Present Values (Basic Concepts) 

"The Future is purchased by the present."

Samuel Johnson

Cash is useful and people are often willing to pay rent for its use. Cash is subject to erosion, in the form of inflation risk, so that when borrowed cash is paid back it may be exchangeable for fewer real goods. There is also a risk that borrowed cash may never be paid back. These and other factors determine the rent or interest that accompanies cash flows. When measuring the value present in cash flows spread over time, this rent or interest must be taken into account. One generally accepted measure of the value present in a series of cash flows is the present value of those cash flows. 

Definition 5.0 The Present Value (PV) of a series of Cash Flows or values CF1, CF2, CF3, CF4, … at times T1, T2, T3, T4,… in the future, respectively, with constant Required Interest RI, is given by 

PV(CF1, CF2, CF3, CF4, …) = CF1/(1+RI)^T1 + CF2/(1+RI)^T2 + CF3/(1+RI)^T3 + CF4/(1+RI)^T4 + … 

The times T1, T2, T3, T4, … are often positive integers, but may be fractional or negative. Cash flows or values can be added or subtracted at will, but they must all be measured from the same time perspective, i.e., with the appropriate adjustment for required interest. 

Discounted cash flows (present values) are a widely used and universally accepted measure, in theory. In practice, there is a reluctance to accept or use future cash flows. To recognize that the future may not correspond to our anticipations, we will use the phrase expected (future) cash flows. Expected cash flows are perfectly accurate and real, as expectations. Expectations are useful, in the present, for dealing with the future. They are also useful, in the future, for dealing with the future. The expected future provides the standard against which we measure developing experience and/or the quality of management judgments. We will see, in later chapters, that expectations will be strictly disciplined before and after the fact. Expectations are no more unreliable than the future is, perhaps less so. 

"Measurement is the process of determining a relevant attribute to quantify an item in monetary units with sufficient reliability. Several measurement alternatives are used. … Present (or discounted) value of future cash flows reports the present or discounted value of future cash inflows (outflows) into (at) which an asset (liability) is expected to be converted (settled) in due course of business less present values of cash outflows necessary to obtain those inflows" 

AFTF measurement is similar to that cited above except that the cash flows are expected cash flows fully discounted for contingencies. Also negative cash flows are separate from positive cash flows so that related costs (liability flows) are not immediately netted against asset flows. With AFTF it is quite easy to look only at related cash flows, for example, a line of business or a particular product. 

The Required Interest is the interest rate or yield that is required by the shareholder for the use of his capital. Usually it is also the minimum interest rate or yield a company requires before it will invest its capital, since the company represents and must compensate the shareholder. This compensation is the market cost of equity capital to the company, which will be divided out as a discount rate. The Required Interest is that required and determined by the capital markets. Hence, it is a market cost of capital and is not dictated by analysts or by company management. We will not introduce a cost of debt capital into the discount rate. Any cost of debt capital will be subtracted out as a periodic cash flow (less taxes). Any decision to employ debt capital will be explicitly evaluated from the shareholder’s perspective like any other decision.

  

The AFTF Perspective 

AFTF is designed for financial reporting by the company to the shareholder. There is a dual aspect in AFTF financial reporting: the company view and the shareholder view. If the company is to represent the shareholders’ interests, those views must be of the same thing. The shareholder is interested in maximizing dividends and minimizing debt cost and the company should be interested in the same thing. The company does not represent the bondholder in the same way as it represents the shareholder. To the shareholder, the decision to borrow is like any other decision; it must be evaluated using expected cash flows and the market cost of equity capital. Note that this discount rate is different from the weighted-average cost of capital, which incorporates the cost of debt capital. In the AFTF model the cost of debt capital is explicitly subtracted as a cash flow. This is a difference from the macro-economic viewpoint, which treats equity capital and debt capital from the same perspective. AFTF adopts the shareholder’s viewpoint. 

