Bonds issued at a discount, faster frequency of interest payments, why the value has fallen by 10

Discounted bonds, with a coupon rate lower than the market rate.

By increasing the frequency of interest payments, the effective annual market interest rate will increase more than the effective coupon rate, and the higher the market interest rate, the lower the value of the bond.

Here's an example. A parity bond with an issue price of 1,000 yuan, a coupon rate of 8%, a market interest rate of 10%, and a maturity of 3 years.

If the interest is paid once a year, then the value of the bond is: 1000*8%*(P a,10%,3)+1000*(P s,10%,3)=100*

If the frequency of interest payment is accelerated and the interest is paid once every six months, the value is: 1000*4%*(p a,5%,6)+1000*(p s,5%,6)=50*

Suppose that the interest rate of the equal risk market is 8%, and the coupon rate of the bond is 6%, both of which are paid once a year, and the interest rate difference between the two is 2%.

At present, based on (1), other conditions remain unchanged, and the interest payment period is changed to semi-annual time.

Then, the effective annual interest rate of an at-the-money bond issued at a market interest rate is; The effective annual interest rate for discounted bonds is >2%. As a result, the value decreases. The principle is the same in the case of premium.

The root of the problem is that you can't just see the effective annual interest rate of the discount bond rising, but you also see the benchmark rate rising because of the faster frequency of interest payments.

The main difference is in the discounted face value. The error of the formula lies in metaphysics, it is obviously the same period, such as a sum of money after 5 years, why bother to make two discount rates according to the interest payment period? Those who believe in this formula do not have brains.

Accounting Tips: Why Do Investors Buy Bonds at a Premium?

The impact of the frequency of bond interest payment on the value of the bond mainly depends on the coupon rate and discount rate.

Judgment of the relationship between the size of the relationship.

A bond is a valuable bond issued by the issuer in order to raise funds, paying a certain percentage of interest at an agreed time, and repaying the principal at maturity. There are several basic concepts of bonds, namely the face value of the bond (100 yuan in China), the coupon rate of the bond and the maturity time of the bond.

Bond value refers to the investment made in bonds.

The present value of cash inflows that investors expect to receive. The cash inflow of bonds mainly consists of interest and the principal or cash received at maturity.

Factors influencing the value of a bond:

1. Bond face value: bond face value (par value), financial management term. Refers to the set par value, which represents the amount that the issuer promises to repay the bondholder at a specific future date.

The coupon rate of a bond is the ratio of the interest that the bond issuer expects to pay to investors to the par amount.

2. Bond issuance price: Bond issuance** is the actual payment of bond investors when subscribing to newly issued bonds**.

3. Coupon rate: corporate bonds.

The coupon rate of the bond must be stated. To a certain extent, the level of coupon rate not only indicates the economic strength and potential of the issuer of corporate bonds, but also one of the factors that can form a sufficient attraction to the public who buy them.

4. Market interest rates.

Market interest rate or bank deposit and loan interest rate.

The impact on fixed-rate bonds is significant. Market interest rates are rising, credit is tightening, investment in securities is decreasing, people are willing to make bank deposits, bond prices are falling (i.e., intrinsic yields are rising, and the market is driving bond yields.

changes in the same direction as bank deposit rates); On the contrary, there is the opposite result.

A discount rate is also needed to calculate the value of a bond, so let's look at the most basic model of bond valuation.

1. If the coupon rate is equal to the discount rate, then no matter whether the frequency of interest payment of the bond becomes higher or lower, it has no effect on the value of the bond.

If the coupon rate is equal to the discount rate, then the value of the bond will not be affected by whether the bond is paid more or less frequently.

2. If the coupon rate is greater than the discount rate, the higher the frequency of bond interest payment will increase the value of the bond; A lower frequency of interest payments will result in a decrease in the value of the bond.

If the coupon rate is greater than the discount rate, then the higher frequency of interest payments will increase the value of the bond; A lower frequency of interest payments will result in a decrease in the value of the bond.

3. If the coupon rate is less than the discount rate, the higher the frequency of interest payment of the bond, the lower the value of the bond; If the interest payment frequency is lower, the bond** will be higher.

