When designing a bonded loan, the company calculates the parameters of the bonds (issue volume, coupon rate, circulation period, etc.), and also calculates the price at which the bonds can be sold on the market. Investors, in turn, evaluate the parameters of the issue and determine the price at which they are willing to purchase these bonds. The issue of bonds will take place only if the interests of the company and investors on the price of bonds coincide.

An investor, when purchasing a bond, expects to receive periodic coupon payments, but at the expiration of the bond to receive its face value. At the same time, the buyer of the bond proceeds from the fact that coupon payments will bring him a certain return on invested capital. However, these payments (coupon payments and redemption at par) will occur in the future, and the bond must be purchased today. Therefore, it is necessary to estimate the future cash receipts from the bond.

Bond price

In general, the current price of a bond can be represented as the value of the expected cash flow, reduced to the current moment in time. The cash flow consists of coupon payments and the face value of the bond paid at maturity. Thus, the price of a bond is the present value of the coupon payments and the lump sum of the bond's face value at maturity.

The price of a bond is determined by the formula

where FROM - coupon payments; G - required return; H is the face value of the bond; P - number of years to maturity of the bond.

If an enterprise issues a three-year bond with a nominal value of 1000 rubles. with a coupon rate of 12%, at which coupon payments are made once a year and the market interest rate for similar bonds is 15% per annum, the entity can calculate the selling price of bonds using the above formula

With a fixed coupon rate of 12%, the company will not be able to sell the bonds at face value. This is due to the fact that the market yield of similar financial instruments is 15% per annum, and the company will pay only 12% on coupons. Therefore, investors will not agree to purchase bonds at face value, the company will have to reduce the price, and when it reaches the equilibrium level of 931.5 rubles. for the bond, then the transaction of purchase and sale of the bond will be completed. If the company wants to save on coupon payments (for example, set them at 8% per annum), then it will have to further reduce the sale price in order for investors to purchase bonds.

Coupon payments can be made several times during the year: quarterly or semi-annually (see Chapter 2). If payments are made several times a year, then the above formula is somewhat modified and looks like this:

where T - number of coupon payments during the year.

Consider the previous example of a three-year bond with the same parameters, but coupon payments are made twice a year. In this case, the price of the bond is:

According to these bonds, the enterprise will make six coupon payments of 60 rubles each during the period of their validity. every. As we can see, the price of the bond with semi-annual coupon payments is higher and amounts to 939.1 rubles. This is due to the fact that coupon payments are made not at the end of each year, but half-yearly. The investor receives funds earlier, which he can use for his needs. Therefore, for earlier arrivals Money he is willing to pay a higher amount for the bond.

Due to the fact that transactions with securities are carried out constantly, bonds are sold (purchased) during the entire period of their circulation. The day of the transaction in most cases does not coincide with the beginning of the coupon period. The bond can be purchased on any day of the current coupon period. Therefore, when determining the price of a bond, it should be taken into account that not an integer, but a fractional number of coupon periods remains before the maturity date, and the seller of the bond must be reimbursed for the accumulated coupon income. In this case, the price of the bond, at which the coupon income is paid once a year, is determined by the formula

where FROM - the amount of coupon payments; G - yield to maturity (discount rate); P - the number of years to maturity of the bond; i- ordinal number of the year from the current date; H is the face value of the bond; k- share of the coupon period from the date of purchase of the bond to the date of its end;

where t- the number of days from the moment of the transaction to the date of payment of the next coupon.

Example. Determine the price of a bond with a par value of 1000 rubles, at which a coupon income of 10% is paid annually. Discount rate - 15%. The bond was purchased on the 60th day of the coupon period. There are 2 years and 305 days left until maturity.

Solution. To find the price of a bond, we calculate the fraction of the coupon period from the date of purchase to the date of coupon payments:

Thus, the investor will receive the income on the first coupon in 305 days from the date of purchase of the bond, which is 0.84 of the duration of the coupon period. The second coupon will be received in 1.84 years and the third - in 2.84 years from the date of purchase.