 

AFTF Bookkeeping 

Under AFTF, bookkeeping would be essentially the same as is currently practiced. There could be a couple of differences. It would not be necessary to book non-cash items. It would not be necessary to book negative entries. Hence AFTF entries would favor the matching concept as opposed to the realization concept. 

 

AFTF Statement of Values 

AFTF is accounting for future cash flows. This accounting involves measurement; the measure of future cash flows is the present value of those cash flows. All future cash flows are included. No non-cash amounts are included. All cash flows are expressed and recognized in nominal terms when they occur. All cash flows will be measured, in the present, in current value terms. AFTF is defined in terms of cash flows into the company, denoted by (+CF) and cash flows from the company, denoted by (-CF). Note that the quantity (-CF) is a disbursement and a positive quantity like any expense item.

 

Definition 5.1 AFTF assets = present value of all future cash flows into the company = PV(+CF). A cash flow into the company is an asset flow. 

Definition 5.2 AFTF equities = present value of all future cash flows from the company = PV(-CF). A cash flow from the company is an equity flow.

As might be expected, 

This result can be thought of as arising in one of two ways, 

First, we can rewrite Equation 5.1 as, 

Where NCF is the net cash flow (+CF) – (-CF) 

Hence, if we can find an Internal Rate of Return (IRR) such that PV(NCF) = 0, then that same IRR will equate AFTF assets and AFTF equities. In most real situations such an IRR exists as a meaningful number. Equation 5.1 will hold true for some IRR, except in unusual pathological cases. 

Second, for a selected interest rate, we can consider any imbalance as an immediate cash flow to or from the shareholder. This is not unlike defining the traditional shareholders’ equity to be the difference between traditional assets and traditional liabilities. The shareholder must make up the difference. Note that the IRR balancing also causes the shareholder to make up the difference through an increased or decreased yield, rather than as an immediate gain or loss. 

Using the IRR, we can algebraically manipulate Equation 5.1 and the equality will be preserved. We can divide cash flows into the company (+CF) into those cash flows from Shareholders (+CFS) and cash flows from Non-Shareholders (+CFNS). Similarly cash flows from the company can be divided into those cash flows to Shareholders (-CFS) and cash flows to Non-Shareholders (-CFNS). 

Hence,

Rearranging,

 Definition 5.3 AFTF Net Capital Cash Flow: PV(NCCF) = present value of all cash flows from the company to shareholders = PV(+CFS) - PV(-CFS). 

Net capital cash flows are primarily dividends, but also include other capital flows, such as, shares purchased or sold by the company. 

Definition 5.4 AFTF Net Operational Cash Flow: PV(NOCF) = present value of all cash flows from non-shareholders to the company = PV(+CFNS) - PV(-CFNS) 

Note that all capital flows are excluded in measuring operational cash flows. 

Hence,

For an interest rate other than the IRR equation 5.2b will not be true. Any imbalance can be thought of as an immediate gain or loss of capital which, when added to the LHS of equation 5.2b, reestablishes the equality.

 

There is another more interesting, perhaps less traditional, way of defining AFTF asset and equities. The curious can see Appendix 6.

It may seem that future cash flows ignore the accumulated NOCF (surplus) from the past. This surplus will be reinvested and will, in the course of time, get translated into future cash flows. 

If the future yield on this surplus exceeds the required interest, that surplus will add value. Its present value, discounted at the required interest, will greater than its current unrealized value. The company should not pay this surplus out as a current dividend and indeed might consider issuing more stock. 

If, however, the future yield obtainable is less than the required interest then the company will lose value unless it pays out this surplus as a dividend. This is not an admission of failure; it is a means of avoiding the failure of losing shareholder value. If the realizable market value is greater than the AFTF value, the asset should converted into a shareholder dividend. Hence AFTF provides a built in criterion and motivation for efficient dividend policy. 

The present value of future net capital cash flows (dividends for the most part) PV(NCCF) is the value of the company to the shareholder. The present values of net operational cash flows PV(NOCF) is the value of the company to the company. Note that these values are equal. 

