Useful Tips

How to calculate bond yields?

Corporate bonds can bring interest to the holder in the form of interest (coupon income) (Article 2 of the Law of April 22, 1996 No. 39-ФЗ).


The amount due to the organization from the issuer of the coupon yield on the bond may consist of:

- coupon income accumulated before the bond became the property of the organization (accumulated coupon income (NDC) paid upon purchase of the security),

- coupon income accrued by the organization during the time of holding the bond.


For accounting and tax purposes, it is not necessary to calculate the amount of accumulated coupon income paid to the seller. It is indicated in the documents for the purchase of bonds (for example, in the contract, settlement documents, documents of trade organizers).


Coupon income for the time of holding the bond for accounting and tax purposes (when calculating income tax on an accrual basis) must be determined. In this case, it is required to calculate:

- based on the results of each month in which the organization owned a corporate bond (both in the conditions of coupon payments and without them),
- based on the results of the sale of a security,
- upon payment by the issuer.


The corporate bond yield pertaining to the reporting month must be determined based on:

- yield declared upon its issue,
- the number of days during which the bond is owned by the organization in a given period.


This procedure follows from paragraph 16 PBU 9/99 and Article 328 of the Tax Code of the Russian Federation.


Calculation Methods


However, the specific procedure for calculating corporate bond income in legislation is not established. Therefore, in practice, you can determine the amount of coupon income per month in different ways. For example:

- calculate the coupon yield based on the term of ownership of the bond in the reporting month and the data established when the issuer issued the bonds (coupon rate, duration of the coupon period, etc.) - direct account method,

- determine coupon income based on the data on the amount of accumulated coupon income (ACI) accrued at the end of the reporting month, at the end of the previous month (or paid to the seller), and the amount of coupon payments in the reporting month - the method applied to state and municipal securities.


Moreover, the amount of coupon income per month does not depend on the method by which it is calculated.


For tax purposes, regulatory agencies recommend calculating coupon yield on corporate bonds in the manner that is established for state and municipal securities (paragraph 5.1 of the letter of the Ministry of Finance of Russia dated October 26, 2005 No. 03-03-02 / 118 and the letter of the Department of the Ministry of Taxes of Russia for Moscow dated February 18, 2004 No. 26-08 / 10738). This is due to the fact that government (municipal) bonds and corporate bonds are similar in terms of the issue and circulation, since the general procedure for the issue of both types of bonds is regulated by Law No. 39-FZ of April 22, 1996 (Article 1 of the Law of April 22, 1996 g. No. 39-FZ). In particular, for both types of bonds additional income is coupon income or discount (Article 2 of the Law of April 22, 1996 No. 39-ФЗ).


Direct counting method


In the issue documents (for example, in the issue prospectus, reports on material facts), the algorithm for calculating the coupon yield on the bond is established (clause 9.1.2 of the Regulation approved by order of the Federal Service for Financial Markets of Russia of October 4, 2011 No. 11-46 / pz-n).


As a rule, in order to fulfill this requirement, the issuer provides a formula with letter designations of indicators. Using it, you can determine the amount of coupon income for the required period of time.


For example, if the coupon yield is determined as a percentage of the face value of the bond and the duration of the coupon period, then its amount per reporting month can be calculated by the formula:

Types of bonds by payment form

Most often coupon bonds are found. A coupon is an interest payment that occurs at a certain frequency: for example, once every six months. Payment dates are known in advance, but the size of coupons may change over time.

There are also discounted securities: coupons are not paid on them, but the securities themselves are sold much cheaper than face value. Income can be obtained if the price rises or if you pay off the bond at par at the end of the term.

Coupon yield

This is money that the issuer is obligated to pay periodically to bondholders. The interest rate on the yield of a coupon bond is easy to calculate:

(Annual Coupons / Face Value) × 100%

Bonds are not always sold at face value: their price changes over time. Therefore, the calculation of the coupon yield does not allow to know exactly how much the investor will earn on bonds.

