The concept of alternative returns and the concept of the weighted average cost of capital. Basic concepts and formulas
Estimating cash flows and bringing them to one point in time can be done on a nominal or real basis.
Nominal cash flows and memorial rates. Nominal cash flows - these are amounts of money 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, a 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 of opening a mini-bakery for baking and selling bakery products, we must take into account the projected increase in prices for bread, flour, etc. in the calculations of expected cash flows. over the life of the project and index the cash flows accordingly raising 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 a period of high inflation, such rates increase in order to compensate investors for losses from inflationary price increases due to increased income. Conversely, 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 estimated without taking into account inflationary price increases (Fig. 3.4). However, cash flows should still be indexed by a decreasing or increasing coefficient if they (or their individual elements) grow faster or slower than inflation.
Rice. 3.4.
The real rate of the alternative (required) return is this is the rate "cleared" of the inflation premium. It reflects the part of the investor's income that is formed in excess of compensation for inflationary price increases.
Real rate (g) 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 at the level of 10%. What is the real rate of return offered by the bank?
Real cash flows are discounted at real rates, nominal - at nominal.
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 pros and cons.
Advantages and disadvantages of the valuation method at constant (fixed) prices. The advantage of estimating on a real basis is that with an aggregated calculation of cash flows there is no need to predict future inflationary price growth - it is enough to know the current level of inflation and current prices in the current period. At the same time, to carry out such a calculation, more or less strict fulfillment of the following hypothesis is necessary: all prices for products, raw materials, materials, etc., taken in determining cash flows, change in the same proportion in accordance with the level of inflation in the economy. Another "minus" - with this approach, there are difficulties in analyzing project financing systems (interest rates on loans provided for the implementation of an investment decision must also be brought to real rates, which gives rise to distrust of the calculation results on the part of creditors). For example, they give money at 14% per annum, and the real rate appears in the calculations - 4%. In addition, the budget of the project, drawn up on a nominal basis, looks more realistic.
Let's consider a principled approach to valuation on a real and nominal basis using an example.
Example. The manager of the company assumes that the project will require investments in the amount 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 growth in product prices and costs. For 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 this project is profitable if the nominal rate of alternative 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:
ypy> Oh, so the project is profitable.
We will evaluate the same project on a real basis. The real alternative rate of return is calculated by the formula
According to the condition, only inflationary growth in prices is expected. Therefore, the subsequent cash flow up to 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 can be seen, both methods gave almost the same result, which is explained by the same assumptions laid down in the conditions of the example for both approaches (the discrepancies are due to the approximation error allowed in the calculations).
We conduct classical fundamental analysis ourselves. We determine the fair price according to the formula. We make an investment decision. Features of the fundamental analysis of debt assets, bonds, bills. (10+)
Classical (fundamental) analysis
Universal formula for a fair price
Classical (fundamental) analysis based on the premise that the investee has a fair price. This price can be calculated using the formula:
Si - the amount of income that will be received from investment in the i-th year, counting from the current to the future, ui - the alternative return on investment for this period (from the current moment to the payment of the i-th amount).
For example, you purchase a bond with maturity in 3 years with a lump sum payment of the entire amount of principal and interest on it. The amount of payment on the bond, together with interest, will be 1,500 rubles. Let us determine the alternative return on investments, for example, by the return on a deposit in Sberbank. Let it be 6% per annum. The opportunity return is 106% * 106% * 106% = 119%. The fair price is equal to 1260.5 rubles.
The above formula is not very convenient, since the alternative return is usually assumed by years (even in the example, we took the annual return and raised it to the third power). Let's convert it to the annual alternative return
here vj is the alternative return on investment for the jth year.
Why are all assets not worth their fair price?
Despite its simplicity, the above formula does not allow you to accurately determine the value of the investment object, as it contains indicators that need to be predicted for future periods. The alternative return on investment in the future is unknown to us. We can only guess what rates will be in the market at that moment. This introduces especially large errors for instruments with long maturities or without them (stocks, consoles). With the amount of payments, too, not everything is clear. Even for debt securities (fixed-income bonds, bills of exchange, etc.), for which, it seems, the payment amounts are determined by the terms of issue, the actual payments may differ from the planned ones (and the formula contains the amounts of real, not planned payments ). This occurs when a debt is defaulted or restructured, when the issuer is unable to pay the full amount promised. For equity securities (shares, shares, shares, etc.), the amounts of these payments generally depend on the performance of the company in the future, and, accordingly, on the general economic situation in those periods.
Thus, it is impossible to accurately calculate the fair price using the formula. The formula gives only a qualitative idea of the factors affecting the fair price. Based on this formula, it is possible to develop formulas for a rough estimate of the asset price.
