Calculation of the actual issue price of the bond, calculation of the issue price of the bond?

There is a formula for calculating the actual issuance of bonds**, where p and f represent what they mean:

p: Issue ** (present value).

f: The final value of compound interest (the sum of principal and interest).

p f, 4%, 10) What do the three parts of this formula mean?

According to the question, p=f*(1+4%) 10

4% is the market interest rate, and 10% is the bond issuance for 10 issues.

1. The coupon rate of the bond.

Bonds are printed on the face value, interest rate. This is the coupon rate of the bond.

2. The effective interest rate of the bond.

There is a certain time interval from the completion of the printing to the actual issuance, for example, the board of directors decided to issue the bonds on January 1, 09 on October 8, 2008, and the printing may have been completed in November. It has been a long time since the actual release. Market interest rates are subject to change during this time.

Suppose the five-year coupon rate of 1,000 yuan is 10%, but by the time of actual issuance, the market risk interest rate has become 9%, and the interest rate of the printed bonds cannot be changed. At this time, it can only be issued at the effective interest rate of 9%, otherwise the effective interest rate is higher than the market interest rate, and the issuer will raise funds with the cost higher than the market interest rate, resulting in losses. Conversely, if the market interest rate becomes 11%, it can only be issued at the effective interest rate of 11%, otherwise the issuance will fail because no one buys the bond.

The answer is supplemented. 3. Issuance of bonds at parity, premium and discount.

At the time of actual issuance, if the market interest rate is exactly the same as the coupon rate (10%), the market value of a bond with a face value of 1,000 yuan is 1,000 yuan, and it can be issued at face value (parity issuance). If the market interest rate is 9%, the market value of a bond with a face value of 1,000 yuan is higher than 1,000 yuan and it needs to be issued at a premium. If the market interest rate is 11%, the market value of a bond with a face value of $1,000 is less than $1,000 and will be issued at a discount.

The answer is supplemented. 4. The actual issuance of bonds**.

The market value of a bond (issue**) is the present value of the principal and interest of the bond (interest per instalment and the principal amount eventually returned) at the market rate.

Actual issuance of bonds** (market value) = a*(p a,i,m) + m*(p s,i,n).

a – interest per period.

i – Market interest rate per annum.

m – face value.

m – the number of interest-bearing periods.

n - the principal repayment period of the bond.

Pro, bond issuance** is composed of two parts, namely the present value of the face value and the present value of interest in each period, the first part is the present value of compound interest calculation, and the latter part is the present value of annuity calculation, both of which are discounted by market interest rates. The solution and formula of this problem are matched. (P a is the present value of compound interest, P a is the present value of annuity).

The formula for calculating bonds**p is p=m(1+rn) (1+rn).

There are two formulas for calculating the actual issuance of bonds, one is to pay interest in installments and repay the principal at maturity, and the other is to calculate interest on an annual basis, and repay the principal and interest at maturity, respectively, as follows:

Issuance of bonds with interest payment in installments** = annual interest rate * annuity present value coefficient + face value * compound interest present value factor.

The issuance of bonds with principal repayment and interest payment at the first touch of the code** = principal and interest at maturity and * present value coefficient of compound interest.

The bond issuing price** refers to the market that the original investor of the bond should pay when the bond is purchased**, which may or may not be consistent with the face value of the bond. Theoretically, a bond issuance** means that the face value of the bond and the annual interest to be paid are based on the market interest rate at the time of issuance.

The present value obtained by discounting. The relationship between coupon rates and market interest rates affects the issuance of bonds**. When the coupon rate of the bond is equal to the market interest rate, the bond issuance** is equal to the face value; When the coupon rate of the bond is lower than the market interest rate, the enterprise will not be able to attract investors if it is still issued at face value, so it is generally issued at a discount. On the contrary, when the coupon rate of the bond is higher than the market interest rate, the issuance cost will increase if the enterprise still issues at face value, so it is generally issued at a premium.

Coupon rate 10% = market interest rate 10%, parity issue PV = 1000 * 10% * P A, 10%, 5) + 1000 * P F, 10%, 5).

1000 (yuan).

The formula for calculating bonds**p is p=m(1+rn) (1+rn).

1.the actual rate of return; 920 = 1000 * 8% * (p a, i, 5) + 1000 * (f p, i, 5), with the interpolation method, when i = 10%, the result is, when i = 12%, the result is, finally i = 10% + (

2.In the general model, the cost of capital of a bond = [par value * coupon rate * (1 - income tax rate)] [issuance *** (1 - issuance expense rate)].

