The concept of net present value. Net Present Value (NPV). Calculation of net present value. Advantages and disadvantages of the net present value method

Many investors have lost sleep and appetite trying to determine the most effective way minimizing investment risks and maximizing profits. However, it is only necessary to increase economic literacy. Net present value will allow you to look at financial issues much more objectively. But what is it?

Cash

Before talking about such an issue as net present value, it is first necessary to understand the related concepts. Positive income represents funds that flow into the business (interest earned, sales, proceeds from stocks, bonds, futures, etc.). Negative flow (i.e. expenses) represents funds that flow from the company's budget (salaries, purchases, taxes). Net present value (absolute net financial flow) is essentially the difference between negative and positive flows. It is this cost that answers the most important and most exciting question of any business: “How much money is left in the cash register?” To ensure dynamic business development, correct decisions regarding the direction of long-term investments are necessary.

Investment Questions

Net present value is directly related not only to mathematical calculations, but also to the attitude towards the investment. Moreover, understanding this issue is not as simple as it seems, and relies primarily on the psychological factor. Before investing money in any project, you need to ask yourself a number of questions:

Will the new project be profitable and when?

Maybe it's worth investing in another project?

The net present value of an investment must be considered in the context of other issues, such as the negative and positive flows of the project and their impact on the initial investment.

Movement of Assets

Financial flow is a continuous process. The assets of an enterprise are considered as uses of funds, and capital and liabilities are considered as sources. The final product in this case is a set of fixed assets, labor, and raw material costs, which are ultimately paid for in cash. Net present value considers exactly

What is NPV?

Many people who are interested in economics, finance, investing and business have come across this abbreviation. What does it mean? NPV stands for NET PRESENT VALUE, and is translated as “net present value”. This is the cost of the project calculated by summing up the income that the enterprise will generate during operation and the costs. The amount of income is then subtracted from the amount of expenses. If, as a result of all calculations, the value is positive, then the project is considered profitable. It can be concluded that NPV is an indicator of whether a project will generate income or not. All future income and costs are discounted at appropriate interest rates.

Features of calculating net present value

Net present value is the determination of whether the cost of a project is greater than the costs spent on it. This value is estimated by calculating the price of cash flows generated by the project. It is necessary to take into account the requirements of investors and the fact that these flows may be subject to trading on securities exchanges.

Discounting

The calculation of net present value is carried out taking into account discounting of cash flows at rates equal to those for investment. That is, the expected rate of return from securities is equal to the same risk that the project under consideration bears. In developed stock markets, assets that are exactly the same in terms of risk are valued in such a way that they have the same rate of return. The price at which investors participating in the financing of a given project expect to receive a rate of return on their investments is obtained precisely by discounting the flows of funds at a rate equated to opportunity costs.

Net present value of the project and its properties

There are several important properties this method of project evaluation. Net present value allows investments to be evaluated using the general value maximization criteria available to investors and shareholders. Financial and foreign exchange operations both in attracting funds and capital and in placing them are subject to this criterion. This method focuses on cash profits, which are reflected in receipts in the bank account, while neglecting accounting income, which is reflected in the financial statements. It is also important to remember that net present value uses the opportunity costs of financial assets for investment. Another important property is compliance with the principles of additivity. This means that it is possible to consider all projects both in total and individually, and the sum of all components will be equal to the cost of the overall project.

Present value indicator

Net present value depends on the present value (PV) indicator. This term refers to the cost of receipts of funds in the future, which relates to the present by discounting. The calculation of net present value usually includes the calculation of the present value indicator. You can find this value using a simple formula that describes the following financial transaction: placement of funds, payment, repayment and lump sum repayment:

where r is the interest rate, which is the fee for the money borrowed;

PV is the amount of funds that are intended for placement on the terms of payment, urgency, repayment;

FV is the amount required to repay the loan, which includes the original amount owed as well as interest.

Net Present Value Calculation

From the current value indicator, you can move on to calculating NPV. As discussed above, net present value is the difference between discounted future cash flows and the amount of total investment (C).

NPV= FV*1/(1+r)-C

where FV is the sum of all future income from the project;

r is the profitability indicator;

C is the total amount of all investments.

Present value

Discounted value expresses the value of future payment streams in terms of the value of current payment streams. The definition of present value is widely used in economics and finance as a tool for comparing streams of payments received at different times. The discounted value model allows you to determine how much financial investment an investor intends to make to receive a certain cash flow over a given period. The discounted value of a future stream of payments is a function of:

the period through which the future flow of payments is expected,
risk associated with a given future flow of payments,
other factors.

The present value indicator is used as the basis for calculating the amortization of financial borrowings.

Explanation

The value of money changes over time. 100 rubles received after five years have a different (in most cases, less) value than 100 rubles that are available. Available funds can be invested in a bank deposit or any other investment instrument, which will provide interest income. That is, 100 rubles. today, they give 100 rubles. plus interest income after five years. In addition, for the available 100 rubles. You can purchase a product that in five years will have a higher price due to inflation. Therefore 100 rub. in five years they will not be allowed to purchase the same product. In this example, the discounted value indicator allows you to calculate how much 100 rubles are worth today. which will be received in five years.

Calculation

where is the flow of payments received in years, is the discount rate determined based on the above factors, is the discounted value of the future flow of payments.

In order to receive an amount equal in years, given that inflation, risk, etc. determine the discount rate equal to , the investor agrees to invest an amount equal to today.

