Question

Bad Wolf Enterprises issues $1 million in 11.4% bonds maturing November 6, 2027. The bond is callable November 6, 2019 at a call premium of 5%. November 6, 2019 the prevailing yield is 6%.

If Bad Wolf Enterprises calls the entire issue and replaces it with 6% bonds also maturing November 6, 2027 then the present value of the decrease in coupon payments is how much? (positive number rounded $ to two places after the decimal)

Answer 1

Existing semiannual coupon = $1,000,000 * 11.4% / 2 = $57,000

New value of bond issue = $1,000,000 * (1+5%) = $1,050,000

New semiannual coupon = $1,050,000 * 6% / 2 = $31,500

Decrease in coupon = $57,000 - $31,500 = $25,500.

Calculation of Present value of decrease in coupon payments:

Nper = 8 * 2 = 16

Rate = 6% / 2 = 3%

PMT = $25,500

FV = 0

Present value of decrease in coupon payments can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(3%,16,-25500,0)
= $320,308.10

Present value of decrease in coupon payments = $320,308.10