This section is from the book "Money And Investments", by Montgomery Rollins. Also available from Amazon: Money and Investments.

First read "Net Return upon the Investment."

The computations involved therein are based upon the principle that the holder of a bond, bought at a premium, is expected to immediately reinvest a sufficient portion of the money derived from the payment of each coupon, and keep it invested at compound interest until the maturity of the bond, so that the face value of the bond added to the accumulation of reinvested interest will, at the maturity of the bond, be exactly equivalent to the original cost of the same.

To illustrate, let us take a 5% bond having 20 years to run, yielding 4 per cent to the investor at a price of 113.68; that is, $1,136.80 for a $1,000 bond. The investor believes that he will receive 4% upon the purchase price of $1,136.80. As a matter of fact, he receives $25 each 6 months, or $50 yearly. At the maturity of the bond, he will receive, besides the last interest payment, only the principal sum of $l,000. There must be some manner, therefore, of accounting for the $136.80 premium originally paid. This is done through the creation of a sinking fund, as follows:

The investor must reckon 4% upon the total cost price of $1,136.80, which would amount to $22.74 for each 6 months' period. The semi-annual coupon being $25, there is left, therefore, a sum of $2.26, which, if immediately invested, will, at the maturity of the bond, added to the principal sum, together with other amounts similarly deposited twice yearly, equal the purchase price.

In the 20 years which the bond has to run there will be 39 times $2.26 deposited, which will have drawn interest, and one like sum taken at the maturity of the bond, which will have no time to draw interest. 40 times $2.26, however, will be the amount set aside, or $90.40, which is $46.40 less than the actual amount sought. This $46.40 is provided for by the interest - and compounded at the investment rate; in the foregoing case, 4 per cent - upon the sums set aside.

It is true that there would be some difficulty in putting this into actual practice, and that the sinking fund plan is seldom carried into effect, but, nevertheless, it does not change the principle that money has a value, so that, if the sums are not set aside and invested, the theory remains the same.

The question naturally arises as to the application of the foregoing principle for determining the yield of a bond bought at a discount. Let us again illustrate: A 5% bond having 20 years to run, if bought at the rate of 88.44, or $884.40 and accrued interest, will net the investor 6%; that is, 6% on the $884.40 invested. As the coupons fall due, he obtains, the same as in the above case, $25 each 6 months or $50 per annum. When the bond matures, he will receive, in addition to the interest, the full principal sum of $1,000, for which he has paid but $884.40. There is, therefore, a difference here of $115.60, by which amount the purchaser will be apparently enriched at the maturity of his bond. If, however, he wishes to avail himself, in the meantime, of the full 6% net return, to which he is entitled, he must anticipate this difference of $115.60, which may be done in this manner: He is entitled to reckon his income at 6% on the $884.40, the original purchase price, which, for each 6 months, would call for $26.53. The coupon which he detaches from his bond provides for but $25 of this. There is, consequently, the sum of $1.53 which he should receive, from some source, to make his full 6% interest. He may anticipate the $115.60 above referred to by taking from some other fund this $1.53 each 6 months. This represents the amount which, if invested at 6% - the same net return as provided for in the investment - will, at the maturity of the bond, added to the $884.40, just equal $1,000.

To explain one more point in this connection, and following the illustration above, where $1.53 is taken each 6 months from some other fund, is there not a loss of interest each time upon that amount until the maturity of the bond? Or, in other words, what provides for the interest on these sums? That comes back at the maturity of the bond, for, it will be noticed, that if $1.53 be multiplied by 40, the number of coupons, the sum equals $61.20. But $115.60. will be received at the end of 20 years, and the difference between these last two sums is $54.40. That is to say, $54.40 represents the compound interest on the $1.53 periodically taken and expended as income.

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