© 2000 John Petroff
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© 2000 John Petroff |
A- General formula of value of financial assets
As developed in Chapter 1 Section B, value stems from the benefits (or use) derived from an asset. These benefits can be looked upon and the value formula state in absolute or relative terms. The two concepts contain equivalent information, but are used differently. An absolute measure of value is used when one must compare it to a nominal amount: purchase price, amount to invest, target sum of money to raise. A relative measure of rate of return is more convenient to use when one wishes to compare one financial asset to a set of numerous alternative assets.
The value V of any asset is the sum of the present value PVk() of future benefits B received in each period t of n periods of asset life, discounted at a discount rate k
V0 = Sum(PVk(Bt))
This formula is used throughout next chapter for concepts of valuation of stocks, bonds, investment projects and price to offer for a company to be acquired. In Chapter 4 it will be shown how a value estimate is compared to a quoted market (or asked) price in order to decide about a proposed purchase. Before applying the value formula, it is necessary to be thoroughly familiar with what it contains.
This general formula requires two processes to be used: an estimation of future benefits and a conversion of these future benefits into today's equivalent. The second process is a mathematically straightforward calculation of present value (also known as discounted value). Section C of this chapter verifies that a great accuracy is easily achieved in the calculation of discounted value. Difficulties do not stem from mathematical steps, but from the selection of an appropriate discount rate. The major difficulty with discount rate is due to the fact that it is an opportunity rate determined by continuously changing financial markets, and not derived on the basis of a given asset alone. Section D of this chapter shows how an acceptable discount rate can be estimated. Forecasting future benefits can be just as difficult as deciding on a discount rate. Guidelines for quantifying those future benefits are outlined in next section.
| Difficulties in financial analysis of Russian firms can be especially significant because financial markets are emerging, and market rates are influenced more than in other countries by numerous factors which have little to do with finance alone. For instance, banking practice is often based on subjective rather objective criteria, government intervenes in currency valuation, and regulations are often not enforced. |
A rate of return is the most commonly used relative measure of value. But there are several others such as profitability index (used in capital budgeting and defined in Chapter 3 Section G-5), earnings multiple (for choosing stocks and described in Chapter 3 Section D-3) and price to sales ratio (used sometimes in merger decision and presented in Chapter 3 Section F-3). Generally, a rate of return states future benefits earned stated on an annual basis as a fraction of current price (or amount invested). Although we shall see that there are many different ways that this rate of return can be calculated, there is only one method to incorporate all useful information about future benefits in a manner consistent with the absolute measure of value previously defined. This is to calculate a total rate of return. The total rate of return is obtained as the discount rate R that equates present value PVx() of future benefits Bt earned over the asset life n, to today's price or (initial investment outlay)P0
R = x
for which P0 = Sum(PVx(Bt))
This formula is used, for instance, in calculations of yield to maturity for bonds, and internal rate of return in capital budgeting. Such a total rate of return is also used for pricing debt instruments. For example, this is true for interest earned on bank loans, and for yields on all money market instruments selling at a discount from their par value. This total rate of return is compared to market yields such as stock required rate of return or cost of obtaining funds. The chosen market yield is the same as the discount rate used in absolute value formulation.
For stocks and other forms of investment
where future benefits are difficult to estimate, this concept
of total rate of return is substituted by simpler measures that
are derived using single period, historical data or expected value
as follows:
- holding period return HPR0 is equal to the sum of
current year dividends D0 (or other distribution) plus
price change from prior period price P-1 to current
price P0 , divided by initial price P-1
HPR0 = (D0 + (P0 - P-1))/ P-1
- annualized rate of return is obtained by specifying the holding period to equal one year, or converting the holding period return above to an annual return equivalent
- arithmetic mean of holding period return over several years
- geometric mean of holding period return over several years (one may note that a geometric mean is mathematically more accurate than an arithmetic mean because finance assets grow at a compounded rate - i.e. multiplying by (1+i), as will be discussed in next section - and are not increased each period by the same amount which an arithmetic mean implies)
- expected rate of return is calculated as the mean of all possible return values for the coming year, with each return assigned a probability
For stocks, there are other even more straightforward return concepts, such as dividend yield (dividends divided by stock price) and earnings per share (total company earnings divided by the number of shares outstanding). These and all the previous concepts of stock rate of return only measure partial performance. They are indicative of a stock potential, but cannot offer a comprehensive magnitude of a stock value. This can only be done if all future benefits are entered into the formula. As noted before, estimating future benefits and required rate of return presents difficulties. These are discussed next.
See review questions Q-2A.1 through Q-2A2.5.
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