Discounted value of a series of payment streams and annuity payments

The discounted value of a series of payment streams is equal to the sum of the discounted values of each of the component payment streams. Thus, the discounted value of a series of payment streams received each year over a period of years is calculated using the following formula:

Discounted value of perpetuities (perpetual annuities)

Based on the formula for calculating the discounted value of annuity payments, you can obtain a formula for the discounted value of perpetuities (perpetual annuities). As the value approaches infinity, the , part of the formula approaches zero. Under such conditions, the formula for perpetuity will have the following form:

The discounted value of perpetual securities with increasing payments, such as stocks with increasing dividend yields, is calculated using the Gordon model

References

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See what “Present Value” is in other dictionaries:

Present value

Present value- (present value) amount (costs, income, etc.) at a base point in time, equal to amounts assessed at other points in time (produced or expected costs, income, etc.). Reduction in time is carried out using... ... Economic-mathematical dictionary

present value- An amount (costs, income, etc.) at a base point in time that is equivalent to amounts estimated at other points in time (produced or expected costs, income, etc.). Reduction in time is carried out using discounting.… … Technical Translator's Guide

present value- The present value of future payments or cash flows, discounted at some compound interest rate ( compound interest). For example, the present value of $1,000 to be received in 10 years is... ... Financial and investment explanatory dictionary

Present value- (PRESENT VALUE) the value of future quantitative quantities reduced to the current moment... Modern money and banking: glossary

Present value- the amount calculated by discounting the future cash flows of the analyzed project at a discount rate equal to the required return. Its value differs from net present value in that the calculations do not include... Glossary of terms on expertise and real estate management

Present value of accounts receivable- (present value of accounts payable) The value of accounts receivable without taking into account the created reserve for doubtful debts, discounted by maturity. Used in preparing separation balance sheets (during separation of companies) ... Economic-mathematical dictionary

Not all investments involve the same risk. An office building project is riskier than investing in government securities, but probably carries less risk than investing in a start-up biotech. Let's say, according to your estimates, the project is associated with the same risk as investing in the stock market (investing in shares), and the return on the latter is projected at 12%. Then 12% is the appropriate value for the opportunity cost of raising capital. This is precisely the return that you give up by not investing in securities comparable in risk to your project. Now you can recalculate the NPV:

NPV = PV − $350,000 = $357,143 − $350,000 = $7,143

If other investors agree with your income forecast of $400,000. and with your assessment of the inherent risk, your property under construction should be worth $357,143. If you tried to sell it for more, you would not find a buyer, because then the expected return on investment in real estate would be lower than the 12% that can be obtained in the stock market. The office building still provides a net increase in value, but it is much less than our previous calculations indicate.

The value of an office building depends on the timing of cash flows and their inherent uncertainty. Income of 400 thousand dollars. would cost exactly 400 thousand dollars if it could be received immediately. If constructing an office building is as safe as investing in government securities, a delay of 1 year reduces the cost to $373,832. If it carries the same risk as investing in the stock market, uncertainty reduces the value by another $16,689, to $357,143.

Unfortunately, estimating the value of assets taking into account time and uncertainty is often much more difficult than our example suggests.

So, we have come to the conclusion that the construction of an office building is a good thing because its value exceeds the costs associated with it, that is, it has a positive net present value. To calculate the cost, we estimated how much you would need to pay to get the same return on investing directly in the securities. The present value of the project is equal to the future revenue from it, discounted by the yield of these securities.

Another way to put the same point is that our real estate project makes sense because its return exceeds its cost of capital. Return on investment is simply the ratio of profit to initial cost:

Costs of capital (costs of raising capital), recall, are equal to the profitability lost due to refusal to invest in securities. If building the office building in our example involves the same risk as investing in the stock market, then there is a lost return of 12%. Since the 14% return on an office building exceeds the 12% opportunity cost, you should proceed with the project.

Here are two equivalent rules to follow when making investment decisions.

1. Net present value rule: make investments that have a positive net present value.

2. Rule of return: make investments whose profitability exceeds their opportunity costs.

The opportunity cost of raising capital is such an important concept that it deserves additional attention and another example. Let's say the following opportunity opens up before you: invest $100 thousand today, so that at the end of the year, depending on the general state of the economy, you will receive a return in the amount of:

You reject optimistic (rise) and pessimistic (decline) forecasts. This leaves you with an expected return of Q = $110,000. , that is, a 10% return on your investment (100 thousand dollars). But what is the correct discount rate?

You start looking for common stocks that have the same risk as your investment opportunity. Shares X turned out to be the most suitable. Their price for next year, in a normal state of the economy, is projected at $110. In case of an economic upswing, the price will be higher, in case of a downturn, lower, but the proportion of changes is the same as for your investment ($140 in an upturn, $80 in a downturn). In general, you conclude that stock X and your investment involve equal risk.

The current price of X stock is $95.65. per share, their expected return is 15%:

This is the same expected return that you give up by investing in your project instead of investing in the stock market. In other words, this is the opportunity cost of your project.

In order to estimate the cost of a project, you need to discount the expected cash flow at these opportunity costs:

This is exactly the amount it would cost investors in the stock market to purchase the expected cash flow of $110,000. (They could get it by buying 1,000 shares of X.) Therefore, that's exactly what investors will be willing to pay you for your project.

We get the net present value of the project by subtracting the initial investment:

NPV = $95,650 – $100,000 = −$4350

The project costs $4,350. less than what was spent on it. There's no point in taking it on.

Note that you would reach the same conclusion by comparing the project's expected return to its inherent cost of capital:

The project's expected return of 10% is less than the 15% that investors expect to earn by investing in the stock market, so, whatever one may say, the project is worthless.

Of course, in real life, the true state of the economy cannot be reduced to just “recession,” “normal,” or “boom.” In addition, we adopted another simplified premise, establishing an absolute correspondence between the return on 1000 shares of X and the proceeds from the investment project. However, the main idea of this example is quite consistent with real life. Remember: the opportunity cost of raising capital (cost of capital) for an investment project is equal to the expected return that investors require from common stock or other securities that are subject to the same risk as the project. By calculating the present value of a project, that is, by discounting its cash flow at opportunity costs, you get the amount that investors (including the shareholders of your own company) are willing to pay for the project. Whenever you find and launch a project with a positive net present value (that is, a project whose present value exceeds the investment required), you make your company's shareholders richer.

For example, this circumstance can be misleading. Imagine that a banker comes to you and says: “Your company is a well-established, reliable enterprise, and you have little debt. My bank is not averse to lending you the $100 thousand needed for the project at 8% per annum.” Does this mean that the cost of capital for the project is 8%? If so, your project is afloat: its present value at a rate of 8% is equal to $110,000/1.08 = $101,852, that is, the net present value is $101,852. — $100,000 = +1852 dollars

But this is not true. First, the interest rate on the loan has nothing to do with the risk of the project: it only reflects the health of your current business. Second, whether you take out a loan or not, you will still have to choose between a project with an expected return of only 10% and a stock that carries equivalent risk but has an expected return of 15%. A financial manager who borrows money at 8% and invests it at 10% is not just stupid, but desperately stupid, if the company or its shareholders have the opportunity to borrow money at 8% and invest with the same risk, but with profitability 15%. So it is the expected stock return of 15% that represents the opportunity cost of raising capital for the project.

