Discount rate. Alternative Return Concept and Weighted Average Cost of Capital Concept Alternative Return Rate Formula

We have understood the concepts of cash flow. Now, in order to calculate the cost of an investment project, we must decide on the procedure for determining the discount rate. Let's consider three main points: alternative rates, the WACC model - a weighted average cost of capital model, the CAPM model - a model for estimating the cost of capital assets.

Discount rate based on alternative rate

As for alternative rates when determining the discount rate, the rate that we will use in , we will present some of them.

Alternative bet based on stock index

You can use the stock index return for the period as the discount rate.

Alternative rate based on investors' desired return

You can conduct a survey among your investors about what kind of return they want to have on their investments. Provided that you have a responsible investor and he thinks about what he does with his funds.

Alternative rate based on average yield

You can perform a market analysis and see what other similar projects have similar risks, and what the discount rates are. In other words, if you invest not in your project that you have chosen, but in some others. What income will you receive? In the market, the average cost of resources is 7%, 6%, 7.2%, 6.4%, you can find the average as an option.

Alternative bet based on no risky return

This might be an option. Determine the risk-free return and add a risk premium to it. In principle, risk-free returns are considered. The risk premium can be determined based on the ratings. If the company that is implementing the project has a rating, then by analogy, comparing the rating with other companies, you can determine the risk premium.

Two words about the risk-free interest rate. As you understand from the name, a risk-free bet means a financial instrument in which you do not bear any risk when investing. Obviously, in practice this is practically impossible and therefore the more common phrase is “maximum risk-free instrument”, respectively, “maximum risk-free bet”. In order to determine the maximum risk-free rate, you need to find an instrument with the lowest risk. The measure of risk is the standard deviation. This is a term from statistics, and it means how much on average the quote fluctuates from the average up and down.

Let's note the following: you use the yield to calculate the standard deviation and your output is the following construction. Example: A stock has an average annual return of 10%, standard deviation of 3%. What does this mean? This means that on average over the year the yield of this security fluctuated in the range from 13% to 7%.

As practice shows, bonds have the smallest standard deviation and these securities are certainly more reliable than stocks. The market value of these securities fluctuates significantly less than the market value of other securities. Accordingly, in order to find a security for which we can determine the maximum risk-free interest rate, we need to choose a bond that will have the smallest standard deviation. Usually, for such calculations, government bonds are immediately taken. Their risk is less than the risks of corporate securities, less than the risks of regional and municipal bonds. If we take countries, we choose American bonds as a basis. In Russia, this could be Russian federal loan bonds.

Discount rate based on the WACC model weighted average cost of capital model

Formula 1 shows that if we take the company’s data as a basis, we can calculate how much it costs this company to attract its capital. Capital consists of two main parts: debt and equity. From stocks and bonds. There may also be long-term credit resources that also need to be taken into account. There are weights in this formula. They correspond to the weight of each source of financing in the capital structure. In this formula, T stands for income tax or corporate tax. The fact is that interest payments on bonds and bank loans are paid from pre-tax profits. And dividends on shares are paid after tax. Therefore, these two parameters, the cost of debt and the cost of shares, will not be comparable. It needs to be brought to a common denominator. In fact, by using the (1-T) multiplier, we make the cost of debt capital comparable to the cost of equity in view. Typically, WACC is calculated based on the balance. Unfortunately, using balance sheet data does not allow you to take into account the risk factor. We will write about this in the next article.

WACC = (1)

– shares of borrowed funds, preferred shares, equity (ordinary shares) of retained earnings;

r – the cost of the corresponding parts of capital

Discount rate based on CAPM capital asset valuation model

This model is mainly designed for stock valuation. She has an interesting destiny. In an attempt to find the most diversified portfolio, foreign scientists came across an interesting fact. The more securities you combine into a portfolio, the lower the risk of the portfolio, expressed by standard deviation. If you look at Chart 1, we have the risk of shares on one axis, and the number of shares in the portfolio on the other. At the moment when there is only one security in the portfolio, the risk of the portfolio is maximum. When two papers are combined, the risk decreases. But what’s interesting is that, starting from a certain point, depending on the market, it can be 100 securities in the portfolio, or 500, the risk stops falling. This has led to a better understanding of the nature of securities risk. It turns out that the risk consists of two parts. The first part is the so-called systemic risk, a risk that cannot be eliminated under any circumstances. And the market pays you for it. The second part of the risk is the risk associated with the issuer itself and can be eliminated. If it can be eliminated, then the market does not pay you for such a risk. If you take both risks, that's your problem. If you want to invest, then you take on two risks: one you get paid for, one you don't get paid for, and you take on an unpaid, excessive risk. Therefore, one needs to build a portfolio and try to avoid unnecessary risk.

Chart 1 Dependence of stock risk on their number in the portfolio

Based on the noted fact that risk consists of two parts, a model called CAPM was built. This is formula 2. The meaning of the model is as follows. There is a direct relationship between the yield of a security and the average return of the market. If the market's profitability changes, then the profitability of your securities changes in a certain way. In order to express this, a special coefficient β was introduced. It is inherently somewhat close to the standard deviation parameter.

CAPM = (2)

r_m – return on the market portfolio (stock index)

r_i – return on company shares

The β coefficient has a simple meaning. Example: A company has a β coefficient of 2. This means that every time the market return changes by one percent, the return on your stock will change by 2%. If the β coefficient is 3. This means every time the market's return changes by 1%, your security's return will change by 3%. Or should change. If β is -1, what does that mean? This means that for every unit the market falls, your security should rise by 1 unit. If your coefficient is 0.5. This means that for every unit of market growth, your security grows by 0.5. This is a good ratio that allows you to select securities in such a way as to build a certain kind of portfolio - aggressive, defensive and others.

We looked at several options for determining the discount rate, and before that we looked at issues related to the definition. In each individual case, you need to conduct separate research and logically justify a particular discount rate. There are no universal rules or formulas for determining the discount rate. After making a choice and analyzing the market, you will have to choose the discount rate that seems most acceptable to you.

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Index funds allow you to earn income from investing in the stock market completely passively. For example, if you invest in a fund based on the S&P 500 index, your money will be invested in the overall market, and you won't have to worry about how to manage your money or whether to sell or buy shares of certain companies. All these points will be managed by the fund, which forms its investment portfolio depending on the state of a particular index.

You can also choose a fund that covers any index. There are funds involved in various business sectors - energy, precious metals, banking, emerging markets and others. All you have to do is decide for yourself that this is what you want to do, then invest the money and relax. From now on, your stock portfolio will run on autopilot.

1. Make videos for YouTube

This area is developing very quickly. You can make videos of absolutely any category - music, educational, comedy, movie reviews - anything... and then post it on YouTube. Then you can connect Google AdSense to these videos, and automatic advertising will appear in them. When viewers click on these ads, you will earn money from Google AdSense.

