and the multiplying fraction
| r | . |
| 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 | |