Simple yield to maturity

Many hold bonds until the maturity date when, together with the last coupon, the investor receives the face value. But it is possible to calculate the yield of a bond at maturity only when the size of all coupons is known.

The repayment rate is calculated using a more complex formula:

((Denomination - Full purchase price + All coupons for the holding period) / Full purchase price) × (365 / Number of days to maturity) × 100%

Effective yield to maturity

If you use the received coupons to purchase additional securities, you can calculate the rate of return on bonds with reinvestment of coupons - approximately as a contribution with capitalization of interest.

It is believed that coupons are invested in new securities at the current rate - the one that was originally. This is an assumption, as the price changes over time and actual returns will vary.

A simple and accurate way to find out effective yield to maturity is to use a bond calculator on the Rusbonds website or on the Moscow Exchange website. For OFZ -26217, this indicator as of October 2 was equal to 7.93% per annum.

Nuances and useful tips

The price of a bond also depends on interest rates in the economy. If the Central Bank raises the rate, investors will want to have instruments with higher returns. They will start selling old papers with a permanent coupon, and they will become cheaper. If the Central Bank reduces the rate, demand for old bonds will increase and they will rise in price. The shorter the time to maturity, the less sensitive are the securities to changes in the key rate.

When choosing between government bonds and corporate bonds, it is important to know that corporate bonds have the highest yield, all other things being equal. More generous coupons compared to state ones are a premium for the risk of losing invested money if things go wrong with the company. If the paper has unusually large coupons or the price has fallen far below face value, then there is a good chance of losing money.

Coupon income on one corporate bond is subject to personal income tax, on others it is not. The list of securities with preferential taxation can be found on the Moscow Exchange website. When comparing the profitability of OFZs, corporate securities and deposits, remember about personal income tax.

It is good if the broker allows you to receive coupons in a bank account, and does not credit them to the IMS. Then the coupons can be independently deposited on the IIS and then receive a deduction from this money.

The essence of discounting

The discounting of cash flows is the reduction of their divergent (related to different calculation steps) values ​​to their value at a certain point in time, which is called the moment of reduction. When solving the problem of calculating the discounted value of bonds for the purposes of RAS 19/02, the date of reduction is the reporting date. The main economic standard used for discounting is the discount rate, expressed in fractions of a unit or in percent per year. The discount rate is set by the enterprise itself, but cannot be arbitrary. Typically, the discount rate is related to inflation, the Bank of Russia refinancing rate, and the return on working assets.

The calculation of the discounted (present) value (PV) of a bond is made on the basis of a formula for calculating compound interest based on the fact that the amount of coupon income accrued for the year is capitalized (that is, it also brings income in the next year):

where PV is the discounted (reduced) value of the bond,

N is the number of years of circulation of the bond,

F - payments on bonds,

r is the discount rate.

Example 1. The company is offered to purchase a bond with a par value of 1000 rubles. repaid in a year, interest income is accrued at the time of repayment at a rate of 12% per annum.

Let the discount rate also be 12% per annum.

Calculate the discounted value of the bond.

In a year, the company will receive the face value of the bond (1000 rubles) and coupon income (120 rubles).

PV = (1000 + 120) / (1 + 0.12) = 1000 (rubles).

The present value is equal to the nominal value, since the discount rate is equal to the coupon rate and the payment of income occurs exactly one year later.

Example 2. The initial conditions are taken from example 1 with the only difference being that the discount rate is 10% per annum.

The discounted value of the bond is:

PV = (1000 + 120) / (1 + 0.10) = 1018.18 (rubles).

The present value is higher than the nominal value, since the discount rate reflecting the expectations of the enterprise is lower than the coupon rate on the bond.

Example 3. We use the conditions of example 1, but the discount rate is 14% per annum.

The discounted value of the bond is:

PV = (1000 + 120) / (1 + 0.14) = 982.46 (rubles).

The present value is lower than the nominal value, since the discount rate reflecting the expectations of the enterprise is higher than the coupon rate on the bond.

