity, that the firm’s optimal dividend policy is such that the legal constraint that dividends be non-negative does not bind. The form of the corporation tax system is central to our analysis, and we assume that it has the two essential features of (a) asymmetry between taxable profits and taxable losses, with the former giving rise to payments to the tax authorities but the latter not resulting in the firm receiving payments from the authorities; and (b) permitting firms who purchase capital goods for the purpose of leasing to other firms to claim tax allowances on them. Specifically we assume that the corporation tax system provides for initial allowances on a fraction u > 0 of the firm’s net purchases of capital stock and allows the remaining (1 -a) to be written off for tax purposes at the

178

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

economic depreciation rate A2 Hence the tax-written-down value of the capital stock owned by the firm at the start of period t, Kf, evolves over time according to ‘ K;+,=(l--G)KT+(l-cr)Z,. The firm’s lease rental payments are deductible against corporation tax, while lease rental receipts are fully taxable. Similarly, the firm’s interest payments are deductible and interest receipts are taxable. Taxable profits are thus given by gross profits from production less net interest payments, net lease rental payments, allowances on the capital stock, and tax losses carried forward from previous periods. This final component reflects the asymmetrical nature of corporation tax systems: if in any period tax allowances exceed taxable receipts the firm makes a tax loss, and the tax loss accrued at the start of period t - 1 is carried forward without interest to be set against taxable receipts at the start of period t. For simplicity we abstract from restrictions on the period for which tax losses can be carried forward by assuming that they can be carried forward indefinitely, and we ignore provisions for carrying back losses.3 These assumed features of the corporation tax system give rise to the following expression for corporation tax payments at the start of period t:

7;= z max(n,W,,4 - A, 01, where z denotes defined as

the corporation

Here L,denotes tax losses carried are determined as follows:

tax rate

forward

(6) and

& denotes

from the start

tax allowances,

of period

t, which

*This particular formation of the capital allowances available is a simplified version of the system applicable in the United Kingdom between 1972 and 1984. Investment in plant and machinery received 100 percent initial allowances (c( = l), while investment in industrial buildings received initial allowances varying between 40 percent and 75 percent at different times, together with annual writing down allowances at a rate of 4 percent (straightline basis). Our assumption that annual writing down allowances are given on a declining balance basis at the economic depreciation rate is made purely for simplicity. The precise form of the capital allowances granted under the corporation tax system does not affect the substantive results obtained in the paper. %arry forward restrictions do not apply in the United Kingdom, while in the United States the per&d for which losses can be carridd-forward is sufficiently long to obviate the need for a detailed analvsis of the restrictions. The provisions for carry back merely affect the definition of taxable pro& in the current period and require that &venues geneiated over the relevant previous periods be included.

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

L, = max Cd+ - dK,, 4,Ol.

179

(8)

In practice firms are uncertain about the value of their taxable profits at the time at which decisions are taken about some of the variables which will affect taxable prolits.4 This is a key feature of our analysis, and to capture it we assume that a one-period decision lag operates with respect to the firm’s choice of its net purchase of capital stock, net addition to its leased capital stock, and stock of outstanding debt. Thus we assume that the firm has to decide the values of I,, ZF and B, at the start of period t- 1 conditional on information available at that time. The firm’s problem is therefore to choose I,, Zk and B, at the start of period t- 1 to maximise the value of the firm’s equity at the beginning of period t- 1. In choosing I, and If- to maximise the value of equity at the beginning of period t- 1 the firm must take account of its expected tax position in both period t, which will depend on L,_l (known to the firm at the start of period t-l), and period t+ 1, which depends on L, (about which the firm is uncertain at the start of period t - 1). Denoting by E,_ 1 the expected value at the start of period t- 1 of a variable (conditional on information available at the time), the expected value at the beginning of period t - 1 of the tax loss carried forward from the start of period t is given by

4 - I CL,1 where g, is defined

=“r’ Cd+ - dK,, Et

~,)lf(dd~,,

(9)

as the value of E, which solves

(10) The expected value at the start of period t - 1 (conditional on information available at that time) of the firm’s tax payments at the start of period t is given by

The firm’s problem at the start of period t - 1 is therefore and B, to maximise the value of its equity at the beginning

to choose I,, Zf of period t - 1

41n the United Kingdom contentious cases have been disputed by the Inland Revenue and the company concerned for up to 10 years. An initial assessment of liabilities may be available around the time that accounts for a year are published but in the course of subsequent appeals significant revisions (frequently in a downward direction) may be made. By the ‘tax due date’ (9 to 21 months after the accounting year end) an assessment will have been made, but the books relating to a particular year will typically not be formally closed for some four years thereafter.

