This gives a working rule whereby it is possible to work back from the known value, par, by successive operations until any desired value is found. The calculation is somewhat as follows for the example used in the schedule:
| 1,000 + (1,000 × .025) | = | 1,025 | = | 1,004.90 |
| 1.02 | 1.02 | |||
| 1,004.90 + (1,000 × .025) | = | 1,029.90 | = | 1,009.71 |
| 1.02 | 1.02 | |||
Similar calculations will develop the other values in the schedule. In the case of a bond with, say, 30 periods still to run, the burdensome nature of the calculation by this method is apparent.
While commercial houses rarely need to use the algebraic formulas for calculating bond values, it is the only really correct method of valuing bonds which are held for long-time investment, and the accountant should be conversant with it. For the balance sheets of savings banks, insurance companies, and other investment concerns, scientific valuation of bonds with the attendant amortization up and down of discounts and premiums is not only theoretically correct but practical considerations, in a market such as prevails in a time of marked but temporary depression, demand that it, or some approximation to it, be used.
A discussion of the valuation of serial and short terminal bonds, or those carrying more than one rate of interest, or those redeemable by lot at various times, is beyond the scope of the present work.
Valuation of Sinking Funds
The section of the balance sheet under consideration usually includes the various funds representing the investment of reserves. Sinking funds, building funds, insurance, pension, endowment funds, and the like, are examples of this class of asset. The use of the term fund should be strictly limited to specific assets set aside for specific purposes. The problem of valuation in connection with funds will be considered under two sets of conditions, viz., when the funds are invested in a concern’s own securities and when invested in outside securities. The practical questions in connection with funds are those of finance rather than of accounting.
The determination of a policy of investment as between the concern’s own and outside securities depends on many considerations, some of which do not come strictly in the purview of the accountant. It is argued that for the sake of immediate availability, investment of funds to be used for a specific purpose at a definite time should be in the securities of other concerns over whom control does not extend. In some cases, however, provision is made in the trust deed of a sinking fund to the effect that the funds set aside shall be used to purchase the bonds to retire which the funds have been created. These bonds may be canceled or held for the sake of their income in the fund till maturity. There would seem to be no choice between a concern’s own and outside securities, provided the same standards of moral obligation are observed in both cases. If the securities purchased for the funds are the concern’s own bonds, they should as a rule be valued at cost and the premium or discount amortized over the remaining life of the security. They may, of course, be carried on the books at par and the premium charged immediately against any income in the fund. The showing on the balance sheet should be in exact accord with the facts. If the bonds have been purchased and canceled together with their coupons, the amount of such cancellations should be shown as a deduction from the bond liability. The fund is thus serving its purpose currently by reducing that liability. Any uninvested balance in the fund should, of course, be shown among the assets. When the bonds are purchased and held uncanceled for the sake of their income, it is probably better to carry them among the assets, indicating, if the information should be considered vital, that the securities in the fund are the concern’s own securities.
If the funds are invested in outside securities, these should be valued on the basis of long-time investments. If bonds, their premiums or discounts should be amortized. If, however, the credit of the issuing concern is such as to cast doubt on its ability to redeem them at maturity, other bases for valuation should be taken. It might even be necessary to set up special reserves to replenish the expected shrinkage upon realization of the securities held in the fund. A final injunction may not be out of place, to the effect that all funds should be definitely labeled so as to show their purpose.
Valuation of Investments in Land