Definition 5.5 AFTF Shareholder Equity = PV(NCCF) = PV(NOCF) 

There is no difference between the shareholder’s concept of value and the company’s concept of value. There can, however, be differences between values perceived or expected by shareholders and by company management. 

Definition 5.5 Market Valuation (MV) of a company is the actual current price of the company’s total outstanding stock. 

The market valuation of a company is the value perceived by the capital markets. It is the present value of all future NCCF expected by the market. It might be argued that the market, or the individual investor, has never heard of NCCF and instead sets prices in reaction to such things as: earnings announcements, interest or inflation rate changes, consumer confidence indications, global capital market fluctuations, and a whole host of other real or perceived factors. This is precisely the point of the Market Valuation concept. Each of these factors implicitly affects perceptions in complex and subtle ways, but the effect is to change real expected returns (NCCF). A goal of AFTF is to make market’s expectations more explicit and more rational, and thereby improve capital market efficiency. AFTF will do this by directly and explicitly providing information about the future. 

Definition 5.6 Company Valuation (CV) of a company is the total value of the company as reported by management 

The company valuation is the value perceived by the company management. It is the present value of all future NOCF expected by management. 

The market valuation will tend to approximate the PV(NCCF) since it is in the shareholder’s interest to estimate as accurately as possible the future dividends or equivalently the PV(NOCF). It is obviously sub-optimal for the shareholder to overestimate future dividends. It is also sub-optimal to underestimate future dividends since no investment is likely to be made. The capital markets are strongly motivated to make accurate market valuations. 

The company valuation will tend to approximate the PV(NOCF) since it is in the company’s interest to estimate as accurately as possible the future net cash flows or equivalently the PV(NCCF). If a company overestimates future net operational cash flows it may not be able to earn an acceptable return. It is also sub-optimal to underestimate future net operational cash flows since no investment is likely to be made. Decisions to issue new stock or repurchase old stock can be profitable or unprofitable depending on the relationship between the share price and the expected NOCF. The company is strongly motivated to make accurate company valuations. 

Hence,

Market valuations will tend to approximate company valuations and both will tend to approximate the value of the company. If they do not, then we have sub-optimization for both the company and the shareholder since they share a common concept of value. 

Efficient capital markets depend on the availability and timely communication of relevant information. If the information flow to and from the capital markets can be improved then capital market efficiency can be improved. In our context this means that management and the shareholder must have common expectations. Management must convey its cash flow expectations to the capital markets. The capital markets must convey its cost of capital expectations to management. These two ingredients (expected cash flow and expected cost of capital) determine the present value and define a major goal of AFTF, i.e., to improve capital market efficiency. That goal can be satisfied by a prospective accounting and reporting system based on present values. 

The value of a company is equally well represented by MV, PV(NCCF), PV(NOCF), or CV. We will, as a practical matter, phrase the value of a company in terms of the company valuation CV. This reflects the fact that the company will do the financial modeling and reporting, and will do so from its own perspective. This perspective should not be different from the market perspective and, as we shall later see, it will not be different. 

We will call future cash flows expected by the company simply expected cash flows. We restate the earlier definitions, 

Definition 5.7 AFTF assets = present value of all expected asset flows. 

Definition 5.8 AFTF equities = present value of all expected equity flows. 

The pure shareholder perspective assumes that all dividends are received. This can result from holding shares forever. Usually, however, shares are held for a period of time and then sold. The selling price of those shares will be the then-present-value of the future dividends, so that the total value of past dividends plus the selling price (terminal dividend) of the shares is equivalent to holding shares forever and receiving all dividends. In this way paid out and retained cash flows may be viewed as dividends. The sum of any normal dividends and the terminal dividend (selling price) is the net capital cash flow (NCCF) defined above. Shareholders in a company like Microsoft, paying no current dividend, receive all their dividends in the form of a present value, i.e., the selling price of the shares. 

The pure company perspective assumes that no dividends are paid. This can result from not paying any dividends. Usually, however, some cash flows are retained and some are paid out in the form of dividends. These payouts may be considered as company investments in the shareholders permanently earning the shareholders required interest. The present value of any investment, yielding the discount rate, is that investment. In this way, both retained and paid out cash flows may be viewed as giving rise to future cash flows with determinable present values. The sum of these cash flows paid out and retained is the net operational cash flow (NOCF) defined above. 