Your main task is to create decent videos, promote them on social networks and maintain a sufficient number of them to provide yourself with income from several clips. Shooting and editing a video is not that easy, but once done, you will have a source of completely passive income that can last for a very long time.

Not sure you'll succeed on YouTube? Michelle Phan combined her love of makeup and drawing with video production, gained more than 8 million subscribers, and now launched her own company with a capitalization of $800 million.

1. Try Affiliate Marketing and Start Selling

This is a passive income technique that is more suitable for owners of blogs and active Internet sites. You can start promoting any products on your website and receive a fixed fee or a percentage of sales.

Making money this way is not as difficult as you might think because many companies are interested in selling their products in as many places as possible.

You can find partnership offers either by contacting manufacturers directly or on specialized websites. It is best if the advertised product or service is interesting to you or matches the theme of the site.

1. Make your photos profitable online

Do you like photography? If so, you may be able to turn this into a source of passive income. Photo banks, such as and, can provide you with a platform for selling photographs. You will receive a percentage or flat rate for each photo sold to a website client.

In this case, each photo represents a separate source of income that can work over and over again. All you need to do is create a portfolio, upload it to one or more platforms, and that's where your active work will end. All technical issues of photo sales are resolved using the web platform.

1. Buy high-yielding stocks

By creating a portfolio of high-yield stocks, you will receive a source of regular passive income with an annual interest rate that is much higher than the interest on bank deposits.

Don't forget that high-yielding stocks are still stocks, so there's always the possibility of capital overvaluation. In this case, you will receive profit from two sources - from dividends and return on invested capital. To purchase these shares and complete the appropriate forms, you will need to create a brokerage account.

1. Write an e-book

Of course, this can be quite a labor-intensive process, but once you write a book and publish it on marketplaces, it can provide you with income for years. You can sell the book on your own website or enter into a partnership agreement with other websites that are similar in theme to the book.

1. Write a real book and get royalties

Just like writing an e-book, there's a lot of work involved at first. But when the work is completed and the book goes on sale, it will become a completely passive source of income.

This is especially true if you manage to sell your book to a publisher who will pay you a royalty on the sales. You will receive a percentage of each copy sold, and if the book is popular, these percentages can add up to significant amounts. Moreover, these payments can last for years.

Mike Piper of ObviousInvestor.com recently did just that. He wrote a book, Investing Plain, which was sold only on Amazon. The first book became so profitable that he created a whole series. These books total .

1. Get cashback on credit card transactions

Many credit cards offer cash back ranging from 1% to 5% of the purchase price. You still go shopping and spend money, right?

Such bonuses allow you to provide yourself with a kind of passive “income” (in the form of reduced spending) from actions that you perform anyway.

1. Sell ​​your own products online

The possibilities in this area are endless: you can sell almost any product or service. It could be something you created and made yourself, or it could be a digital product (software, DVDs, or instructional videos)

For trading, you can use a specialized resource, if suddenly you do not have your own website or blog. In addition, you can enter into a partnership agreement by offering goods to sites on relevant topics or using platforms like (American marketplace for selling digital information products - editor's note).

You can learn how to sell products online and earn quite a lot from it. This may not be completely passive income, but it is certainly more passive than a regular job that you have to go to every morning.

1. Invest in real estate

This method falls more into the category of semi-passive income, since investing in real estate involves at least a small level of activity. However, if you have a property that you're already renting out, it's mostly just a matter of maintaining it.

Additionally, there are professional property managers who can manage your property for a commission of approximately 10% of the rent. Such professional managers help make the process of receiving profits from such investments more passive, but they will take part of it.

Another way to invest in real estate is to pay off a loan. If you take out a loan to buy a property that you will rent out, your tenants will pay off that debt a little each month. When the full amount is paid, your profits will increase dramatically, and your relatively small investment will turn into a full-fledged program for quitting your day job.

1. Buy a blog

Thousands of blogs are created every year, and many of them end up abandoned after some time. If you can acquire a blog with enough visitors—and therefore enough cash flow—it can be a great source of passive income.

Most blogs use Google AdSense, which pays once a month for advertising placed on the site. To provide additional income, you can also enter into partnership agreements. Both of these income streams will be yours if you own a blog.

From a financial perspective, blogs typically sell for 24 times the monthly income the blog can generate. That is, if a site can earn $250 per month, most likely you can buy it for $3,000. This means that by investing $3,000, you can receive $1,500 annually.

You may be able to buy the site for less money if the owner really wants to get rid of this asset. Some sites contain “eternal” materials that will not lose relevance and will generate income years after publication.

Bonus tip: If you buy such a site and then fill it with fresh content, you will be able to increase your monthly income, and you will be able to sell the site again after some time for a significantly higher price than you paid when buying it.

Finally, instead of purchasing a blog, you can create your own. This is also a good way to earn money.

1. Create a website that sells

If there is a product that you know a lot about, you can start selling it on a specialized website. The technique is the same as when selling a product of your own making, except that you do not have to deal with the production itself.

After some time, you may find that you can add similar products. If this happens, the site will begin to generate significant profits.

If you can find a way to ship products directly from the manufacturer to the buyer, you won't even have to get your hands dirty. This may not be 100% passive income, but it’s very close to it.

1. Invest in real estate investment trusts (REITs)

Let's say you decide to invest in real estate, but you don't want to devote any attention or time to it. Investment trusts can help you with this. They are something like a fund that owns various real estate projects. The funds are managed by professionals, so you don't have to interfere with their work at all.

One of the main advantages of investing in REITs is that they typically pay higher dividends than stocks, bonds and bank deposits. You can also sell your interest in the trust at any time, making such assets more liquid than owning real estate on your own.

1. Become a passive business partner

Do you know a successful company that needs capital to expand its business? If so, you can become something of a short-term angel and provide that capital. But instead of giving a loan to the owner of the company, ask for a share of the shares. In this case, the owner of the company will manage the work of the company, while you will be a passive partner, also taking part in the business.

Every small business needs a source of referrals to support sales. Make a list of entrepreneurs whose services you use regularly and whom you can recommend for cooperation. Contact them and find out if they have a system for paying for referrals.

The list could include acquaintances: accountants, landscape designers, electricians, plumbers, carpet cleaners—anyone. Be prepared to recommend the services of these people to your friends, relatives and colleagues. You can earn a commission on every referral just by talking to people.

Don’t underestimate referral programs in the professional sphere either. If the company you work for offers bonuses for referring new employees or new clients, take advantage of it. This is very easy money.

1. Rent out your unused property on Airbnb

The concept appeared only a few years ago, but very quickly spread throughout the world. Airbnb allows people to travel the world and pay much less to stay than in regular hotels. By participating in Airbnb, you can use your home to host guests and earn extra money just from renting.

The amount of income will depend on the size and condition of your home and its location. Naturally, if your home is located in an expensive city or near a popular resort, the income will be much higher. This is a way to make money from free spaces in your home that would otherwise be empty.

1. Write an application

Apps can be an incredibly lucrative source of income. Think about how many people have smartphones today. Yes, almost everything! People are downloading apps like crazy—and for good reason.