Rationale for the net present value rule

So far, our knowledge of net present value has remained very superficial. The phrase “increasing value” as a company goal sounds quite reasonable. But the net present value rule is more than just a requirement of basic common sense. We need to understand what this rule is all about and why managers look to the bond and equity markets to determine the opportunity cost of raising capital.

In our previous example, only one person (you) invested 100% of the money in a new office building and received 100% of the return on it. But in a corporation, investments are made on behalf of and at the expense of thousands of shareholders with different appetites for risk and different preferences regarding the choice between today's and future income (and therefore consumption). What if a project that clearly has a positive net present value for Ms. Smith turns out to be a deep loss for Mr. Jones? Could it happen that the goal of maximizing the value of the company will be unacceptable to some of them?

The answer to both questions is the same: no. Both Smith and Jones will always be able to come to an agreement if they have unfettered access to the capital market. We will show this with another simple example.

Suppose you are able to foresee your future earnings in advance. Without the ability to save from current income or take out a loan against future income, you will be forced to postpone consumption until you receive it. And this is a very inconvenient thing, to say the least. If the bulk of the income that is due to you in your life falls in some more or less distant future, then the result may be that today you are in danger of hunger, and tomorrow (or sometime later) - excessive consumption. This is where the capital market comes in handy. Simply put, a capital market is a market in which people exchange current and future money among themselves. Thanks to him, you can eat normally now and in the future.

We will now show how a well-functioning capital market can help investors with different income schedules and consumption patterns come to a consensus about whether a particular investment project is worth undertaking. Let's imagine two investors with different tastes and aspirations. One of them is Ant, who prefers to save money for the future; the other is Dragonfly, who squanders all her income with extraordinary ease, not caring at all about the future. Now let's assume that they both have the same opportunity: to purchase a stake in a $350,000 office building project that will yield a guaranteed return of $400,000 at the end of the year. (i.e. the yield is about 14%). The interest rate is 7%. At this rate, both Ant and Dragonfly can borrow or lend money in the capital market.

No doubt Ant would be happy to invest in an office building. Every hundred dollars invested in this project today will allow him to spend $114 at the end of the year, while the same hundred invested in the capital market will bring him only $107.

What would Dragonfly, who wants to spend money right now, and not in a year, do? Perhaps she will neglect the investment opportunity and immediately squander all her cash? It’s unlikely, since the capital market allows you to both lend and borrow money. Every hundred dollars that Dragonfly invests in an office building will bring her $114 at the end of the year. Any bank, aware that Dragonfly will have a guaranteed income at the end of the year, will not hesitate to lend her $114/1.07 = $106.54 today. Therefore, if Dragonfly invests in an office building and then takes out a loan against future income, today she will be able to spend not 100, but 106.54 dollars.

The figure clearly illustrates this example (our heroes are designated here as M and C, respectively). The horizontal axis represents the amount of money that can be spent today; the vertical axis shows next year's expenses. Let’s say that initially both the Ant and the Dragonfly have the same amounts - 100 dollars each. If each of them fully invests their $100. on the capital market, then at the end of the year both will receive $100 for expenses. x 1.07 = 107 dollars. The straight line connecting these two points (in the figure this is the line closest to the origin) displays combinations of current and future consumption for the following possible options: when nothing is invested, when this or that part of the cash is invested, and when all available funds are invested on the capital market at 7% per annum. (The interest rate determines the slope of this line.) Any intermediate point on the line (between the points of intersection with the coordinate axes) is reached when one or another part of the cash is $100. today is spent and the rest is invested in the capital market. Let's say someone might prefer to spend $50. today and 53.50 dollars. next year. But our Ant and Dragonfly unanimously rejected such intermediate (“residual”) consumption patterns.

The straight line with the arrow (highlighted) in the figure represents the proceeds from the investment of $100. in an office building construction project. The return on this investment is 14%, so today's $100. will turn into 114 dollars in a year.

The Dragonfly (C) wants to consume right now, while the Ant (M) wants to wait. But each of them is happy to invest. M prefers to invest not at 7, but at 14%, which increases the point of intersection of the straight line with the arrow (which is highlighted in blue) with the vertical axis. C also invests (at the same 14%), and then borrows money at 7%, thereby turning $100 intended for current consumption into $106.54. Thanks to his investment, C will have $114 in one year to pay off his debt. The net present value of this investment is $106.54. — 100 dollars. =+6.54 dollars

The inclined straight line on the right in the figure (the one that is located farthest from the origin) reflects the increase in the planned expenses of Ant and Dragonfly if they decide to invest their $100. to an office building. A tight-fisted Ant who does not intend to spend anything today can invest $100. in the construction of an office building and at the end of the year receive 114 dollars. for expenses. Lazy Dragonfly also invests $100. to an office building, but at the same time takes 114 dollars/1.07 = 106.54 dollars. for future income. It is clear that there is nothing stopping these spending plans. Indeed, the right straight line represents all possible combinations of current and future spending available to an investor who invests $100. in the construction of an office building and at the same time takes out a loan against some part of the future income.

From the figure it is easy to see that the present value of Dragonfly and Ant's participation in the office building project is $106.54, and the net present value is $6.54. (this is the difference between $106.54 present value and $100 initial investment). Despite the differences in tastes between Dragonfly and Ant, both of them benefit from investing in an office building and then using the power of the capital market to achieve the desired ratio between today's consumption and consumption at the end of the year. In fact, in making their investment decisions, both of them seem willing to follow two equivalent rules, which we formulated rather superficially at the end of the section. Now we can rephrase them as follows.

1. Net Present Value Rule: Invest in any project with a positive net present value. The latter is the difference between the discounted, or present, value of future cash flow and the amount of the initial investment.

2. Rule of profitability: invest in any project whose profitability exceeds the profitability of equivalent investments in the capital market.