In this case, the bond price can be calculated as follows:

If coupon payments are made several times during the year, then the above formula is slightly modified. Instead of the number of full years, it is necessary to take the number of coupon payments. In this case, the fractional part of the coupon period is determined taking into account the number of days in the coupon period. If the number of coupon payments per year T, then in the formula for determining the price of a bond, the indicators i And P are multiplied by T, and the value k is determined by the formula

where t- the number of days from the date of the transaction to the date of the next coupon payments; T - number of days in the coupon period.

When borrowing for a short period of time, enterprises sometimes resort to the issuance of non-counon bonds, which are sold to investors at a discount but at a price below par. A zero-counon bond can be thought of as a special case of a coupon bond, except that all coupons are zero. Therefore, the price of a zero-coupon bond is calculated by the formula

A distinctive feature of zero-coupon bonds, as mentioned above, is a short circulation period (up to a year). In this case n> which in the formula shows the number of years to maturity, is obtained as a fractional value. In order not to raise to a fractional power, in practice a simplified formula for calculating the cost of zero-coupon bonds is widely used:

where t- the number of days until the maturity of the bond; G - market annual return.

Example. Determine the price of a zero-coupon bond with a face value of 1000 rubles, which is issued by a company with a circulation period of 182 days. The market interest rate for bonds of the same type is 15% per annum. Under these conditions, the price of the bond

Bonds have a face value (nominal) and a market price. The face value of the bond is printed on the face of the security itself and indicates the amount that is borrowed and payable at the end of the circulation period. As a rule, bonds are issued with a high face value and are designed for wealthy investors. In this they also differ from shares, the value of which is calculated for the acquisition of a wide range of persons, while if for shares the par value is a rather conditional value (since shares are sold and bought at a price that is in no way related to the par value), then for bonds the par value is very important parameter. This is due to the fact that according to the initially fixed value of the nominal value, the bonds will be redeemed at the end of their circulation period.

From the moment of issue to maturity, bonds are sold and bought at market prices. The market price at the time of issue may be below par, equal to it, or higher. From the moment of issue, the market price of bonds is determined based on the situation on the market, as well as two main elements:

• 1) prospects to receive the face value upon redemption (the closer the maturity date, the higher the market price of the bond);
• 2) rights to a regular fixed income (the higher the interest income, the higher the market price).

Determining the market price of a bond depends primarily on the form of income that it brings to its owner. In this regard, there are:

1) zero-coupon bonds, or discount bonds, on which the investor receives income in the form of a discount. The pricing of a zero-coupon bond consists in determining the value of the elementary stream of payments, according to known values ​​of the face value, the risk-free interest rate (or expected return), and the investment period. Thus, the current price of the bond is:

where N is the face value of the bond.

At the same time, the market price of this bond will never exceed the nominal value, since upon redemption, the investor will receive only the nominal value of the bond.

The nominal value of a zero-coupon bond is 1,000 rubles. In the market, the return on an investment with a level of risk corresponding to this bond is estimated at 20%. The maturity of the bond is 3 years. Calculate the current (market) value.

2) bonds with constant coupon income. The coupon rate on such bonds is fixed and remains unchanged throughout the entire period of its circulation. The market price of such a bond is determined as

where C - coupon;

N - face value;

n is the number of years to maturity of the bond;

r - yield to maturity.

The market price of these bonds can be either higher or lower than the face value, depending on the investor's expected yield and the coupon rate. In formula (21), such a concept as yield to maturity (yield to maturity) appeared - this is the yield per year that an investor will provide himself if, having bought a bond, he holds it until maturity.

The nominal value of the bond is 10,000 rubles, the coupon is 20%, the yield to maturity is 15%, three years remain until maturity. Calculate the market price of the bond.

