- Email: [email protected]
Bias from decision assessment by reported profit
OMEGA The Int. Jl of Mgmt Sci., Vol. 9. No. 1. pp. 91 to 101 © Pergamon Press Ltd 1981. Printed in Great Britain
0305-0483/81/0101-0091502.00/0
Bias from Decision Assessment by Reported Profit THE P R E S U M P T I O N COMPLAINT is often made by investors, particularly in times of inflation, that companies are undergeared. Similarly, there has long been a widespread view that managers and directors are often over-inclined to retain earnings for future investment rather than to distribute them in dividends. This article develops a simple model to show how the common assumptions made in the use of profit figures may lead to such non-optimal investment and financing decisions of under-gearing and over-investing as those criticised above. Much of the very recent literature on financial accounting theory (e.g. [l, 2]) uses the assumption that external reporting enables owners to monitor the performance of managers of an enterprise. It might, therefore, be assumed that the profit measurement system should work in such a way that the owners' welfare is maximised when the reported profit is maximised. Further, it should follow that managers who maximise owners' welfare will be more valuable than those who do not, and will thereby command higher salaries, enhancing their own welfare. We will now develop a simple model in order to see the effect of using these assumptions.
In purchasing power terms (period n units) Profit on borrowing and investing = A[(I + a ) " (1 + b)"] i.e. the purchasing power of the cash surplus at the end of the investment period. This, it will be noted, is identical with the gain reported under the historical cost reporting system. However, splitting this gain into its two const~uent elements (1) The profit on investing in the assets = A[(l + a)~ -(1 + i)~] (i.e. cash proceeds from sale of assets less purchasing power equivalent of the original cost of the assets), and (2) The profit on borrowing = AI-(I + i)~ - (1 + by'] (i.e. purchasing power equivalent of the original loan less cash cost of repaying that loan). Thus, although the total reported profit from the transactions is unaffected by the reporting method, which tempts us to conclude that no different bias than that introduced by HC reported profit will arise, the constituent elements are different in that (a) C P P reported profit on investing in the assets is less than the HC reported profit on investing in the assets, and (b) C P P reported profit on borrowing is greater than the HC reported profit on borrowing.
HISTORICAL COST (HC) R E P O R T E D PROFIT
Thus, as we state in detail below, there may be different bias from HC and C P P reported profit. Since the borrowing and investment decisions are separate, it is clear that HC reporting will enhance the reported profit on investing in assets, thereby encouraging it to an extent greater than would be the case if C P P reporting was used. Similarly, there will be less encouragement for management to borrow if HC reporting is used rather than C P P reporting as the gain from borrowing will appear to be less.
Consider a firm which is able to borrow at 100b% per period and uses this borrowing to finance assets whose value increases at 100a~o per period. These assets are purchased solely for capital gain and serve no other purpose. The specific index for these assets was 1 at the beginning of period 1 and will be (1 + a)" at the end of period n. If the firm borrows A to buy these assets, sells the assets at the end of period n and pays off the loan and interest, at 100b% per period, with the proceeds, the reported profit is given by HC is A[(I + a)" (1 + b)"]. This can be split into two separate elements, (1) The profit on investing in the assets A[(I + a)" - I] (2) The profit on borrowing money A[(1 - ( I + b)"] (usually negative)
O W N E R S WELFARE R E P O R T E D PROFIT In assessing their own welfare the owners will introduce, in addition to a purchasing power adjustment, a further adjustment to take account of their own time preference rate. Thus, if their time preference rate is 100p% per period, the current welfare equivalent at the end of period n of 1 unit of currency at the beginning of period 1 will be (1 + i)"(1 + p)". Thus we can state that in welfare terms. Profit on borrowing and investing = A[(I + a ) " (1 + b)"] again the cash surplus at the end of the investment period. This may be broken down into the constituent parts
C U R R E N T P U R C H A S I N G P O W E R (CPP) REPORTED PROFIT If we continue to report on the profit from borrowing and investing, but report in a way which reflects the change in purchasing power that accrues to the owners, we will need to use their purchasing power index. This may be the inverse of the general price level index, and if this price level index increases by 100i% per period, it will increase 4"rom 1 at the beginning of period 1 to (I + i)" at the end of period n. Thus the purchasing power of I unit of currency in period 1 will be equal to (1 + i)" times the purchasing power of 1 unit of currency in period n.
