Question

Assume that Bunch Inc. Has an issue of 18-year $1,000 par value bonds with 7% of annual coupon rate. The coupon is paid semi-annually. Further assume that today's Yield to Maturity (YTM) on these bonds is 5%. How much would these bonds sell for today?

Please show work on how to get answer.

Answer 1

Face Value = $1,000

Annual Coupon Rate = 7%
Semiannual Coupon Rate = 3.50%
Semiannual Coupon = 3.50% * $1,000
Semiannual Coupon = $35

Time to Maturity = 18 years
Semiannual Period to Maturity = 36

Annual YTM = 5%
Semiannual YTM = 2.50%

Price of Bond = $35 * PVIFA(2.50%, 36) + $1,000 * PVIF(2.50%, 36)
Price of Bond = $35 * (1 - (1/1.025)^36) / 0.025 + $1,000 / 1.025^36
Price of Bond = $35 * 23.55625 + $1,000 * 0.41109
Price of Bond = $1,235.56

So, bonds are selling at $1,235.56