Estimation of the fair price of a debt asset (with fixed payments), bonds, promissory notes
In the new formula, Pi is the amount promised to be paid in the relevant period, ri is the discount based on our assessment of the reliability of investments. In our previous example, let us estimate the reliability of investments in Sberbank as 100%, and the reliability of our borrower as 90%. Then the estimate of the fair price will be 1134.45 rubles.
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When evaluating the effectiveness of investment projects, theory, in some cases 1 , recommends using WACC as the discount rate. At the same time, it is proposed to use the profitability of alternative investments (projects) as the price of equity capital. Alternative profitability (profitability) is a measure of lost profit, which, according to the concept of alternative costs based on the ideas of Friedrich von Wieser about the marginal utility of costs, is considered as an expense when evaluating options for investment projects intended for implementation. At the same time, a wide range of authors understand alternative income as the profitability of projects that have low risk and guaranteed minimum profitability. Examples are given - rent of land and buildings, foreign currency bonds, time deposits of banks, government and corporate securities with a low level of 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 with the profitability of project B, but taking into account risks.
This method allows us to make more intelligent decisions about the feasibility 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 from the profitability of project A the profitability of project B. (50% - 20% = 30%).
Now let's compare the same indicators, but taking into account the risks of projects.
Profitability of project A = 30% * (1-0.5) = 15%.
Profitability of project B - 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 the usual, 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 assessment described above, based on the theory of opportunity costs, is quite reasonable and is not rejected by practitioners.
But, can alternative incomes be considered as capital expenditures 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 the expenses of the project A, they did not cease to be income.
The calculation considered in Table No. 1 only says that in order to fulfill your desire to receive a yield of 15%, you need to ensure a return on assets of 11.5% or more. Once again, we emphasize that a yield of 15% is only your desire.
But what is your cost of equity? Maybe they are only 5% of the capital invested and why shouldn't you be happy with a 10% return like Molly's?
In this case, the weighted cost of capital will not be 11.5%, but 9%, but there is an income! Profit - yes! (9% minus 5%).
Reduce your capital costs, get more of it out of circulation and grow rich!
So what can 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 amounts transferred by you for goods, not money paid to employees and not the cost of raw materials and materials included in the costs of manufactured and sold products. All this does not take away from you your property, your benefits.
An expense is a decrease in the value of assets or an increase in liabilities.
The owner, when using his own capital, will incur expenses in two cases:
1. Payments from profit, for example: dividends, bonuses and other payments, such as taxes, etc.
2. If part or all of the own capital is not involved in business turnover.
Let's dwell on this in more detail.
Let us turn to the mentioned concept of opportunity costs and the theory of the dependence of the cost of money and time.
The concept of opportunity costs proposes to use as their income from investments in a business that has the least risk and guaranteed profitability. If we continue this logic, it will become clear that the least risk will occur when refusing to invest in this business. In this case, the income will be the least. They will both be zero.
Of course, financial analysts, and just sane people, will immediately say that both the real and the relative consumption of assets during inactivity will be inevitable.
Real costs are caused by the need to maintain the quantitative and qualitative preservation 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, and the neighbor's capital functions properly and brings him income, then the more 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 the measure of the neighbor's wealth growth and your relative losses. In other words, if you do not provide a return above the market average, then your share in the total volume of capital operating in the capital market has decreased. So you have incurred expenses.
What will be their size?
The calculation can be done like this.
Capital expenditure 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 lost 3%. These are your relative costs. This is the relative price of your capital.
Since sectoral profitability indicators do not have significant fluctuations, 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 cost of equity calculations than using alternative returns, since there are a lot of alternative options for investing in a business that has a low risk and guaranteed return.
2. The proposed approach limits the liberties, and therefore, in our opinion, increases objectivity when comparing the effectiveness of various options for investment projects.
3. Perhaps this will reduce the distrust 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 profitability? The cost of equity will become equal to zero? Theoretically - yes, if there are no payments from the profit. Our welfare relative to the state of the business community will not change. In practice, this is not achievable. Because there are bound to be payments and obligations arise that reduce the value of our own capital and, accordingly, reduce the assets owned by us. Even if the enterprise does not work, it must pay property taxes, etc.
Therefore, the price of the company's equity capital should consist not only of the price calculated on the basis of the industry average return on assets, but also the price determined on the basis of dividend payments and other payments from profit, possibly including payments to the budget and extra-budgetary funds. It may be correct to take into account the costs associated with the stakeholder business model when calculating the WACC.
When calculating WACC, factors that reduce the price of capital sources should also be taken into account. For example, the price of a source of financing, such as accounts payable, is the amount of penalties paid by the company for late payments to suppliers. But doesn't the company receive the same penalty payments from buyers for late payments on receivables?
