Question

Yan Yan Corp. has a $5,000 par value bond outstanding with a coupon rate of 4.2 percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 4.4 percent.What is the price of the bond?

Answer 1

:

The price of the Bond is $4887

Step-by-step explanation:

Bond price can be defined as the present discounted value of future cash stream generated by a bond. In other words, it is the sum of the present values of all likely coupon payments plus the present value of the par value at maturity. To calculate the bond price, one can apply the formula stated below.

Bond Price =
`(C*(1-(1+r)^(-n) )/(r)`+
`(F)/((1+r)^(n) )`

Where,

F = The face/par value

C = Coupon payment

n = Number of periods till maturity

r = Yield to maturity

From the question

C = $5,000 *4.2% = $210

F = $5,000

n = 16

r = 4.4%

now (1+r) = 1+0.044 = 1.044

`(1+0.044)^(16)`=
`1.044^(16)` =1.9916

`(1+0.044^(-16)` =
`1.044^(-16)` =0.502

Substituting into the formula we have

Bond Price =
`(210*(1-(1+0.044)^(-16) )/(0.044)` +
`(5000)/((1+r)^(16) )`

Bond Price =
`(210*(1-0.502))/(0.044)` +
`(5000)/(1.9916)`

= 2376.8 +2510.54 =4887.358

The price of the Bond is $4887