180

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

subject to the constraints represented by eqs. (2), (3), (5) and (8). The value of the firm’s equity at the start of period t - 1 is given by

r/;_,=E,_,

{&Dt+V’}(‘+“)I;

where tI denotes the after-tax amount received by shareholders if fl is paid out by the firm as a dividend5 and p denotes the (risk-neutral) shareholders’ discount rate, which, from the condition for equilibrium in the capital market, can be written as6 p=(l

-m)r/(l--2).

(12)

To solve the firm’s dynamic optimisation problem a maximum value function value of the 5tKj+ 19KjL, 1, KjT, 1, B,, Lj) is defined, giving the maximised tit-m’s equity at the start of period j as a function of the predetermined variables at that time. Using the fundamental recurrence relation of dynamic programming, the solution of the firm’s dynamic optimisation problem at the start of period t- 1 must satisfy the following equation:

=(I

+j)-’

max E,_r It. 1:. &

. (13)

~D,+~(K,+I,K:il,K:,I,B,,L,) 1

Thus by substituting from eqs. (2)411) into (13), the firm’s choice of I,, 1: and B, can be analysed as a straightforward unconstrained maximisation problem, the first-order necessary conditions for which are that aq_,/aZ,, sThe variable 0 is one that enables alternative forms of corporation tax system to be accommodated in the general framework: see King (1977). Under a classical system O= 1 -WI, while under an imputation system 0 = (1 - m)/( 1 -s). % shareholders are risk-neutral, then equilibrium in a perfect capital market requires that the after-tax return that shareholders expect to receive on their holdings of equity (comprising dividends and capital gains) must equal the after-tax amount that could have been obtained if shareholders had sold their shares and invested the proceeds at the safe rate of interest, i.e.

~~-~~~~=~~,C~,+~l+~~--z~C~,C~+~II-~l. If a suitable terminal condition is imposed, this equation can be rewritten to give the value of equity as the expected stream of future dividends multiplied by O/( 1 -z) and discounted at a rate (1 - m)r,‘( 1 -z). the shareholders’ discount rate p [l+(l-m)r/(l-z)]-‘.

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost

ofcupltal

181

~~_,/c?Z~ and ~C_,/C?Z?, should all equal zero. Details of the derivation of these first-order conditions are given in the appendix to the paper. The first-order conditions for the firm’s choice of I, and If- both involve terms relating to the expected tax liability on the returns from marginal investment, which is dependent on the proportion of returns that accrue in of the analysis tax loss states when rc_,(K,+,,~,+r) < 4,+r. The presentation is greatly simplified, but not altered in substance, if it is assumed that in any period the returns to marginal investment, &/(K, + 1, E,+ l)/dK, + 1 = nK,t + 1, are independent of the random variable E,+ 1. This will be the case if gross profits from production, K,, r(K,+ r, E,+ r), can be written as ic(K,+ ,) +E,+, . In these circumstances

where St+

F t+l=

I

J &+Ad~,+l

represents the probability (as perceived at the beginning of period t- 1) of tax exhaustion at the start of period t + 1. Given this assumption, the lirstorder necessary conditions for the firm’s choice of I,, Zk and B, can be written as follows (see the appendix for details of the derivation):

Ll%,t+l=

P(1-as:)+cc(t,*,l-rT)+6 l-C+1

2

(15)

~f-l%,r+l=~f+l~

(16)

r(1 -~,*,~)=p.