In this case, the price of the bond was higher than the par value. This situation is explained by the fact that, according to the conditions of the example, the market requires a yield to maturity of the bond at the level of 15% per annum. However, it pays a higher coupon - 20%. How can an investor get a lower return than 20%? This is only possible if he purchases the bond at a price above par. When the bond is redeemed, he will only be paid face value. Therefore, the amount of the premium that he paid in excess of face value will reduce the profitability of his operation to 15%. Since the denominations of different bonds differ, the exchange rate is used to compare the market prices of bonds. The rate of a bond is the value of the market price of a bond, expressed as a percentage of its face value:

where K is the bond rate;

P is the market price of the bond;

N is the nominal price of the bond.

Calculate the bond rate if it is known that the market price of the bond is 500 rubles, and the nominal price is 600 rubles.

A bond is characterized by a nominal value and a market price.

nominal value(nominal price) - the face value indicated on the bonds or announced by the issuer when placing the bonds. The face value is the base value for calculating the income generated by the bond. Bonds are redeemed at the initially fixed par value.

Purchase and sale of bonds is carried out at prices established in the market. Factors that shape the market price of a bond:

The situation in the financial market as a whole;

The prospect of receiving the face value of the bond upon redemption (the closer the maturity date of the bond at the time of purchase, the higher its market value);

The right to a regular fixed income (the higher the income, the higher the market value of the bond).

Bond rate- the value of the market price of the bond, expressed as a percentage of its face value:

where Ko is the bond rate;

Рр - the market price of the bond;

H is the face value of the bond.

The total return on a bond is made up of the following elements:

Periodically paid interest (coupon income) - a series of payments made at fixed time intervals for a certain number of periods (annuity);

Changes in the value of the bond for the relevant period;

Income from the reinvestment of interest received.

When evaluating bonds, it is of primary importance the concept of current (present) value, which, in general, is understood as the amount of money that an investor must pay for a financial asset so that at certain intervals this asset brings him the required amount of money. The basis for determining the current value is the discounting formula:

, (3.2)

where Po is the current value of the bond at some point in time (t=0);

Ct - periodic coupon payments on the bond;

H is the face value of the bond;

i - percentage discount rate;

n is the number of periods after which coupon payments are made.

To determine the current value of a bond, four parameters must be known:

* amount of coupon payments and face value;

* the frequency of receipt of coupon payments, determined by the value of t;

* Duration of the bond circulation period;

* interest rate i, at which cash flows are discounted.

If the bond is a discount (with a zero coupon), then the formula for calculating the present value is as follows:

. (3.3)

If coupon payments on bonds are made several times a year (m times), then the formula for calculating the present value takes the following form:

. (3.4)

The current value of bonds is a benchmark for the formation of market prices.

Bond yield. In general, profitability is a relative indicator that characterizes the income per unit of costs. Bond yields can be calculated in various ways:

Current yield;

Yield to maturity (full or final yield).

Current yield characterizes the annual (current) receipts on the bond relative to the costs incurred during its acquisition. The current yield of a bond is calculated as follows:

The current yield is the simplest characteristic bonds. Using only this indicator, it is impossible to choose the most effective bond for investing funds, since the calculation of the current yield does not reflect the change in the value of the bond over the period of its ownership.

Yield to maturity (full yield) characterizes the total income on the bond attributable to the unit of costs for its acquisition. This indicator is calculated as follows:

where n is the number of years the investor has owned the bond.

The change in the value of a bond is equal to the difference between the par value and the purchase price if the investor holds the bond to maturity. If an investor sells a bond without waiting for maturity, then the change in value is measured by the difference between the sale and purchase price of the bond.

A bond is an interest-bearing debt instrument, a security that evidences a loan has been granted by its holder. A bond is a security that certifies a loan relationship between its owner (creditor) and the person who issued it (borrower).

The current Russian legislation defines a bond as an emissive security that secures the right of its holder to receive from the issuer of the bond, within the period stipulated by it, its nominal value and the percentage of this value fixed in it or other property equivalent. Thus, a bond is a debt certificate, which includes two main elements: the obligation of the issuer to return to the bondholder at the expiration of the amount indicated on the face of the bond; the obligation of the issuer to pay the bondholder a fixed income in the form of a percentage of the face value or other property equivalent.

