After Quota-Tions Have Been Marked X D.. The Ensuing Dividends Begin To Accrue, And Stock Is Quoted Cum Div

Immediately after the quotation is marked x d. the ensuing dividend begins to accrue and to increase the price; that is to say, the dealings are made cum dividend so far as the subsequent dividend or interest is concerned; the price instantly is reduced when it is quoted x d. - no extraneous events affecting the value of the stock having meantime occurred - by the amount of the dividend or interest paid or shortly payable. Thus a stock bearing 3 per cent interest, payable half-yearly, stands at £150, we will assume (in-cluding the current six months' dividend): on the next day it is, say, quoted x d., and the price falls to 148½, being reduced by the half-year's dividend paid. If sold on the former day the seller obtains £150, but hands over the £1½ (the half-year's dividend) to the buyer, or if sold on the following day the vendor receives £148½ and retains the £1½; he is, accordingly, in precisely the same position (at the level of £150) in each case and sustains no loss. If there be no apprehension or unfavourable news in the market extrinsically affecting the stock individually, or affecting it in conjunction with other securities, the price of 148½ by simple efflux of time gradually rises from the moment it is declared x d.t by the accruing increment of the current interest, so that at the end of four months from that date it will stand at 149½, being the 148½, plus the accrued interest for the one-third of the year expired.

IV. Sinking Funds: Their Formation And Uses

The Wisdom Of Forming Sinking Funds

I have already recorded the sound advice of a financial authority - that every investor, however substantial be his securities and trustworthy the rate of interest which they yield, should appropriate a portion of the annual income as a sinking fund1 for possible loss of capital during the course of his investments. Investments of successful issue will certainly, even with the most vigilant and competent exercise of judgment and caution, be interspersed with investments resulting in a loss or diminution of capital; and the maintenance of an average level of value in the whole range of the selected securities demands the appropriation of part of the proceeds of prosperous ventures to the formation of a sinking fund, or a reserve.

1 A fund, in its original literal sense, is a bottom, or foundation (Latin, fundus); a banking fund, for example, is the foundation of its financial operations; the word thus acquired the sense of capital. Sinking is derived from sink, and one of its meanings is "to be reduced in value or extent"; hence, a sinking fund is a fund or capital devoted to the gradual sinking or reduction and extinction of any debt.

The Ordinary Form Of Sinking Fund Not Adapted To Small Investors

A sinking fund, in the ordinary form, is not generally feasible for an ordinary investor of moderate means, if only on the ground that the continuous reinvestment of small sums at compound interest cannot usually be attempted with success; but a sinking fund in the form of a reserve - applicable to the retrieval of losses - should be the practice of a prudent man.

The Nature Of Sinking Funds Proper

It will be of interest to describe the customary nature and process of what are termed sinking funds proper. A sinking fund consists of a yearly (or other periodical) sum set apart and invested at compound interest (with the reinvestment of each payment of interest as it is received) for the purpose of recouping any loss of money which may occur, or with the object of providing the means for discharging a specific pecuniary obligation which may have been accepted. A few examples will show the operation of the process.

Sinking Fund Applied To A Security Redeemable At The End Of Thirty Years

1. A security is purchased on the Stock Exchange which is redeemable at the end of thirty years (from the date of purchase) at par; that is, at the nominal capital-value which it expresses - usually £100 or some multiple of £100. Owing to favourable circumstances affecting the security and its prospects at the time of purchase, the security is in great demand, and the investor pays a price of £104, or he purchases at a premium of

4 per cent. Since the bond will be redeemed or paid off at £100 only, provision should bo made for the certain loss of the £4. Every sinking fund should be calculated at such a rate of interest as may, after allowance for income tax, depreciations of value, or actual losses on the securities in which its instalments are invested, be expected with reasonable confidence to be continuously realised throughout the duration of the period for which the service of the fund is required. This selection of the rate depends upon the sagacity and closeness of our predictions of the probable future course of the money market, and the influences by which it is affected, based upon a survey of the experience of the past. But, in any event, the rate chosen for the accumulation of the fund should be low, and the securities in which its instalments are invested, and in which the interest derived from the investments of past instalments are reinvested, should be of the soundest and most stable character.

This condition in itself implies a low rate of accumulating interest. It is obvious that where the term over which the sinking fund is to extend is short, a comparatively higher rate of interest may be legitimately adopted than can be prudently assumed when the period is a lengthy one, and accordingly comprises a greater number of possibilities of fluctuation of values. Foresight is more competent to a brief than to a prolonged range of vision. In the case now under consideration let us assume that a clear rate of 3 per cent may be depended upon as safe. Apart from adverse variations in the values of the securities selected for the investment of the instalments, and looking simply for illustration to the element of income tax, the adoption of 3 per cent implies a realised rate of about £3 3s. 2d. per cent, since £3 3s. 2d. reduced by an income tax at 1s. produces the required 3 per cent. From a book of tables of compound interest we perceive that, at 3 per cent, an annual sum of £1 will accumulate to £47 l1s. 6d. by the end of thirty years, so that by proportion, the sinking fund for restoration of the premium of £4 per cent will be about 1s. 8d. This result, as has been stated, demands that at least £3 3s. 2d. per cent is realised throughout upon the investment of each instalment of the sinking fund and upon the reinvestment of the interest obtained thereon. Hence, from the interest derived from the bond, the yearly sum of 1s. 8d. should be set aside and invested in respect of each £100 which the bond expresses. The security is thus rendered complete and exempt from loss, since £100 will be received on repayment of the bond, and the balance of the purchase money (or the £4 per cent) will be provided by the accumulated amount of the sinking fund.