Apps make people's lives easier. Whether it's helping you post pretty pictures or keeping track of tasks, there's always an app that's useful to someone.

You might ask: If there are so many apps out there, why would you try to create another one. Is there too much competition? This is all true, but fresh, creative ideas can benefit. If you can come up with something unique, you can make money from it.

Don't know how to program? No problem, you can learn. There are a lot of different courses on the Internet, including free ones. Alternatively, you can hire a developer to create an app based on your idea.

The end result is an application that will potentially generate relatively passive income.

1. Create online courses

Every person is an expert in something. Why not create an online course about your passion?

There are several ways to create and deliver your own online courses. One of the easiest ways is to use sites like

Profitability. The most significant parameter, knowledge of which is necessary when analyzing transactions with stock values, is profitability. It is calculated by the formula

d = ,(1)
Where d- profitability of operations, %;

D- income received by the owner of the financial instrument;

Z - the cost of its acquisition;

 is a coefficient that recalculates profitability for a given time interval.

Coefficient  has the form

 =  T /t (2)

where  T- time interval for which profitability is recalculated;

t- the time period during which the income was received D.

Thus, if an investor received income in, say, 9 days ( t= 9), then when calculating profitability for the financial year ( T= 360) the numerical value of the coefficient t will be equal to:

 = 360: 9 = 40

It should be noted that usually the profitability of transactions with financial instruments is determined based on one financial year, which has 360 days. However, when considering transactions with government securities (in accordance with the letter of the Central Bank of the Russian Federation dated 09/05/95 No. 28-7-3/A-693) T is taken equal to 365 days.

To illustrate the calculation of the profitability of a financial instrument, consider the following model case. Having carried out a purchase and sale operation with a financial instrument, the broker received an income equal to D= 1,000,000 rubles, and the market value of the nth financial instrument Z= 10,000,000 rub. The profitability of this operation in annual terms:
d ==
=
= 400%.

Income. The next important indicator used in calculating the efficiency of operations with securities is the income received from these operations. It is calculated by the formula

D= d +  , (3)

Where d- discount part of income;

 is the percentage of income.

Discount income. The formula for calculating discount income is

d = (R etc - R pok), (4)

Where R pr - the selling price of the financial instrument with which transactions are carried out;

R pok - purchase price of a financial instrument (note that in the expression for profitability R pok = Z).

Interest income. Interest income is defined as income received from interest charges on a given financial instrument. In this case, it is necessary to consider two cases. The first is when interest income is calculated at a simple interest rate, and the second when interest income is calculated at a compound interest rate.

The scheme for calculating income at a simple interest rate. The first case is typical when calculating dividends on preferred shares, interest on bonds and simple interest on bank deposits. In this case, an investment of X 0 rub. after a period of time equal to P interest payments will result in the investor having an amount equal to

X n-X 0 (1 +  n). (5)

Thus, interest income in the case of a simple interest calculation scheme will be equal to:

 = X n - X 0 = X 0 (1 +  n) - X 0 = X 0  n,(6)

where X n - the amount generated by the investor through P interest payments;

X 0 - initial investment in the financial instrument in question;

 - interest rate;

P- number of interest payments.

Scheme for calculating income at a compound interest rate. The second case is typical when interest is calculated on bank deposits using a compound interest scheme. This payment scheme involves the accrual of interest on both the principal amount and previous interest payments.

Investment of X 0 rub. after the first interest payment they will give an amount equal to

X 1 -X 0 (1 + ).

On the second interest payment, interest will accrue on the amount X 1 . Thus, after the second interest payment, the investor will have an amount equal to

X 2 – X 1 (1 + ) - X 0 (1 + )(1 + ) = X 0 (1 + ) 2.

Therefore, after n- interest payment from the investor will be an amount equal to

X n = X 0 (1 +) n . (7)

Therefore, interest income in case of accrual of interest according to the compound interest scheme will be equal to

 = X n -X 0 = X 0 (1+ ) n – X 0 . (8)

Income subject to taxation. The formula for calculating the income received by a legal entity when performing transactions with corporate securities has the form

D = d(1-  d) + (1- p), (9)

where  d is the tax rate on the discount part of income;

 n - tax rate on the interest part of income.

Discount income of legal entities (d) subject to taxation in accordance with the general procedure. Tax is levied at the source of income. Interest income () is taxed at the source of this income.

The main types of tasks encountered when carrying out transactions on the stock market

The tasks that are most often encountered when analyzing the parameters of operations on the stock market require answers, as a rule, to the following questions:

• 
  What is the yield of a financial instrument or which financial instrument has a higher yield?
• 
  What is the market value of securities?
• 
  What is the total income that the security brings (interest or discount)?
• 
  What is the period of circulation of securities that are issued at a given discount in order to obtain an acceptable yield? and so on.

The main difficulty in solving this type of problem is to compile an equation containing the parameter of interest to us as an unknown. The simplest tasks involve using formula (1) to calculate profitability.

However, the bulk of other, much more complex problems, with all the diversity of their formulations, surprisingly, have a common approach to solution. It lies in the fact that with a normally functioning stock market, the profitability of various financial instruments is approximately equal. This principle can be written as follows:

d 1 d 2 . (10)

Using the principle of equality of returns, you can create an equation to solve the problem, revealing the formulas for profitability (1) and reducing the factors. In this case, equation (10) takes the form

=
(11)
In a more general form, using expressions (2)-(4), (9), formula (11) can be transformed into the equation:


. (12)

By transforming this expression into an equation to calculate the unknown unknown in the problem, you can obtain the final result.

Algorithms for solving problems

Problems for calculating profitability. The technique for solving such problems is as follows:

1) the type of financial instrument for which the profitability needs to be calculated is determined. As a rule, the type of financial instrument with which transactions are made is known in advance. This information is necessary to determine the nature of the income that should be expected from this security (discount or interest), and the nature of the taxation of the income received (rate and availability of benefits);

2) those variables in formula (1) that need to be found are clarified;

3) if the result is an expression that allows you to create an equation and solve it with respect to the unknown unknown, then this practically ends the procedure for solving the problem;

4) if it was not possible to create an equation for the unknown unknown, then formula (1), sequentially using expressions (2)-(4), (6), (8), (9), leads to a form that allows you to calculate the unknown quantity .

The above algorithm can be represented by a diagram (Fig. 10.1).

Profit comparison problems. When solving problems of this type, formula (11) is used as the initial one. The technique for solving problems of this type is as follows:

Rice. 10.1. Algorithm for solving the problem of calculating profitability
1) financial instruments are determined, the profitability of which is compared with each other. This means that in a normally functioning market, the profitability of various financial instruments is approximately equal to each other;

• 
  the types of financial instruments for which profitability needs to be calculated are determined;
• 
  known and unknown variables in formula (11) are clarified;

• 
  if the result is an expression that allows you to create an equation and solve it relative to the unknown unknown, then the equation is solved and the procedure for solving the problem ends here;

• 
  if it was not possible to create an equation for the unknown unknown, then formula (11), sequentially using expressions (2) - (4), (6), (8), (9), leads to a form that allows you to calculate the unknown quantity.

