A company issues a ten-year bond at par with a coupon rate of 6.2 % paid semi-annually. The YTM at the beginning of the third year of the bond (8 years left to maturity) is 9.5 %. What is the new price of the bond?

What is the new price of the bond?

Price $817,95

Explanation:

To know the new Price of the bond we need first to calculate the Present Value of the Principal and then through the annuity method calculate the Present Value of the coupons.

Bond Value

Principal Present Value = F / (1 + r) ^t

Coupon Present Value = C x [1 - 1 / (1 + r) ^t] / r

The price of this bond it's $475,92 + $342,03 = $817,95

Bond $1,000

Coupon $62,00

SemmiAnnual Coupon $31,00

SemmiAnnual Rate 3,1%

YTM 9,5%

Semiannual YTM Rate 4,75%

Years 8

Periods 16

Present Value of Bonds $475,92 = $1,000 / (1+0,0475) ^16

Bond $1.000

Coupon $62,00

SemmiAnnual Coupon $31,00

SemmiAnnual Rate 3,1%

YTM Rate 9,50%

Semiannual YTM Rate 4,75%

Years 8

Periods 16

Present Value of Coupons $342,03 = $31 (Coupon) x 11,03

11,03 = [1 - 1 / (1+0,0475) ^16 ] / 0,0475