Question

A 7 year maturity corporate bond has coupon rate of 7% and pays coupon semi-annually. Considering Par value of $1000, what would be the bond price if Effective Annual Yield is 10%?

Please explain all steps, Thanks!

Answer 1

Face Value = $1,000

Annual Coupon Rate = 7.00%
Semiannual Coupon Rate = 3.50%
Semiannual Coupon = 3.50% * $1,000
Semiannual Coupon = $35

Time to Maturity = 7 years
Semiannual Period = 14

Effective Annual Yield = 10%

1 + Effective Annual Yield = (1 + Semiannual YTM)^2
1.10 = (1 + Semiannual YTM)^2
1.0488 = 1 + Semiannual YTM
Semiannual YTM = 0.0488 or 4.88%

Price of Bond = $35 * PVIFA(4.88%, 14) + $1,000 * PVIF(4.88%, 14)
Price of Bond = $35 * (1 - (1/1.0488)^14) / 0.0488 + $1,000 / 1.0488^14
Price of Bond = $35 * 9.97503 + $1,000 * 0.51322
Price of Bond = $862.35

So, price of the bond is $862.35