Accounting theory and practice, Volume 2 (of 3)

by Roy B. Kester

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.

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: