Question

Knowledge Check 01 Zeta Corporation issues $100,000 of 8% bonds maturing in 10 years on January 1, Year 1, when the market rate of interest is 9%. The bonds were issued at a discount, Market interest rates drop to 7% by December 31, Year 1. The company retires these bonds on December 31, Year 1. How much did it cost the company to retire them? Multiple Choice $106,595 $100,000 o oo $93,496

Answer 1

A.$106,595.

bonds will be retired at value of the bonds at the time of retirement:

value = [present value of annuity factor * interest payment] + [present value factor * face value]

here,

present value of annuity factor = [1 -(1+r) ^(-n)]/r

here,

r = 7% per year =>7% *6/12 =>3.5%=>0.035.

n = 9 years remaining *2 semi annual periods=>18

=> [1-(1.035)^(-18)]/0.035

=> 0.4616389/0.035

=>13.1896829

interest payment = $100,000*8%*6/12 =>$4000

present value factor = 1/(1.035)^18

=>0.53836114.

par value = $100,000.

=>[13.1896829*$40] + [0.53836114*100,000]

=>52,758.7316+53,836.114

=>$106,595.