What would happen if the interest rate were not 7%, but 14.3%? In this case, the net present value of the office building would be zero:

In addition, the profitability of the project is $400,000/$350,000. - 1 = 0.143, or 14.3%, would be exactly equal to the capital market interest rate. In this case, both of our rules show that the project is balancing on the edge “between light and darkness,” and this means that investors should be indifferent whether the company takes it on or not.

As you can see, if the interest rate were 14.3%, neither the Dragonfly nor the Ant would gain anything from investing in an office building. Ant would have the same amount of money to spend at the end of the year regardless of how he initially used his money - whether he invested it in an office building or invested it in the capital market. In the same way, Dragonfly would not receive any benefit by investing in an office building with a yield of 14.3% and at the same time taking out a loan at the same 14.3%. She might as well spend all her original cash at once.

In our example, Dragonfly and Ant invested the same funds in an office building construction project and willingly took part in it. This unanimity is explained by their equal opportunities to both borrow and lend money. Whenever a firm discounts cash flow at financial market rates, it is making the implicit assumption that its shareholders have free and equal access to competitive capital markets.

It is easy to see that the absence of a well-functioning capital market undermines the logic of our net present value rule. For example, let’s assume that Dragonfly does not have the opportunity to take out a loan against future income or that there is such an opportunity in principle, but the price of the loan is too high to take advantage of it. In such a situation, Dragonfly would likely prefer to use up his cash immediately rather than invest it in an office building and wait until the end of the year to start spending the money. If Dragonfly and Ant were shareholders of the same company, it would be difficult for the manager to reconcile their conflicting interests and goals.

No one would unequivocally assert that capital markets are characterized by perfect competition. Taxes, transaction costs, and other factors limiting perfect competition should be taken into account when making financial decisions. But by and large, capital markets operate quite efficiently. This is at least one good reason why net present value should be relied upon when setting corporate goals. Another reason is that the net present value rule simply agrees with common sense; Later we will see that it leads to obviously ridiculous results much less often than its main “competitors” - other common criteria for making investment decisions. For now, having only briefly touched on the problems of market imperfections, we, like a shipwrecked economist, will simply assume that we have a life jacket, and, mentally dressing ourselves up in it, we will calmly swim to the shore.

So far, our rationale for the net present value rule has been limited by two assumptions: that cash flows extend over only two time periods and that cash flows are inherently certain. However, the rule is also true for uncertain cash flows that continue into the distant future. The following arguments can be given to support this.

1. The financial manager must act in the interests of the owners of the company, that is, its shareholders. Every shareholder strives for three goals:

a) be as rich as possible, that is, maximize your real wealth;

b) convert this wealth into any temporary consumption model desired by him (or her);

c) have freedom in choosing the risk characteristics of this consumption model.

2. But shareholders do not need the help of a financial manager to achieve the best temporary consumption pattern. They can handle this themselves if they have easy access to competitive capital markets. In addition, they are free to choose the risk characteristics of their consumption patterns by investing in more or less risky securities.

3. How then can a financial manager help the company's shareholders? Only one way: by increasing the market value of each shareholder's share in the company. To do this, he must take advantage of any investment opportunity that has a positive net present value.

Shareholders, although they have different preferences, show remarkable unanimity regarding the amounts they are willing to invest in real assets. On this basis, they can unite into one company and entrust the management of affairs to professional managers without risk to themselves. Managers do not need to know anything about the tastes and preferences of shareholders and should not indoctrinate them with their own tastes and preferences. Their goal is to maximize net present value. Once they have succeeded, managers can sit back and rest with the confidence that they have done their best work in the best interests of their shareholders.

This implies a fundamental condition for the successful functioning of a modern capitalist economy. The separation of ownership from management is of great importance for most corporations, so delegation of management authority is essential. It's nice to know that all managers can be given one simple instructions: Maximize net present value.

Sometimes you hear managers argue that their corporations have different goals. Thus, a manager might say that his job is to maximize profits. Well, that sounds pretty meaningful. After all, don't shareholders prefer a profitable company to an unprofitable one? However, it is unreasonable to proclaim pure profit maximization as a corporate goal. There are several reasons for this.

1. The task of “maximizing profit” immediately gives rise to the question: “What year’s profit?” Shareholders may not want the manager to boost next year's profits at the expense of later years' profits.

2. The company can increase future profits by reducing dividend payments and investing this money in investment projects. But given the low returns on such investments, this goes against the interests of shareholders.

3. Different accountants use different methods profit calculations. You may find that a decision that improves profits from one accountant's perspective makes them worse from another's perspective.

Principal corollary

We show that managers best serve shareholders' interests by investing in projects with positive net present value. But this brings us back to the principal-agent problem. How can shareholders (principals) make sure that managers (agents) are not solely pursuing their own interests? Shareholders cannot constantly monitor managers to see if they are shirking their responsibilities or maximizing the value of their own wealth. However, there are several organizational mechanisms that more or less ensure that the manager's heart is in the shareholders' pocket.

Members of a company's board of directors are elected by shareholders and are supposed to represent their interests. True, sometimes the board of directors is portrayed as a weak-willed extra, always siding with management. However, when a company's operations are in trouble and managers don't come up with a viable turnaround plan, the board of directors does its job. In recent years, companies such as Eastman Kodak, General Motors, Xerox, Lucent, Ford Motors, Sunbeam, and Lands End have seen senior executives resign from their positions as profitability declined and the need to revamp their business strategy became clear. .

Considering that the performance of the corporation leaves much to be desired, and the members of the board of directors are not energetic enough in calling managers to order, shareholders may try to change the board of directors at the next election. If this succeeds, the new board of directors will recruit a new management team. However, such attempts to re-elect the board of directors are quite expensive and thankless (rare of them are successful). Therefore, dissident shareholders usually do not engage in an unequal battle, but instead simply sell their shares.

However, the sale of shares itself carries a very powerful message. If enough holders dump a stock, the price of the stock goes down. This hurts the reputation of managers and their earnings. CEOs receive part of their compensation in the form of earnings-related bonuses or stock options, which pay well when stock prices rise but are worthless when stock prices fall below a certain threshold. In theory, this should encourage managers to increase profits and increase share prices.

Do managers protect the interests of shareholders?