What does the WACC score reflect in the end? 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, as the organization receives economic profit. The same applies to investment projects.
The value of WACC within the range of change in return on assets from zero to the value of industry average values indicates that the business is profitable, but not competitive.
A WACC that exceeds the industry average return on assets indicates a loss-making business.
So, the end of the discussion about WACC? No. Ahead of the mysteries of corporations.
“If you don’t cheat, you won’t sell, so why frown?
Day and night - a day away. Further, how to get "
We have dealt with the concepts of cash flow. Now, in order for us to calculate the cost of an investment project, we must decide on the procedure for determining the discount rate. Consider three main points: alternative rates, the WACC model - the weighted average cost of capital model, the CAPM model - the model for estimating the cost of capital assets.
Discount rate based on alternative rate
As for alternative rates in determining the discount rate, the rate that we will use in , we will give some of them.
Alternative rate based on stock index
You can take the return of the stock index for the period as the discount rate.
Alternative rate based on investors' desired return
You can conduct a survey among your investors on the subject of what they want to have a return 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 analyze the market and see what other similar projects, with the same risk, and what are the discount rates. 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 7%, 6%, 7.2%, 6.4% can be found as an average as an option.
Alternative rate based on no risky return
There may be such an option. Determine the risk-free return and add a risk premium to it. Risk-free returns are, in principle, calculable. The risk premium can be determined based on ratings. If the company that implements 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 rate is understood as such a financial instrument, investing in which you do not bear any risk. It is obvious that in practice this is practically unrealistic, and therefore the phrase “maximally risk-free instrument” is more common, respectively, “maximum risk-free rate”. In order to determine the maximum risk-free rate, you need to find an instrument with the least risk. The measure of risk is the standard deviation. This is a term from statistics, and it means how much the quote fluctuates on average from the average value up and down.
We note the following, you use yield to calculate the standard deviation and you get the following construction at the output. Example: A stock has an average annual return of 10%, a standard deviation of 3%. What does this mean? This means that the average annual yield of this security fluctuated in the range from 13% to 7%.
As practice shows, bonds have the smallest standard deviation, and these papers are certainly more reliable than stocks. The market value of these securities fluctuates much 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, government bonds are immediately taken for such calculations. Their risk is less than the risks of corporate papers, less than the risks of regional and municipal bonds. If we take countries, then we choose American bonds as a basis. In Russia, this may be Russian federal loan bonds.
Discount rate based on WACC model weighted average cost of capital
Formula 1 shows that if we take the data of the company as a basis, we can calculate how much the capital raised by this company costs. 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. This formula has weights. They correspond to the weight of each funding source in the capital structure. In this formula, T stands for income tax or corporation tax. The fact is that interest payments on bonds and bank loans are paid out of profit before tax. A dividend on shares is paid after tax. Therefore, these two parameters, the cost of debt and the value of shares will not be comparable. It needs to be brought to a common denominator. In fact, using the (1-T) multiplier, we bring the cost of debt capital to a comparable to the cost of shares in view. Usually WACC is calculated based on balance. Unfortunately, the use of balance data does not allow taking 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 is the value of the respective parts of the capital
Discount rate based on the CAPM capital asset valuation model
This model is mainly for stock valuation. She has an interesting history. 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 as a standard deviation. If we look at Chart 1, we have stock risk on one axis, and the number of stocks 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 is reduced. But what is interesting, starting from some 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, the risk of which cannot be eliminated under any circumstances. And the market pays 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 risk. If you take both risks, that's your problem. If you want to invest, you are taking on two risks: one you get paid, one you don't get paid, and you take unpaid, excessive risk. Therefore, one should build a portfolio and try to avoid unnecessary risk.
Graph 1 Dependence of the risk of shares on their number in the portfolio
Based on the noted fact that the 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 the paper and the average yield of the market. If the yield of the market changes, then the yield 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 - profitability of the company's shares
The coefficient β carries a simple meaning. Example: A company has a β coefficient of 2. This means that every time the market yield changes by one percent, your paper's yield will change by 2%. If the β coefficient is 3. This means every time the market returns change by 1%, your security returns change by 3%. Or should change. If the coefficient β is -1, what does it mean? This means that for every unit the market falls, your stock must rise 1 unit. If you have a coefficient of 0.5. This means that for every unit of market growth, your stock grows by 0.5. This is a good ratio, it allows you to choose securities in such a way as to build a certain kind of portfolios - aggressive, defensive and others.
We considered several options for determining the discount rate, and before that we analyzed issues related to the definition. In each individual case, you need to conduct separate studies and logically justify one or another discount rate. There are no universal rules, formulas for determining the discount rate. Having made a choice, market analysis, you have to choose the discount rate that seems to you the most acceptable.
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