A Farther Method Of Computation

A clearer plan would be to suppose that he sold to some person the right to the bonus of £5. At 3 per cent, the present value he would receive would be £2 7s. 9d.; and laying out this sum in the purchase of an annuity enduring for the twenty-five years, he obtains each year the sum of 2s. 9d.t as in the preceding calculation. The same result is thus arrived at. As previously computed, apart from the bonuses, the investor receives £3 3s. 2d. per cent; adding the equivalent annuity in respect of the reversionary £5, or 2s. 9d., we obtain the complete return shown of £3 6s. Or he may regard his position in another way. He has invested £95 ; the sum of £5 is worth in present value £2 7s. 9d.: hence he will receive his capital of £95 intact when the bond is redeemed, and he also possesses a permanent additional capital of £2 7s. 9d., which he can apply to productive uses.

Method Of Computation When A Security Has Been Bought At A Premium

But assume that instead of buying the bond at a discount he purchased at a premium: let him give £105, where he loses £5 on each £100 of the bond on redemption. It is not likely that this price would be paid where the bond only bore a rate of 3 per cent. We accordingly presume that the rate attached is 3½ per cent. The bond is again assumed to be repayable on the expiration of twenty-five years from the date of purchase.

Proceeding as before, we have the proportion: as £105 is to 3½, so is £100 to the return actually obtained as a percentage. The result is £3 6s. 8d. per cent. But a sinking fund must be established (or assumed to be established) for recouping the loss of the £5 at the end of the period. As £1 per annum will at 3 per cent compound interest (this rate being appropriate to the formation of such a fund) accumulate to £36 9s. 2d. in twenty-five years' time, an annual sum of 2s. 9d. is necessary to restore the extinguished £5. Hence for the £105 expended the investor receives £3 10s. in interest, and diminishing this income by the sinking fund provision, the net amount is £3 7s. 3d. Then as £105 is to £3 7s. 3d., so £100 is to the actual rate per cent realised, or £3 4s. Id. Receiving the return of £3 4s. Id. per cent, he also secures the full £105 when the bond is discharged, namely, £100 from the bond, and the £5 from the accumulated amount of the sinking fund.

Foreign Bonds Redeemable By Annual Drawings By Lot

Reference may be briefly made to certain foreign loans (which require, if they be selected, the exercise of special knowledge and judgment) which are redeemable by what is termed an accumulative sinking fund; that is to say, where the bonds are repayable annually by drawings by lot with a bonus, since they are usually issued at a discount and repayable at par. If an investor's bond be drawn for redemption at an early stage in the duration of the loan, he realises, it is evident, by this speedy receipt of the bonus a very substantial rate of interest on the investment, while if the drawing of his bond be deferred for a considerable time, the remunerative rate becomes less and less, though, of course, always higher than the rate of interest which the bonds bear. If he invested in a very large number of bonds, he might reasonably assume that his bonds would be drawn for repayment year by year (and thus be able to estimate the probable total realised rate) in the proportion which the aggregate amount of such bonds bore to the total amount of the loan.

Objections To Foreign Securities Redeemable By Annual Drawings By Lot

But, as a rule, the investor who simply wishes for a sure and steady income in stable securities should exclude from his survey investments with this mode of redemption. A further practical objection lies in the fact that if the bond be drawn he is burdened with the cost and trouble of discovering a fresh security; and although the compensation might be adequate where an early drawing ensued, the occurrence of a speedy redemption is, of course, entirely a matter of chance, which, in the case of a single bond or of a small holding, cannot be fixed otherwise than as an insecure question of probabilities.

III. Ex Dividend (X D.) And Ex Interest (X In.)

It has already been mentioned that the symbols x d. or x in. will at periodical intervals be found attached to the quotation of prices in the official list; and as the subject is usually perplexing to the investor, and of some practical consequence (at all events in the way of preventing a disappointed expectation sometimes entertained) it is desirable to furnish an explicit explanation.