(1) Profit of investing in assets = A[(I + a)" - (1 + i)" (1 + p)"] (i.e. the cash proceeds from the sale of the assets less the welfare equivalent of their original purchase price) (2) Profit on borrowing = A[(I + i)"(1 + p)" (1 + b)"] (i.e. the welfare equivalent of the original 91
Memoranda
92
sum of money borrowed less the cash paid to redeem the loan). Thus both HC and C P P reporting correctly give the gain in welfare for the owners from such a borrowing and investment transaction, but they both distort the source of the gain, attributing more than is appropriate to the holding of assets and less than is appropriate to the borrowing of funds, given that the owners have a positive marginal time preference rate. This effect is brought about because the elements of reported profit take no account of the fact that shareholders are only able to benefit from that profit when it is made available to them for consumption or for them to choose to reinvest. (They will choose to reinvest only when the real return offered for reinvestment is greater than their real marginal time preference rate.) Thus for any non-zero money marginal rate of time preference (i.e. (1 + i)(1 + p) d: 1) the HC reporting system will lead to bias in the welfare value of the reported profit, and for any non-zero marginal rate of time preference (i.e. p g: 0) C P P reporting system will similarly lead to bias. DECISION RDLES BASED O N R E P O R T I N G SYSTEM If HC reporting is used, then it is clear that investment in assets will take place whenever they are expected to appreciate faster than the cost of borrowing (i.e. Invest if a > b). However, from the owners' point of view, investment should only take place when the rate of appreciation of assets is greater than the owners' marginal rate of time preference (i.e. when (1 + a) > (1 + i)(1 + p)) regardless of the cost of borrowing (b). It is also clear that borrowing will only occur when this will lead to a reported profit, i.e. a > b, but for the maximisation of owners' welfare borrowing should take place whenever the owners' marginal rate of time preference is greater than the cost of borrowing (i.e. when (1 + i)(1 + p) >
(1 + b)) regardless of the level of the rate of appreciation of assets (a). A normal expectation is that the larger the amount of funds to be invested in assets (for a holding gain), the lower will be the expected rate of holding gain; while the larger the amount of funds to be borrowed, the higher the cost of borrowing. These relationships may be plotted as in Fig. 1 for a single period model. The decision rule for maximising HC reported profit would lead to the borrowing and investing up to Ao showing a reported profit of the area boaoA'o. The elements of profit are a gain on investing, area OaoA'oAo and a loss on borrowing of OboA'oAo. Thus management can increase reported profit by not borrowing but instead using owners' funds which in the HC reporting model are treated as free of cost. If, however, the owners' marginal money time preference rate (I + i)(1 + p) - I is taken into account, we can observe an owners' welfare measure of gain. If this rate (t) is the same as the equilibrium rate for the enterprise (i.e. to = a(Ao)= b(Ao)) then the total gain is given by the area boaoA'o, (i.e. the welfare gain is the same as the reported profit and no bias is introduced by the use of reported profit). The elements of this profit are a gain from investing of toaoA'o and a gain from borrowing of botoA'o. If the owners' money marginal rate of time preference is greater than this equilibrium rate (i.e. tl > a(Ao) = b(Ao)), then the required optimal level of investment will be 11 which is less than Ao and the required optimal level of borrowing will be B~ which is greater than A0. The difference (B~-II) must be paid to the owner for consumption. The reported profit on the investment will be area Oaol'olt but the real gain to the owners will be area t~aol't; the reported cost of the borrowing will be area OboB'lBl but the real gain to the owners will be area bot~B'~. Thus the reported profit will be area boaol'~l'~' minus area I~I~B'~B~ which is less than the previously reported profit of area boaoA'o, while the real gain to the owners is area t~aol'l plus area bot~B'~ which is
b - b (A) Merg
%/100 O, bff
Oo
z;
e,'
I i
i I
~--O(Ao)=b(Ao)
.
bo
t
.
.
.