The above algorithm is shown in Fig. 10.2.

Let's consider several typical computational problems that can be solved using the proposed methodology.

Example 1. The certificate of deposit was purchased 6 months before its maturity date at a price of RUB 10,000. and sold 2 months before the maturity date at a price of RUB 14,000. Determine (at a simple interest rate excluding taxes) the annualized profitability of this operation.

Step 1. The type of security is specified explicitly: certificate of deposit. This security issued by the bank can bring its owner both interest and discount income.

Step 2.

d =
.

However, we have not yet received an equation for solving the problem, since in the problem statement there is only Z– the purchase price of this financial instrument, equal to 10,000 rubles.

Step 3. To solve the problem, we use formula (2), in which  T= 12 months and  t= 6 – 2 = 4 months. Thus,  = 3. As a result, we obtain the expression

d =
.

Step 4. From formula (3), taking into account that  = 0, we obtain the expression

d =
.

Step 5. Using formula (4), taking into account that R pr = 14,000 rub. And R pok = 10,000 rubles, we get an expression that allows us to solve the problem:

d =(14 000 - 10 000) : 10 000  3  100 = 120%.

Rice. 10.2. Algorithm for solving the problem of comparing yields
Example 2. Determine the listing price Z the bank of its bills (discount), provided that the bill is issued in the amount of 200,000 rubles. with due date  t 2 = 300 days, bank interest rate is (5) = 140% per annum. Take the year equal to the financial year ( T 1 = T 2 = t 1 = 360 days).

Step 1. The first financial instrument is a deposit in a bank. The second financial instrument is a discount bill.

Step 2. In accordance with formula (10), the profitability of financial instruments should be approximately equal to each other:

d 1 = d 2 .

However, this formula is not an equation for an unknown quantity.

Step 3. Let us detail the equation using formula (11) to solve the problem. Let us take into account that  T 1 = T 2 = 360 days,  t 1 = 360 days and  t 2 = 300 days. Thus,  1 = l and  2 = 360: 300 = 1.2. Let us also take into account that Z 1 = Z 2 = Z. As a result, we obtain the expression

= 1,2.

This equation also cannot be used to solve the problem.

Step 4. From formula (6) we determine the amount that will be received from the bank when paying income at a simple interest rate of one; interest payment:

D 1 =  1 = Z = Zl,4.

From formula (4) we determine the income that the owner of the bill will receive:

D 2 = d 2 = (200 000 - Z).

We substitute these expressions into the formula obtained in the previous step and get

Z =
l,2.
We solve this equation with respect to the unknown Z and as a result we find the price of placing the bill, which will be equal to Z= 92,308 rub.

Particular methods for solving computational problems

Let's consider particular methods for solving computational problems encountered in the process of professional work on the stock market. Let's start our review by looking at specific examples.

Own and borrowed funds when making transactions with securities

Example 1. The investor decides to purchase a share with an expected increase in market value of 42% over the six months. The investor has the opportunity to pay at his own expense 58% of the actual value of the share ( Z). At what maximum semi-annual percentage () should an investor take out a loan from a bank in order to ensure a return on invested own funds of at least 28% for the half-year? When calculating, it is necessary to take into account the taxation of profits (at a rate of 30%) and the fact that interest on a bank loan will be repaid from profits before taxation.

Solution. Let us first consider solving this problem using the traditional step-by-step method.

Step 1. The security type (share) is specified.

Step 2. From formula (1) we obtain the expression

d =
100 = 28%,

Where Z- market value of the financial instrument.

However, we cannot solve the equation, since from the problem conditions we only know d- the return on a financial instrument on invested own funds and the share of own funds in the acquisition of this financial instrument.

Step 3. Using formula (2), in which  T = t= 0.5 years, allows us to calculate  = 1. As a result, we obtain the expression

d = 100 = 28%.
This equation also cannot be used to solve the problem.

Step 4. Taking into account that the investor receives only discount income, we transform the formula for income taking into account taxation (9) to the form

D = d(1 -  d) =  d0,7.

Hence, we present the expression for profitability in the form

d =
= 28%.

This expression also does not allow us to solve the problem.

Step 5. From the problem conditions it follows that:

• 
  in six months, the market value of the financial instrument will increase by 42%, i.e. the expression will be true R pr = 1.42 Z;

• 
  the cost of purchasing a share is equal to its cost and the interest paid on the bank loan, i.e.

R pok = 0.58 Z + (1+ )  0,42 Z = Z +   42 Z .

The expressions obtained above allow us to transform the formula for discount income (4) to the form

d = (P etc - R pok) = 42 Z(1 - ).

We use this expression in the formula obtained above to calculate profitability. As a result of this substitution we get

d =
= 28%.

This expression is an equation for . Solving the resulting equation allows us to obtain the answer:  = 44.76%.

From the above it is clear that this problem can be solved using the formula for solving problems that arise when using own and borrowed funds when making transactions with securities:

d =
(13)

Where d- profitability of a financial instrument;

TO - increase in exchange rate value;

 - bank rate;

 - share of borrowed funds;

 1 - coefficient taking into account income taxation.

Moreover, solving a problem like the one given above will come down to filling out a table, determining the unknown with respect to which the problem is being solved, substituting known quantities into the general equation and solving the resulting equation. Let's demonstrate this with an example.

Example 2. An investor decides to purchase a share with an expected increase in market value of 15% per quarter. The investor has the opportunity to pay 74% of the actual cost of the share using his own funds. At what maximum quarterly percentage should an investor take out a loan from a bank in order to ensure a return on invested own funds of at least 3% per quarter? Taxation is not taken into account.

Solution. Let's fill out the table:

d	TO			 1
0,03	0,15	?	1 – 0,74 = 0,24	1

The general equation takes the form

0,03 = (0,15 -  0,26) : 0,74 ,

which can be converted into a form convenient for solving:

 = (0,15 – 0,03 . 0,74) : 0,26 = 0,26 ,

or as a percentage  = 26%.

Zero coupon bonds

Example 1. The zero-coupon bond was purchased on the secondary market at a price of 87% of par 66 days after its initial placement at auction. For participants in this transaction, the yield to auction is equal to the yield to maturity. Determine the price at which the bond was purchased at the auction if its circulation period is 92 days. Taxation is not taken into account.

Solution. Let us denote  - the price of the bond at auction as a percentage of the face value N. Then the yield to the auction will be equal to

d a =
.

The yield to maturity is

d n =
.

We equate d a And d P and solve the resulting equation for  ( = 0.631, or 63.1%).

The expression that was used to solve problems that arise when making transactions with zero-coupon bonds can be represented as a formula

= K

,

Where k- ratio of yield to auction to yield to redemption;

 - the cost of GKOs on the secondary market (in shares of the nominal value);

 - the cost of state bonds at auction (in shares of the face value);

t- time elapsed after the auction;

T- bond circulation period.

