Bonds

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Bonds also known as “Fixed Income Security” are financial instruments that help governments, companies or other issuer of the bond to borrow money from the market.  Bonds are considered to be debt instruments unlike equities (Shares); Equity gives an investor opportunity to be a partner in the business thus shares profit and losses proportionally, whereas while investing in a bond; investor acts as a creditor.

Why Bonds named as Fixed Income Security? : Bonds are known as fixed income as bonds make a periodic stream of interest payments to investors while repaying the principal sum on a specified maturity date.

Bonds can be considered as financial contract between the lender (Investor) of the money and the borrower (Government or Corporations) as per which the borrower of the money would make regular interest payment on the amount borrowed. On the date of maturity borrower would payback principal borrowed along with final interest payment.

Valuation of Bonds: While investing in bonds; investor calculates the present value of the bond which is sum of the all the expected cash flows. Bond valuation process involves the following three steps:

  1. Estimation of the expected cash flows.
  2. Determine the appropriate interest rate that could be used to discount the future cash flows.
  3. Finally; discount all the expected cash flows with the appropriate discount rate.

Key Bond Characteristics: Before we understand the valuation process; it will be helpful if we understand few key terminologies.

  1. Face Value: The face value (also known as the par value) of a bond is the price at which the bond is sold to investors when first issued; it is also the price at which the bond is redeemed at maturity. In the U.S., the face value is usually $1,000 or a multiple of $1,000.
  2. Coupon Rate: The coupon rate, which is generally fixed, determines the periodic coupon or interest payments. It is expressed as a percentage of the bond’s face value. It also represents the interest cost of the bond issue to the issuer.
  3. Coupon: The coupon payments represent the periodic interest payments from the bond issuer to the bondholder. The annual coupon payment is calculated be multiplying the coupon rate by the bond’s face value. Since most bonds pay interest semiannually, generally one half of the annual coupon is paid to the bondholders every six months.
  4. Date of Maturity: The maturity date represents the date on which the bond matures, i.e., the date on which the face value is repaid. The last coupon payment is also paid on the maturity date.
  5. Yield to Maturity: The rate of return that an investor would earn if he bought the bond at its current market price and held it until maturity. Alternatively, it represents the discount rate which equates the discounted value of a bond’s future cash flows to its current market price.

Valuation of a Bond: Below is the formula used for the valuation of bond.

Where

C = coupon payment

i = interest rate, or required yield (Yield to Maturity)

M = value at maturity (par value + final coupon payment)

n = number of payments

As per above formula; price of a bond is the present value of its promised cash flows.

Market interest rate (to be used as Yield to Maturity or discount rate as investor expects bond should give return at least equal to market interest rate); impacts the price of the bond. Below given three scenarios help us to understand.

As an example, suppose that a bond has a face value of $1,000, a coupon rate of 4% and a maturity of four years and bond makes annual coupon payments.

From above results, we could infer following three scenarios:

  1. If i > coupon rate, P < face value.
  2. If i = coupon rate, P = face value.
  3. If i < coupon rate, P > face value.

These results also demonstrate that there is an inverse relationship between yields and bond prices:

  1. When yields rise, bond prices fall.
  2. When yields fall, bond prices rise.

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