Fundamental properties of bonds: 1) Certificate of loan; 2) The final maturity date; 3) Seniority before the shares in the payment of% and in liquidation; 4) Do not give the right to manage; 5) Mandatory payments%.

Advantages and disadvantages of issuing bonds for the issuer

Advantages: 1) Cheaper way of borrowing compared to a bank loan. 2) Longer borrowing period compared to bank loans. 3) The possibility of attracting significant amounts of resources. 4) Flexibility of financing. 5) No need to secure bond loans with the issuer's assets. 5) Creation of a public credit history issuer.

Disadvantages: 1) The need for market research. 2) Possible increase in transaction costs associated with the placement and servicing of the bond issue. 3) Problems arising from the possible restructuring of the issuer's company.

Bond collateral. Such securities are issued under the pledge of specific property - land or securities owned by the issuing company. In case of non-payment of the debt and interest on it, the pledge is sold, the proceeds from which go to satisfy the claims of the bond holder. A mortgage is issued - a type of debt obligation under which the creditor, in the event of non-repayment of the debt by the borrower, receives one or another real estate (land, buildings) or financial collateral (securities of securities of other companies owned by the issuer). Covered bonds are senior bonds. Depending on the type of collateral, bonds are distinguished: 1) with collateral in the form of securities and real estate; 2) with a guarantee; 3) with a bank guarantee; 4) with a state or municipal guarantee.

Types of bonds. There is a wide variety of bonds, to describe their types, we classify bonds according to a number of features. We can propose the following classification: 1. Depending on the issuer, bonds are distinguished 1) state, 2) municipal, 3) corporate, foreign.

2. Depending on the terms for which the loan is issued, there are: 1) bonds with a specified maturity date (short-term, medium-term, long-term); 2) bonds without a fixed maturity (perpetual, callable bonds, redeemable bonds, renewable bonds, deferred bonds).

3. Depending on the order of ownership: 1) registered (ownership rights are confirmed by entering the name in the text of the bond); 2) bearer (possession rights are confirmed by a simple presentation of the bond).

4. According to the purposes of the bonded loan: 1) ordinary (issued to refinance the issuer's debt); 2) targeted (funds from the sale of these bonds are used to finance specific investment projects).

5. According to the method of placement 1) freely placed, 2) forcedly placed.

6. Depending on the form in which the borrowed amount is reimbursed 1) with reimbursement in cash, 2) with reimbursement in kind.

7. According to the nominal redemption method: 1) redemption by a single payment; 2) repayment for a certain period of time; 3) sequential repayment with a fixed share of the total.

8. Depending on the payments made by the issuer: 1) bonds on which only interest is paid; 2) bonds on which capital is returned at face value, but interest is not paid; 3) bonds on which interest is not paid until maturity; 4) bonds for which a fixed income and the nominal value of the bond are periodically paid when it is redeemed.

9. By the nature of circulation 1) non-convertible, 2) convertible - exchange of bonds for shares of this issuer.

10. Depending on the collateral 1) unsecured, 2) secured by collateral.

11. Depending on the degree of protection of investors' investments: 1) reliable bonds worthy of investment; 2) junk bonds of a speculative nature.

12. Periodic payment of income on bonds in the form of interest is made on coupons. A coupon is a cut coupon with a coupon (interest) rate indicated on it. According to the methods of payment of coupon income, bonds are allocated: 1) with a fixed coupon rate; 2) with a floating coupon rate; 3) with a uniformly increasing coupon rate over the years of the loan; 4) at minimum or zero coupons; 5) with payment by choice.

A bond has the following price characteristics: face value (or nominal price), issue price, redemption price, market price. The cost characteristics of bonds include: nominal price; issue price; redemption price; bond rate; market price; market value of the bond.

