he took advantage of an opportunity then offered to dispose of $5,500 of his bonds at par flat net, and thus extinguished his indebtedness. Now, except for detail, the foregoing was an entirely commonplace case, and the principles of accounting that were involved were of the most elementary nature. The rate of interest and frequency of compounding were first agreed upon; after that the man was charged interest on what he actually owed. He at all times had the privilege of making deposits of any amount and stopping interest to that extent, and it merely happened that he deposited uniform amounts at regular intervals. The position occupied by the brokers was that of a money lender, or what is the same thing-an investor. They lent their customer $5,826.50 and did not even know when, how soon, or in what or how many installments it would be repaid them, but where is the accountant, or "reinvestment" apostle even who would undertake to say that the account did not pay" the brokers 4 per cent., compounded semi-annually? Is it necessary for us to know what disposition the brokers made of the several sums they retained as they collected the coupons from the bonds they were holding as collateral, or is it none of our business? 66 This amount $5,826.50 is what $5,000 of these bonds would have cost at 116.53, and if each item in the account be divided by 50 we will have the following: which is the correct record of the purchaser of the $100 Bridge bond would have had of his investment, if he had done what is imperatively necessary for any and every one to do who buys bonds at any other price than par, viz: KEEP BOOKS! Instead of buying a $100 bond he lent INVESTMENT $116.53, which was charged to its account. Feb. 1, 1905, six months interest was due, which was promptly charged up, making the balance due $118.87. The same day, however, INVESTMENT called and made a deposit of $3.00, which was placed to its credit, leaving a net balance of $115.87. This is the tabular value of the bond when having four years to run, hence thus far we have a complete reconciliation of INVESTOR'S books and the tabulated values, and it would be a waste of time to go on and show that this may be continued to the end, at which time INVESTOR'S books would show that INVESTMENT owed him $110. There is absolutely no particle of difference between the case of the advance of the brokers and the purchase of this $100 bond, except the fifty-fold ratio of the amounts involved. In each case there was a gradual repayment of principal, but a uniform rate of interest received on the principal outstanding, and the interest was collected, not in cash, but by bookkeeping. Having now satisfied ourselves that the tables were "right we will consider the manner in which they were computed, for there is no denying that an unusual feature is involved, and that it is at least necessary to make some modification in the usual methods for valuing bonds. The purest and most logical method of all is to totally banish all such confusing and misleading ideas as 6 per cent. interest, 10 per cent. premium, $100 bond, etc. and regard it as being what it really is, viz., a batch of non-interest bearing promissory notes, maturing as follows: Their aggregate face value is $137, which is their FUTURE WORTH,* but as we are now at August 1, 1904, and as it will be from 6 to 54 months before all this fruit will be ripe, we are more interested in knowing their PRESENT WORTH, which proves to be as follows: This is the theory upon which these tables were "figured," although a much more expeditious method was employed for calculating the different Present Worths and afterwards ascertaining their sum, which said more expeditious method owed There was an actual case a year or so ago of a bond and set of coupons selling at their FUTURE WORTH when Union Pacific Convertible 4's crossed 125 or thereabouts in an upward movement. The flat market price was exactly equal to the face value of the bond and all of its coupons, representing an 0% basis. its existence solely to the fact that (with one exception) the notes happened to be for uniform amounts, and also matured at regular intervals. The tabulated matter shown above is not a calculation at all unless an intelligent use of the repeat key of an adding machine and the proper locating of the decimal point be designated as such. The various sequences of digits that appear were copied exactly as they were found in Reussner's True Discount Tables, and the total that the machine yielded certainly warrants the assertion that the tables are still "right." In fact the expression, "The tables were right" is now ambiguous, as it is the Point of View only that determines which tables are referred to the Bridge Bond Tables, the True Discount Tables, or Vega's Logarithms; indeed if a reciprocally mutual verification club is to be formed, even the adding machine could probably present some very strong claims for admission. There is another totally different manner of regarding the subject; equally sound and affording the same final results, and this plan, although a little inconvenient, nevertheless possesses the advantage that the valuation sought may be derived from tables for ordinary bonds; whereas nothing could be done by the former method if logarithms or Present Worth tables were not available, except at the cost of a prodigious amount of arithmetical work, if the time to run exceeded a few years. This bond is not a $100 bond at all, but a $110 bond, and for it to be 6 per cent. the coupons should be for $3.30. They are, however, for $3.00 only; hence it is not a 6 per cent. bond, but a bond at some other, and of course lower rate, which is found by division to be 5.4545 plus per cent. To be sure no published tables are to be found that give the values at sight for a bond bearing such a cash rate, but we can derive the proper value therefor in the same manner as we would for a 3.65 per cent. or a 9 per cent. bond. Consulting the ordinary tables we find: Value for a 5 per cent. bond... 104.0811 100.0000 4.0811 This 4.0811 is the constant difference representing a change of I per cent. in the cash rate when the basis is 4 per cent. semiannual, and the time to run 41⁄2 years. By subtracting same from par we would have the value of a 3 per cent. bond, and by adding it to 104.0811 we would have the value for a 6 per cent. bond, hence it is evident that if we add thereof to 104.0811 we 45450 1000 should obtain the value for a 5.4545 plus per cent. bond. Performing this multiplication, and using a liberal amount of decimals in the repetend we obtain Add value of 5 per cent. bond 1.8550 104.0811 Value for a 5.4545 plus per cent. bond ... 105.9361 ...... which will no doubt be quite a disappointment to those who fully expected that the result to be obtained in this manner would be in the neighborhood of 1162. 811 10000 However this value of 105.9361 is correct. The 104.0811 that we found in the tables did not mean that a bond for $100 was worth one hundred and dollars, but on the contrary was an abstract ratio on a scale of 100, to be multiplied into the face value of the security it was desired to evalue, and consequently was equally applicable to a real estate note for $3,864.93 or a £200 Mexican bond, and the same may be said of the 100.0000 that was the value for a 4 per cent. bond. Inasmuch as we were working with abstract ratios, the 105.9361 that we derived from the 104.0811 and the 100.0000 is also 1059361 and not $105.9361; neither was the 116.53, $116.53, but and to find in dollars and cents the actual cost of a $100 Bridge bond, August I, 1904, we must perform the operation of $116.53. 10000 11653 11653 X$100= What we now wish to know is the actual cost in dollars and cents of a 5.4545 plus per cent. bond for $110; hence we perform the operation: 1059361 X$110 $116.5297. The tables are still "right." There is yet another way of looking at the problem-the most expeditious of the three, and still possessing the virtue of being untainted with any usual assumptions or presuppositions regarding sinking funds or reinvestments respectively. This bond is not a straight 40 year bond, but a 20-40, and as it is selling above par, we must assume that it will run the minimum time, hence its value, according to the ordinary tables is, 108.1622 But we are working on the theory that whoever owns this bond when it is paid off is to receive a present of |
