Chapter 10, Problem 3AP

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.

$\begin{array}{c}\text{Cash interest payment}=\text{Face value}\times \text{Coupon rate}\times \text{Interest time period}\\ =\$2,000,000\times 6\%\times 1\\ =\$120,000\end{array}$

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 7% for 5 periods (b)	4.10020
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$492,024

Table (1)

Note: The present value factor for 5 periods at 7% interest would be 4.10020 (Refer Appendix E (Table E.2) in the book for present value factor).

Step 3: Calculate the present value of single principal payment of $2,000,000 (principal amount) at 7% for 5 periods.

Particulars	Amount
Single principal payment (a)	$2,000,000
PV factor at annual market interest rate of 7% for 5 periods (b)	0.71299
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$1,425,980

Table (2)

Note: The present value factor for 5 periods at 7% interest would be 0.71299 (Refer Appendix E (Table E.1) in the book for present value factor).

Step 4: Calculate the issue price of the bonds.

$\begin{array}{c}\text{Issue price of the bonds }=\left(\begin{array}{c}\text{Present value of interest payment} \\ +\text{ Present value of single principal payment}\end{array}\right)\\ =\left(\begin{array}{l}\text{\$492,024}\left(\text{from table 1}\right)\\ +\text{\$1,425,980}\left(\text{from table 2}\right)\end{array}\right)\\ =\text{\$1,918,004}\end{array}$

Conclusion

Hence, The issuance price of the bonds on January 1 of this Year is $1,918,004.

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.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\left(\text{issue price}\right)\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$1,918,004}\times 7\%\times 1\\ =\$134,260\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31 of this year is $134,260.

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.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= }\left(\$1,918,004+\left(\$134,260-\$120,000\right)\right)\times 7\%\times 1\\ =\$135,258\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31 of next year is $135,258.

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.

$\begin{array}{c}\text{Cash paid}=\left(\begin{array}{l}\text{Face value of bond }\times \text{coupon rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$2,000,000}\times 6\%\times 1\\ =\$120,000\end{array}$

Conclusion

Hence, amount of cash that should be paid on December 31 of this year is $120,000.

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.

$\begin{array}{c}\text{Cash paid}=\left(\begin{array}{l}\text{Face value of bond }\times \text{coupon rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$2,000,000}\times 6\%\times 1\\ =\$120,000\end{array}$

Conclusion

Hence, amount of cash that should be paid on December 31 of next year is $120,000.

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.

$\begin{array}{c}\begin{array}{l}\text{Book value of bond on }\\ \text{December 31 of this year}\end{array})\text{ =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ \text{+}\text{Discount amortized on December 31 of this year}\end{array}\right)\\ =\left(\$1,918,004+\left(\$134,260-\$120,000\right)\right)\\ =\$1,932,264\end{array}$

Conclusion

Hence, the book value of the bonds on June 30 of this year is $1,932,264.

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.

$\begin{array}{c}\begin{array}{l}\text{Book value of bond on }\\ \text{December 31of next year}\end{array})\text{ =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ \text{+}\text{Discount amortized on December 31 of this year}\\ \text{+Discount amortized on December 31 of next year}\end{array}\right)\\ =\left(\begin{array}{l}\$1,918,004+\left(\$134,260-\$120,000\right)\\ +\left(\$135,258-\$120,000\right)\end{array}\right)\\ =\$1,947,522\end{array}$

Conclusion

Hence, the book value of the bonds on December 31 of next year is $1,947,522.