Sinking funds

The method the issuer chooses to fulfill the sinking fund requirement is a function of the interest rate level. If interest rates have risen since the bond was issued, depressing the bond s price, the issuer will purchase the required amount of bonds in the open market. If interest rates have fallen, it will call the specified amount at par. As an illustration, consider the hypothetical ABC bond whose terms are listed in FIGURE 11.15. 

According to the terms in figure 11.15, the ABC bond pays an 8 percent coupon and is set to mature in 2019. It also contains a provision stating that the issuer will redeem 50 million of the bond s 100 million 

FIGURE 11. la M hypOTflf Issuer Ticai finnn wirn a. iinianp Minn ABC pic 

ABC has in effect embedded ten European options in the bond, each relating to 5 million nominal of the bonds and each expiring on December 1 of a different year, starting in 2009 and ending with 2018. The decision to exercise the options as they mature is made using the binomial-tree method discussed earlier. 

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DecoveTj of Capital. In Figure 1, the annual book depreciation is used to retire the fixed capital investment. Whereas this accounting model does not correspond to the typical money flow, it is one possible model for recovery of capital. This model assumes that the investment is reduced each year by the amount of the annual depreciation. Another model (22) assumes that a uniform yearly book depreciation payment is made to an interest-bear sinking fund that accumulates to the depreciable fixed capital amount at the end of the venture. Using this second model, the investment is outstanding throughout the lifetime of the project. This also does not correspond to the actual money flow in most cases. ProfitabiUty analysis utilizes a third model based on discounted cash flows. 

A fourth method of computing depreciation (now seldom used) is the sinking-fund method. In this method, the annual depreciation A is the same for each year of the life of the equipment or plant. The series of equal amounts of depreciation Aq, invested at a fractional interest rate i and made at the end of each year over the life of the equipment or plant of s years, is used to build up a future sum of money equal to (Cpc S). This last is the fixed-capital cost of the equipment or plant minus its salvage or scrap value and is the total amount of depreciation during its useful life. The equation relating i Fc S) and Ao is simply the annual cost or payment equation, written either as... 

In the sinking-fund method of depreciation, the effect of interest is to make the annual decrease of the book value of the equipment or plant less in the early than in the later years with consequent higher tax due in the earlier years when recovery of the capital is most important. 

Sometimes a company uses a sinking fund to retire a bond. A series of equal annual payments A, invested at a fractional interest rate i and made at the end of each year over a period of n years, is equivalent to a sum of money of present value P, given by... 

The inverse of the right-hand side of Equation (3.6) is known in economics as the sinking fund deposit factor, that is, how much a borrower must periodically deposit with a trustee to eventually pay off a loan. 

Sinking fund An accounting procedure computed according to a specified procedure to provide capital to replace an asset. 

Now This method for determining depreciation is based on an ordinary annuity and is known as the sinking-fund method.)... 

The original cost for a distillation tower is 24,000 and the useful life of the tower is estimated to be 8 years. The sinking-fund method for determining the rate of depreciation is used (see Example 5), and the effective annual interest rate for the depreciation fund is 6 percent. If the scrap value of the distillation tower is 4000, determine the asset value (i.e., total book value of equipment) at the end of 5 years. 

Derivation of the formulas for the sinking-fund method can be accomplished by use of the following notations in addition to those already given ... 

Since the value of R represents the annual depreciation cost, the yearly cost for depreciation is constant when the sinking-fund method is used. As shown in Fig. 9-3, this method results in book values which are always greater... 

Asset values of property when depreciated by interest (sinking fund) and no-interest (straight-line) methods. 

Although the sinking-fund viewpoint assumes the existence of a fund into which regular deposits are made, an actual fund is seldom maintained. Instead, the money accumulated from the depreciation charges is put to work in other interests, and the existence of the hypothetical fund merely serves as a basis for this method of depreciation accounting. 

The same approach used in the sinking-fund method may be applied by analyzing depreciation on the basis of reduction with time of future profits obtainable with a property. When this is done, it is necessary to use an interest rate equivalent to the annual rate of return expected from the use of the property. This method is known as the present-worth method and gives results similar to those obtained with the conventional sinking-fund approach. The sinking-fund and the present-worth methods are seldom used for depreciation cost accounting but are occasionally applied for purposes of comparing alternative investments. 

Comparison of the various depreciation methods shows that the declining-balance and the sum-of-the-years-digits methods give similar results. In both cases, the depreciation costs are greater in the early-life years of the property than in the later years. Annual depreciation costs are constant when the straight-line, sinking-fund, or present-worth method is used. Because interest effects are included in the sinking-fund and present-worth methods, the annual decrease in asset value with these two methods is lower in the early-life years than in the... 

The original cost of a property is 30,000, and it is depreciated by a 6 percent sinking-fund method. What is the annual depreciation charge if the book value of the property after 10 years is the same as if it had been depreciated at 2500/year by the straight-line method ... 

A company may use a sinking fund in a variety of ways, but the simplest is to pay a fixed amount A at the end of each year to buy and retire bonds until after n years all the bonds have been retired. This annual payment may prove a significant strain on the resources of a company. Failure to make the payment could result in bankruptcy. In the case of income bonds, a company is required only to pay interest when it earns it. 

Singular and plural in reports, use of 474 Sink, capital, 150-152 Sinking-fund method for determining depreciation, 283-285 Site-improvement costs, 175-176... 

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