Examples 1–3 are schematic, showing the effect of the discount rate on the present value of a bond. Now we calculate the discounted value of the bond, if the circulation period of the latter is more than a year.

Example 4. The company is offered to purchase a bond with a par value of 1000 rubles. with maturity after 4 years, interest income is accrued at the end of each year at a rate of 12% per annum.

Let the discount rate be 12% per annum.

Calculate the discounted value of the bond.

The present value is equal to the nominal value, since the discount rate is equal to the coupon rate and income is paid annually.

When they talk about the discount rate, they usually mean the annual rate, which is formed when paying income exactly one year later. If the company will be offered a different asset, for example, a bond at 12% per annum with a quarterly coupon payment, then at a discount rate of 12% per annum this investment will exceed the expectation of the company on the basis that the more frequent (often once a year) payment of the coupon allows you to reinvest funds with obtaining additional income.

If several interest payments are provided during the year, then the conversion formula is used:

where m is the number of interest payments in a year,

r is the annual discount rate,

is the discount rate corresponding to the period m.

The validity of the formula is easy to verify. Let the annual rate be 12% per annum, then the quarterly rate corresponds to it:.

Thus, according to the recalculation formula, the annual discount rate of 12% corresponds to the quarterly rate of 2.87373%, and the quarterly rate of 3% corresponds to the annual rate of 12.55088%.

Example 5. The company is offered to purchase a bond with a par value of 1000 rubles. repaid one year later, interest income is paid quarterly at a rate of 12% per annum in the amount of 30 rubles. (1000 rub. X 12% / 4).

Let the discount rate be 12% per annum.

Calculate the discounted value of the bond.

All calculations with fractional degrees are carried out using Excel spreadsheets (mathematical function degree).

The discounted value is higher than the nominal value, since even though the discount rate coincides with the coupon rate, the coupon is paid more often than once a year.

Example 6. The company is offered to purchase a bond with a par value of 1000 rubles. with maturity after 2 years, interest income is paid at maturity at a rate of 12% per annum.

Let the discount rate also be 12% per annum.

Calculate the discounted value of the bond.

The discounted value is lower than the nominal value, since even though the discount rate coincides with the coupon rate, the coupon is paid less than once a year.

For accounting purposes, it is required to calculate the discounted value of a bond not at the time of its issue, but at the reporting date. How will this change the calculations? An incomplete year of circulation will arise, which should be taken into account in the calculations. If you reduce the calculation step to 1 day (this formula is proposed by the Bank of Russia in Guidelines N 2008-U), then neither the frequency of payments, nor the period before their execution interferes with settlements. In this case, the discounted (reduced) value formula will take the following form:

where PV is the discounted (reduced) value of the bond,

N is the number of years of circulation of the bond,

F - payments on bonds,

r is the discount rate,

dn - date of payment on the bond,

do - reporting date.

Example 7. We will use the terms of example 5 (the company is offered to purchase a bond with a par value of 1000 rubles, repaid in a year, interest income is paid quarterly at a rate of 12% per annum in the amount of 30 rubles), but we will calculate using the last formula.

As you can see, the result in examples 5 and 7 is the same.

And now we will consider how the present value of the bond is calculated at the reporting dates.

Example 8. March 14, 2013 the company during the initial placement bought a bond with a par value of 1000 rubles. with maturity on March 14, 2014, interest income is paid at the time of maturity at a rate of 12% per annum.

Let the discount rate be 12% per annum.

We calculate the present value of the bond at the acquisition date, maturity date and reporting dates.

Discounted value of bonds for March 14, 2013:

The discounted value of the bond is equal to the nominal value, since the discount rate is equal to the coupon rate, and exactly one year is left before the payment of the bond.

Discounted value of bonds in the statements for the I quarter of 2013:

Discounted value of bonds in the statements for the I half of 2013:

Discounted value of bonds in the reporting for 9 months of 2013:

Discounted value of bonds in the financial statements for 2013:

Discounted value of the bond for March 14, 2014:

As they mature, the discounted value of the bond approaches its nominal value plus interest receivable.

