Determine the current value of a municipal bond from a portfolio of securities of a commercial bank.

The par value of the bond is 300 thousand rubles.

Four years to maturity.

The annual coupon rate on bonds, respectively: 5%, 6%, 6%, 7%.

Market interest rate - 8% per year.

The present value of a bond can be defined as the value of the expected cash flow reduced to the current point in time. Cash flow consists of two components: coupon payments and the bond amount paid at maturity. That is, the price of the bond will be equal to the present value of the annuity and the lump sum of the face value.

The formula for calculating the current value of the bond will be as follows:

C - coupon payments

i - market interest rate in period t (yield in alternative financial instruments),

H is the face value of the bond,

n is the number of periods during which coupon income is paid.

We calculate coupon payments. The absolute value of annual yield is calculated by the formula:

r is the annual coupon rate on the bond,%,

R_{nom} - face value of the bond.

Coupon payment for the first year:

Coupon payment for the second and third year:

Fourth year coupon payment:

Thus, the current value of a municipal bond from a portfolio of securities of a commercial bank will be equal to:

## Bond options

What options do bank deposits have? Typically, these are interest on the deposit, the term of the deposit, the maximum and minimum amount, the possibility of replenishment and withdrawal. Debt securities have a wider spectrum:

- face value
- market price,
- circulation period
- coupon size and type,
- frequency of payments
- 2 types of profitability,
- type of bonds
- offer
- duration
- credit rating.

Briefly go over them, for a better understanding.

### nominal cost

Each bond has a face value that will remain constant. Typically, the face value of bonds traded on Russian exchanges is 1,000 rubles. This is the so-called deposit body. Bonds were issued for 1 thousand apiece, but their value may change over time. For example, there will be great demand and for them they can give more. Such bonds are easily sold 10-20% above their face value.

The converse is also true. In adverse situations, the price in the market may be below face value.

The bond is always repaid at par.

Regardless of the price at which you buy the bond - at the end of the circulation period, the issuer will pay you the amount equivalent to the face value of the paper.

### Circulation period

All bonds are issued for a limited period, it can be 1 year and 5 years, or even 10-30 years. During this time, the owner is paid a coupon income. At the end of the term, the nominal value of the bond is returned to him.

Buying bonds with a long circulation period, investors will receive a predetermined income during the time of ownership, which can be very profitable.

In early 2016, when the refinancing rate jumped sharply, federal loan bonds maturing in 10-15 years yielded a yield of 15-16% per annum. Having acquired them at that moment, it was possible to fix high profitability for the entire circulation period.

### Income Payment Form

**Discount** - are placed on the exchange at a price below par, and are paid off at par. This difference just forms the investor’s income. For example, a company sells a bond for 800 rubles with a par value of 1000 rubles. At the time of repayment, the investor receives a face value or 200 rubles of profit, which is 25% of the return.

**Coupon** - the bond is issued at par. It provides for the payment of a certain percentage (coupon). Frequency can be once a quarter, six months or a year. Coupon income is accrued every day. But it is paid to the owners only on the coupon payment date, which is known in advance.

For example, a bond with a par value of 1,000 rubles with a coupon yield of 12% per annum and payments 2 times a year means that every six months you get 6% or 60 rubles.

The amount of coupon income accumulated on a bond but not yet paid to the owner is called accumulated coupon income (NDC). It is embedded in the price of a bond, making it more expensive. At the time of payment of the coupon on time, the coupon is reset and begins to accumulate until the next payment date.

When selling, without waiting for payment of the coupon, the buyer is obliged, in addition to the cost of the bond itself, to pay its owner and for the accumulated coupon income. And vice versa, buying a bond - its price increases by NKD. This allows you to not lose accrued profits to the owners and maintain high liquidity in the debt market.

**Typically, newcomers have difficulty understanding the principle of NKD. Therefore, here is a small example for you.**

A bond for 1000 rubles. Profitability 12% per annum. Coupon payments 2 times a year or 6% (60 rubles) every six months. After the coupon is paid, the next day a new coupon income begins to accumulate. Every day, NKD is increasing. For a month by 1%, for 3 months - 3% and so on. If you decide to sell the bond a month before the coupon payments, then in addition to the cost of 1,000 rubles, you will receive another 5% or 50 rubles from the buyer in the form of accumulated coupon income (for 5 months of ownership since the last payment).

The buyer, having paid you NKD - 50 rubles, in a month - will receive the full coupon size - 60 rubles (6%), thereby compensating for their costs and making a profit in proportion to the time of ownership.

NKD allows you not to lose accrued but not yet paid income in connection with the early sale. This is one of the main advantages over bank deposits.

### Profitability

Profitability can be of two types:

- nominal or coupon
- to repayment.

At nominal, the yield is calculated based on the amount of profit received on coupon payments. If the coupon is paid once a year in the amount of 120 rubles at a nominal price of the bond - 1000 rubles, then we get 12% per annum.

But as a rule, the market price is always different from the nominal. Therefore, it is better to use the yield to maturity. This parameter shows your profit for each invested ruble.