Note that if we assume that dividends save (or earn) required interest then the timing of dividends is immaterial. We will therefore conveniently assume that all dividends are paid at year-end and not during the year.

 

Change in Values: Value Added 

The AFTF balance sheet probably seemed somewhat familiar. The change in the AFTF balance sheet will probably seem somewhat unfamiliar. It is important to understand its nature. 

In traditional retrospective accounting, the income statement bridges the gap between successive balance sheets. The period change in the traditional surplus account (before dividends) equals period net income. 

The period change in the AFTF shareholder equity does not equal the period net income. It more closely resembles the change in "income". Instead of measuring income velocity it measures income acceleration. We define, 

Definition 5.7 AFTF Value Added (VA) is the change in the value of a company during the current period. 

We phrase value added in terms of the company valuation CV. Note that any dividends (or other capital flows) paid at the end of the current year are not subtracted from the current company valuation since they are not paid during the current year. Note that any dividends (or other capital flows) paid at the end of the prior year are subtracted from the prior company valuation since they are not paid during the current year. We will use the notation CV’ to denote the company valuation after dividends are paid. If we are determining the value added as of year-end (time T=0) then the we need to subtract the prior year company valuation CV’(-1) from the current company valuation CV(0). Recall that we can only combine values at different times with an appropriate interest adjustment. Hence the value added is given by 

Where RI is the capital market’s Required Interest on its investment. We will investigate this required interest in more detail in a later chapter, but for now it may be considered to be approximately the Internal Rate of Return IRR used in the prior section. Note that we do not separately subtract a cost of capital, as with other economic value-added systems; the cost of capital is inherent in the present value concept. Hence AFTF is technically different, in this regard, from most value-added schemes. An accounting system that incorporates the cost of capital as a discount rate will seamlessly integrate the company’s equity financing into its general operation. 

If, for a particular period, the company has Earned Interest, EI, on its prior value then 

and by substituting into Equation 5.3, 

If EI = RI then the value added is zero. We illustrate two special cases for such a steady state company, 

Case 1. Steady State Paying Full Current Dividend: If EI = RI then from Equation 5.4 we have, 

The full dividend CV’(-1)* RI must be subtracted in determining CV’(0).

Hence,

As long as a full dividend is paid the company value will be frozen.

 

For example, if the company value CV’(-1) is $100,000,000 and the required interest is 15%, then annual dividend would be $15,000,000 and the company value 30 years later would be CV’(29) = CV’(-1) = $100,000,000. This would be the terminal dividend from the sale of shares 30 years later. The present value (at time t = -1) of this terminal dividend and all prior dividends is PV(NCCF) and is exactly $100,000,000  

Case 2. Steady State with No Dividend: If no dividend is paid then CV = CV’. Again by equation 5.4, 

CV(1) = CV(0)*(1+RI) = CV(-1)*(1+RI)*(1+RI) = CV(-1)*(1+RI)^2

For example, if the company value CV(-1) is $100,000,000 and the required interest is 15%, then the company value 30 years later, CV(29) = CV(-1)*(1+RI)^30 = $100,000,000*(1.15)^30 = $6,621,177,195. The present value of this amount is exactly $100,000,000. The present value (at time t = -1) of all future net operational cash flows PV(NOCF) is exactly $100,000,000 

In both Case 1. and Case 2., no value has been added although the final company values are dramatically different. Paying or not paying dividends does not affect the value added (assuming the company can continue to earn the required rate), but it does point out the need for careful consideration of any dividend cash flows. The value-added concept makes companies paying dividends and not paying dividends directly comparable. Not only is the value added independent of dividends, but the current company valuation itself is independent of future dividends; recall that PV(NOCF) excludes capital flows. This does not mean, however, that future company valuations are independent of the dividend, as was illustrated by cases 1 and 2. Case 1 can be reconciled to case 2 by considering the company and shareholder as a unit. This is the pure company perspective and this enlarged unit will be valued just as in case 2.