If a company's leaders fail to maximize value, they are always exposed to the threat of a hostile takeover. The lower the price of a company's shares falls (as a result of inept management or due to incorrect policies), the easier it is for another company or group of investors to buy a controlling stake in its shares. In such a situation, the old management team will likely be left behind, and new managers will take their place, ready to make the changes needed to realize the true value of the company.

The mechanisms described go a long way toward ensuring that there are few executives at the top of large American corporations who are lazy or shareholder-neglected. Moreover, these mechanisms contain strong incentives for managers to work harder.

We conceptualized managers as agents working for the shareholders of their firms. But perhaps it is worth asking: “Is it desirable for managers to act in the selfish interests of shareholders?” Doesn't the focus on enriching shareholders mean that managers should behave like greedy traders, cruelly trampling on the weak and helpless? Don't they have a broader responsibility—to their employees, to their customers, to their suppliers, and to the community where the firm is located?

The bulk of this book is devoted to financial policies that increase firm value. None of the varieties of such a policy requires the infringement of the weak and helpless. In most cases, doing the right thing (maximizing value) is not at all inconsistent with doing the good thing. If a firm is profitable, then it is one whose customers are satisfied and whose employees are loyal; those firms whose customers and employees are dissatisfied with them are likely to experience declining profits and declining stock prices.

Of course, in business, as in any area of life, ethical issues arise; and when we call the firm's goal to maximize shareholder wealth, we do not mean that everything else should be left to chance. Laws partially prevent managers from engaging in obviously dishonest behavior, but for most managers it is not just the letter of the law or the provisions of formal employment contracts that are important. In business and finance, as in other everyday activities, there are unwritten and unspoken rules of behavior. In order to work fruitfully together, we must trust each other. The largest financial transactions are often “finalized” with a simple handshake, and each party knows that in the future, even if events turn out badly, the other party will not break its word. Any incident that weakens this mutual trust is detrimental to us all.

Should managers defend the interests of shareholders?

In many financial transactions, one party may be better informed than the other. It is very difficult to obtain complete and reliable information about the quality of the assets or services that you are purchasing. This situation opens up wide scope for dubious financial manipulations and illegal scams, and since unscrupulous businessmen are much more likely than honest entrepreneurs to jump from place to place, airport registration lists are replete with traces of financial scammers.

Honest firms counter this with a demonstrated commitment to long-term client relationships, a good name in the business and financial integrity. Large banks and investment companies are well aware that their most valuable asset is their business reputation. They do not miss an opportunity to emphasize the long history of their existence and their consistently responsible behavior. Any event that undermines this reputation can cause them enormous material damage.

Consider, for example, the Salomon Brothers stock exchange scandal that erupted in 1991. A company trader tried to circumvent the rules limiting its participation in a Treasury bond auction; To do this, he submitted bids on behalf of several Salomon Brothers clients without notifying them of this and without obtaining their consent. When the forgery was discovered, Salomon Brothers had to fork out a fair amount to settle the case: almost $200 million. went to pay the fine and another 100 million dollars. - to establish a special fund to satisfy claims in civil suits. In addition, the value of Salomon Brothers shares immediately decreased by more than $300 million. In fact, the shares fell in price by almost a third, reducing the company's market value by $1.5 billion.

What explains such a dramatic decline in the value of Salomon Brothers? Mainly from the fears of investors, who felt that the company's business would suffer from the loss of customers who had lost confidence in it. The damage Salomon Brothers suffered as a result of its tarnished reputation was far greater than the obvious costs of the scandal, and hundreds or even thousands of times greater than the benefits that the company could have gained from illegal participation in the auction.

In this chapter we introduced the concept of present value as a tool for asset valuation. Calculating present value (PV) is simple. All you need to do is discount the future cash flow at an appropriate rate r, usually called the opportunity cost of capital, or marginal return:

Net present value (NPV) is equal to the sum of the present value and the original cash flow:

Recall that C 0 is negative if the initial cash flow represents an investment, that is, a cash outflow.

The discount rate is determined by the yield prevailing in the capital markets. If future cash flow is absolutely certain, the discount rate is equal to the interest rate on risk-free securities such as U.S. government debt. If the magnitude of future cash flow is subject to uncertainty, then the expected cash flow should be discounted by the expected return of securities with similar risk.

Cash flows should be discounted for two simple reasons: first, because a dollar today is worth more than a dollar tomorrow, and second, because a safe dollar is worth more than a risky one. The present value and net present value formulas express these ideas in numerical terms. The capital market is a market where the purchase and sale of reliable and risky future cash flows takes place. That's why we look at the rates of return prevailing in the capital markets to determine what discount rate to use given timing and cash flow risk. When we calculate the present value of an asset, we are actually estimating what people would pay for it given that alternative investment opportunities exist in the capital markets.

The concept of net present value supports the rationale for separating ownership from control within a corporation. A manager who invests only in assets with a positive net present value best serves the interests of each of the firm's owners—despite their differences in wealth and tastes. This is possible thanks to the capital market, which allows each shareholder to form their own investment portfolio in accordance with their needs. In particular, the firm does not need to adjust its investment policy so that subsequent cash flows correspond to shareholders' preferred temporary consumption patterns. Shareholders themselves are perfectly capable of moving funds forward or backward in time as long as they have free access to competitive capital markets. In fact, their choice of a particular temporary consumption pattern is limited by only two circumstances: their personal wealth (or lack thereof) and the interest rate at which they can borrow or lend money. The financial manager is not able to influence the interest rate, but he has the power to increase the wealth of shareholders. This can be done by investing in assets with a positive net present value.

There are several organizational mechanisms that provide some assurance that managers are paying close attention to the value of the firm:

the work of managers is closely monitored by the board of directors;
It is difficult for lazy people and hacks to hold on to their positions under the pressure of more energetic managers. Such competition often arises within an individual company, but it also operates externally: poorly performing firms very often become targets of hostile takeovers; as a result, as a rule, the management team is completely renewed;
Managers are motivated by incentive schemes such as stock options, which pay handsomely when the stock price (and therefore shareholders' wealth) rises, but depreciate when it doesn't.

