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Bond is recognition of a debt given out for a long period of time, usually by means of a public, or private company, or a government to raise additional capital or financing by borrowing. An investor becomes a creditor of an issuer, but they are not normally entitled to ownership rights of the person who issues. In case the issuer is not able to meet the obligations of the bond agreement or contract, the bondholder has a greater claim over the issuer’s assets (similar to other credit cases). A bond should be exchanged at a higher price than nominal (par) value (i.e. sold at a premium), or at a price below its par value (i.e. sold at a discount).

It is of considerable importance for investors to understand the theory behind valuation of bonds. It will indicate the expected yield, should he or she elect to purchase the bond. Pricing of bonds can equally be at a premium, discount or at par. If the price with which the bond sells at is higher than the par value, the bond will be sold at a premium. Such situation arises where the current market (prevailing) rates are lower than the bond interest rate (coupon rate). Similarly, where a bond sells at a discount, it means that prevailing market rates are higher than the bonds interest rate. When investors calculate the price of a bond, they normally want to determine the maximum affordable price one would want to pay for that specific bond. They give the bonds coupon rates relative to the prevailing market rates. For a bond to become attractive to investors, the required yield or required rate of return should be higher or equal to the market interest rates at the time. (Brealey et al , 2003)

Vanilla bond is a bond without any unusual features, and it is issued with no warranty or conversion clauses, normally interests are paid at a fixed rate, and with a pre-determined maturity or redemption dates (Smith, 2008). Fundamentally, the value of a bond is the present values of all coupon (interest) payments plus the present value of the bond, once, it is mature. For bond valuation the interest rate is the required yield or rate of return.

Therefore, Bond Price = PV of all coupons received over the bond period + PV of Redemption Value (Par Value)

Where; C = Coupon Payments

i= Required yield or interest rate

n= No. of payments

From Annuities formulae, the above tedious calculations can be simplified to:

PV OF Coupons received = Coupon Payments * ( 1 – (1+i)-n)/i

PV of Redemption Value = PV of Par Value/(1+i)n

Therefore the Bond Value = C*( 1-(1+i)-n)/i + Par Value/(1+i)n

## Example 1

Company A located in Illinois, Chicago has issued a Bond with a par value of $1,000.00 redeemable after 10 Years, coupon rate is 10% and a required yield is 12%. Bond interest is payable quarterly.

Required: Coupon amount, and the Bond price.

Interest amount = .25*10%*1000=$25

Yield = .25*12% = 3%

Bond price = 25*(1-1/(1+.03)40)/.03 + 1000/(1+.03)40=$884.43

Example 2

Company B located in Baltimore issued a zero-coupon bond which is meant to mature in five years, has a par value of $1,000 and a required yield of 6%.Calculate the price.

Bond Price = PV .(1 + i)n1000 .(1 + 0.03)10 = $744.09

The first company is receiving a better bond price.

It is crucial to determine the price of a bond, because, it will indicate the yield received in the future. Lower prices mean higher costs to borrowers. The prices that buyer prefers to pay for a bond may be influenced by prevalent interest rates. If prevalent interest rates get higher than at the time issuing the bonds, the cost of the bonds drops down. That is due to new bonds being issued with coupon rates at higher level as the interest rates increase, thus, making the old bonds unattractive, unless they can be purchased at a lower price. When interest rates become higher it means lower pricing for present bonds. When interest rates get reduced, bond prices of present bonds rise: it means, an investor may sell a bond for higher than the start price. Some investors pay a premium for a beneficial bond, which has higher interest payment, it is called a coupon. Investors mostly want to pay less for a bond which has lower coupon rates in comparison with the prevailing interest rates. Also, buyers would more willingly pay for a bond with high coupon rate than for one with the prevalent interest rates.

Bankers would be safe to assume that company B will be able to repay the loan. It is because a low bond price is due to lower interest rate, which guarantees, that the bonds will rise faster. This is a positive effect; it enables even a struggling company to get back on its feet once again. When the credit rating of the company is low, the bond’s price move better than those of the company with a good credit rating. The first company, therefore, has a lower credit rating and subsequently lower interest rates. Prices of bonds are highly affected by interest rates. When interest rates are high, prices of bonds are charged less, than when the interest rates are low. Higher credit rating tells an investor that, the company is stable, but stagnant at its current situation. Lower credit rating, however, tells an investor that, it has higher volatility and is more profitable.