CHAPTER XXV

THE SINKING FUND Origin and Use The sinking fund is a recognized and well-established instrument for the financing of business. A great deal has been written about the subject, and over some of its phases much wordy warfare has raged. As usual, however, the controversy has had little or no effect on the practical application of the principle of the fund. The sinking fund seems to have been first used as a practical instrument for the repayment of debt in the year 1716, although the idea germinated some time before this. At first its application was limited entirely to public finance. Through the efforts of Sir Robert Walpole, legislation was enacted in England which made certain specified taxes perpetual. Any surplus remaining after applying them to the purpose for which they were levied was to be put into a sinking fund for the purpose of paying off the public debt. Due to bad administration of the fund, it was not successful. Its use was attempted a second time in 1786 by William Pitt, at the instance of a Dr. Price. Since then it has had a rather checkered career in public finance. In some fields, notably among municipal corporations, the device has been very successful. Through the extension of the principle to the field of business the sinking fund found the use to which it was best adapted. Definitions A sinking fund may be defined as “a fund formed by the investment of annual savings or other contributions with a view to the ultimate application of the moneys so accumulated in the payment of a previously incurred ... debt.” An English accounting authority defines a sinking fund as “a fund set aside out of _assets_ and accumulated at interest for the purpose of meeting a debt.”[67] This latter definition draws attention to the fact that the sinking fund is a fund of assets—not simply a book account set up to indicate recognition by the board of directors of the _need_ of providing for payment of a debt, but certain definite assets set aside and, after accumulation, to be used for that purpose. Attention should also be called to the fact that usually the fund is not dependent solely for its increase upon interest accretions. As generally handled, the fund is added to at regular intervals by setting aside more or less regular amounts of assets to be applied to the same purpose. Frequently the contract agreement entered into between the company and the creditors holding the debt to be repaid governs in detail the way in which the fund is to be provided and the way in which it is to be handled. [67] George Lisle in “Accounting in Theory and Practice.” A sinking fund may be used for other purposes than the payment of debt. Thus, occasionally one finds it created for the purpose of providing funds for the retirement of capital stock issues, notably preferred stocks of various kinds. It may be well again to point out the unfortunate lack of uniformity in the use of the term. Thus “Sinking Fund” as an item in the balance sheet is found sometimes among the debits and sometimes among the credits. Other titles under which the item appears are: Sinking Fund Account, Sinking Fund Reserve, Sinking Fund Investments, Sinking Fund Trustee, and Sinking Fund Cash. While in this chapter the term will be used to indicate assets set aside in a definite fund—and limitation to this use is growing among the best authorities—explanation will also be given of what the other uses indicate as to financial policy and the manner of booking such policy. Mathematical Principles on which Based The mathematical principles on which the computation of the sinking fund rests will first be explained. The problem involved here is the calculation of the amount which set aside periodically and invested at compound interest will provide a sum sufficient to pay off the debt when it matures. Needless to say, the sinking fund is usually applied only to the redemption of long-term debts, as only over a comparatively long period is the real potency of the compound interest principle secured. For the solution of the problem it must be known whether the periodic increments to the fund are set aside at the end or at the beginning of the period. It is usually understood to be at the end of the period unless otherwise specified. Assume, therefore, that a bond issue is made with maturity in n years and that the contract with the bondholders calls for the creation of a sinking fund with payment thereinto at the end of each period. It is required to find the amount to be paid into the fund periodically. We will assume that: P = the principal sum to be redeemed at maturity n = the number of periods till redemption A = the amount paid into the sinking fund at the end of each period r = the rate per cent per period at which the moneys in the sinking fund are invested at compound interest R = 1 + r Reference to Chapter XV, page 271, gives the amount, A, of a sum of money put at compound interest at r% for a term of n years, as A(1 + r)ⁿ⁻¹. It is evident here that the sum, A, paid into the fund will accumulate for n-1 years and that each succeeding payment remains at interest one year less than the next preceding amount, the last amount earning no interest. Accordingly, the first A—we will denote it as A₁—will amount to A(1 + r)ⁿ⁻¹; A₂ will amount to A(1 + r)ⁿ⁻²; A₃ to A(1 + r)ⁿ⁻³; etc. The sum of all these amounts must be equal to P, the debt to be redeemed. Therefore, the equation may be formed: A(1 + r)ⁿ⁻¹ + A(1 + r)ⁿ⁻² ... + A(1 + r) + A = P or A(Rⁿ⁻¹ + Rⁿ⁻² ... + R + 1) = P, whence ( Rⁿ - 1) A(--------) = P and ( R - 1 ) P(R - 1) Pr A = -------- or ------, Rⁿ - 1 Rⁿ - 1 which being interpreted means that the theoretical amount to be set aside at the end of each period can be found by multiplying the amount of the debt by the fraction r ------- . Rⁿ - 1 If the annual payment is made into the fund at the beginning of each period instead of at the