If managers strive to increase shareholder value, this does not mean that they are neglecting other, broader responsibilities to society. Managers act honestly and fairly towards employees, customers and suppliers partly because they see it as the common good, but partly for very pragmatic reasons: they are well aware that a company's most valuable asset is its reputation. Of course, there are ethical issues in finance, and every time some unscrupulous manager abuses his position, we all start to trust each other a little less.

The first works on net present value:

I. Fisher. The Theory of Interest. 1965 (reprint of 1930 edition). J. Hirshleifer. On the Theory of Optimal Investment Decision // Journal of Political Economy. 66: 329-352. 1958. August.

For a more detailed presentation of the subject, see:

E. F. Fama and M. H. Miller. The Theory of Finance. New York: Holt, Rinehart and Winston, 1972.

If you want to delve deeper into how you can motivate managers to maximize shareholder wealth, we suggest looking at the following works:

M. C. Jensen and W. H. Meckling. Theory of the Firm: Managerial Behavior, Agency Costs, and Ownership Structure // Journal of Financial Economics. 3: 305-360. 1976. October.

E. F. Fama. Agency Problems and the Theory of the Firm // Journal of Political Economy. 88: 288-307. 1980. April.

However, needless to say, there are some types of real estate, the value of which is practically impossible for an appraiser to determine; for example, no one knows the potential price at which the Taj Mahal, or the Parthenon, or Windsor Castle could be sold.

Hereinafter as symbols terms in the text and formulas use abbreviations derived from English names: PV - from present value (present value), NPV - from net present value (net present value), DF - from discount factor (discount factor), D - from debt (debt, indebtedness), E - from equity (own, or share capital), etc. (Full list of terms in Russian and English languages, as well as the corresponding abbreviations (symbols) are contained in the Subject Index at the end of the book.) - Note. editor.

Let's check ourselves. If you invest $373,832. at 7% per annum, then at the end of the year your original investment will be returned to you plus interest income in the amount of 0.07 x $373,832. = $26,168 The total amount you will receive is $373,832. + $26,168 = $400,000 Pay attention to this: 373,832 x 1.07 = 400,000.

We'll define "expected" more precisely in Chapter 9. For now, it's enough to understand that expected revenue reflects a realistic forecast, not an optimistic or pessimistic forecast.

You can verify for yourself the equivalence of these rules. Let's express them differently: if the yield of 50,000/350,000 is greater than r, then the net present value -350,000 + 400,000/(1+r) must be greater than zero.

These rules may conflict with each other when cash flows extend beyond two periods. We'll tackle this problem in Chapter 5.

We assume that a decline and a rise are equally probable, that is, that the expected (average) outcome is $110 thousand. Let, for example, the probabilities of recession, normal state and rise - that is, each of these probabilities - be equal to V3. Then the expected return: Q = ($80,000 + $110,000 + + $140,000)/3 = $110,000.

The exact relationship between current and future consumption that each person chooses depends on his individual preferences. Readers familiar with economic theory will know that such choices can be shown by superimposing indifference curves specific to each individual. The preferred combination will be at the intersection of the interest rate line and the individual's indifference curve. In other words, each individual will borrow or lend up to the point where 1 plus the interest rate equals the marginal rate of time preference (ie the slope of the indifference curve). For a more rigorous presentation of graphical analysis of investment decisions and choices between current and future consumption, see the Braley-Myers website at www://mhhe.com/bm/7e.

Some managers, for fear of displeasing any stakeholder group, deny that they are profit or value maximizers. We recall one survey of businessmen in which they were asked to answer whether they were trying to maximize profits. Interviewees indignantly rejected this suggestion, arguing that their responsibilities extended far beyond the narrow and selfish task of making a profit. But when the question was modified slightly and the businessmen were asked whether they could increase their profits by increasing or decreasing the selling price of their products, they replied that none of these changes would lead to a further increase in profits. (See: G. J. Stigler. The Theory of Price. 3rd. ed. New York: Macmillan Company, 1966.)

Under US law, a contract can be valid even if it is not in writing. Of course, it is more reasonable to keep the necessary documentation, but an oral agreement is recognized as valid if it can be proven that the parties have reached complete and unconditional mutual understanding and agreement. For example, in 1984, Getty Oil executives verbally agreed to a proposed merger with Pennzoil. Texaco then came out with a better offer and outbid. But Pennzoil sued, alleging that Texaco had breached a valid contract, and won.

For more details on this issue, see: A. Schleifer and L. H. Summers. Breach of Trust in Corporate Takeovers // Corporate Takeovers: Causes and Consequences. Chicago: University of Chicago Press, 1988.

See: Clifford W. Smith, Jr. Economics and Ethics: The Case of Salomon Brothers // Journal of Applied Corporate Finance. 5. 1992. Summer. P. 23-28.

Net present value (NPV) is one of the main indicators on the basis of which financial decisions are made. Typically NPV is used to evaluate the performance of an investment over the long term. This indicator is most often used in the field of corporate finance, but it is also useful for daily monitoring of the financial situation. Net present value is calculated using the formula (P / (1 + i) t) – C, where t is the number of time periods, P is the flow of payments, C is the amount of initial investment, i is the discount rate.

Steps

Part 1

NPV calculation

Determine the amount of initial investment. Investments are often made to generate profits over the long term. For example, a construction company might buy a bulldozer to take on larger projects and make more money from them. Such investments always have an initial size.

For example, let's say you own an orange juice stand. Are you thinking about purchasing an electric juicer that will help you increase your juice production. If a juicer costs $100, then $100 is an initial investment. Over time, this initial investment will allow you to earn more money. By calculating the NPV, you will determine whether the juicer is worth purchasing.