;
i
;
:
;
8~
/'1
A,
8~
Z~
o.oTA) A
Amount of funds
FIG. I. Borrowing and investment in a single period model
Omega, Vol. 9, No. I greater than the previously ascertained gain of area
boaoAo. If, however, the owners' marginal money time preference rate, (t2) is less than the previously determined equilibrium rate (to) (i.e. t2 < a(Ao) = b(Ao)) then the optimal solution will require less borrowing and more investment than the original solution (i.e. the required investment will be 12 which will be greater than A0 and the reported profit is given by the area 0a0I'212 whilst the gain to the owners from the investment is given by the area t2aoI'2). The required borrowing will be B 2 which will be less than Ao showing a reported cost of the area OboB'2B2 but a real gain of area bot2B'2 accruing to the owners. Thus the reported total profit will be the area Oaol':I 2 minus area OboB'2B2 which far exceeds the original reported profit boaoA'o. The real gain to the owners is given by the area t2aol'2 plus area bot2B'l which though greater than the original gain boaoA'o is not greater by as much as the reported profit exceeds the original reported profit. This occurs because the difference between the required investment 12 and the borrowing B 2 is assumed to be provided by the owners and no interest charge for this cash injection is levied in arriving at reported profit. CONCLUSIONS Whilst the profit reporting procedures treat owners' funds as free, the maximisation of reported profit will not maximise owners' welfare unless the owners' marginal time preference rate happens to be equal to the equilibrium rate for investment and borrowing by the enterprise. Where the owners' marginal money time preference rate is below this equilibrium level, the maximisation of reported profit will not greatly militate against the owners' interests, but where their marginal money time preference rate is above the equilibrium level, their welfare will be harmed by the maximisation of reported profit. In most cases enterprises are able to borrow at lower interest rates for given amounts than are the owners and it would, therefore, be reasonable to assume that owners' marginal time preference rate will be greater than the equilibrium rate for the enterprise. In these cases the enterprise will be over-investing, underborrowing and paying out too little to its owners for their welfare maximisation. Increased borrowing and increased dividends should be encouraged to enhance owners' welfare. Within the context of the cost of borrowing for the firm, it must be remembered that there may be fixed costs, such as that on the flotation of securities. These fixed costs on flotation will increase the firm's cost of borrowing above the required rate being paid and will therefore distort the picture. The retention of earnings does not lead to such a cost and will therefore appear attractive to the firm. Such an operation will only be attractive to the shareholders if they would have invested any dividend returned to them in securities rather than using the dividend for consumption.
O.M.k.9/I ¢;
93
From the point of view of the owners of the company it may be necessary to distinguish between private and institutional shareholders since it is difficult to determine a marginal time preference rate for an institutional shareholder, whilst that of the private shareholder may be shown to be measurable at least by an opportunity cost approach. However, it would seem that individuals must ultimately have an interest in the income of institutional shareholders, therefore it may be assumed that there will be a positive marginal time preference rate for such shareholders. Where, however, a problem does arise is that the cost of borrowing for institutional shareholders may well be very similar to that for the firm, while the cost of borrowing for individuals is usually higher than that for the firm. If the institutional shareholders are able to borrow more cheaply than the firm, there is no determinate solution to the optimal borrowing level of the firm for owner welfare maximisation. However, where the institutional shareholders are not able to borrow more cheaply than the firm, it is clear that the firm should borrow at least until its marginal cost of borrowing is equal to the minimum cost of borrowing of its institutional shareholders. It has been shown therefore that the ideal method of assessing management's decisions is in terms of owners' welfare but that present profit reporting practices will lead to bias in the investment and financing decisions of enterprises where ownership and control are divorced. Only where the owners' marginal money time preference rate concurs with that of the enterprise will the owners' welfare be maximised and optimal decisions be taken by management, given that management will be assessed by the profit that is reported. There will, however, be a solution available to the owners other than changing the profit reporting system, and that is to invest only in enterprises whose equilibrium discount rate is the same as the owners' marginal time preference rate. This clientele effect will work only to a limited extent and this article has shown that reported profit may not be a good proxy for use in assessing management decisions about investment and its financing.
REFERENCES 1. FELLINGHAMJC • NEWMAN DP (1979) Monitoring decisions in an agency setting. Jl Busin. Fin. Acct,q 6(21, 203-222. 2. WATTS RL & ZIMMERMAN JL (1979) The demand and supply of accounting theories: the market for excuses. Acct 9 Rec, LIV(2), 273 305.