Nominal price - the value in monetary units, which is indicated on the bonds. Bonds, as a rule, are issued with a fairly high par value compared to other securities. The issue price is the price at which bonds are sold to their first owners. It can be equal to, less than or greater than the face value, this is determined by the type of bond and the terms of issue. The redemption price is the price paid to bondholders at the end of the loan term. In most cases, the redemption price of a bond is equal to its face value (the redemption price level is fixed at the time of issue), but may differ from the nominal price. Bond rate - the ratio of the market price of a bond to its face value, expressed as a percentage.

Market price is the market price at which bonds are sold in the secondary bond market. Although each bond has a strictly defined face price, issue price, and redemption price (the level of which is fixed when the bond is issued) of the loan, the market price of a bond in the free market can change significantly over the life of the bond - it fluctuates relative to the theoretical market value of the bond, which, according to essentially, acts as the estimated market price of the bond.

The market value of a bond is the calculated theoretical value, the most likely expected price for a possible sale at a given moment in the free market. The market value is usually calculated by a professional appraiser commissioned by the investor. The general approach to determining the theoretical (market) value of any security is as follows: in order to determine how much, in the opinion of a given investor, an appraiser should cost a security at a given point in time, it is necessary to discount all income that the owner expects to receive during the time of possession of the security.

Depending on the method of paying interest income, two types of bonds can be distinguished:

Bonds with periodic payment of interest income (coupon bonds);

Zero-coupon (or discount) bonds, the income on which is formed from the difference between the redemption price of the bond and the issue price and is paid when the bond is redeemed.

Bonds have a face value (face value) and a market price. The nominal price of the bond is printed on the bond itself and indicates the amount that is borrowed and repayable at the expiration of the bond loan. The nominal price is the base value for calculating the income generated by the bond.

The interest on the bond is set to the face value, and the increase (decrease) in the cost of the bond for the corresponding period is calculated as the difference between the nominal price at which the bond will be redeemed and the purchase price of the bond.

The market price of bonds also depends on a number of other conditions, the most important of which is the reliability (degree of risk) of investments.

Since the denominations of different bonds can differ significantly from each other, there is often a need for a comparable measure of market prices for bonds. This indicator is the course.

The rate of a bond is the value of the market price of a bond, expressed as a percentage of its face value.

In practice, quite often, for example, when the issuer determines the parameters of the issued bonded loan, the investor chooses when buying a particular bond and the formation of optimal investment portfolios by professional market participants, there is a need to establish the financial efficiency of a bonded loan, which boils down to determining the yield of bonds.

In general, profitability is a relative indicator and represents the income per unit of costs. Distinguish between current yield and full, or final, yield of bonds. The current yield indicator characterizes the annual (current) receipts on the bond relative to the costs incurred to purchase it.

The current yield of a bond is the simplest characteristic of a bond. Using only this indicator, it is impossible to choose the most effective bond for investing funds, since another source of income is not reflected in the current yield - the change in the value of the bond over the period of its ownership. Therefore, on bonds with a zero coupon, the current yield is zero, although they bring income in the form of a discount.

Both sources of income are reflected in the indicator of the final, or full, yield, which characterizes the total income on the bond per unit of cost for the purchase of this bond per year. There are two important factors that affect bond yields. It's inflation and taxes. If the yield on the bond is 14% per year, and the inflation rate is 13%, then the real yield will be only 1%. If the inflation rate rises to 14% or more, then investors - holders of bonds with a fixed income of 14% - will have the prospect of receiving zero income or even incur losses. Therefore, under conditions of inflation, investors avoid investing in long-term bonds (although issuers are undoubtedly interested in them) in order to maintain the return on their own investments at a level commensurate with the base rate of return - the refinancing rate. Taxes reduce the yield on bonds, and hence their yield. Given all of the above, the real yield of certain bonds should be calculated after deducting taxes paid from income, taking into account inflation. These profitability indicators should be compared, choosing the most effective objects for investment.