Decide what time period you will analyze. For example, if a shoe factory buys additional equipment, then the purpose of this purchase is to increase production and make more money over a certain period of time (until the equipment fails). Therefore, to calculate NPV, you need to know the period of time during which the investment must pay off. A period of time can be measured in any time unit, but in most cases one time period is considered to be one year.
- In our example, the warranty on the juicer is given for 3 years. In this case, the number of time periods is 3, since after 3 years the juicer will most likely break down and will not be able to generate additional profit.
Determine the flow of payments during one time period, that is, the cash receipts that are generated due to the investments made. The payment stream can be a known value or an estimate. If this is an estimate, then companies and financial firms spend a lot of time and hire relevant specialists and analysts to obtain it.
- For our example, let's say you think that purchasing a $100 juicer will generate an additional $50 in the first year, $40 in the second year, and $30 in the third year (by reducing the time your employees spend juicing and the associated wage costs). . In this case, the payment flow is: $50 for year 1, $40 for year 2, $30 for year 3.
Determine the discount rate. In general, any amount has more value now than in the future. You can put this amount in the bank today and receive it in the future with interest (that is, $10 today is worth more than $10 in the future, since you can invest $10 today and get more than $11 in the future). To calculate NPV, you must know the interest rate on an investment account or investment opportunity with a similar level of risk. This interest rate is called the discount rate; To calculate NPV it must be converted to a decimal fraction.
- Companies often use the weighted average cost of capital to determine the discount rate. In simple situations, you can use the rate of return on a savings account, investment account and so on (that is, an account into which money can be deposited at interest).
- In our example, let's say that if you don't buy a juicer, you invest the money in the stock market, where you will earn 4% per annum on the amount invested. In this case, 0.04 (4% as a decimal) is the discount rate.
Discount cash flow. This can be done using the formula P / (1 + i)t, where P is cash flow, i is interest rate and t is time. Now you don’t have to think about the initial investments - they will be useful in further calculations.
- In our example, the number of time periods is 3, so use the formula three times. Calculate the annual discounted cash flows as follows:
  - Year 1: 50 / (1 + 0.04) 1 = 50 / (1.04) = $48,08
  - Year 2: 40 / (1 +0.04) 2 = 40 / 1.082 = $36,98
  - Year 3: 30 / (1 +0.04) 3 = 30 / 1.125 = $26,67
Add up the resulting discounted cash flows and subtract the initial investment from the total. What you end up with is the NPV, which is the amount of money the investment will make compared to the amount that alternative investments would make you at the discount rate. In other words, if it is a positive number, then you will make more money from the investment than from the alternative investment (and vice versa if the number is negative). But remember that the accuracy of the calculation depends on how accurately you estimate future cash flows and the discount rate.
- In our example, NPV is calculated as follows:
  - 48,08 + 36,98 + 26,67 - 100 = $11,73
If NPV is a positive number, then the project will be profitable. If the NPV is negative, then you should invest the money somewhere else or reconsider the project. In the real world, NPV allows you to decide whether it is worth investing in a particular project at all.
- In our example, NPV = $11.73. Since this is a positive number, you will most likely decide to buy a juicer.
- Note that this figure does not mean that the electric juicer will only net you $11.73. What this actually means is that the juicer will earn you $11.73 more than what you would get by investing in the stock market at 4% per annum.
Part 2
Using the formula to calculate NPV
1. By calculating the NPV of several investment projects, you can compare their effectiveness. Investments with high NPV are more effective, so invest in projects with the highest NPV (unless you have sufficient funds to invest in each project).
  - For example, you are considering three investment projects. One has an NPV of $150, the second has an NPV of $45, and the third has an NPV of -$10. In this situation, invest in a project with an NPV of $150, and only then invest in a project with an NPV of $45. Do not invest in a project with NPV = -$10, since a negative value indicates that it is better to invest in an alternative project with a similar level of risk.
2. Use the formula PV = FV / (1+i)t to calculate the "present" and "future" value of an investment. In this formula, i is the discount rate, t is time, FV is future value, PV is present value.
  - For example, let's calculate the value of a $1,000 investment after five years. Let's assume that these funds can be invested (as an alternative) at 2% per annum. In this case i = 0.02; t = 5, PV = 1000.
    - 1000 = FV / (1+0.02) 5
    - 1000 = FV / (1.02) 5
    - 1000 = FV / 1.104
    - 1000 x 1.104 = FV = $1104 .
3. Find out what assessment methods exist to get more exact value NPV As noted above, the accuracy of the NPV calculation depends on the accuracy of the quantities you use to estimate the discount rate and future payment streams. If the discount rate is close to the interest rate of an alternative investment (with a similar level of risk), and the future cash flows are close to the amounts you will actually receive (as a result of the investment), then the calculated NPV value will be quite accurate. To estimate the required values as accurately as possible, learn about the corporate valuation methods that are used by large corporations when analyzing huge multi-million dollar investment projects.
- Always remember that there are other, non-financial factors (such as environmental or social) that need to be taken into account when making any investment decision.
- NPV can also be calculated using a financial calculator or NPV tables, which are useful if you don't have a financial calculator.

Investing is a direction of financial activity that or loss. It all depends on many factors and risks that such an investment carries. Therefore there are directions investment analysis, where many indicators are calculated and analyzed, including the present value of the flow.

An investment project is assessed by many indicators, but the main one is the return on investment funds. Also, when investing, each analyst evaluates incoming and outgoing cash flows, which ultimately help evaluate the inflow or outflow at the end of the project.

Cash flow is denoted in theory and practice by CF. This abbreviation is entirely in English. language - cash flow. These are receipts from the project of cash resources, their equivalents, as well as expenses incurred during the duration of the investment. However, not everyone knows that investment activities, already being investment activities, are divided into three main subtypes:

Flow from investment activities. As a rule, this includes funds received or spent as a result of the acquisition or other intangible assets that are sold or purchased.
Flow from the financial direction. Includes all flows that are associated with attracting credit funds; with the payment of interest on them, the acquisition and sale of securities, etc.
Flow from the operating area of activity. Includes income from services, sales finished products; expenses for materials, inventories and other components that form.

As a rule, the movement of funds from operating activities is the main one in an enterprise, since it is directly related to its economic activities.

Incoming and outgoing cash flows

Cash flow is the basis for calculating the investment attractiveness of the investment itself, and therefore at each stage of the analysis of this indicator the following components are taken into account:

How much income was credited to the account of such a project.
How many expenses were incurred as a result of the sale?
What is the investment balance: positive or negative.

At the initial stage of investment implementation, flows are predominantly outgoing, and the balance is negative. To calculate the balance, you need to clearly separate what is included in incoming and outgoing flows.