(17)

In eqs. (15) and (17) the terms SF and r:+ 1 denote the effective rate of corporation tax in periods t and t + 1, respectively, as perceived at the start of period t - 1. The effective rate in period t + 1 is defined as $+r=t(l-F,+r)+t’-F,+r Ml-z) where ,u~+i denotes the effect, as perceived at the start of period t - 1, on the maximised value of the firm’s equity in period t + 1 of an additional unit of tax loss carried forward from period t+ 1. An analogous definition applies to the effective rate of corporation tax in period t. The effective rate of corporation tax takes account of the probability of the firm being taxexhausted in some future period: it is a weighted average of the statutory rate of corporation tax and the value of a marginal unit of tax loss carried forward, adjusted by a term reflecting the personal tax system’s discrimi-

182

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

nation between dividends and retained profits, with the weights being the probabilities of being tax-paying and tax-exhausted, respectively. Eq. (15) shows that in equilibrium the firm will equate the expected marginal return from an additional unit of capital stock it uses at the start of period t + 1 to the one-period cost of capital for retention-financed assets, which depends on the shareholders’ discount rate, the effective rates of corporation tax in periods t and t + 1, and the initial and depreciation allowances granted by the tax system. Eq. (16) shows that in equilibrium the firm will also equate the expected marginal return from an additional unit of capital stock used by the firm at the beginning of period t + 1 to the lease rental rate at the start of t + 1. Eq. (17) shows the relationship between the costs of debt and retained profits finance when the firm’s capital structure is in equilibrium. If p> )}, then the firm will, at the start of period t 1, choose to &,{r(l -r:+1 increase the amount of debt used to finance investment at the beginning of period t and reduce the amount of retained profits used for this purpose. The additional interest deductions against tax at the start of period t+ 1 associated with a larger stock of outstanding debt at the beginning of period t will raise 4,+ r, hence increase g,, 1 [from (lo)], and thus reduce t,*+ 1 [from (18)]. This process will continue until eq. (17) is satisfied. Similarly, if )} the firm will use retained profits to buy bonds at the P<&r{r(l--z,*,r start of period t until the interest earned on these bond holdings has increased expected taxable profits at the start of period t + 1 sufficiently to raise z,*, 1 to the value at which eq. (17) is satisfied. Eq. (17) can be used to substitute for p in (15) to give a general expression for the one-period cost of capital for assets financed by debt or retained profits finance, or in other words the cost of capital for assets owned by the firm. Thus eq. (15) becomes:

(19)

Eqs. (16) and (19) imply that in equilibrium the cost of capital for assets owned by the firm equals the lease rental rate, and that these are both equal to the expected marginal return from an additional unit of capital stock used by the firm. These expressions will be used in section 3 to analyse the firm’s investment, financing and leasing decisions in the presence of a market for the transfer of taxable capacity via leasing, and the equilibrium properties of this leasing market. 3. Equilibrium in the leasing market As we have already

noted,

the firm will, at the start

of period

t - 1, take

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

183

decisions about its borrowing or lending at the beginning of period t which ensure that eq. (16) holds. The firm’s optimal financial policy at the start of period t - 1 therefore fixes z,*+~ at the value which makes the costs of debt and retained profit finance equal. From eq. (16), recalling (12), this value is

z* =(m-4/(1--4,

(20)

t+1

which will be positive given our assumptions represented by eqs. (la) and (lb).7 Eq. (20) means that as far as the firm’s decisions (taken at the start of period t - 1) about its investment and leasing in period t are concerned, rF+ 1 is a constant, being maintained at this fixed value by the firm’s optimal financial policy. The equality between the cost of capital for assets owned by the firm and the lease rental rate determines the firm’s total net purchases of capital goods at the start of period t, which can either be used in its own production or leased to other firms. To see this, recall that

(21) and note that, as pLt= aI/;/aL,, value function gives

&z)

-==z;“+1/(1

straightforward

differentiation

+p),

of the maximum

(22)

showing that, conditional on information available at the start of period t - 1, an additional unit of tax losses carried forward from period t will be expected to raise the maximised value of equity in period t by the discounted value of the effective corporation tax rate in period t + 1 which is expected to rule given information available in period t- 1, adjusted by the term reflecting the personal tax system’s discrimination against dividends. Using eqs. (7), (lo), (20) and (22) in (21) we have, for z: >O,

aq/aI, c 0.

(23)

The cost of capital for assets owned by the tirm is given by the right-hand side of eq. (19): using (23) in (19) and remembering that r:+ 1 is a constant it can be seen that, so long as the firm’s effective corporation tax rate in period t is expected, at the start of period t - 1, to be positive, the cost of capital for assets owned by the firm increases with additional investment because of the ‘For this to be feasible it is necessary

to assume

that (m-2)/(

1 -z) 5~.

