Valuation of Bonds -Price and performance

How to value  a Bonus at primary and secondary market

Introduction

Suppose that a company needs money to finance its operations, so it goes to funding sources. A bank may be the best alternative if the company is large and has access to preferential rates and terms; shareholders can have very high expectations in terms of performance required; A third source is the issuance of bonds under certain conditions. Suppose the firm has good performance, is known and therefore will have no difficulty placing bonds.

Calculations

Initial data: = $ 1,000 par value, term = five years, at a nominal annual coupon rate of 10% voids, bond type = bullet.

First, we calculate the annual cash flow considering coupons. It is observed that the discounted 10%, the interest rate paid by the issuer for financial equivalence, the value should be 1000, the nominal value. 

If the coupon is semiannual, the calculation is similar except that the number of periods, fees doubles and the discount rate is half the annual rate since this nominal fee. The calculations are shown in the table below 

Now we consider the initial investor who buys the bond issuer. Money certainly has an opportunity cost, that defines the rate of return. If you think that the performance of 6% is suitable, it would pay US $ 1168.5, i.e. greater than the face value of the bond (price above the par or premium price) wreck; on the contrary, if you think the performance should be 12%, the price you pay will be $ 927.9, lower than the nominal value of the bond (below the par or discounted price). It is important to note that when paying above the par, the initial investor does not lose, simply the gain keeps financial equivalence. That is, does not care to pay the sender $ 1168.5 now to receive the cash flows shown for 5 years because 6% is its opportunity cost. 

Note that whatever the rate set by the investor, the interest rate and thus the amount of the coupon, do not vary. They are two separate fees that may or may not be equal,

Suppose now that the initial investor needs liquidity and cannot demand the return to sender, go to the secondary market, which is the secondary investor who has money and an opportunity cost. This time, the bond is valued at a market price that depends on the rate of return required by the investor side.
In the table below, it is observed that if the investor believes that its opportunity cost is 14% require this fee as a financial return on their investment in the purchase of the bond. The price of $ 862.7 is undoubtedly lower than the nominal value (under the par or at a discount). 

Like the primary investor, the secondary investor can pay more than the face value (above the par), because his opportunity cost is low or for other reasons; if anything, pay more than the nominal value does not mean loss.

The secondary investor has two options trading: market information may have on the price of bonds with similar characteristics so decides to negotiate the price setting, so it is necessary to calculate the rate of return associated; moreover, you can set the rate of return and discount cash flows at this rate, to determine the price you pay.

In conclusion, it appears that for the issuer, the cash flow consists of initial income, coupons and final payment (redemption of the bond); the interest rate to calculate the coupon and the discount rate are the same. 

In the case of the primary investor, the values ​​are the same except the initial value can be lower, equal or greater than the initial value of the issuer (nominal value). The interest rate or yield determined by the investor  is i1.

For the secondary investor, also flows are similar except that the initial value is the price paid for the bond. The discount rate r determines the price paid. 

In summary, the issuer is willing to pay an interest rate i (coupon rate), the initial investor can accept that rate or different (i1 = i, i1 <i, i1> i); secondary investor has a rate of return that can be also equal, higher or lower than the initial interest rate (r=i, r<i, r>i).