David S Simon (May 1980) University of Hull Department of Accounting Hull HU6 7RX UK
0305-0483/81/0101-0091502.00/0
Bias from Decision Assessment by Reported Profit THE P R E S U M P T I O N COMPLAINT is often made by investors, particularly in times of inflation, that companies are undergeared. Similarly, there has long been a widespread view that managers and directors are often over-inclined to retain earnings for future investment rather than to distribute them in dividends. This article develops a simple model to show how the common assumptions made in the use of profit figures may lead to such non-optimal investment and financing decisions of under-gearing and over-investing as those criticised above. Much of the very recent literature on financial accounting theory (e.g. [l, 2]) uses the assumption that external reporting enables owners to monitor the performance of managers of an enterprise. It might, therefore, be assumed that the profit measurement system should work in such a way that the owners' welfare is maximised when the reported profit is maximised. Further, it should follow that managers who maximise owners' welfare will be more valuable than those who do not, and will thereby command higher salaries, enhancing their own welfare. We will now develop a simple model in order to see the effect of using these assumptions.
In purchasing power terms (period n units) Profit on borrowing and investing = A[(I + a ) " (1 + b)"] i.e. the purchasing power of the cash surplus at the end of the investment period. This, it will be noted, is identical with the gain reported under the historical cost reporting system. However, splitting this gain into its two const~uent elements (1) The profit on investing in the assets = A[(l + a)~ -(1 + i)~] (i.e. cash proceeds from sale of assets less purchasing power equivalent of the original cost of the assets), and (2) The profit on borrowing = AI-(I + i)~ - (1 + by'] (i.e. purchasing power equivalent of the original loan less cash cost of repaying that loan). Thus, although the total reported profit from the transactions is unaffected by the reporting method, which tempts us to conclude that no different bias than that introduced by HC reported profit will arise, the constituent elements are different in that (a) C P P reported profit on investing in the assets is less than the HC reported profit on investing in the assets, and (b) C P P reported profit on borrowing is greater than the HC reported profit on borrowing.
HISTORICAL COST (HC) R E P O R T E D PROFIT
Thus, as we state in detail below, there may be different bias from HC and C P P reported profit. Since the borrowing and investment decisions are separate, it is clear that HC reporting will enhance the reported profit on investing in assets, thereby encouraging it to an extent greater than would be the case if C P P reporting was used. Similarly, there will be less encouragement for management to borrow if HC reporting is used rather than C P P reporting as the gain from borrowing will appear to be less.
Consider a firm which is able to borrow at 100b% per period and uses this borrowing to finance assets whose value increases at 100a~o per period. These assets are purchased solely for capital gain and serve no other purpose. The specific index for these assets was 1 at the beginning of period 1 and will be (1 + a)" at the end of period n. If the firm borrows A to buy these assets, sells the assets at the end of period n and pays off the loan and interest, at 100b% per period, with the proceeds, the reported profit is given by HC is A[(I + a)" (1 + b)"]. This can be split into two separate elements, (1) The profit on investing in the assets A[(I + a)" - I] (2) The profit on borrowing money A[(1 - ( I + b)"] (usually negative)
O W N E R S WELFARE R E P O R T E D PROFIT In assessing their own welfare the owners will introduce, in addition to a purchasing power adjustment, a further adjustment to take account of their own time preference rate. Thus, if their time preference rate is 100p% per period, the current welfare equivalent at the end of period n of 1 unit of currency at the beginning of period 1 will be (1 + i)"(1 + p)". Thus we can state that in welfare terms. Profit on borrowing and investing = A[(I + a ) " (1 + b)"] again the cash surplus at the end of the investment period. This may be broken down into the constituent parts
C U R R E N T P U R C H A S I N G P O W E R (CPP) REPORTED PROFIT If we continue to report on the profit from borrowing and investing, but report in a way which reflects the change in purchasing power that accrues to the owners, we will need to use their purchasing power index. This may be the inverse of the general price level index, and if this price level index increases by 100i% per period, it will increase 4"rom 1 at the beginning of period 1 to (I + i)" at the end of period n. Thus the purchasing power of I unit of currency in period 1 will be equal to (1 + i)" times the purchasing power of 1 unit of currency in period n.
