Question

Chinook Inc. has available for issue a $3,270,000 bond due in eight years. Interest at the rate of 6.50% is to be paid semiannually. Calculate the issue price if the market interest rate is: (Do not round intermediate calculations. Round the final answers to the nearest whole dollar amount.)
a.5.50%

b.6.50%

c.7.25%

Answer 1

Solution:

Par value of bond = $3,270,000

Coupon rate = 6.50%, 3.25% semi annual

Period = 8 year, 16 semiannual period

a. Market rate of interest = 5.50%, Semiannual rate = 2.75%

Issue price of bond = Present value of future cash flows discounted at market rate of interest

= ($3,270,000*3.25%)*Cumulative PV Factor at 2.75% discount rate for 16 periods + $3,270,000* PV factor at 2.75% for 16^th period

= $106,275*12.80457 + $3,270,000*0.647874 = $3,479,354

b. Market rate of interest = 6.50%, Semiannual rate = 3.25%

Issue price of bond = Present value of future cash flows discounted at market rate of interest

= ($3,270,000*3.25%)*Cumulative PV Factor at 3.25% discount rate for 16 periods + $3,270,000* PV factor at 3.25% for 16^th period

= $106,275*12.32435 + $3,270,000*0.599458 = $3,270,000

c. Market rate of interest = 7.25%, Semiannual rate = 3.625%

Issue price of bond = Present value of future cash flows discounted at market rate of interest

= ($3,270,000*3.25%)*Cumulative PV Factor at 3.625% discount rate for 16 periods + $3,270,000* PV factor at 3.625% for 16^th period

= $106,275*11.98136 + $3,270,000*0.565675 = $3,123,076