What does the incoming flow of cash resources include:

products, goods and services
Obtaining loan funds from the bank and other lenders
Issue and sale of securities
Other operating income
Income from the sale or rental of fixed assets and other intangible assets
Profit from investments in securities

What does outgoing cash flow include:

for purchase necessary materials, raw materials, stocks, semi-finished products, etc.
Employee wage costs
Purchase of fixed assets, production facilities
Funds invested in working capital
Interest payments on the loan
Other operating expenses

Based on the results of such indicators, the balance of cash flow of resources can be calculated, which will show the result of investing funds in the business.

Present value: what is it?

Since we are studying such a concept as the present value of the cash flow itself, it is correct to study not only the essence of the cash flow, but also the essence of the concept of “present value”.

Present value allows you to find out the current value of an investment, that is, what we will receive in the future, but subject to the current exchange rate. Present value allows you to determine how much money needs to be invested for a period at interest in order to receive a certain amount of money in the future. In this case, the calculation of present value takes into account compound rather than simple interest.

Why is NPV calculation needed?

If they mean present value, then they mean only the net value. This concept is differently referred to in the world literature as NPV. This completely sounds like Net Present Value. This concept implies the current real amount of monetary resources that are necessary to receive in the near future an amount equal to the income from the sale of this investment.

In simple language: with a deposit interest of 10%, 100 rubles today will equal 110 rubles by the end of the year. As a result, such an example of a deposit is equivalent to the profitability of an investment project.

If the investment involves investments not for one year, but for several years, then it is necessary to calculate the present value not at the end of the entire period, but at the end of each reporting year. It is necessary to determine what amount will be returned to the investor at the end of each year in comparison with the investments made in that year.

NPV: is this the same as NPV?

It should also be taken into account that in Russian literature one can often find such an abbreviation as NPV - this is the same thing and is simply deciphered not from English, but from Russian - net present value.

Based on the results of the study, we can conclude that the NPV is the total for all realized cash flows, which is calculated taking into account the current period of time. Present value is always the opposite indicator of future value, which is so often taken as a basis when calculating investment attractiveness.

Algorithm and formula for calculating NPV

NPV = sum of results for each year of investment CF / ((1 + r) to the power of t),

where the designations have the following meaning:

CF – cash flow balance, calculated as the difference between what the company received and what it spent
t – number of years for which the calculation is made
r – investment discount rate
n – duration of implementation of the investment project itself

When studying cash flows and their present value, it is very important to approach the choice of discount rate directly. When making its choice, it is necessary to take into account not only the features of the theory of the value of money over time, but also take into account the risk of uncertainty. It is better to choose the weighted average of the investment in the investment project as the discount rate. As a result of this choice, there is a pattern: the greater the risks of uncertainty, the greater the bet itself will be, and vice versa.

NPV of projects: which one to choose

There are two investment projects with investments of 10 thousand rubles. The cash flows for each project by year are known. Project A: 5, 4, 3, 1. Project B has the following cash flows: 1, 3, 4, 6. Discount rate is 10%. Which project is better?

5 / (1 + 0.1) to the 1st power = 4545.5
4 / (1 + 0.1) to the 2nd power = 3305.8
3 / (1 + 0.1) to the 3rd power = 2253.9
1 / (1 + 0.1) to the 4th power = 683.0

According to the results of calculating the NPV of the flow for investment project A for 4 years will be: 10788.2 (all NPV for four years are summed up: 4545.5 +…+ 683). If we subtract the initial investment, then NPV = 10788.2 – 10000 = 788.2.

By analogy, the NPV for project B is calculated, where it will be 491.5.

Conclusion: you can invest money in both projects, but it is more profitable to invest in project A.

Analysis of the results obtained

Thus, NPV is a way of studying the investment profitability of a project that allows you to understand today how much money needs to be invested and what the return will be from it. You can also understand how much the project will pay off.

How to analyze results

The implementation of the NPV method is based on the following principles:

Discounting of cash flows occurs as a whole at the cost of the capital invested. Before carrying out the calculation, it is always necessary to find the size of both incoming and outgoing flows reduced to the current time period, and only after that calculate the NPV.
All values for discounted cash flows must always be added in order to then evaluate the result obtained.
The resulting flow is assessed. If the resulting NPV is greater than 0, the investment project can be implemented in reality. If this value is equal to 0, then everything is at the discretion of the investor: the project can be accepted or rejected. This is due to the fact that NPV = 0 indicates that the flows will cover the invested capital and may even provide a small rate of profit, but there will be no further benefits for the investor. The project's share price will not change in the future.

Selection criteria

Based on the results of studying the issue, the criteria for selecting an investment project can be presented as follows:

If we take into account any investment project, then if the net present value is greater than zero, the project is unconditionally accepted. If such an indicator is negative in the calculation, then the project is clearly rejected. With a value of zero, the investor does not care whether the project is implemented or not.
If several projects are simultaneously being considered by the investor, then the investment project that has the highest present value is selected from the list, that is, the straightforward selection method is used.
If there are a lot of projects under consideration, all of which are accepted for implementation by the investor, then if a negative NPV is received, the project must be rejected.

Pros and cons of the method

The main advantage of calculating NPV is that this technique allows the analyst to now estimate the value that will be additionally created in the future, but taking into account modern realities.

This allows the investor to understand the situation and make an informed decision. But we cannot completely say that this method does not have drawbacks; there are some.

Among these controversial issues are the following:

Incorrect assessment of the discount rate, its sensitivity to changes. Present value calculations are based on the assumption that all investments will be reinvested at the applicable discount rate. But this is absolutely impossible to predict 100%. Interest rates are constantly changing in the financial market, and therefore the one that applies is not a fact that will not change in the future.
Limitation of project implementation deadlines. Investments can be long-term when it is impossible to estimate cash flows in the future. And the present value may be negative at the time of calculation or at the time of the planned end of the project, and in fact the state of affairs will change a year after the evaluation period.
Management decisions. The project is assessed for a specific period, but no one appreciates the fact that, given the circumstances and market conditions, top managers can implement creative solutions and change the results of the investment. The manager's reaction can greatly change the magnitude of all flows.

Every investor to implement the right choice project, assessing its cost, profitability, etc. Flows of cash resources are the fundamental criterion for calculation, and this is an indisputable fact. Present value helps to assess the state of future flows, which is important in the realities of interest capitalization.

Of course, the method is not without its drawbacks, but everyone must make their own decisions about which method to use.

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