Question

TR issues 6.9%, 5-year bonds with a total face amount of $1,000,000. The market interest rate for bonds of similar risk and maturity is 6.8%. Interest is paid semi-annually. DO NOT ROUND YOUR ANSWERS UNTIL YOU FULLY COMPLETE THE PROBLEM SET (input your answers after you’ve completed the entire problem).

4.    $___________ (rounded to nearest dollar). What is the issue price of the bond?      

5.    $___________ (rounded to nearest dollar). When the company records the first interest payment, how much will the company record for interest expense?                                                                                                                                                                                                                                                                               

6.    $___________ (rounded to nearest dollar). What is the bond liability (carrying amount) after the first interest payment?                                                                                                                                                                          

7.            $___________ (rounded to nearest dollar). When the company records the second interest payment, how much will the company record for interest expense?                                   

Answer 1

Answer to Part 1.
Face Value of Bonds = $1,000,000

Annual Coupon Rate = 6.90%
Semiannual Coupon Rate = 3.45%
Semiannual Coupon = 3.45% * $1,000,000
Semiannual Coupon = $34,500

Time to Maturity = 5 years
Semiannual Period = 10

Annual YTM = 6.80%
Semiannual YTM = 3.40%

Issue Price of Bonds = $34,500 * PVIFA(3.40%, 10) + $1,000,000 * PVIF(3.40%, 10)
Issue Price of Bonds = $34,500 * (1 - (1/1.034)^10) / 0.034 + $1,000,000 * (1/1.034)^10
Issue Price of Bonds = $34,500 * 8.358682 + $1,000,000 * 0.715805
Issue Price of Bonds = $1,004,180

Answer to Part 2.
Interest Expense = Beginning Carrying Value * Market Rate of interest
Interest Expense in First interest payment = $1,004,180 * 6.80% * 6/12
Interest Expense in First interest payment = $34,142

Answer to Part 3.
Interest Paid = 34,500
Interest Expense = $34,142
Premium Amortized = Interest paid – Interest Expense
Premium Amortized = $34,500 - $34,142
Premium Amortized = $358

Carrying Amount = Beginning Carrying Value – Premium Amortized
Carrying Amount after first interest = $1,004,180 - $358
Carrying Amount after first interest = $1,003,822

Answer to Part 4.
Interest Expense = Beginning Carrying Value * Market Rate of interest
Interest Expense in Second interest payment = $1,003,822 * 6.80% * 6/12
Interest Expense in Second interest payment = $34,130