As an example, consider the following problem.

Example 2. The zero-coupon bond was purchased through an initial placement (at auction) at a price of 79.96% of the nominal value. The bond's circulation period is 91 days. Specify the price at which the bond should be sold 30 days after the auction so that the yield at auction is equal to the yield at maturity. Taxation is not taken into account.

Solution. Let's present the problem condition in the form of a table:

		T	t	k
?	0,7996	91	30	1

Substituting the table data into the basic equation, we obtain the expression

( - 0,7996) : (0,7996  30) – (1 - ) : (  61).

It can be reduced to a quadratic equation of the form

 2 – 0,406354 - 0,3932459 = 0.

Solving this quadratic equation, we obtain  = 86.23%.

Discounted Cash Flow Method

General concepts and terminology

If, when comparing yields, the yield of a deposit in a bank is chosen as an alternative, then the stated general method of alternative yield coincides with the discounted cash flow method, which until recently was widely used in financial calculations. This raises the following main questions:

• 
  the commercial bank deposit rate taken as the base rate;

• 
  scheme for accruing money in a bank (simple or compound interest).

The answer to the first question is usually formulated as follows: “the rate of a reliable, stably operating bank should be chosen as the base rate.” However, this statement is true for Russian conditions with a certain degree of approximation. Everyone knows examples of “reliable, stably operating banks” that did not withstand the test of the crisis and went bankrupt. Sometimes the refinancing rate of the Central Bank of the Russian Federation is considered as a base level. However, this choice also raises objections due to the fact that the value of this indicator is not formed by the market, but is used by the Central Bank of the Russian Federation to influence the market. However, it comes to the rescue that when solving many problems, usually the bank rate, which should be taken as the base one, is specified specifically.

The second question is easier to answer: both cases are considered, i.e. accrual of interest income at simple and compound interest rates. However, as a rule, preference is given to the scheme of calculating interest income at a compound interest rate. Let us remind you that in the case of accrual of funds according to the simple interest income scheme, it is accrued on the principal amount of money deposited in the bank deposit. When accruing funds according to the compound interest scheme, income is accrued both on the original amount and on the interest income already accrued. In the second case, it is assumed that the investor does not withdraw the amount of the principal deposit and interest on it from the bank account. As a result, this operation is more risky. However, it also brings in more income, which is an additional payment for greater risk.

For the method of numerical estimation of parameters of transactions with securities based on cash flow discounting, its own conceptual apparatus and its own terminology have been introduced. We will now briefly outline it.

Increment And discounting. Different investment options have different payment schedules, which makes direct comparison difficult. Therefore, it is necessary to bring cash receipts to one point in time. If this moment is in the future, then this procedure is called increment, if in the past - discounting.

Future value of money. The money available to the investor at the present time provides him with the opportunity to increase his capital by placing it on deposit in a bank. As a result, the investor will have a large amount of money in the future, which is called future value of money. In the case of accrual of bank interest income according to the simple interest scheme, the future value of money is equal to

P F= P C(1+ n)

For a compound interest scheme, this expression takes the form

P F= P C (1 + ) n

Where R F - future value of money;

P C - the original amount of money (the current value of money);

 - bank deposit rate;

P- the number of periods of accrual of cash income.

Coefficients (1+ ) n for compound interest rate and (1 + n) for a simple interest rate are called growth rates.

The original cost of money. In the case of discounting, the problem is the opposite. The amount of money that is expected to be received in the future is known, and it is necessary to determine how much money must be invested at the present time in order to have a given amount in the future, i.e., in other words, it is necessary to calculate

P C=
,

where is the factor
- called discount factor. Obviously, this expression is valid for the case of accruing a deposit according to the compound interest income scheme.

Internal rate of return. This rate is the result of solving a problem in which the current value of investments and their future value are known, and the unknown value is the deposit rate of bank interest income at which certain investments in the present will provide a given value in the future. The internal rate of return is calculated using the formula

 =
-1.

Discounting cash flows. Cash flows are the returns received at different times by investors from investments in cash. Discounting, which is the reduction of the future value of an investment to its present value, allows you to compare different types of investments made at different times and under different conditions.

Let's consider the case when any financial instrument brings at the initial moment of time an income equal to C 0 for the period of the first interest payments - WITH 1 , second - C 2, ..., for the period n-x interest payments - WITH n . The total income from this operation will be

D=C 0 +C 1 +C 2 +… + C n .

Discounting this scheme of cash receipts to the initial point in time will give the following expression for calculating the value of the current market value of a financial instrument:

C 0 +
+
+…+
=P C. (15)

Annuities. In the case when all payments are equal to each other, the above formula simplifies and takes the form

C(1 +
+
+…+) =
P C.

If these regular payments are received annually, they are called annuities. The annuity value is calculated as

C =
.

Nowadays, the term is often applied to all the same regular payments, regardless of their frequency.

Examples of using the discounted cash flow method

Let's look at examples of problems for which it is advisable to use the discounted cash flow method.

Example 1. The investor needs to determine the market value of the bond, on which interest income is paid at the initial point in time and for each quarterly coupon period WITH in the amount of 10% of the nominal value of the bond N, and two years after the end of the bond's circulation period - interest income and the nominal value of the bond equal to 1000 rubles.

As an alternative investment scheme, a bank deposit is offered for two years with the accrual of interest income according to the scheme of compound interest quarterly payments at a rate of 40% per annum.

Solution. For To solve this problem, formula (15) is used,

Where P= 8 (8 quarterly coupon payments will be made over two years);

 = 10% (annual interest rate equal to 40%, recalculated per quarter);

N= 1000 rub. (face value of the bond);

WITH 0 –C 1 = WITH 2 - … = WITH 7 = WITH= 0,1N– 100 rub.,

C 8 = C + N= 1100 rub.

From formula (15), using the conditions of this problem, to calculate

C(1+++…+)+=(N+C
).

Substituting the numerical values ​​of the parameters into this formula, we obtain the current value of the market value of the bond, equal to P C = 1100 rub.

Example 2. Determine the price for a commercial bank to place its discount bills, provided that the bill is issued in the amount of 1,200,000 rubles. with a payment term of 90 days, bank rate - 60% per annum. The bank accrues interest income monthly using a compound interest scheme. A year is considered equal to 360 calendar days.

First, let's solve the problem using the general approach (alternative return method), which was discussed earlier. Then we solve the problem using the discounted cash flow method.

Solving the problem using the general method (alternative yield method). When solving this problem, it is necessary to take into account the basic principle that is fulfilled in a normally functioning stock market. This principle is that in such a market the profitability of various financial instruments should be approximately the same.

The investor at the initial moment of time has a certain amount of money X, to which he can:

• 
  or buy a bill and after 90 days receive 1,200,000 rubles;

• 
  or put the money in the bank and receive the same amount after 90 days.