end, then Pr r A will be -------- and the multiplying fraction --------- . R(Rⁿ - 1) R(Rⁿ - 1) It is evident that in practice some allowance will usually have to be made for failure to keep all payments in the fund and interest accretions thereto constantly invested at the calculated rate. This is not a matter of serious import, however, for small inaccuracies can be adjusted during the last period or the last few periods by increasing or decreasing the annual payments as may appear necessary at those times. From a financial standpoint it should be borne in mind that there is no absolute necessity for the accumulations in the fund to be sufficient in all cases to retire the entire debt. Refunding a portion of it may be resorted to. Other conditions being equal, it should be a much easier task to borrow only a portion as compared with borrowing the original amount. Accumulation Based on Agreement It is necessary to call attention to the inapplicability of the above method to all cases. Of course, where the contract between the borrower and the lender makes definite provision for the manner of creating and handling the sinking fund, that contract must therefore govern. However, in the case of a concern operating wasting assets, a frequent provision of the trust agreement in the case of a bond issue is that the periodic payments into the fund shall be proportional to the amount of the natural product extracted or used. Thus in the coal mining industry the trust agreement may provide that, say, five cents for every ton mined shall be placed in a sinking fund. In determining the amount for each ton, the total amount of the debt to be extinguished is divided by the estimated number of tons of coal in the mine. This gives the amount of the debt which each ton must bear. Conservatism and business prudence require an ample allowance for mistakes in the estimate of tonnage which it will be profitable to mine and, also, for a liberal margin of safety. The relation between the life of the bonds and the estimated annual output has an important bearing also, for the charge per ton must be sufficient on the basis of the tonnage mined during the period covered by the bonds to retire the bonds at their maturity, regardless of how much coal there is still in the mine at that time—unless a refunding operation is contemplated. Similarly in the case of timber properties, sinking fund payments are usually roughly proportional to the amount of timber cut; in earthwork or quarry enterprises, to the amount of material removed or quarried; in real estate development companies, to the number of divisions made ready for the market. In such cases the compound interest method, scientifically accurate, often gives place to annuity methods more or less roughly calculated, under which, by trust agreement, definitely named sums, approximately sufficient to accomplish redemption at maturity, are set aside periodically. Other methods fix the amount as so many per cent of gross or net profit, of the bonds outstanding, of total business done, etc. Oftentimes, scientific accuracy, even if desirable, is impossible because of provisions in the trust agreement to the effect that the moneys in the sinking fund are to be used for the purchase of the company’s own bonds at market but providing a maximum price above which none are to be bought. This involves purchases at a premium, or possibly a discount, unknown at the time the periodic amount must be calculated. An amount figured on the maximum price would be conservative; or the amount may be based on par with the stipulation that the difference between par and market shall be handled each period through the profit and loss. Effect of Settlement of Debt As an introduction to the discussion which will follow of the relation of the sinking fund to profits, we will first consider the several ways in which a debt may be settled. For that purpose there is nothing which makes clear the principle involved better than the fundamental schedule of debit and credit, showing the interplay of all transactions as they are brought onto the books. At the risk of unnecessary repetition, that schedule is accordingly set up here for ease of reference. SCHEDULE OF DEBIT AND CREDIT =============================================================== _Debit:_ | _Credit:_ (1) Increase of assets | (a) Decrease of assets (2) Decrease of liabilities | (b) Increase of liabilities (3) Decrease of proprietorship | (c) Increase of proprietorship From this it is seen that the redemption of a debt—a number (2) transaction—may be accompanied, and therefore accomplished, by any one of the three offsetting credits or by a combination of them. A debt may be settled (a) by the conversion of an asset; (b) by the creation of another liability; or (c) by an increase in net worth. Cash or other assets may be used for the purpose, resulting in a decrease of assets, as in (a) of the schedule. It should be noted that the borrowing of, say, $1,000 and its repayment in cash leaves the borrower in the same relative financial condition as before, except for the gain derived from the use of the money borrowed. Such loans, to be repaid in this way, are usually of a temporary nature, to tide over an emergency—such as the handling of the load of seasonal activity, or other similar situation. This method of settlement is, of course, not confined to payment of debts for money borrowed, but includes debts contracted for merchandise purchased on credit and other current liabilities. Again, a debt of one kind may be settled by the creation of a debt of another kind, as in (b) of the above schedule. Thus, an open account payable may be converted into a note or acceptance payable. Here, the liability canceled and the new one created are usually of the same class, viz., current liabilities, and the need for a more or less permanent increase in working funds is not