Chapter 14, Problem 6BTN

To determine

Issue of bond at premium:

When the coupon rate or contract rate of a bond is higher than the market interest rate, the bond is being issued at premium. If the bond is issued at premium, the selling price of the bond will be higher than the face value of the bond.

Effective interest method:

Effective interest method aims at computing an accurate interest expense. In case of issue of bonds on premium, the carrying value of the bonds payable inclusive of premium amortized is used to determine the interest expense during a particular period. Hence the interest expense decreases as the carrying value of the bonds decrease.

To determine:

1. Preparation of format of amortization table for bond premium using effective interest method.

2 Allocating the amounts in their respective columns

3. Determine the final number in each column.

4. Computation of total bond interest expense over the life of the bonds.

5. Prepare similarities and differences between the amortization table for premium and discount.

Answer to Problem 6BTN

Solution:

1.

Period Ending	Cash Interest Paid	Bond Interest Expense	Premium Amortization	Unamortized Premium	Carrying Value

2.

Period Ending	(A) Cash Interest Paid 4.5% X Par Value	(B) Bond Interest Expense 4% X Prior (E)	(C) Premium Amortization (A) − (B)	(D) Unamortized Premium Prior (D) − (C)	(E) Carrying Value Par Value + (D)
01/1/2015				$4,100	$104,100
06/30/2015	$4,500	$4,164	$336	$3,764	$103,764
12/31/2015	$4,500	$4,151	$349	$3,415	$103,415
06/30/2016	$4,500	$4,137	$363	$3,052	$103,052
12/31/2016	$4,500	$4,122	$378	$2,674	$102,674
06/30/2017	$4,500	$4,107	$393	$2,281	$102,281
12/31/2017	$4,500	$4,091	$409	$1,872	$101,872
06/30/2018	$4,500	$4,075	$425	$1,447	$101,447
12/31/2018	$4,500	$4,058	$442	$1,005	$101,005
06/30/2019	$4,500	$4,040	$460	$545	$100,545

3. Final numbers of each column

12/31/2019	$4,500	$3,955	$545	0	$100,000
	$45,000	$40,900	$4,100

4. The total interest expense over the life of the bonds is $40,900.

5.

Similarities	Issue of bonds on premium	Issue of bonds on discount
Cash Interest Payment	Constant over the bonds’ life	Constant over the bonds’ life
Unamortized Discount / Premium	Diminishing periodically till maturity	Diminishing periodically till maturity
Differences
Bond Interest Expense	Decreases periodically over the life of the bonds.	Increases periodically over the life of the bonds.
Discount /Premium Amortization	Premium amortization per period is computed by deducting the interest expense from the cash interest payment.	Discount amortization per period is computed by deducting the cash interest payment from the interest expense.
Carrying Value	The carrying value decreases periodically till it becomes equal to par value at the maturity. (Par Value + Unamortized Premium)	The carrying value increases periodically till it becomes equal to par value at the maturity. (Par Value - Unamortized Discount)

Explanation of Solution

Explanation:

2.
  $\begin{array}{l}\text{Premium }onBondsPayable=Issuepriceofthebond–Parvalueofthebond\hfill \\ =\$104,100*-\$100,000\hfill \\ \begin{array}{l} =\$4,100\\ *IssuePrice=\$100,000X1.041=\$104,100\end{array}\hfill \end{array}$

Same steps are followed through all the period till the maturity of the bonds.

4.

Computation of total interest expense
Amount to be repaid at maturity:
Total Interest Payment	$45,000
Par Value of Bonds	$100,000
Total amount to be repaid	$145,000
Less : Selling Price of the Bonds	$104,100
Total Bond Interest Expense	$40,900

  $\begin{array}{l}*InterestPayment=\$4,500X\text{ 10 }=\$45,000\hfill \\ *SemiannualInterestPayment=\$100,000X0.045=\$4,500\hfill \end{array}$

Conclusion

Conclusion:

Thus, from the above we can clearly understand the differences and the similarities between the amortization table for premium and discount.