A typical example is the accountant's need as decision maker to estimate the future market value of an income-producing asset when its book value figure is not suitable or no objective measure for doing so exists. The problem arises in such decisions as lease versus purchase, the valuation of a going-concern, or an income producing intangible asset, capital budgeting or abandonment analysis, or when considering the sale or replacement of an existing asset at some future time period. While there is no foolproof approach to future value estimation, elementary financial/economic theory provides a sound, logical basis for making this challenging projection when alternative methods are either inappropriate or unavailable. This simple, practical technique can be referred to as Amortized Residual Value (ARV).

The logic underlying the ARV technique is grounded in fundamental financial/economic concepts. A brief review of these principles enriches the discussion and illustration that follow.

The Financial Concept of Value

In finance, the value of any income-producing asset is a function of the discounted amount (present value) of the asset's expected cash flows. The discounting process involves adjusting expected future cash flows to a present value using the prospective buyer's or seller's required rate of return as the discount rate. The rate of return or discount rate should be sufficient to provide compensation for the opportunity cost of waiting (time value of money) and for the degree of risk inherent in the asset's expected cash-flow stream. This concept can be illustrated with a simple example.

Assume the Friendly Bank makes a $50,000, 6-year term loan to XYZ Corporation. The loan is to be amortized quarterly at the current 12% market-rate of interest, and requires interest and principal payments each period of $2,952.37. Initially, the discounted or amortized value of the future stream of quarterly loan payments (cash flows) would be the outstanding or remaining principal of $50,000. This amount is determined as follows using the present value factor from a standard annuity table for 12% and 24 quarters, and the quarterly cash flow stream of $2,952.37.

AmortizedValue=AnnuityPaymentx

PresentValueAnnuity

Factor

=$2,952.37x16.93554

=$50,000

The discounted or present value of the loan at any other point in time can be calculated in the same manner, or determined more easily from a traditional loan-amortization schedule. The "Ending Balance" figures on an amortization schedule represent the present value of the remaining cash flows from the loan and, as such, the market value of the loan at a 12% discount rate.

This illustration reflects three important properties of the amortized-value concept: in competitive, highly efficient financial markets, income-producing assets of the same risk class will have the same required rate of return; the required rate of return will be the same for all owners or prospective buyers of the asset; and, the value of the loan at any interim point in its life span is the same regardless of who owns the note.

To illustrate, assume that after one year Friendly Bank wishes to sell the paper to another creditor rather than hold it to maturity. If the market rate of interest at the date of sale is again 12%, this percentage would be the required rate of return for both buyer and seller. At this rate of return, the selling price (market value) of the loan would be the present of amortized value of XYZ's remaining payments as originally established in the amortization schedule.

From this example, it is clear that the amortization schedule provides a realistic measure of future value when an asset's risk class and the required rate of return are known. It is also clear that the illustration begs the question of how this information can be obtained for the valuation estimate made in the typical business decision: decisions involving physical assets such as buildings, machinery, and equipment that are not traded in competitive, highly efficient, financial markets, and for which valuation estimates are not readily available. Fortunately, elementary economic theory provides guidelines for addressing this question.

The Economics of Competitive

Industries

A cornerstone of economic theory suggests that as competitive industries mature, the rate of return that member firms earn on industry-related investment projects stabilizes. Competition, along with the free movement of capital into and out of an industry, forces the rate of return to approach a level that is commensurate with the opportunity cost and risk exposure of invested capital. Thus, the rate of return that is earned on typical investments in the industry will be roughly the same for all member firms, and this rate serves as each firm's required rate of return.

Using this principle to establish a firm's required rate of return, the accountant is in a position to prepare the asset-amortization schedule necessary to estimate future value. The following example illustrates the procedure.

A Capital Budgeting Decision

Assume that XZY Corporation, a manufacturing firm, is considering a one-time, four-year agreement to produce parts for a prime government contractor. Included in the capital budgeting analysis surrounding

TABULAR DATA OMITTED

the decision is the cash flow associated with the purchase and resale of specialized machinery costing $100,000. This equipment is vital to the manufacture of the parts, but it is useless to XYZ after completion of the contract. Management anticipates that the equipment would be sold at that time. The machinery falls in the 3-year MACRS category, but has an estimated productive life of six years. When making capital budgeting decisions of this type, XYZ's management uses 18% as the required or hurdle rate of return.

Because the asset is assumed to have additional productive life and, therefore, resale value at the end of the four-year contract period, the cash inflow from its sale is an important consideration in deciding the economic feasibility of the project. This means that a justifiable market value for the equipment four years hence must be established today when the decision is under consideration. In the absence of a more substantive measure, the equipment's Amortized Residual Value serves as a realistic proxy for the future market or resale value at that date. As shown in Table 1 at the 18% required rate of return, the amortized value of the machinery at the end of the fourth year is $44,763.29.

The simple mechanics required to construct the amortization schedule shown in Table 1 are outlined below. It should be noted that the schedule is easily prepared manually or can be constructed using any of the popular electronic spreadsheet programs.

1. The number of periods (years in the illustration) is the economic or productive life of the asset.

2. The "Initial Balance" figure is the cost of the asset -- in the illustration this is $100,000.

3. The "Amortized Amount" is the payment required to amortize the Initial Balance over its estimated productive life. It is calculated using the present value annuity factor for the life of the asset and the firm's required rate of return. In the illustration this is six years and 18% respectively. The payment is calculated as follows.

AmortizedAmount=InitialBalance/Present

ValueAnnuityFactor

=$100,000/3.4976

=$28,591.01

Note that this calculation is a built-in function in most electronic spreadsheet programs. For example, in Lotus 1-2-3 the calculation is made automatically using the "@ Payment" function.

4. The "Yield" values represent the return on the initial investment each period. They are analogous to the interest portion of a loan payment in a typical loan amortization schedule. The Yield values are calculated by multiplying the Initial Balance for the period by the required rate of return and by the time period for which the Initial Balance was outstanding. Because the illustration reflects a one-year amortization schedule, the yield portion of the Amortized Amount is calculated as:

Yield = Initial Balance x .18 x 1

5. The "Toward Principal" values represent the periodic return of the initial investment. These values are analogous to the portion of each loan payment that goes toward the reduction of principal in a typical loan amortization schedule. The Toward Principal values are calculated as the Amortized Amount minus the Yield value for that period.

Amount Toward Principal = Amortized Amount - Yield

6. The "Residual Value" amounts represent the remaining portion of the asset's economic value, and are calculated as the Initial Balance for the period minus the Toward-Principal value.

Residual Value = Initial Balance -- Toward Principal

Specifying the Required Rate of

Return

The percentage rate used to produce the Amortized Residual Value schedule should be the same hurdle rate used to evaluate the firm's investment projects. Financial theory recommends the firm's cost of capital as appropriate for these purposes. While a detailed discussion of the cost of capital is beyond the scope of this article, it should be noted that this percentage is, as explained in a typical business finance text, a weighted average of the cost of the various types of financing used by the firm. Because these costs to raise capital are determined in the marketplace, a weighted average of these values represents the rate of return that the suppliers of capital expect the firm to earn. As such, it is the appropriate opportunity cost for the firm's valuation decisions.

Rational, Appealing Basis

When the occasional requirements of the firm's decision process include projecting the future value of an income producing asset, the Amortized Residual Value technique provides a rational, appealing basis for making this elusive estimate. Without it, the accountant is faced with the undesirable choice of using an improper book-value figure, if available, or a guesstimate that has no tenable foundation.