The profitability in both cases should be the same.

In the first case (purchase of a bill), the income is equal to: D= (1200000 – X), expenses Z = X. Therefore, the return for 90 days is equal to

d 1 =D/Z=(1200000 – X)/X.

In the second case (placing funds on a bank deposit)

D= X(1 + ) 3 – X, Z = X.

d 2 - D/Z= [ X(1+) 3 - X/X.

Note that this formula uses  - the bank rate recalculated for 30 days, which is equal to

 - 60  (30/360) = 5%.

d 1 = d 2), we get the equation for calculating X:

(1200000 - X)/X-(X 1,57625 - X)/X.

X, we get X = RUB 1,036,605.12

Solving the problem using the discounted cash flow method. To solve this problem we use formula (15). In this formula we will make the following substitutions:

• 
  interest income in the bank was accrued over three months, i.e. n = 3;
• 
  the bank rate recalculated for 30 days is  - 60  (30/360) - 5%;
• 
  No intermediate payments are made on the discount bill, i.e. WITH 0 = WITH 1 = WITH 2 = 0;
• 
  after three months, the bill is canceled and a bill amount equal to 1,200,000 rubles is paid on it, i.e. C 3 = 1200000 rub.

It is necessary to determine what the price of placing a bill of exchange is, i.e. magnitude P C .

Substituting the given numerical values ​​into formula (15), we obtain the equation R With = 1,200,000/(1.05) 3 , solving which we get

P C = 1,200,000: 1.157625 - 1,036,605.12 rub.

As can be seen, for problems of this class the solution methods are equivalent.

Example 3. The issuer issues a bond loan in the amount of 500 million rubles. for a period of one year. A coupon (120% per annum) is paid upon redemption. At the same time, the issuer begins to form a fund to repay this issue and the interest due, setting aside at the beginning of each quarter a certain constant amount of money in a special bank account, on which the bank accrues quarterly interest at a compound rate of 15% per quarter. Determine (excluding taxation) the size of one quarterly installment, assuming that the moment of the last installment corresponds to the moment of repayment of the loan and payment of interest.

Solution. It is more convenient to solve this problem using the cash flow increment method. After a year, the issuer is obliged to return to investors

500 + 500  1.2 = 500 + 600 = 1,100 million rubles.

He should receive this amount from the bank at the end of the year. In this case, the investor makes the following investments in the bank:

1) at the beginning of the year X rub. for a year at 15% of quarterly payments to the bank at a compound interest rate. From this amount he will have at the end of the year X(1,15) 4 rub.;

2) after the end of the first quarter X rub. for three quarters under the same conditions. As a result, at the end of the year, from this amount he will have X(1.15) 3 rubles;

3) similarly, an investment for six months will give at the end of the year the amount of X (1.15) 2 rubles;

4) the penultimate investment for the quarter will give X (1.15) rubles by the end of the year;

5) and the last payment to the bank in the amount X coincides in terms of the problem with loan repayment.

Thus, having invested money in the bank according to the specified scheme, the investor at the end of the year will receive the following amount:

X(1,15) 4 + X(1,15) 3 + X(1,15) 2 + X(1,15) +X= 1100 million rubles.

Solving this equation for X, we get X = 163.147 million rubles.

Examples of solving some problems

Let us give examples of solving some problems that have become classic and are used in studying the course “Securities Market”.

Market value of financial instruments

Task 1. Determine the price for a commercial bank to place its bills (discounted) under the condition: the bill is issued in the amount of 1,000,000 rubles. with a payment term of 30 days, bank rate - 60% per annum. Consider a year to be equal to 360 calendar days.

Solution. When solving this problem, it is necessary to take into account the basic principle that is fulfilled in a normally functioning stock market. This principle is that in such a market the profitability of various financial instruments should be approximately the same. The investor at the initial moment of time has a certain amount of money X, to which he can:

• 
  or buy a bill and after 30 days receive 1,000,000 rubles;
• 
  or put money in the bank and receive the same amount after 30 days.

The profitability in both cases should be the same. In the case of purchasing a bill of exchange, the income is equal to: D= 1000 000 - X . Costs are: Z = X .

Therefore, the profitability for 30 days is equal to

d 1 = D/Z- (1 000 000 - X)/X.

In the second case (bank deposit), similar values ​​are equal

D - X(1+) - X; Z= X; d 2 = D/Z=[X(1+) - X]/X.

Note that this formula uses  - bank rate, recalculated for 30 days and equal to:  = 60  30/360 = 5%.

Equating the returns of two financial instruments to each other ( d 1 = d 2), we get the equation for calculating X :

(1 000 000 - X)/X- (X 1 ,05 - X)/X.

Solving this equation for X, we get

X= RUB 952,380.95

Task 2. Investor A bought shares at a price of 20,250 rubles, and three days later sold them at a profit to investor B, who, in turn, three days after the purchase, resold these shares to investor C at a price of 59,900 rubles. At what price did investor B buy the specified securities from investor A, if it is known that both of these investors secured the same profitability from the resale of shares?

Solution. Let us introduce the following notation:

P 1 - the price of shares at the first transaction;

R 2 - value of shares in the second transaction;

R 3 - value of shares in the third transaction.

The profitability of the operation that investor A was able to secure for himself:

d a = ( P 2 – P 1)/P 1

A similar value for the operation performed by investor B:

d B = (R 3 - R 2)/R 2 .

According to the conditions of the problem d a = d B , or P 2 /P 1 - 1 = R 3 /R 2 - 1.

From here we get R 2 2 = R 1 , R 3 = 20250 - 59900.

The answer to this problem: R 2 = 34,828 rub.

Profitability of financial instruments

Task 3. The nominal value of JSC shares is 100 rubles. per share, current market price - 600 rubles. per share. The company pays a quarterly dividend of 20 rubles. per share. What is the current annualized return on JSC shares?

Solution.

N= 100 rub. - par value of the share;

X= 600 rub. - market price of the share;

d K = 20 rubles/quarter - bond yield for the quarter.

Current annualized yield d G is defined as the quotient of income per year divided D on the cost of purchasing this financial instrument X:

d G = D/X.

Income for the year is calculated as the total quarterly income for the year: D= 4 d G - 4  20 = 80 rub.

Acquisition costs are determined by the market price of this financial instrument X = 600 rubles. The current yield is

d G = D/X= 80: 600 = 0.1333, or 13.33%.

Task 4. The current yield of a preferred share, the declared dividend of which upon issue is 11%, and the par value is 1000 rubles, this year amounted to 8%. Is this situation correct?

Solution. Notation adopted in the problem: N= 1000 rub. - par value of the share;

q = 11% - declared dividend of preferred shares;

d G = 8% - current yield; X = market price of the share (unknown).

The quantities given in the problem conditions are related to each other by the relation

d G = qN/X.

You can determine the market price of a preferred share:

X - qN/d G - 0.1 1  1000: 0.08 - 1375 rub.

