Question

Explain, conceptually, how bonds are priced. Provide an example of a bond and explain how bond yields are calculated.

Answer 1

pricing of a bond:

a bond can be sold at par,above par, or below par. A bond provides payments in the form of coupons to the investor.

these payments can be either annually,semi annually or quarterly.

The yield is the rate ,which the investor demands for the issuer for purchasing the bond.

the bonds tenure can be any number of years during which the investor holds the bond. let me explain this to you with the help of an example.

suppose,

the FV of a bond is 1000

the coupon payments are 50( coupon rate 5%)

the tenure of the bond is 3 years. ytm is 6%

now,discounting these cash flows back at the YTM , we get the PV of the bond.

50/1.06 + 50/1.06^2 + 1050/1.06^3

so the pv of the bond is : 47.16 +44.49 +881.16

= $972.81

the present value of the bond is less,as the bond is being sold at a discount to attract investors. the rate at which the coupon payments are discounted back i.e the current yield is higher than the coupon payments received.

calculating bond yields:

investors often calculate bond yields which is the minimum amount they want from the money they have invested in purchasing the bond.

the investor will receive coupon payments ,suppose a bond which will pay 5 % coupon payments it par value is 100. it is presently trading at 90.

the YTM can be calculated as :

coupon payments = 5%100 = 5

5/90 * 100 = 5.55%

this is a approximate number,

now taking into consideration the price movements, the $100 bond is currently trading at 90 and the time to maturity is 4 years, so the adjustment factor

(100 -90)/4 = 2.5

so the YTM is 5.55.+2.5 = 8.05