184

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

resulting increased probability of tax-exhaustion at the beginning of period t [recall that decisions about I, are taken at the start of period t- 1 when rr,(K,,~,) is uncertain]. The firm will thus adjust I,, its total net purchases of capital goods at the start of t, until the cost of capital for assets it owns equal the lease rental rate. Given the firm’s decision about its total net purchases of capital goods, the equality between its expected marginal return from an additional unit of capital stock used and the lease rental rate establishes its leasing decision. It is easiest to see how the firm’s leasing decision is determined in terms of a diagram. Fig. 1 illustrates the decisions, taken at the start of period t- 1, of two firms about their overall investment and leasing in period t, i.e. I, and 1:. The two firms have identical schedules representing the cost of capital for assets they own: this is depicted as ABCDE in the diagram, and is upwardsloping since iir~/c?l,
r(l-or)

+

'q+l

0

pt+1-‘) + 6

Rt+l

r+6

\

I" k,t+l

A

-‘.‘

Et-1

Expected marginal return from investment, lease rental rate

H

I'

I

Et-l

Fig. 1

J

/

C

\_\_\//I

\

K

\

/ r<

L

186

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

method of financing that part of its total new capital goods used in its production. In fig. 1 there are lower and upper bounds on the firm’s cost of capital for investment in assets it owns, which are derived as follows. The firm’s optimal financial policy fixes T:+,, at the value given by eq. (20). From eq. (19) with z;“+1 constant the cost of capital is decreasing in 7:. Eqs. (21) and (22) imply that z: is contained in the set [z,*,~ /( 1 +p), T]. Hence the firm’s cost of capital for investment in assets its owns attains a minimum when T: =T, which will be the case when the firm is certain at the beginning of period t - 1 that it will be fully tax-paying at the start of period t (i.e. F,=O). This lower bound on the cost of capital for assets the firm owns is [from (19)] r(l - cLT)+E(T,*,, - T)/(1 -T;“+ 1)+ 6, which is lower than the cost of capital in the absence of taxation, r+ 6, as T:+ 1 =CT. It is also lower than the cost of capital when there are no asymmetries in the treatment of taxable profits and losses, r( 1 -UT) + 6, unless z,*+1 = z, when it is the same. The reason for this latter point is that capital allowances are claimed at a higher effective rate of corporation tax than subsequent returns are charged. At the other extreme, the maximum value of the firm’s cost of capital for assets it owns is attained when T: = T,*+I/(1 +p), which will be the case if the firm is certain at the start of period t- 1 that it will be tax-exhausted at the beginning of period t (i.e. F,= 1). From eq. (19) this upper bound is equal to r +6 irrespective of the length of time for which it expects to be taxexhausted. In other words, tax exhaustion in the period when investment is undertaken delays the claim of initial allowances on capital goods to the same period in which returns accrue, thereby eliminating the tax privilege of initial allowances and creating a cost of capital equal to that in the absence of taxation. An interesting feature of this analysis is that a firm’s overall investment at the start of period t will, for given tax, interest and lease rental rates, depend on the probability distribution of gross profits from production at the start of period t [again, recall that nt(Kt,@ is uncertain at the time when decisions about I, are made]. An increase in the expected value (conditional on information available at the beginning of period t - 1) of gross profits from production at the start of period t, with the other parameters of the distribution unchanged, will raise T: for a given I,, shift ABCDE in fig. 1 to the right, and raise the firm’s level of net purchases of capital goods at the start of period t. A mean-preserving spread of the probability distribution (at the beginning of period t- 1) of returns on K, which increases the weight of the distribution in the tail corresponding to taxable losses (i.e. raises F,) reduces 7: and thus desired levels of overall purchases of capital goods. The firm’s demand for capital goods for use in its own production only determines the al!ocation of these purchases between leasing and use in the firm’s own production. The asymmetrical treatment of taxable profits and