If the coupon rate is less than the discount rate, then the higher the frequency of interest payments on the bond, the lower the value of the bond; If the interest payment frequency is lower, the bond** will be higher.

Faster frequency of interest payments, effective interest rates.

If it must be higher, then the value of the bond calculated at the discount of the higher interest rate must be lower.

The present value of the face value of the bond The present value of the annuity of the interest The present value of the face value of the bond, as the frequency of interest payment increases, the real interest rate gradually increases, so the present value of the face value of the bond gradually decreases.

When the coupon rate of a bond is less than the necessary rate of return (discount**), the interest is relatively less, and the increase in the present value of the interest is less than the decrease in the present value of the principal, and the value of the bond decreases.

When the coupon rate of the bond is equal to the necessary rate of return (parity**), the increase in the present value of the interest is equal to the decrease in the present value of the principal, and the value of the bond remains unchanged; When the coupon rate of the bond is greater than the necessary rate of return (premium**), relatively speaking, the interest is more, and the increase in the present value of the interest is greater than the decrease in the present value of the principal, and the value of the bond increases.

If the coupon rate is less than 10, the value of the bond with semi-annual interest payment is less than the value of the bond with annual interest payment, that is, the value of the bond decreases. A bond is a bond in which the interest is paid evenly over a period of maturity. The frequency of payments may be annual, semi-annual, or quarterly, among others.

The value of a bond is made up of two parts: the present value of the interest paid in the future, and the present value of the principal paid in the future. "Flattening bonds"。

Most of the bonds issued by ** and corporates are flat bonds, and they are paid only on the closed maturity date, and regular cash payments are also made between the issuance date and the maturity date.

PV is the value of the bond; m is the number of interest payments per year; i is the interest payable per annum; n is the number of years of expiration; i is the necessary rate of return per year; m is the face value or the amount paid on the due date.

Effective Annual Percentage Rate.

As the frequency of interest payments accelerates, the value of bonds rises, and the value of bonds becomes lower and lower.

Bonds** means bonds at the time of issuance. Theoretically, the face value of a bond is **. But in fact, due to various considerations of the issuer or the supply and demand in the capital market, the interest rate.

The market for bonds** is often detached from par, sometimes above par, sometimes below par. In other words, the face value of a bond is fixed, but it changes frequently. The issuer's interest repayment is based on the face value of the bond, not on its **.

Bonds are mainly divided into issuance and trading.

The bond market** is also determined by the relationship between capital and bond supply. When the economic development is on the rise, enterprises generally want to increase equipment investment, so on the one hand, they will throw bonds because they are in urgent need of funds, and on the other hand, they will borrow from financial institutions or issue corporate bonds, which will make the market tighten the funds and increase the supply of bonds, thus causing bonds. When the economy is sluggish, the demand for funds by production enterprises will decline, and financial institutions will have surplus funds due to the reduction of loans, thereby increasing the investment in bonds, resulting in the first bond.

And when the ** bank.

When the financial department and the foreign exchange management department carry out macroeconomic regulation and control of the economy, it often causes changes in the supply of funds in the market, which is generally reflected in the changes in interest rates and exchange rates, which causes the rise and fall of bonds.

The interest payment method refers to the way in which the debtor pays interest to the creditor at certain intervals during the validity period of the bond. Interest payment methods can generally be divided into two types: one-time interest payment and installment interest. Medium- and long-term bonds can be paid in instalments.

Short-term bonds can be paid in a lump sum.

The annual interest rate refers to the interest rate on deposits for one year.

The interest rate is the abbreviation of "interest rate", which refers to the ratio of the amount of interest to the principal of the deposit or loan over a certain period of time. It is usually divided into annual interest rate and monthly interest rate.

and daily interest rates. The annual interest rate is expressed as a percentage of the principal, the monthly interest rate is expressed in thousandths, and the daily interest rate is expressed in thousandths.

Why the effective annual interest rate remains the same, and the value of the bond rises as the frequency of interest payments increases.

