Chapter 10, Problem 10.6P

Recording and Reporting Bonds Issued at a Discount (AP10-3)

L010-4 PowerTap Utilities is planning to issue bonds with a face value of $1,000,000 and a coupon rate of 10 percent. The bonds mature in 10 years and pay interest semiannually every June 30 and December 31. All of the bonds were sold on January 1 of this year. PowerTap uses the effective-interest amortization method. Assume an annual market rate of interest of 12 percent.

Required:

1. 1. What was the issue price on January 1 of this year?
2. 2. What amount of interest expense should be recorded on June 30 and December 31 of this year?
3. 3. What amount of cash should be paid to investors June 30 and December 31 of this year?
4. 4. What is the book value of the bonds on June 30 and December 31 of this year?

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.

$\begin{array}{c}\text{Cash interest payment}=\text{Face value}\times \text{Coupon rate}\times \text{Interest time period}\\ =\$1,000,000\times 10\%\times \frac{1}{2}\\ =\$50,000\end{array}$

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

Particulars	Amount
Interest payment (a)	$50,000
PV factor at annual market interest rate of 6% for 20 periods (b)	11.4699
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$573,495

Table (1)

Note: The present value factor for 20 periods at 6% interest would be 11.4699 (Refer Appendix E (Table E.2) in the book for present value factor).

Step 3: Calculate the present value of single principal payment of $1,000,000 (principal amount) at 6% for 20 periods.

Particulars	Amount
Single principal payment (a)	$1,000,000
PV factor at annual market interest rate of 6% for 20 periods (b)	0.31180
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$311,800

Table (2)

Note: The present value factor for 20 periods at 6% interest would be 0.31180 (Refer Appendix E (Table E.1) in the book for present value factor).

Step 4: Calculate the issue price of the bonds.

$\begin{array}{c}\text{Issue price of the bonds }=\left(\begin{array}{c}\text{Present value of interest payment} \\ +\text{ Present value of single principal payment}\end{array}\right)\\ =\left(\begin{array}{l}\text{\$573,495}\left(\text{from table 1}\right)\\ +\text{\$311,800}\left(\text{from table 2}\right)\end{array}\right)\\ =\text{\$885,295}\end{array}$

Conclusion

Hence, The issuance price of the bonds on January 1 of this Year is $885,295.

To determine

Calculate the amount of interest expense that should be recorded on June 30 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 June 30 of this year.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\left(\text{issue price}\right)\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$885,295}\times 12\%\times \frac{1}{2}\\ =\$53,118\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on June 30 of this year is $53,118.

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.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= }\left(\$885,295+\left(\$53,118-\$50,000\right)\right)\times 12\%\times \frac{1}{2}\\ =\$53,305\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31 of this year is $53,305.

To determine

Calculate the amount of cash that should be paid to investors on June 30 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 to investors on June 30 of this year.

$\begin{array}{c}\text{Cash paid}=\left(\begin{array}{l}\text{Face value of bond }\times \text{coupon rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$1,000,000}\times 10\%\times \frac{1}{2}\\ =\$50,000\end{array}$

Conclusion

Hence, amount of cash that should be paid to investors on June 30 of this year is $50,000.

To determine

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

$\begin{array}{c}\text{Cash paid}=\left(\begin{array}{l}\text{Face value of bond }\times \text{coupon rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$1,000,000}\times 10\%\times \frac{1}{2}\\ =\$50,000\end{array}$

Conclusion

Hence, amount of cash that should be paid to investors on December 31 of this year is $50,000.

To determine

Calculate the book value of the bonds on June 30 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 June 30 of this year.

$\begin{array}{c}\text{Book value of bond on June 30 =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ \text{+}\text{Discount amortized on June 30}\end{array}\right)\\ =\left(\$885,295+\left(\$53,118-\$50,000\right)\right)\\ =\$888,413\end{array}$

Conclusion

Hence, the book value of the bonds on June 30 of this year is $888,413.

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.

$\begin{array}{c}\text{Book value of bond on December 31 =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ \text{+}\text{Discount amortized on June 30}\\ \text{+Discount amortized on December 31}\end{array}\right)\\ =\left(\begin{array}{l}\$885,295+\left(\$53,118-\$50,000\right)\\ +\left(\$53,305-\$50,000\right)\end{array}\right)\\ =\$891,718\end{array}$

Conclusion

Hence, the book value of the bonds on December 31 of this year is $891,718.