For example, if the coupon is 12% of the face value of one thousand or 120 rubles and at the same time the market value of the bond will be 1,100 rubles, then buying them at that price reduces the yield to maturity. You invest 100 rubles more, and get the same income.

120 rubles of profit with investments of 1100 rubles corresponds to a real return of 10.9% per annum.

Important. There is a guaranteed opportunity to additionally receive 13% profit from the purchase of bonds, in addition to coupon income.

The yield to maturity is divided into 2 types:

- simple - without reinvestment of coupon payments,
- effective - taking into account reinvestment.

### Bonds classification

Depending on the issuer, debt securities are divided into 4 types. Each of them has its own rating of reliability and profitability.

- State - issued by the government. In Russia, they are called federal loan bonds or federal loan bonds. The initiator of the release is the Ministry of Finance.
- Municipal or sub-federal - issuer, local (regional) authorities. For example, bonds of the Tomsk region (Moscow, Leningrad).
- Corporate - commercial companies, for example, Sberbank, Gazprom.
- Eurobonds - denominated in foreign currency (usually dollars and euros). Due to the high cost of one lot (from $ 100,000), they will not be entirely interesting for private investors.

**Federal loan bonds**

The most demanded debt securities on the Russian market. Issued for a period of 1 year to 30 years. Denomination - 1 000 rubles. The main difference in coupon income payments.

Government securities are of the following types:

- OFZ-PD (constant income) - the coupon size is fixed for the entire circulation period.
- OFZ-FK (fixed coupon) - one coupon size is set for several years in advance (for example, 8% for 3 years), then it changes by 7%.
- OFZ-IN (indexed face value) is a fixed coupon size, but the face value of a bond is constantly changing depending on inflation.
- OFZ-AD (debt amortization) - periodic repayment of the principal amount of the debt at the time of coupon payments.

#### The content of the article

In general terms, the current price of bonds can be represented as

**value of expected cash flow reduced to the current point in time**

. Cash flow consists of two components: coupon payments and the face value of the bond paid upon maturity. Thus, the bond price is the present value of the annuity and the lump sum of the face value. Consider the factors that affect the price of bonds. In the stock market, bonds are sold at prices that differ from their face value in one direction or another.

### What factors affect the price of bonds

A bond is an issue (issued) debt security, securing the rights of its holder to receive from the issuer (issuing person) within the stipulated time period its nominal value and a percentage of this value or other property equivalent fixed in it. Bonds are issued for the purpose of borrowing capital, and the buyer of the bond acts as a creditor, receiving interest on invested capital at a predetermined time, and after the bond has expired, its nominal value.

A bond rating is a valuation of a non-material product, and its value is determined by the value of the rights that it gives to its owner. Bond owners are creditors, not owners of the enterprise, and do not have the right to participate in its management. Most of the bonds are not secured and do not give the right to participate in management. Bonds are issued by the state, local authorities, credit organizations and companies in the form of securities with a fixed or variable interest rate.

### Bond income is independent of the issuer's financial performance

The yield on bonds is usually lower than on shares, since it is more reliable and does not depend on the issuer's financial results. Bond income is paid out of net profit. If net profit is not enough, then payment is made at the expense of the reserve fund. The creation of a reserve fund is mandatory for the joint-stock company that issued the bonds.

The bond market is divided into three echelons:

The first issue for a total amount of 3 billion rubles.

The second from 3 billion to 1 billion rubles.

The third is less than 1 billion rubles.

### What is the income from an irrevocable bond with a constant income coupon

Irrevocable bond with a constant income coupon. The cash flow in this case is the sum of the same income over the years and the face value of the bond paid at maturity. In developed countries, bonded loans with semi-annual interest payments are very common. Such loans are more attractive, since the investor in this case is more protected from inflation and, in addition, has the opportunity to receive additional income from reinvesting the interest received.

Revocable bond with a constant income coupon. A revocable bond differs from an irrevocable bond by the presence of two additional characteristics: the redemption price and the term of protection against early repayment. In the period when the bond is protected from early repayment, the assessment of its current intrinsic value may vary not only depending on the acceptable profit margin included in the calculation, but also on the probability of early repayment being estimated.

### What value does the bond have

Bonds may have various values: common (nominal), conversion, redemption and market.

The face value is printed on the bond itself and is most often used as a base for calculating interest. This indicator matters only in two cases: at the time of issue of the bond when setting the offering price, as well as at the time of interest calculation, if the latter are tied to the face value. During the placement of a bond loan, the price of a bond, as a rule, coincides with its face value.

Conversion value is a calculated indicator characterizing the value of a bond, under the conditions of issue of which it is possible to convert it into ordinary shares of the issuer's company under certain conditions.

### Redemption of a bond by the issuer is made at an early repayment price

Redemption price (cost), prepayment price, call price - this is the price at which the issuer redeems the bond at the expiration of the bond loan or until this point, if such a possibility is provided for by the loan conditions. This price coincides with the face value, as a rule, if the loan does not involve early repayment. Therefore, from the assessment point of view, two types of loans are divided: without a right and with a right to early repayment.