(1) Profit of investing in assets = A[(I + a)" - (1 + i)" (1 + p)"] (i.e. the cash proceeds from the sale of the assets less the welfare equivalent of their original purchase price) (2) Profit on borrowing = A[(I + i)"(1 + p)" (1 + b)"] (i.e. the welfare equivalent of the original 91
Memoranda
92
sum of money borrowed less the cash paid to redeem the loan). Thus both HC and C P P reporting correctly give the gain in welfare for the owners from such a borrowing and investment transaction, but they both distort the source of the gain, attributing more than is appropriate to the holding of assets and less than is appropriate to the borrowing of funds, given that the owners have a positive marginal time preference rate. This effect is brought about because the elements of reported profit take no account of the fact that shareholders are only able to benefit from that profit when it is made available to them for consumption or for them to choose to reinvest. (They will choose to reinvest only when the real return offered for reinvestment is greater than their real marginal time preference rate.) Thus for any non-zero money marginal rate of time preference (i.e. (1 + i)(1 + p) d: 1) the HC reporting system will lead to bias in the welfare value of the reported profit, and for any non-zero marginal rate of time preference (i.e. p g: 0) C P P reporting system will similarly lead to bias. DECISION RDLES BASED O N R E P O R T I N G SYSTEM If HC reporting is used, then it is clear that investment in assets will take place whenever they are expected to appreciate faster than the cost of borrowing (i.e. Invest if a > b). However, from the owners' point of view, investment should only take place when the rate of appreciation of assets is greater than the owners' marginal rate of time preference (i.e. when (1 + a) > (1 + i)(1 + p)) regardless of the cost of borrowing (b). It is also clear that borrowing will only occur when this will lead to a reported profit, i.e. a > b, but for the maximisation of owners' welfare borrowing should take place whenever the owners' marginal rate of time preference is greater than the cost of borrowing (i.e. when (1 + i)(1 + p) >
(1 + b)) regardless of the level of the rate of appreciation of assets (a). A normal expectation is that the larger the amount of funds to be invested in assets (for a holding gain), the lower will be the expected rate of holding gain; while the larger the amount of funds to be borrowed, the higher the cost of borrowing. These relationships may be plotted as in Fig. 1 for a single period model. The decision rule for maximising HC reported profit would lead to the borrowing and investing up to Ao showing a reported profit of the area boaoA'o. The elements of profit are a gain on investing, area OaoA'oAo and a loss on borrowing of OboA'oAo. Thus management can increase reported profit by not borrowing but instead using owners' funds which in the HC reporting model are treated as free of cost. If, however, the owners' marginal money time preference rate (I + i)(1 + p) - I is taken into account, we can observe an owners' welfare measure of gain. If this rate (t) is the same as the equilibrium rate for the enterprise (i.e. to = a(Ao)= b(Ao)) then the total gain is given by the area boaoA'o, (i.e. the welfare gain is the same as the reported profit and no bias is introduced by the use of reported profit). The elements of this profit are a gain from investing of toaoA'o and a gain from borrowing of botoA'o. If the owners' money marginal rate of time preference is greater than this equilibrium rate (i.e. tl > a(Ao) = b(Ao)), then the required optimal level of investment will be 11 which is less than Ao and the required optimal level of borrowing will be B~ which is greater than A0. The difference (B~-II) must be paid to the owner for consumption. The reported profit on the investment will be area Oaol'olt but the real gain to the owners will be area t~aol't; the reported cost of the borrowing will be area OboB'lBl but the real gain to the owners will be area bot~B'~. Thus the reported profit will be area boaol'~l'~' minus area I~I~B'~B~ which is less than the previously reported profit of area boaoA'o, while the real gain to the owners is area t~aol'l plus area bot~B'~ which is
b - b (A) Merg
%/100 O, bff
Oo
z;
e,'
I i
i I
~--O(Ao)=b(Ao)
.
bo
t
.
.
.