After we have considered simplified examples, we will complicate the conditions, bringing them closer to real ones. Typically, coupon payments on bonds are made quarterly, and the bonds have a maturity period of several years.

Example 9. The company has on the balance sheet bonds of Comet Comet with a par value of 1000 rubles. The coupon rate on the bond is 12% per annum. The coupon is paid by the issuer 4 times a year, the maturity of the bond is 03/20/2017. We calculate the discounted value of the bond at the reporting dates, if there is a payment schedule for the issuer, and the discount rate is 12%.

The discounted value of bonds in the statements for the I quarter of 2013

The discounted value in the statements for the I half of 2013

The discounted value of bonds in the reporting for the 9 months of 2013

The present value of the bond in the financial statements for 2013

For reference, the discounted value for all subsequent reporting dates (without calculations) is indicated below.

Since there is an equal period of time between the reporting dates, the discounted value for these dates only shows a decrease in value due to a decrease in the number of interest payments. Inside the reporting period, the discounted value increases by the time interest income is paid and falls after this payment.

So, in 2017, the discounted value will have the following dynamics:

  • 12/31/2016 - 1,004.64 rubles.,
  • 01/31/2017 - 1014.36 rubles,
  • 02/28/2017 - 1023.22 rubles.,
  • 03/20/2017 - 1029.59 rubles.

All considered examples are based on the traditional discount method. In most examples, the discount rate is equal to the nominal rate on the bond. This is done specifically to demonstrate how factors other than the discount rate (time remaining to maturity, frequency of coupon payments) affect the present value.

Discount Methods

There are two main discount methods: the traditional method and the expected cash flow method. The traditional method assumes that the discount rate includes all expectations regarding future cash flows and the corresponding risk premium. Therefore, when using the traditional method, the main emphasis is placed on choosing the discount rate.

Examples of using the expected flow method are given in Appendix 2 to RAS 8/2010 and paragraphs A7 - A14 of Appendix A to IAS 36. As follows from the descriptions of these paragraphs, the expected flow method is mainly used when there is no market neither for the object of evaluation, nor for a comparable object.

The traditional method is more suitable for bonds, since both the size and frequency of cash flows are known in advance. However, there are situations where the expected flow method is appropriate, for example, if there is a likelihood of default on the bond. Поскольку дисконтирование при расчете приведенной стоимости по традиционному методу не может отражать неопределенностей в распределении по времени, этот пробел восполняется методом ожидаемого потока.

Пример 10. Предприятие имеет на балансе облигацию номиналом 1000 руб., срок обращения облигации - 2 года, процентный доход выплачивается в момент погашения по ставке 12% годовых. Дата выпуска облигации - 24.10.2011, дата погашения - 24.10.2013.

09/05/2013 the company received a letter from the issuer stating that, by the due date, the bond is most likely not to be redeemed, and with a proposal to restructure the debt.

On the eve of reporting for 9 months of 2013, the financial service of the enterprise provided the chief accountant with information about the expected cash flows.

Let the discount rate be 9%.

Based on paragraphs. “a” paragraph A3 of Appendix A to IAS 36, the discount rate is reduced by 3% to exclude credit risk, which is accounted for in expected cash flows.

Discount rate

In conclusion, we return once again to the issue of substantiating the discount rate used to calculate the present value of the bond. In particular, paragraphs A17 - A18 of Appendix A to IAS 36, it is recommended to use the following rates as a starting point:

(a) the weighted average cost of capital of an entity as determined using methods such as a valuation model for long-term assets,

(b) incremental interest rate on borrowed capital,

(c) other market borrowing rates.

However, these rates must be adjusted:

(a) taking into account how the market would assess the specific risks associated with measuring the cash flow of an asset,

(b) to exclude risks that are not relevant to the estimated estimate of the cash flow of the asset or to which the estimated estimate of cash flows has already been adjusted.

Risks such as country, currency and price should be considered.