In the first case, the bonds are redeemed after the period for which they were issued. In the second case, it is possible to recall bonds from the market (early repayment). As a rule, the initiative for such a recall belongs to the issuer.

### Market conditions determine the exchange value of the obigation

The market (exchange rate) price (value) of a bond is determined by market conditions. The value of the market price of a bond as a percentage of face value is called the bond rate. From the time a bond is issued to the maturity date, its price fluctuates in accordance with changes in market conditions or credit quality. In addition, any change in interest rates generally has an immediate and predictable effect on bond prices. When market interest rates rise, the prices of bonds in circulation decrease so that the yield of these securities matches the yield of new issues with higher rates.

Conversely, in the event of a fall in market rates, the prices of previously issued bonds increase, so that their yield decreases to the level corresponding to the yield of new bonds with lower interest rates.

### Assessment of the quality parameters of the company

In addition to these indicators, an assessment is made of the solvency of the company, liquidity of assets, profitability of operation and other quality parameters of the company.

The valuation of bonds is expressed in the fact that to calculate the current market value, the bonds are discounted and summed up cash flows generated by coupon income, and then added to the discounted face value of the bonds. The peculiarity is that the totality of payments that the bond owner must receive is extended in time, and therefore, all future cash flows must be discounted by the time point for which the bond value is being estimated. As an indicator of discount, it is necessary to take the yield of similar financial instruments.

### Based on a thorough analysis, the discount rate is determined

When evaluating the value of bonds, special attention is paid to determining the discount rate, for this purpose a thorough analysis of the issuer's financial condition is carried out, and its solvency is determined.

Bonds ensure the safety of investments and a fixed additional income, which makes this tool attractive for cautious investors. At the same time, there is always the possibility of default on obligations and therefore the analysis of the issuer's reliability is the most important and often laborious task in assessing the value of bonds.

### What is needed to determine the cost and timing of bond valuation

The list of necessary documents and information for determining the cost and terms of work on the evaluation of bonds:

1. The purpose of the assessment (what is the purpose of the evaluation report).

2. Estimated date of valuation (date of determination of value).

3. Information on the participation of the state or other state, regional, municipal entities and institutions in the organization (issuer) that issued the bond.

4. A copy of the bond from all sides.

5. The balance sheet (form 1) of the organization (issuer) that issued the bond at the last reporting date, as well as for the last year.

6. Profit and loss statement (form 2) of the organization (issuer) that issued the bond at the last reporting date, as well as for the last year.

## How and where to buy paper

The purchase of bonds is possible only after concluding an agreement with a broker providing access to the stock market, where securities are actually circulated. The whole process consists of 3 stages:

- Conclusion of a contract with a broker
- Depositing money into an account
- Purchase of securities

The state will withhold 13% tax from the income received on bonds. Subject to taxation:

- coupon payments
- exchange rate difference between buying and selling.

The issuer transferred the coupon income to you - 100 rubles, the state takes 13 rubles. And so every time, while payments are made on bonds.

Тоже самое касается курсовой разницы. Купили облигацию за 1000 рублей, через год продали за 1200. С вашей прибыли в 200 рублей — нужно оплатить 13% или 26 рублей в казну.

По ОФЗ налог на прибыль от купонного дохода не взимается.

Так как брокер является налоговым агентом, то налоги будут удержаны с вас автоматически. В момент получения денег по купону. In other cases, the total amount for withholding in the form of taxes is formed at the end of the year as the total profit for the entire period.

## Where to look at the data

All information on the current parameters of the bond on the market is available in the trading terminal. When you conclude a contract with a broker, you will have access to the stock market. In the program it is convenient to sort and find the necessary securities according to the given conditions (profitability, size and date of coupon payment, current value, duration and much more).

OFZs are sorted in the picture by current yield, for quick selection of the best conditions.

Current yield on government bonds

There are also several sites specializing specifically in bonds. There is also much to be found. From quotes to the latest news. There are special conditions for the selection of interesting papers. You can see current yields, upcoming coupon payments, as well as planned new issues.

List of sites for bonds:

Part of the functionality is paid and is available only by subscription. But the basic information, which is quite enough for ordinary investors in the free access.

## Finally

Buying bonds is a great alternative to bank deposits. In almost all respects (risk-free profitability, maximum profit, liquidity, breadth of choice, minimum investment), debt securities are far ahead of banking products.

The only negative is the lack of risk insurance. Deposits are protected by the DIA for 1.4 million rubles. Bonds, at least corporate ones, do not have such an opportunity. In the event of bankruptcy, all available funds of the company are distributed among creditors. And bondholders have one of the primary rights to receive money.

But on the other hand, if you choose the right paper, not chasing the high profitability that junk bonds give, and opt for the largest companies, then the risk of losing money will be unlikely.

It is probably hard to imagine that such giants of the Russian economy as Gazprom, Sberbank or Lukoil will be in a bankruptcy stage.

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