The issuance ** is 60 million yuan, and the capital cost of the bond = [5000*10%*(1-40%)] [6000*(1-3%)]=

The issuance ** is 60 million yuan, and the capital cost of the bond = [5000*10%*(1-40%)] [4000*(1-3%)]=

The bond's ** is determined by a combination of face value, coupon rate, repayment period and market interest rate.

The cash flow of a zero-coupon bond is very simple, with only the **p paid for buying the bond now and the principal fv received at maturity in the future.

p = fv / (1+y)^t

In the above formula, y is the interest rate and t is the term.

For example, a zero-coupon bond with a par value of $100 and a maturity of 3 years has an interest rate of 5%. The bond is now **p= 100 (1+5%) 3 = yuan.

What if it's a bond with a coupon? We calculate it as follows**.

p = c / (1+y) +c / (1+y)^2 + c / (1+y)^t + fv / (1+y)^t

where p is the ** of the bond, c is the coupon, y is the interest rate of the bond, and t is the maturity of the bond.

The above formula is not simple enough? Let's take an example.

A bond with a face value of $100, a maturity of 3 years, a coupon of 3%, and an interest rate of 5%. The cash flow of this bond is as follows:

p +3 +3 +103

0 hours Year 1 Year 2 Year 3.

Bonds**p = 3 (1+5%) 3 (1+5%) 2 + 103 (1+5%) 3 = RMB.

This question is more professional, and I also studied it to understand, and I used to think that it was issued according to the face of the ticket.

A bond issuance** is what a bond investor actually pays when subscribing to a new issue**.

In practice, the maturity and interest rate of the bond are usually determined first, and then fine-tuned according to the market interest rate level at the time to determine the actual issuance**.

It is generally impossible to complete the issuance of a batch of bonds in one day, and subscribers have to buy the same type of bonds at different times. There may be different levels of market interest rates.

In order to protect the interests of investors and ensure the smooth issuance of bonds, it is necessary to constantly adjust the interest rate and issuance of bonds**.

Generally speaking, when there is a large change in the level of market interest rates, the method of changing interest rates is adopted; When the market interest rate level is relatively stable, the fine-tuning method of issuance is adopted.

There are also times when interest rate changes and issuance** fine-tuning are used in combination. In short, when an investor subscribes to a new bond with a face value of 200 yuan, the actual amount paid can be 200 yuan, 199 yuan or 198 yuan, or 201 yuan or 202 yuan.

The above three methods are called parity issuance, discount issuance and premium issuance.

A company issues a five-year corporate bond with a face value of 1,000 yuan, a coupon rate of 8%, and interest paid once a year.

1) The market interest rate at the time of bond issuance is 10%.

Issuance** = present value of the face value of the note + present value of annual interest = 1000 (1+10%) 5 + 1000 * 8% * (1 - (1 + 10%) 5)) 10% =

2) The market interest rate at the time of bond issuance is 8%.

Issuance** = present value of the face value of the note + present value of annual interest = 1000 (1+8%) 5 + 1000 * 8% * (1 - (1 + 8%) 5)) 8% = 1000

3) The market interest rate at the time of bond issuance is 5%.

Issuance** = present value of the face value of the note + present value of annual interest = 1000 (1+5%) 5+1000*8%*(1-(1+5%) 5)) 5%=

Further Information: Conditions for Bond Issuance:

The conditions of bond issuance refer to the relevant factors that must be considered when the bond issuer issues bonds to raise funds, including the issuance amount, face value, term, repayment method, coupon rate, interest payment method, issuance, issuance costs, whether there is a guarantee, etc., because corporate bonds are usually classified by the issuance conditions, therefore, the determination of the conditions for the completion of the divergence is also to determine the type of bond issued.

The issuer of the bond must submit a declaration to the bond management department in accordance with the regulations before issuance; **The issuance of bonds is subject to the approval of the national budget review and approval authority (e.g. National Assembly). The terms and regulations stated by the issuer in the declaration form are the conditions for the issuance of bonds, the main contents of which are: the number of bonds to be issued, the issuance of **, the repayment period, the coupon rate, the interest payment method, whether there is a guarantee and so on.

The issuance conditions of bonds determine the yieldability, liquidity and safety of bonds, which directly affect the level of financing costs of issuers and the amount of investment returns of investors. For investors, the most important issuance conditions are the coupon rate, repayment period and issuance of bonds**Because they determine the investment value of bonds, they are called the three basic conditions for bond issuance, and for issuers, in addition to the above conditions, the number of bonds issued is also more important, because it directly affects the scale of financing. If the number of issuances is too large, it will cause difficulties in selling and even affect the credibility of the issuer and the transfer of bonds in the future**.