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

ts7

losses is therefore seen to introduce a direct relationship between the returns on the firm’s capital stock in a particular time period and its overall level of capital expenditure in that time period. The equilibrium lease rental rate at the start of period t+ 1, R,+l,is determined by equating the change between periods t and t + 1 in the demand for capital goods for use in firms’ production, summed across firms, with the sum across firms of firms net purchases of capital goods for own use or leasing. The former is negatively related to R,,1.From eq. (16) a firm’s desired stock of capital goods for use in its own production is given by the condition that the expected marginal return from an additional unit of capital stock used in production at the start of period t + 1 should equal the lease rental rate. Firms are assumed to have downward-sloping expected marginal profit schedules, so that the higher is R,,, the lower is the firm’s desired capital stock for own use. This relationship is written as

so that the change in the demand for capital goods for own use, Kf+,(1 - 6)K,, also falls as R,,1 increases. A firm’s desired net purchase of capital goods is obtained by finding the value of I, which, via its effects on r:, makes the firm’s cost of capital for assets it owns equal to R, + r. The higher is R,+l, then the lower must be r: in eq. (19) to maintain this equality (recalling that r:+ 1 is constant), and hence, as &:/aI, ~0, the higher must be I,. The relationship between desired net purchases of capital goods and R,+l is written as

C=dR,+,),

g’>O.

The equilibrium lease rental rate is therefore given by the value of R,+1, which solves

i$lCWC+,)-(1-W,1=

f:dR,+d,

i=l

(24)

where i is the index of firms and n is the total number of firms. Fig. 2 illustrates the determination of the equilibrium lease rental rate in terms of schedules of aggregate expected marginal return and aggregate cost of capital for investment in assets owned by firms. There are a number of interesting features of the equilibrium. First, the aggregate level of investment and the equilibrium lease rental rate are affected by the total level of gross profits but not by their distribution across firms. Mean shifts in the density functions of individual firm profits in

188

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

189

offsetting directions that leave total profits unchanged do not affect the equilibrium. However, the elasticity of the schedule of the cost of capital for debt/equity financed investment is dependent on the second and higher moments of the profits density function. For example, a mean-preserving spead increases this elasticity and makes aggregate net purchases of capital goods more responsive to aggregate profits. Thus a careful description of the profits density function is required to characterise the relationship between profits and investment. Secondly, leasing will not in general be used to extinguish corporate tax liabilities. The following expression for the effective corporation tax rate in period t that is expected at the beginning of period t - 1 can be derived from eqs. (16), (17) and (19):

$=(r+S-R,+,)L

r-p ___

r!x(l +p)+‘(l

+p)’

(25)

In eq. (25) p, r and c1are all positive, and given the assumptions represented by eqs. (la) and (lb) r>p so that the second term on the right-hand side of (25) is positive. The upper bound on the equilibrium lease rental rate has been seen to be r+S, so that the first term on the right-hand side of (25) will be non-negative. Thus r: > 0, which means that in equilibrium firms attach a positive probability at the beginning of period t - 1 to being in a tax-paying state at the start of period t. The existence of both tax-paying and taxexhausted firms is thus consistent with a market for leased assets which can be used to transfer taxable capacity. Thirdly, it is clear from fig. 2 that the equilibrium lease rental rate can take any value between the upper and lower bounds on firms’ cost of capital for investment in assets they own. In particular it is possible for the equilibrium lease rental rate to fall below r(1 -ar) +6, the cost of capital that would obtain in the absence of tax exhaustion. Such an outcome would occur in periods when aggregate investment opportunities, as represented by the sum of firm’s expected marginal profit schedules, were low relative to the aggregate supply of debt and retained profit funds for investment, which is what is represented by the sum of firms’ schedules of cost of capital for assets they own. Fourthly, it is not the case that the existence of the leasing market necessarily increases aggregate investment by comparison with the situation where leasing does not occur, as would be the case, for instance, if capital allowances were not available on assets that were purchased to be leased to other firms. If leasing results in an effective net transfer of finance from firms with a high elasticity of demand for capital goods to firms with a low elasticity of such demand, then leasing may actually lower the total level of