contemplated. So also, a current liability, or a group of them, may be converted into a funded debt. This may be deemed advisable when it is seen that there will be a permanent, or at least a long-term, need for funds which have up to this point been provided by short-term borrowings and credits. Again, a refunding operation would have the effect of a decrease of one liability offset by the increase of another. Finally, a debt may be canceled through an increase of proprietorship, as in (c) of the schedule. By this means the redemption of the debt may be direct or indirect. Capital stock, either treasury or previously unissued stock, may be accepted by creditors in satisfaction of their claims. They thus change their status from creditors to proprietors and the result is an increase of the concern’s net worth. Indirectly a debt may be settled by the reservation of profits. Instead of distributing the profits as dividends, they may be retained in the business and so provide funds, i.e., assets, for the redemption of debts. In either case the settlement of the debt has been effected by means of increased net worth evidenced by new issues of stock or by reserved profits. In these various ways, therefore, a debt may be settled. As pointed out above, the first method contemplates no permanent need for increased working funds and the extinguishment of the debt leaves the borrower in approximately the same position financially as before its incurrence. Under the second method, the relative positions before and after are the same excepting in the case of funding a floating debt. Here a permanent or long-term increase in working funds is secured. With the third method a permanent increase is secured in the capital funds available for use in the business. Financial policy, governed by the needs of the business and its markets, will always dictate the method to be used for extinguishing or contracting a debt. Relation of Fund to Profits The relation of the sinking fund to profits will next claim our attention. This point has been much debated, reaching the acrimonious stage at times. It is variously contended: (1) that there is a necessary relationship between profits and the payment of a debt; (2) that for final settlement only assets will suffice; and (3) that the policy of reserving profits to an amount equal to the sinking fund is a policy not dictated by any fundamental principle of relationship between profits and debt redemption. With regard to the first claim, it is sufficient to call attention to the discussion above where the various ways of paying a debt were considered. As there pointed out, a reservation of profits may offer the only available means of providing assets with which to redeem debts. Accordingly, at least an indirect relationship between profits and debt redemption is established. As regards the second point, that only assets can be used for the final payment of debts, this also is seen to be too broad a claim, for the issue of new stock may accomplish the same end—directly, as where issued to creditors, or indirectly, as where sold and the proceeds applied to liquidate the claims of creditors. As to the third claim, it might be said with equal relevance that there is no basic relationship between debt redemption and any _method_ of settlement. The assertion can be made with little fear of contradiction that so long as the claims of creditors are satisfied, the manner of doing it is of small importance. Of course, only the currency of the realm is a legal tender for debts but, if other forms of payment prove satisfactory and are accepted, the matter ends. It is therefore solely a question of financial policy, no principles of accounting are involved, and the only point in which accounting is concerned is in making the record so as truthfully to show what is taking place, i.e., to reflect accurately the financial policy adopted. If the needs of the business require a permanent addition to the capital, as mentioned above, that can be secured in only two ways, viz.: (1) the sale of stock and (2) the reservation of profits. If, on the other hand, the debts to be repaid have provided funds for the emergency or purpose for which they were contracted and that emergency or purpose no longer exists, then the repayment of those funds to the creditors is the business policy dictated. Under these circumstances, to load the business with capital funds not needed in the enterprise might well be the height of business folly. According to the conditions to be faced, there may or may not be any necessary connection between debts and profits. It should be pointed out that the kind of debt—i.e., the long-term obligation—for the settlement of which the sinking fund method is often employed, is almost invariably an indication of the need of a larger capital fund. Recognition of this is frequently evidenced by the provisions of the trust agreement requiring the payment into the sinking fund _out of profits_ of the periodic contributions. This forces the ultimate increase of capital to be made by the owners. Two other alternatives are open, viz.: borrowing again at the maturity of the debt—a refunding operation—and securing additional capital through the sale of stock. Conditions of the financial market at the time the funds are needed, the policy of the concern as to the admission of other owners, and the relative bargaining strength of the two parties to the loan—these are determining factors in the financial policy to be adopted. Accounting for Sinking Fund The various problems met in accounting for the sinking fund will now be discussed. First among these is the manner of showing its status on the balance sheet. This may be done in four different ways. Here, also, the chief problem involved is an accounting problem only so far as it concerns the best manner of setting forth truthfully the facts of financial policy.