;
i
;
:
;
8~
/'1
A,
8~
Z~
o.oTA) A
Amount of funds
FIG. I. Borrowing and investment in a single period model
Omega, Vol. 9, No. I greater than the previously ascertained gain of area
boaoAo. If, however, the owners' marginal money time preference rate, (t2) is less than the previously determined equilibrium rate (to) (i.e. t2 < a(Ao) = b(Ao)) then the optimal solution will require less borrowing and more investment than the original solution (i.e. the required investment will be 12 which will be greater than A0 and the reported profit is given by the area 0a0I'212 whilst the gain to the owners from the investment is given by the area t2aoI'2). The required borrowing will be B 2 which will be less than Ao showing a reported cost of the area OboB'2B2 but a real gain of area bot2B'2 accruing to the owners. Thus the reported total profit will be the area Oaol':I 2 minus area OboB'2B2 which far exceeds the original reported profit boaoA'o. The real gain to the owners is given by the area t2aol'2 plus area bot2B'l which though greater than the original gain boaoA'o is not greater by as much as the reported profit exceeds the original reported profit. This occurs because the difference between the required investment 12 and the borrowing B 2 is assumed to be provided by the owners and no interest charge for this cash injection is levied in arriving at reported profit. CONCLUSIONS Whilst the profit reporting procedures treat owners' funds as free, the maximisation of reported profit will not maximise owners' welfare unless the owners' marginal time preference rate happens to be equal to the equilibrium rate for investment and borrowing by the enterprise. Where the owners' marginal money time preference rate is below this equilibrium level, the maximisation of reported profit will not greatly militate against the owners' interests, but where their marginal money time preference rate is above the equilibrium level, their welfare will be harmed by the maximisation of reported profit. In most cases enterprises are able to borrow at lower interest rates for given amounts than are the owners and it would, therefore, be reasonable to assume that owners' marginal time preference rate will be greater than the equilibrium rate for the enterprise. In these cases the enterprise will be over-investing, underborrowing and paying out too little to its owners for their welfare maximisation. Increased borrowing and increased dividends should be encouraged to enhance owners' welfare. Within the context of the cost of borrowing for the firm, it must be remembered that there may be fixed costs, such as that on the flotation of securities. These fixed costs on flotation will increase the firm's cost of borrowing above the required rate being paid and will therefore distort the picture. The retention of earnings does not lead to such a cost and will therefore appear attractive to the firm. Such an operation will only be attractive to the shareholders if they would have invested any dividend returned to them in securities rather than using the dividend for consumption.
O.M.k.9/I ¢;
93
From the point of view of the owners of the company it may be necessary to distinguish between private and institutional shareholders since it is difficult to determine a marginal time preference rate for an institutional shareholder, whilst that of the private shareholder may be shown to be measurable at least by an opportunity cost approach. However, it would seem that individuals must ultimately have an interest in the income of institutional shareholders, therefore it may be assumed that there will be a positive marginal time preference rate for such shareholders. Where, however, a problem does arise is that the cost of borrowing for institutional shareholders may well be very similar to that for the firm, while the cost of borrowing for individuals is usually higher than that for the firm. If the institutional shareholders are able to borrow more cheaply than the firm, there is no determinate solution to the optimal borrowing level of the firm for owner welfare maximisation. However, where the institutional shareholders are not able to borrow more cheaply than the firm, it is clear that the firm should borrow at least until its marginal cost of borrowing is equal to the minimum cost of borrowing of its institutional shareholders. It has been shown therefore that the ideal method of assessing management's decisions is in terms of owners' welfare but that present profit reporting practices will lead to bias in the investment and financing decisions of enterprises where ownership and control are divorced. Only where the owners' marginal money time preference rate concurs with that of the enterprise will the owners' welfare be maximised and optimal decisions be taken by management, given that management will be assessed by the profit that is reported. There will, however, be a solution available to the owners other than changing the profit reporting system, and that is to invest only in enterprises whose equilibrium discount rate is the same as the owners' marginal time preference rate. This clientele effect will work only to a limited extent and this article has shown that reported profit may not be a good proxy for use in assessing management decisions about investment and its financing.
REFERENCES 1. FELLINGHAMJC • NEWMAN DP (1979) Monitoring decisions in an agency setting. Jl Busin. Fin. Acct,q 6(21, 203-222. 2. WATTS RL & ZIMMERMAN JL (1979) The demand and supply of accounting theories: the market for excuses. Acct 9 Rec, LIV(2), 273 305.
David S Simon (May 1980) University of Hull Department of Accounting Hull HU6 7RX UK