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

$106,595

Step-by-step explanation:

Given:

Initial market rate = 9%

Dropped market interest rate, r = 7% per year

or

= 7% × [6 ÷ 12]

= 3.5% = 0.035

Remaining time, n = 9 years = 18 semi annual periods

Now,

Value of the bond at the retirement

= [ PVAF × Interest payment] + [ PVF × face value]

here,

Present value of annuity factor, PVAF =
`(1 -(1+r) ^(-n))/(r)`

or

PVAF =
`(1 -(1+0.035) ^(-18))/(0.035)`

or

PVAF = 13.189

And,

Interest payment = $100,000 × 8% × [6 ÷ 12 ] [since, 8% bonds]

= $4000

Present value factor =
`(1)/(1.035^(18))`

= 0.538

par value = $100,000

= [13.189 × $40] + [0.538 × 100,000]

= 52,758.7316 + 53,836.114

= $106,595

Hence,

The correct answer is option $106,595