If the EI > RI then value will be added. If RI < EI then value will also be added. In other words we can increase value added in two ways: increase earnings or decrease the required interest. With AFTF we may be able to do both more effectively. 

If value is being added, it provides a clear signal to add more value by expanding the investment or exploiting similar investments. This may be difficult to do unless the long-term value is measured by management. In practice, it may also be difficult to continue to add value because of diminishing returns, competition, substitutions, or market saturation. If the cost of capital (required interest) is high then it can be lowered by communicating management’s views clearly to the capital markets. This may be difficult to do unless long-term value is reported to the shareholder. AFTF measures and reports long-term value. 

If the EI < RI then value will be lost. This provides a clear signal to lose less value by contracting the investment. This may be difficult to do unless the long-term value is appreciated. In practice, it may also be difficult because of inertia, tradition, exit costs. A losing line of business should be sold, but only if the sales price exceeds the value present. This may happen if a buyer can do better with the line of business, or thinks he can. A losing line should not be abandoned regardless of the cost. This is jumping from the frying pan into the fire. 

In an efficient-omniscient capital market, any factors that would create superior yields (EI>RI) would be known and the market valuation of the enterprise would increase so that the yield EI, based on that valuation, would fall and converge on RI. The efficient-omniscient market would also adjust for inferior yields so that EI<RI would be fleeting. Markets do not generally have perfect knowledge and for many reasons may not act rationally or instantaneously to knowledge. The shareholder or management who makes the market more efficient generally profits in the process. Those who create or condone inefficiency pay the penalty.  

Case 3. Earnings Exceed Interest Required: Assume that EI = RI + G the by Equation 5.5 

VA = CV’(-1)*(EI - RI) = CV’(-1)* (RI+G-RI) = CV’(-1)*G Equation 5.6

 Since the starting value was CV’(-1) the growth rate in the company valuation is 

CV’(-1)*G / CV’(-1) = G  

Definition 5.8 The AFTF Growth Rate is the excess of the Interest Earned over the Required Interest = EI - RI 

Value Added is the absolute residual growth of the company, i.e., the growth rate times the starting value. Value added is a relativistic concept in that growth depends on expectations as expressed through the required interest. 

 

Gordon Growth Model 

The Gordon growth model gives the present value of all future dividends that grow at a constant annual rate G starting with an absolute dividend D(0) = (1+G)*D(-1) and based on a discount rate equal to the Required Interest RI. This present value is PV(NCCF) and is the value of the company. Hence, by the model, 

For a given required interest RI and a given AFTF growth rate G we can determine the value of the company based on the starting dividend D(0). More to the point is that G = IE – RI giving two ways to affect G and the company value. 

If D(0) = $15,000,000 then by Equation 5.7 the company value will follow the patterns shown below for various growth rates and interest required. It seems that lowering the cost of capital is somewhat more productive in adding value then striving for growth. For example, with RI at 15% it takes 10% growth (a total IE of 25%) to produce a $300,000,000 company valuation. In contrast, if RI is 5% then no growth whatsoever will produce the same $300,000,000 company valuation. 

 

The Gordon Growth model will not be used to determine company values since it depends on the existence of a dividend and assumes constant growth. It does provide a simple illustration of the behavior of the company valuation and value added. In particular it shows the sensitivity of the company valuation to both the cost of capital and to the assumed growth rate

  

Conclusions 

The normal present value calculations automatically take into account the cost of capital in defining AFTF value added. The AFTF value perspective is that of the shareholder. The AFTF valuation perspective is that of the decision. Bookkeeping is essentially unchanged for cash flows. Assets and liabilities are defined as present values of expected cash flows into and from the company. The market value and the company valuation are both close approximations to the underlying value of the company, which is defined as the present value of net operating cash flows. Value added is defined as the time-adjusted difference between consecutive company valuations before current year dividends are paid.

   

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