Basic principles of bond pricing

The present value of future cash inflow of bonds is called bond value or bond intrinsic value. Bonds as investment products. Cash outflow is its purchase price, and cash inflow is interest and returned principal, or cash obtained at the time of sale. Bond value is one of the main indicators of bond investment decision. Only when the value of a bond is greater than the purchase price is it worth buying.

1. Value calculation model of installment bonds (basic model)

Under normal circumstances, bonds have a fixed interest rate, and the interest is calculated and paid every year, and the principal is returned at maturity. According to this model, the basic model of bond value calculation is:

In the above formula, p is the bond value (present value); Ct is annual interest; F is the principal (face value) at maturity; I is the market interest rate or the minimum rate of return required by investors; T is the number of years before the bond matures.

situation

Investor A intends to purchase the corporate bonds of Company A as an investment, with the face value of 65,438+0,000 yuan, with coupon rate accounting for 5%. The term is 3 years, the interest is paid once a year, and the principal is repaid at maturity. The current market interest rate is 6%. When calculating the issue price of the bond, it is suitable for investors to buy.

Answer:

The distribution of future cash flows is as follows:

1, 1000×5%=50 yuan at the end of the year.

At the end of the second year, 1000×5%=50 (yuan)

At the end of the third year1000× 5%+1000 =1050 (yuan)

The market price of this bond is

2. Bond value calculation model with one-time repayment of principal and interest without compound interest.

Many bonds in our country belong to one-time debt service without compound interest. Bonds also have a fixed interest rate, which is calculated and accrued every year, but they are paid together with the principal at maturity. The value calculation model is as follows:

Where p is the bond value (present value); C is the annual fixed interest; F is the principal (face value) at maturity; I is the market interest rate or the minimum rate of return required by investors; T is the number of years before the bond matures.

3. zero coupon bond's value calculation model

The so-called zero coupon bond, also known as pure debt, refers to the at discount when the bond is issued. Without coupon rate, it will be repaid at face value at maturity. The value calculation model of this bond is

Where p is the bond value (present value); F is the principal (face value) at maturity; I is the market interest rate or the minimum rate of return required by investors; T is the number of years before the bond matures.

situation

Investor A intends to buy corporate bonds of Company A as an investment. The face value of the bonds is 65,438+0,000 yuan, and that of coupon rate is 5%. The interest is simple, the term is 3 years, and the principal and interest are repaid in one lump sum. If the current market interest rate is 6%, it is suitable for investors to buy when calculating the issue price of bonds.

Answer:

The future cash flow distribution is as follows

At the end of the third year 1000×5%×3= 150 (yuan)

In other words, the price of corporate bonds is

It is worth noting that the coupon rate of some bonds is floating interest rate, and the interest of such bonds will change with the change of floating interest rate. Because the future floating interest rate is unknown, it is difficult to evaluate. Usually, the floating interest rate is estimated and the discounted cash flow method is used to price such floating interest rate bills.

02

Five theorems of bond pricing

1962, Melzi put forward five theorems of bond pricing after studying bond price, bond interest rate, maturity date and yield to maturity. These five theorems are still regarded as the classics of bond pricing theory.

Theorem 1: The market price of bonds is inversely proportional to yield to maturity. When yield to maturity rises, bond prices will fall; On the contrary, when yield to maturity falls, bond prices will rise.

Theorem 2: When the bond yield is constant, that is, the difference between coupon rate and bond yield is fixed, the maturity of bond is directly proportional to the fluctuation range of bond price. The longer the term, the greater the price fluctuation; Conversely, the shorter the term, the smaller the price fluctuation.

Theorem 3: As the maturity date of bonds approaches, the fluctuation range of bond prices decreases, and it decreases at an increasing rate; On the contrary, the longer the maturity, the greater the fluctuation of bond prices, and it is increasing at a decreasing rate.

Theorem 4: For fixed-term bonds, the decline in yield leads to a higher bond price than the increase in yield in the same range.

Theorem 5: For a given yield, the coupon rate of a bond is inversely proportional to the fluctuation range of the bond price. The higher the coupon rate, the smaller the fluctuation of bond prices.