Question

Suppose that General Motors Acceptance Corporation issued a bond with 10 years until​ maturity, a face value of

$ 1 comma 000$1,000​,

and a coupon rate of

7.9 %7.9%

​(annual payments). The yield to maturity on this bond when it was issued was

6.3 %6.3%.

Assuming the yield to maturity remains​ constant, what is the price of the bond immediately after it makes its first coupon​ payment?

Answer 1

Answer - Price of the bond after 1 year will be 1120.92

Workings

YTM = [C + (F-P)/N] / (F+P)/2

Where:

YTM = Yield to Maturity

C = Annual Coupan Payment

F = Face Value of the Bond

P = Purchase Price OR Current Market Price of the Bond

N = Number of years remaining to maturity

Step 1 - Calculation of Number of Years N

After making the first coupan payment number of years left for the bond to mature = 9 Years (N=9)

Step 2 - Calculation of Bond price

Coupan C = 1000 * 7.9% = 79

Face Value F = 1000

N = 9 Years

YTM = 6.3%

Current Price of the Bond = P

YTM = [C + (F-P)/N] / (F+P)/2

0.063 = [79 + (1000-P)/9] /(1000+P)/2

0.063*[(1000+P)/2] = 79 + (1000-P)/9

0.063*[500 + 0.5P] = 79 + 111.11 – 0.11P

31.5 + 0.0315P = 190.11 – 0.11P

0.1415P = 158.61

P = 1120.92

Price of the bond after 1 year = 1120.92