190

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

investment. Fig. 3 illustrates an extreme example in which there are two firms in the leasing market. Both firms have supply of debt or retained profit finance curves given by the upward-sloping schedule of the cost of capital for assets owned by the firms, CC. Firm 1 has a highly elastic demand for capital goods for its own use, represented by the schedule E,_l(nK,r+ 1)1 while firm 2 has a highly inelastic demand for capital goods for its own use, represented by the schedule Et_l(~K,l+ 1)'.In the absence of leasing, firm 1 purchases OA capital goods for its own use, and lirm 2 purchases OB for its own use. If leasing occurs, the equilibrium lease rental rate, R,+l, is given by the intersection of the schedules of aggregate demand for capital goods for own use and aggregate supply of debt or retained profits finance, as shown in the diagram. At this lease rental rate both firms purchase OE capital goods. Firm 1 reduces its own use of capital goods from OA to OC, while firm 2 increases its use of capital goods from OB to OD. The difference between firm l’s use of capital goods and its purchase of capital goods, CE, represents the amount of capital goods which it leases out to firm 2, and of course this equals the excess of firm 2’s use of capital goods over its purchase of them, ED, which firm 2 leases from firm 1. Aggregate investment when leasing occurs is OE + OE: in the absence of leasing it is equal to OA + OB. Thus when leasing occurs there is a fall in aggregate investment. It is clear that empirical information about the relative sizes of the elasticity of demand for capital goods of lessees and lessors is required in order to establish whether or not the existence of a leasing market stimulates aggregate investment by comparison with the situation where no leasing takes place. Of course the existence of a leasing market in our model results, if social and private evaluations of the costs and benefits of investment coincide, in an efficient amount of investment being undertaken.* The equilibrium when leasing can occur is characterised by the marginal return from the use of capital goods being the same for all firms and equal to the marginal cost of capital for investment in capital goods owned by the firm, which is of course also the same for all firms. These efficiency conditions are not satisfied by the equilibrium when leasing does not occur, as inspection of fig. 3 will confirm. However, concern about the aggregate level of investment is often based on the view that social and private evaluations of the costs and benefits of investment do not coincide: more generally there are a number of complex issues involved in consideration of the efficient level of investment for an economy which we do not wish to pursue here. Our point is simply that there is no a priori basis for the view that the existence of a leasing market sThis statement ignores the complications that arise in analysing the effects of opening a new market on efficiency when the market structure is incomplete. Hart (1975) shows that it is possible that opening a new market or markets results in a Pareto deterioration: this possibility can only be ruled out if enough new markets are opened to make the market structure complete in the Arrow-Debreu sense.

191

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

m

iz” 0

m

4J

w

2

v

0

192

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

will necessarily increase investment by comparison with the situation when no leasing occurs. Finally, it should be noted that even in the presence of a competitive leasing market firms will in general be earning rents from acting as lessors. The upward slope of firms’ schedules of cost of capital for assets they own means that rents will be earned on intra-marginal leasing: only on marginal leasing activity will lessors earn no more than normal profits. This observation helps to resolve the apparent contradiction between the theoretical conclusion of Miller and Upton (1976) that lessors should not earn rents in competitive leasing markets and the empirical documentation of just such rents [Edwards and Mayer (1983)].

4. Conclusion This paper has developed a model that integrates leasing into a theoretical literature on taxation and the cost of capital that has found wide application. The paper has shown how differences in the tax payment position of different firms arising from the asymmetric tax treatment of profits and losses give rise to incentives for tax transfer activities in the form of leasing. Of course leasing may occur whenever there are differences between firms in their tax position, so that different tax rules applied to different firms may also provide an incentive for tax transfer via leasing. The emphasis in this paper on asymmetric treatment of taxable profits and losses as a reason for leashing is due to the importance of this feature of corporate tax systems in several countries over the past decade and the associated growth in leasing, which has attracted considerable attention from policymakers. Equilibrium in the model of firm behaviour with possible tax exhaustion and leasing presented in this paper has the feature that the lease rental rate is equal to both the marginal return from the use of capital goods by the firm and the cost of capital for assets that the firm owns. The latter depends in general on the firm’s expected tax payment position, and so is difficult to measure for the purposes of empirical work: the analysis in this paper suggests that it may be possible to use the more easily observable rental rates in the leasing market as a basis for measuring a firm’s cost of capital with potential tax exhaustion. The analysis of leasing, taxes and the cost of capital in this paper has produced a number of conclusions that are of relevance for public policy in this area. The asymmetrical treatment of taxable profits and losses has been shown to introduce a positive relationship between a firm’s returns on existing assets and new investment which would not otherwise exist and so may exacerbate fluctuations of investment over the cycle. The equilibrium lease rental rate, to which firms equate the marginal return from the use of capital goods in their own production, has been shown to fall, in certain