With the acceleration of interest payment frequency, the value of bonds issued at a discount gradually decreases, and the value of bonds issued at a premium gradually increases. The value of bonds issued at parity remains unchanged. In the case of bonds that pay interest in instalments, if the "effective annual coupon rate effective annual discount rate", the value of the bond is the face value of the bond; Among them, the effective annual coupon rate (1 coupon rate m) m 1, the effective annual discount rate (1 discount rate m) m 1, "m" indicates the number of interest payments per year, that is, the frequency of interest payments. (1) For bonds issued at parity, the coupon rate is the discount rate, therefore, the effective annual coupon rate is the effective annual discount rate, so the change in the frequency of interest payment will not affect the value of the bond, and the value of the bond is always equal to the face value of the bond; (2) For bonds issued at a premium, the discount rate, therefore, the effective annual discount rate, the effective annual coupon rate 1, and the higher the frequency of interest payment, the greater the value of the "effective annual coupon rate effective annual discount rate", so the value of the bond is higher and higher than the face value of the bond, and the value of the bond is getting higher and higher; (3) For bonds issued at a discount, the coupon rate discount rate, therefore, the effective annual coupon rate effective annual discount rate, the effective annual coupon rate effective annual discount rate <1, and the higher the frequency of interest payment, the smaller the value of the "effective annual coupon rate effective annual discount rate", so the value of the bond is lower and lower than the face value of the bond, and the value of the bond is lower and lower.

The ** of a bond is the cash flow that is expected to be generated in the future.

The present value of the annuity, i.e., the present value of the annuity for future periods.

the sum of the present value of compound interest at maturity, and this discount rate.

is the current market interest rate. The coupon rate can only be used to calculate the coupon interest.

When the market interest rate is equal to the coupon rate, the bond is issued at par, ** equal to the face value.

The market interest rate is the average opportunity cost rate of investors and the investor's investment project.

The average rate of return that can be achieved on investment. When the coupon rate of the bond is exactly equal to the market interest rate, the investor can obtain the same average return from investing in the bond as other projects in the market, and is naturally only willing to buy the bond at face value, so the bond is issued at parity.

Summary. Hello dear, I'm glad to answer for you, bond issuance at a premium or discount is very common in Western countries, and of course it is also in financial textbooks. In reality, the bonds issued by China are all issued at a parity (except for treasury bonds issued at short-term discounts).

The reason for the issuance of bonds at a discount is that after the interest rate of the company has been determined, such as the central bank raises the interest rate, then the company may not be able to issue the interest rate originally determined, which means that the company can only issue bonds at a discount. Or if the central bank cuts interest rates, the company can also issue at a premium in order to reduce the cost of borrowing. Amortization of discount premium is financially necessary, because in this way it can truly reflect the company's operating costs in the current year, otherwise when the premium is issued, the first year will appear to be highly profitable.

Amortization will only affect the relative profit of each year during the duration of the bond, and after the duration period, the total profit of the next few years will not change regardless of whether it has been amortized before.

Why bonds are issued at parity, at a premium and at a discount.

Hello dear, I'm glad to answer for you, bond issuance at a premium or discount is very common in Western countries, and of course it is also in financial textbooks. In reality, the bonds issued by China are all issued at a parity (except for treasury bonds issued at short-term discounts). The reason for the issuance of bonds at a discount is that after the interest rate of the company has been determined, such as the central bank raises the interest rate, then the company may not be able to issue the interest rate originally determined, which means that the company can only issue bonds at a discount.

Or if the central bank cuts interest rates, the company can also issue at a premium in order to reduce the cost of borrowing. The amortization of the premium is necessary financially, because in this way it can truly reflect the company's operating costs in the current year, otherwise the first year will be highly profitable when the premium hair mask is noisy. Amortization will only affect the relative profit of each year during the duration of the bond, and after the duration period, the total profit of the next few years will not change regardless of whether it has been amortized before.

Debt rebate bonds are issued by debtors such as enterprises and banks in accordance with legal procedures in order to raise funds and promise to creditors to repay principal and interest on a specified date. [It is a kind of financial contract, which is a creditor's right and debt certificate issued to Shouyou investors when **, financial institutions, industrial and commercial enterprises, etc. directly borrow funds from the society, and promise to pay interest at a certain interest rate and repay the principal according to the agreed conditions. The essence of a bond is a certificate of debt, which has the force of law.

The bond purchaser or investor and the issuer have a creditor-debt relationship, the bond issuer is the debtor, and the investor (the bond purchaser, Shihuai) is the creditor.