Cost characteristics of the bond. Bonds tend to have a relatively high par value and are targeted at wealthy individual and institutional investors. This is one of their differences from shares, whose par value is set for a wider range of investors. If for shares the nominal value is a rather conditional value, because. Since they are bought and sold mainly at prices that are not tied to face value, then for bonds the face value is an important parameter, the value of which does not change during the entire term of the bonded loan.

1. Bond rate. From the moment bonds are issued to maturity, they are sold and bought at market prices. The market price at the time of issue may be below the face value, equal to it, or exceed the face value. In the future, the market price of bonds is determined based on the situation prevailing in the stock and financial markets, as well as depending on the two main qualities of the loan itself. Namely: a) Prospects for obtaining the nominal value of the bond when they are redeemed (the closer the maturity date at the time of purchase of the bond, the higher its market price.) b) The right to receive a regular fixed income (the higher the income generated by the bond, the higher its market price).

The market price of a bond also depends on other factors. For example, the risk of investment, the reliability of the issuing company. Since the denominations of various bonds can vary significantly, there is often a need for a comparative measurement of their market prices. Such a measure is the bond rate, which is the value of its market price, expressed as a percentage of the face value.

Ko \u003d Tsr / But * 100%, Ko - bond rate; Цр is the market price of the bond; But is the face value of the bond.

2. Discount and interest income on the bond. Bonds, like other securities, are an object of investment and bring income to their owners. The total income on the bond includes the following components: a) periodically paid interest b) change in the value of the bond for a certain period of time; c) income from the reinvestment of interest paid. Bonds provide holders with a fixed current income. It is a so-called permanent annuity, i.e. the right to receive a fixed amount of money for a number of years. Bonds typically pay interest once or twice a year. The more often they (%) are paid, the more potential income the bonds bring, since the interest received can be reinvested.

The amount of interest income on a bond depends primarily on its reliability, i.e. on the stability of the company that issued it - the issuer. The more stable the issuer and the more reliable the bond, the lower the percentage of payments on it. There is also a relationship between the maturity of a bond and the amount of interest income - the longer the circulation period of a bond, the higher the percentage of income on it. However, bonds can be zero-coupon and sold at a price below par. When buying and selling such bonds, it is required to determine the optimal price at which the bond should be sold today, if the amount of income that will be received in the future and the current rate of return on the financial market are known (the refinancing rate is taken as the basis). The process of determining this price is called discounting, and the price itself is called the present value of future income.

Cd = But/ (1+ Λ*Ps/100%), Cd is the selling price of the bond with a discount; But - face value; Λ is the number of years of repayment; Ps - the rate of loan interest.

3. Bond yield. The total return generated by bonds is generally lower than for other types of securities. This is due to the higher reliability of bonds, compared, for example, with shares.

When determining the parameters of bonded loans, choosing bonds by investors, etc. there is a need for a comparative assessment of the effectiveness of bonded loans. This assessment comes down mainly to determining the yield of bonds.

The yield of bonds is divided into current and full.

The current yield is the simplest characteristic of a bond and characterizes the amount of income received from the bond for the current period of time, usually a year.

Dt = (Pg / Tsr) * 100%, Dt - current yield, Pg - the amount of interest for the year, Tsr - market price.

The total yield of bonds. This indicator takes into account both sources of income brought by bonds and characterizes the total income on a bond per unit of cost when it is purchased.

Дп = (П+Дд) /(Цр* Λ) * 100%, Дп - total yield, Total interest income, Дд - bond discount size, Λ - number of years, Цр - market price.

There are also more complex algorithms for calculating the total return, in particular, taking into account the third factor of the total return brought by the bond. However, in any case, the rate of inflation has a significant impact on bond yields.

More on the topic Bonds: types, valuation and yield of bonds:

1. 4.4. REQUIREMENTS OF THE EXTERNAL INVESTOR TO THE INNOVATIVE PROJECT
2. VI. GLOSSARY OF USED TERMS ON ACADEMIC DISCIPLINE (GLOSSARY)
3. 4.3 Criteria for the effectiveness of the use of working capital and the formation of its optimal structure

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