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

193

circumstances, below the cost of capital that would exist if there were no asymmetries in the tax system. This means that it is possible for aggregate investment to be higher if there is asymmetrical treatment of taxable profits and losses and leasing than if the treatment of taxable profits and losses is symmetrical. It does not follow, however, that the existence of a leasing market when there are asymmetries in the tax system necessarily increases aggregate investment by comparison with the situation when there are asymmetries but leasing does not occur. If leasing transfers funds from firms with highly inelastic demands for capital goods for own use to those with highly inelastic demands aggregate investment may decrease. It has also been shown that even in a competitive leasing market lessors will be earning rents on their intramarginal leasing activity, which is likely to have an effect on how the tax authorities view such leasing profits. Appendix

In this appendix we present the details of the derivation of the first-order necessary conditions (15), (16) and (17) in the main text. The fundamental recurrence relation of dynamic programming means that the solution to the firm’s problem at the start of period t- 1 satisfies

The first-order necessary conditions for the choice of I,, 1: and B, are that c?~_,/c~Z,=O, 8~_,/aZ~=O, and d~_,/~B,=O. 1. ac_,/ar,=o. Using eqs. (2) and (11) of the main text in (A.l), we have that

+=(l+p)-lE,l f

64.2) Note that (A.2) contains no terms in (8g,/34,)(a&/CM,), because although g, depends on C#J, which in turn depends on I, [see eqs. (7) and (10) of the main text], any such terms are evaluated at rrt(K,,g,) - &, which is zero by

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J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

detinition. Expressions for the expected values of af$dK,+, and a@aKT+, can be obtained from the fundamental recurrence relation (A.l), updated one period, as follows:

aK+, gt+l ah+,

E,_,----=ar/; aKT+ 1

s ?I.,~+I/(&~+~)d&~+~+~(l-s)

Et+,

r+2

(A.3)

(1 +p)-lE,-,

++3F,,, t+1

+$+

t+2

(A.4)

Note that (A.3) contains no terms in agf+l/aKf+l even though g,+ I depends on K+r, because any such terms are evaluated at rc,+l(K,+ l,g,+ 1) - 4,+ 1, which is zero by definition. As t is a maximum value function it follows that E,_,afQar,+,=o, SO that we have, on updating (A.2) one period and rearranging,

E,-,~=Et-l{i+J’-m(l-F,,,)) 1+2

(A.3 Using (A.3), (A.4) and (AS) in (A.2), and defining aq/;lZJL,=p,, aF+ ,/aL,+, z pt+l, we have that

+=(l t

+p)-lE,-,

&~~(~-F~)--I)+PPF,

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost

+(1-d)

~(l-ar(l-F,+~))-~~+~~~~+~-~

2+2

(

+(1-a)

z+2

19.5

(1 --a) 1

.

(l-6)

~r6(l-F,,I)fH+16F,,,+~ (

ofcapital

b4.6)

Ii

Using the assumption represented by eq. (14) of the main text and the definitions of r: and r;“+r in eqs. (21) and (18) of the main text, (A.6) can be simplified and then set equal to zero to obtain the first-order condition given by eq. (15) of the main text. 2.

(A.7)

The expected value of at/LJKF+l is found in the same way as (A.3) and (A.4): substituting the expression so obtained together with (A.3) in (A.7) gives:

J.P.E.-

C

J.S.S. Edwards and C.P. Mayer, Leasing, taxes, and the cost of capital

196

(A.81 As t is a maximum value function, Et_ 1 ~J~/c~I~+~ =O, so that (A.7) can be updated one period and used in (A.8), together with (14) and (18) of the main text, to give an expression which, when set equal to zero, gives the first-order condition represented by eq. (16) of the main text. 3.

a~_,/C%?,=o.

gi=(l+p).-‘E,-, f The expected value of a@i3B, is obtained in the same manner (A.4), and when substituted in (A.9) this gives

(A.9)

as (A.3) and

(A.lO)

Using (18) in (A.lO) gives an expression which, when set to zero, yields the first-order condition represented by eq. (17) of the main text.

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