Thus, the situation described in the conditions of the problem is correct, provided that the market price of the preferred share is 1375 rubles.

Task 5. How will the yield on an auction of a zero-coupon bond with a maturity of one year (360 days) change as a percentage compared to the previous day if the bond rate on the third day after the auction does not change compared to the previous day?

Solution. The bond yield for the auction (annualized) on the third day after it is determined by the formula
d 3 =

.

Where X- auction price of the bond, % of par value;

R- market price of the bond on the third day after the auction.

A similar value calculated for the second day is equal to

d 2 =
.

Change in percentage compared to the previous day in the bond yield at the auction:

= -= 0,333333,

or 33.3333%.

The yield of the bond before the auction will decrease by 33.3333%.

Task 6. A bond issued for a period of three years, with a coupon of 80% per annum, is sold at a discount of 15%. Calculate its yield to maturity without taking into account taxes.

Solution. The bond's yield to maturity without taking into account taxes is equal to

d =
,

Where D- income received on the bond for three years;

Z - costs of purchasing a bond;

 - coefficient recalculating profitability for the year.

The income for three years of the bond's circulation consists of three coupon payments and discount income at maturity. So it is equal

D = 0,8N3 + 0,15 N= 2,55 N.

The cost of purchasing a bond is

Z= 0,85N.

The annualized profitability conversion factor is obviously  = 1/3. Hence,

d =
= 1, or 100%.

Task 7. The share price increased by 15% over the year, dividends were paid quarterly in the amount of 2,500 rubles. per share. Determine the total return on the stock for the year if at the end of the year the exchange rate was 11,500 rubles. (taxation is not taken into account).

Solution. The return on a stock for the year is calculated using the formula

d= D/Z

Where D- income received by the owner of the share;

Z is the cost of its acquisition.

D- calculated by the formula D= + ,

where  is the discount part of income;

 - percentage of income.

In this case = ( R 1 - P 0 ),

Where R 1 - share price by the end of the year;

P 0 - share price at the beginning of the year (note that P 0 = Z).

Since at the end of the year the price of the share was equal to 11,500 rubles, and the increase in the market value of the shares was 15%, then, therefore, at the beginning of the year the share cost 10,000 rubles. From here we get:

 = 1500 rub.,

 = 2500  4 = 10,000 rub. (four payments in four quarters),

D=  +  = 1500 + 10,000 = 11,500 rub.;

Z = P 0 = 10000 rub.;

d = D/Z= 11500: 10000 = 1.15, or d= 115%.

Task 8. Bills of exchange with a maturity date 6 months from issuance are sold at a discount at a single price within two weeks from the date of issuance. Assuming that each month contains exactly 4 weeks, calculate (as a percentage) the ratio of the annual yield on bills purchased on the first day of their placement to the annual yield on bills purchased on the last day of their placement.

Solution. The annual yield on bills purchased on the first day of their placement is equal to

d 1 = (D/Z) - 12/t = /(1 - )  12/6 = /(1 - ) . 2,

Where D- bond yield equal to D= N;

N- bond par value;

 - discount as a percentage of the nominal value;

Z- the cost of the bond upon placement, equal to Z = (1 - ) N;

t- circulation time of a bond purchased on the first day of its issue (6 months).

The annual yield on bills purchased on the last day of their placement (two weeks later) is equal to

d 2 = (D/Z)  12/ t = /(1 - ) - (12: 5,5) = /(1 - ) . 2, 181818,

where  t- the circulation time of a bond purchased on the last day of its issue (two weeks later) is equal to 5.5 months.

From here d 1 /d 2 = 2: 2.181818 = 0.9167, or 91.67%.

Cash flows can be assessed and reduced to one point in time on a nominal or real basis.

Nominal cash flows and premium rates. Nominal cash flows - These are monetary amounts expressed in prices that change due to inflation, i.e. payments that will actually be paid or received at various future points (intervals) of time. When calculating them, the constant increase in the price level in the economy is taken into account, and this affects the monetary assessment of the costs and results of making an investment decision (Fig. 3.3).

For example, having decided to implement a project to open a mini-bakery for baking and selling bakery products, we must take into account the projected increase in prices for bread, flour, etc. when calculating expected cash flows. over the life of the project and index cash flows accordingly increasing coefficient.

Rice. 3.3.

Nominal rate of alternative (required) return is the rate that actually exists in the market for investment decisions of a given level of risk. During periods of high inflation, such rates increase in order to compensate investors for losses from inflationary price increases through increased income. On the contrary, nominal rates are relatively low during periods of price stabilization. Based on this, these rates are said to include inflation premium.

Real cash flows and real discount rates. Real cash flows - These are flows expressed at a constant price scale in effect at the time the investment decision is justified. Thus, they are assessed without taking into account inflationary price increases (Figure 3.4). However, cash flows must still be indexed by a decreasing or increasing factor if they (or their individual elements) grow faster or slower than inflation.

Rice. 3.4.

The real rate of alternative (required) return - This is the rate “cleared” of the inflation premium. It reflects the part of the investor's income generated in excess of compensation for inflationary price increases.

Real rate (r) calculated by the formula

Where gr - real rate; G - nominal rate; To - inflation rate. All rates are expressed in fractions of a unit.

Example. The bank interest rate on deposits is 6%, and inflation during this period is expected to be 10%. What is the real rate of return offered by the bank?

Real cash flows are discounted at real rates, nominal - at nominal rates.

The basic calculation rule is that:

• o real cash flows should be discounted at real alternative rates of return;
• o Nominal cash flows should be discounted using nominal discount rates.

Thus, there are two approaches to estimating cash flows, each of which has its own pros and cons.

Advantages and disadvantages of the valuation method in constant (fixed) prices. The advantage of an assessment on a real basis is that with an aggregated calculation of cash flows there is no need to predict future inflationary price increases - it is enough to know the current level of inflation and prices in force in the current period. At the same time, to carry out such a calculation, it is necessary to more or less strictly fulfill the following hypothesis: all prices for products, raw materials, materials, etc., accepted when determining cash flows, change in the same proportion in accordance with the level of inflation in the economy. Another “minus” is that with this approach, difficulties arise in analyzing project financing systems (interest rates on loans provided to implement an investment decision must also be adjusted to real rates, which creates distrust in the calculation results on the part of creditors). For example, they give money at 14% per annum, but the real rate appears in the calculations - 4%. In addition, the project budget drawn up on a nominal basis looks more realistic.

Let's look at the principle approach to valuation on a real and nominal basis using an example.

Example. The company manager assumes that the project will require investments of 350 million rubles. and in the first year of implementation will give a cash flow of 100 million rubles. In each subsequent year for five years, cash flow will increase by 10% due to inflationary increases in product prices and costs. In the sixth and final year, a total cash flow of 123 million rubles will be received from the sale of equipment. It is necessary to determine whether a given project is profitable if the nominal alternative rate of return is 20% per annum.

The cash flow for the project, taking into account inflationary growth, is shown in table. 3.6.

