Тема 4. Вступ до розуміння часової вартості грошей.

The evaluation of any investment opportunity involves three discrete steps:

1. Estimate the relevant cash flows.
2. Calculate a figure of merit for the investment.
3. Compare the figure of merit to an acceptance criterion.

A figure of merit is a number summarizing an investment’s economic worth.

A common figure of merit is the rate of return. Like the other figures of merit to be discussed, the rate of return translates the complicated cash inflows and outflows associated with an investment into a single number summarizing its economic worth. An acceptance criterion, on the other hand, is a standard of comparison that helps the analyst determine whether an investment’s figure of merit is attractive enough to warrant acceptance. It’s like a fisher who can keep only fish longer than 10 inches. To the fisher, the length of the-fish is the relevant figure of merit, and 10 inches is the acceptance criterion.

Difficulties range from commonplace concerns with depreciation, financing costs, and working capital investments to more arcane questions of shared resources, excess capacity, and contingent opportunities. And pervading the whole topic is the fact that many important costs and benefits cannot be measured in monetary terms and so must be evaluated qualitatively.

To begin our discussion of figures of merit, let’s consider a simple numerical example. Pacific Rim Resources, Inc., is contemplating construction of a container-loading pier in Seattle. The company’s best estimate of the cash flows associated with constructing and operating the pier for a 10-year period appears in Table 5.1 

Table 5.1.

The company’s best estimate of the cash flows associated with constructing and operating the

pier for a 10-year period

Although determining figures of merit and acceptance criteria appears to be difficult on first exposure, the first step, estimating the relevant cash flows, is the most challenging in practice. Unlike the basically mechanical problems encountered in calculating figures of merit and acceptance criteria, estimating relevant cash flows is more of an art form, often requiring a thorough understanding of a company’s markets, competitive position, and long-run intentions.

Figure 5.1 presents the same information in the form of a cash flow diagram, which is simply a graphical display of the pier’s costs and benefits distributed along a time line.

Despite its simplicity, I find that many common mistakes can be avoided by preparing such a diagram for even the most elementary investment opportunities. We see that the pier will cost $40 million to construct and is expected to gen­erate cash inflows of $7.5 million annually for 10 years. In addition, the company expects to salvage the pier for $9.5 million at the end of its useful life, bringing the lO th-year cash flow to $17 million.

Pacific’s management wants to know whether the anticipated benefits from the pier justify the $40 million cost. As we will see shortly, a proper answer to this question must reflect the time value of money. But before addressing this topic, let’s consider two commonly used, back- of-the-envelope-type figures of merit that, despite their popularity, suf­fer from some glaring weaknesses. One, known as the payback period, is defined as the time the company must wait before recouping its orig­inal investment. For an investment with a single cash outflow followed by uniform annual inflows.

The pier’s payback period is 5½ years, meaning the company will have to wait this long to recoup its original investment (5½ = 40/7.5).

The second widely used, but nonetheless deficient, figure of merit is the accounting rate of return, defined as

Ac. rate of return is 21.1 %  (7,5 x 9 + 17)

The problem with the accounting rate of return is its insensitivity to the timing of cash flows. For example, a postponement of all of the cash inflows from Pacific’s container-loading pier to year 10 obviously reduces the value of the investment but does not affect the accounting rate of return. In addition to ignoring the timing of cash flows, the payback period is insensitive to all cash flows occurring beyond the payback date. Thus, an increase in the salvage value of the pier from $9.5 million to $90.5 million clearly makes the investment more attractive. Yet it has no effect on the payback period, nor does any other change in cash flows in years 6 through 10.

In fairness to the payback period, I should add that although it is clearly an inadequate figure of investment merit, it has proven to be useful as a rough measure of investment risk. In most settings, the longer it takes to recoup an original investment, the greater the risk. This is especially true in high-technology environments where management can forecast only a few years into the future.

An accurate figure of merit must reflect the fact that a dollar today is worth more than a dollar in the future. This is the notion of the time value of money, and it exists for at least three reasons. One is that inflation reduces the purchasing power of future dollars relative to current ones; another is that in most instances, the uncertainty surrounding the receipt of a dollar increases as the date of receipt recedes into the future. Thus, the promise of $1 in 30 days is usually worth more than the promise of $1 in 30 months, simply because it is customarily more certain.

The third reason money has a time value involves the important notion of opportunity costs. By definition, the opportunity cost of any investment is the return one could earn on the next best alternative. A dollar today is worth more than a dollar in one year because the dollar today can be productively invested and will grow into more than a dollar in one year. Waiting to receive the dollar until next year carries an opportunity cost equal to the return on the forgone investment. Because there are always productive opportunities for investment dollars, all investments involve opportunity costs.