Chapter 10, Problem 6AP

1.

To determine

Calculate the issuance price of the bonds on January 1 of this Year.

Explanation of Solution

Bonds Payable: Bonds payable are referred to long-term debts of the business, issued to various lenders known as bondholders, generally in multiples of $1,000 per bond, to raise fund for financing the operations.

Effective-interest method of amortization: It is an amortization model that apportions the amount of bond discount or premium based on the market interest rate.

Present Value: The value of today’s amount expected to be paid or received in the future at a compound interest rate is called as present value.

Determine the issuance price of the bonds.

Step 1: Calculate the cash interest payment for bonds.

$\begin{array}{c}\text{Cash interest payment}=\text{Face value}\times \text{Coupon rate}\times \text{Interest time period}\\ =\$4,000,000\times 9\%\times 1\\ =\$360,000\end{array}$

Step 2: Calculate the present value of cash interest payment.

Particulars	Amount
Interest payment (a)	$120,000
PV factor at annual market interest rate of 6% for 5 periods (b)	4.21236
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$1,516,450

Table (1)

Note: The present value factor for 5 periods at 6% interest would be 4.21236 (Refer Appendix E (Table E.2) in the book for present value factor).

Step 3: Calculate the present value of single principal payment of $4,000,000 (principal amount) at 6% for 5 periods.

Particulars	Amount
Single principal payment (a)	$4,000,000
PV factor at annual market interest rate of 6% for 5 periods (b)	0.74726
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$2,989,040

Table (2)

Note: The present value factor for 5 periods at 6% interest would be 0.74726 (Refer Appendix E (Table E.1) in the book for present value factor).

Step 4: Calculate the issue price of the bonds.

$\begin{array}{c}\text{Issue price of the bonds }=\left(\begin{array}{c}\text{Present value of interest payment} \\ +\text{ Present value of single principal payment}\end{array}\right)\\ =\left(\begin{array}{l}\text{\$1,516,450}\left(\text{from table 1}\right)\\ +\text{\$2,989,040}\left(\text{from table 2}\right)\end{array}\right)\\ =\text{\$4,505,490}\end{array}$

Conclusion

Hence, the issuance price of the bonds on January 1 of this Year is $4,505,490.

2.

To determine

Calculate the amount of interest expense that should be recorded on December 31 of this year.

Explanation of Solution

Bonds: Bonds are long-term promissory notes that are issued by a company while borrowing money from investors to raise fund for financing the operations.

Interest Expense: The cost of debt which is occurred during a particular period of time is called interest expense. The interest amount is payable on the principal amount of debt at a fixed interest rate.

Calculate the amount of interest expense that that should be recorded on December 31 of this year.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\left(\text{issue price}\right)\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$4,505,490}\times 6\%\times 1\\ =\$270,329\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31 of this year is $270,329.

To determine

Calculate the amount of interest expense that should be recorded on December 31 of next year.

Explanation of Solution

Bonds: Bonds are long-term promissory notes that are issued by a company while borrowing money from investors to raise fund for financing the operations.

Interest Expense: The cost of debt which is occurred during a particular period of time is called interest expense. The interest amount is payable on the principal amount of debt at a fixed interest rate.

Calculate the amount of interest expense that that should be recorded on December 31 of next year.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= }\left(\$4,505,490-\left(\$360,000-\$270,329\right)\right)\times 6\%\times 1\\ =\$264,949\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31 of next year is $264,949.

3.

To determine

Calculate the amount of cash that should be paid on December 31 of this year.

Explanation of Solution

Bonds: Bonds are long-term promissory notes that are issued by a company while borrowing money from investors to raise fund for financing the operations.

Calculate the amount of cash that should be paid on December 31 of this year.

$\begin{array}{c}\text{Cash paid}=\left(\begin{array}{l}\text{Face value of bond }\times \text{coupon rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$4,000,000}\times 9\%\times 1\\ =\$360,000\end{array}$

Conclusion

Hence, amount of cash that should be paid on December 31 of this year is $360,000.

To determine

Calculate the amount of cash that should be paid on December 31 of next year.

Explanation of Solution

Bonds: Bonds are long-term promissory notes that are issued by a company while borrowing money from investors to raise fund for financing the operations.

Calculate the amount of cash that should be paid on December 31 of next year.

$\begin{array}{c}\text{Cash paid}=\left(\begin{array}{l}\text{Face value of bond }\times \text{coupon rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$4,000,000}\times 9\%\times 1\\ =\$360,000\end{array}$

Conclusion

Hence, amount of cash that should be paid on December 31 of next year is $360,000.

4.

To determine

Calculate the book value of the bonds on December 31 of this year.

Explanation of Solution

Bonds: Bonds are long-term promissory notes that are issued by a company while borrowing money from investors to raise fund for financing the operations.

Determine the book value of the bonds on December 31 of this year.

$\begin{array}{c}\begin{array}{l}\text{Book value of bond on }\\ \text{December 31 of this year}\end{array})\text{ =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ -\text{Premium amortized on December 31 of this year}\end{array}\right)\\ =\left(\$4,505,490-\left(\$360,000-\$270,329\right)\right)\\ =\$4,415,819\end{array}$

Conclusion

Hence, the book value of the bonds on June 30 of this year is $4,415,819.

To determine

Calculate the book value of the bonds on December 31 of next year.

Explanation of Solution

Bonds: Bonds are long-term promissory notes that are issued by a company while borrowing money from investors to raise fund for financing the operations.

Determine the book value of the bonds on December 31 of next year.

$\begin{array}{c}\begin{array}{l}\text{Book value of bond on }\\ \text{December 31of next year}\end{array})\text{ =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ -\text{Premium amortized on December 31 of this year}\\ -\text{Premium amortized on December 31 of next year}\end{array}\right)\\ =\left(\begin{array}{l}\$4,505,490-\left(\$360,000-\$270,329\right)\\ -\left(\$360,000-\$264,949\right)\end{array}\right)\\ =\$4,320,768\end{array}$

Conclusion

Hence, the book value of the bonds on December 31 of next year is $4,320,768.