Question

A software company has 11 percent coupon bond on the market with 20 years to maturity, and the par value of $1,000. The bonds make semi-annual coupon payments and currently sell for $1,125. What is the YTM? If the bond with the same maturity and similar risk pays 8% annual coupon (pays semi-annually), what should be the market price of the second bond?

Answer 1

CALCULATION OF YTM OR YIELD TO MATURITY OF FIRST BOND:

FORMULA:

=(C+(F-P)/n)/(F+P)/2)

WHERE;

C=COUPON

F=FACE VALUE

P=PRICE OF BOND

n= YEARS TO MATURITY

Over here, Calculations to be done because it is semi annually:

COUPAN=F*COUPAN RATE/2

=1000*11%/2

=55

n= Number of years*2

=20*2

=40

SUM:

=((55+(1000-1125)/40)/((1000+1125)/2)

=0.0488 OR 4.88%

MARKET PRICE OF SECOND BOND:

Bond Price = ∑(C_n / (1+YTM)ⁿ )+ P / (1+i)n

=∑(40n/ (1+0.034706)ⁿ )+ 1000 / (1+i)n

=($1113.57)

The value of bond at 8% coupon rate (semi annually) is ($1113.57).

NOTE: BELOW IS THE CALCULATION OF BOND IN EXCEL.