TABLE 3.6.

Net present value is calculated as follows:

YRU> Oh, that means the project is profitable.

We will evaluate the same project on a real basis. The real alternative rate of return is calculated using the formula

According to the condition, only inflationary price increases are expected. Therefore, the subsequent cash flow until the sixth year will be stable and equal to 100: 1.1 = 90.91 million rubles. The cash flow of the last year, calculated on a constant price scale, is equal to

As you can see, both methods gave almost the same result, which is explained by the same assumptions laid down in the example conditions for both approaches (the discrepancies are associated with the approximation error allowed in the calculations).

When assessing the effectiveness of investment projects, the theory, in a number of cases 1, recommends using WACC as a discount rate. In this case, it is proposed to use the profitability of alternative investments (projects) as the price of equity capital. Alternative return (profitability) is a measure of lost profits, which, according to the concept of alternative costs based on the ideas of Friedrich von Wieser on the marginal utility of costs, are considered as expenses when evaluating options for investment projects proposed for implementation. At the same time, a wide range of authors understand alternative income as the profitability of projects that have low risk and a guaranteed minimum profitability. Examples are given - lease of land and buildings, foreign currency bonds, time deposits of banks, government and corporate securities with low risk, etc.

Therefore, when evaluating two projects - analyzed A and alternative B, we must subtract the profitability of project B from the profitability of project A and compare the result obtained with the profitability of project B, but taking into account the risks.

This method allows us to make more intelligent decisions about the advisability of investing in new projects.

For example:

The profitability of project A is 50%, the risk is 50%.

The profitability of project B is 20%, the risk is 10%.

Let us subtract the profitability of project B from the profitability of project A (50% - 20% = 30%).

Now let’s compare the same indicators, but taking into account the project risks.

Profitability of project A = 30% * (1-0.5) = 15%.

The profitability of project B is 20% * (1-0.1) = 18%.

Thus, wanting to get an additional 15% return, we risk half of our capital invested in the project. At the same time, by implementing familiar and therefore low-risk projects, we guarantee ourselves an 18% return and, as a result, the preservation and increase of capital.

The approach to investment evaluation described above, justified by the theory of opportunity costs, is quite reasonable and is not rejected by practitioners.

But can alternative income be considered as capital raising costs when calculating WACC?

In our opinion no? Despite the fact that we subtracted the income of the alternative project B from the income of the evaluated project A, conditionally considering them as expenses of project A, they did not cease to be income.

The calculation discussed in table No. 1 only says that in order to fulfill your desire to receive a return of 15%, you need to ensure a return on assets of 11.5% or higher. We emphasize once again that a profitability of 15% is only your desire.

But is this your cost of equity? Maybe they are only 5% of your invested capital and why wouldn't you be happy with a 10% return like Molly?

In this case, the weighted cost of capital will not be 11.5%, but 9%, but there is income! There is profit! (9% minus 5%).

Reduce your expenses on capital, get more of it from circulation and get rich!

So how can you reduce the cost of raising equity capital to zero? Can. And this is not sedition, if you look closely at what we mean by the term “expenses”.

Expenses are not the amounts transferred by you for the goods, not the money paid to employees and not the cost of raw materials included in the costs of manufactured and sold products. All this does not take away your property, your benefits.

Expenses are a decrease in assets or an increase in liabilities.

The owner, when using his own capital, will incur expenses in two cases:

1. Payments from profits, for example: dividends, bonuses and other payments, such as taxes, etc.

2. If part or all of the equity capital is not involved in business turnover.

Let's look at this in more detail.

Let us turn to the mentioned concept of opportunity costs and the theory of the relationship between the cost of money and time.

The concept of opportunity costs suggests using as their income the income from investments in a business that has the least risk and guaranteed profitability. If we continue this logic, it becomes clear that the least risk will occur if we refuse to invest in this business. At the same time, the income will be the least. They will both be zero.

Of course, financial analysts, and simply sensible people, will immediately say that both real and relative loss of assets due to inactivity will be inevitable.

Real costs are caused by the need to maintain the quantitative and qualitative safety of capital.

Relative costs are associated with changes in the market price of assets and changes in the welfare of the company under study, relative to the welfare of other entrepreneurs.

If your capital does not work, but your neighbor’s capital functions properly and brings him income, then the greater this income, the richer the neighbor becomes relative to you. Together with your neighbor, you will receive a certain average profitability for your business, which is precisely a measure of the growth of your neighbor’s wealth and your relative losses. In other words, if you do not provide returns above the market average, then your share in the total volume operating on the capital market has decreased. This means you have incurred expenses.

What will be their size?

The calculation can be done like this.

The cost of capital is equal to the difference between the return on assets in the industry under study and the return on assets of the company.

For example. Return on assets of the manufacturing industry is 8%. Your company's return on assets is 5%. This means you have lost 3%. These are your relative expenses. This is the relative price of your capital.

Since industry profitability indicators do not fluctuate significantly, it is quite possible to predict their values ​​using the usual trend.

What does this give us? In our opinion, the following:

1. Greater opportunities for standardizing the calculation of the price of equity capital than using alternative returns, since there are quite a lot of alternative options for investing capital in a business that has low risk and guaranteed profitability.

2. The proposed approach limits liberties, and therefore, in our opinion, increases objectivity when comparing the effectiveness of various investment project options.

3. Perhaps this will reduce the mistrust of practitioners in the calculations of financial analysts. The simpler the better.

Let's go further. What happens if the company's return on assets is equal to the industry average? Will the price of equity become zero? Theoretically, yes, if there are no payments from profits. Our well-being relative to the state of the business community will not change. In practice this is unattainable. Since, there are necessarily payments and obligations arise that reduce the amount of our own capital and, accordingly, reduce the assets belonging to us. Even if the enterprise does not operate, it must pay property taxes, etc.

Therefore, the price of a company’s equity capital should consist not only of the price calculated based on the average industry return on assets, but also the price determined on the basis of dividend payments and other payments from profits, possibly including payments to the budget and extra-budgetary funds. It may be appropriate to take into account the costs associated with the stakeholder business model when calculating WACC.

When calculating WACC, factors that reduce the price of capital sources should also be taken into account. For example, the price of such a source of financing as accounts payable is the amount of fines paid by the company for late payments to suppliers. But doesn’t the company receive the same penalty payments from customers for late payments on accounts receivable?

What does the WACC indicator ultimately reflect? In our opinion, it is a measure of the economic efficiency of an existing business or investment project.

A negative WACC value indicates the effective work of the organization's management, since the organization receives economic profit. The same applies to investment projects.

The WACC value within the range of changes in return on assets from zero to industry average values ​​indicates that the business is profitable, but not competitive.

The WACC indicator, the value of which exceeds the industry average return on assets, indicates an unprofitable business.

So, end of the WACC speculation? No. Corporate mysteries lie ahead.

“If you don’t deceive, you won’t sell, so why frown?
Day and night - a day away. Next, how will it turn out"