Chapter 10, Problem 1CON

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 current value of an amount that is to be paid or received in future is called as present value.

Determine the issuance price of the bonds.

Step 1: Calculate the cash interest payment for bonds.

$\begin{array}{c}\text{Cash interest payment}=\text{Face value}\times \text{Coupon rate}\times \text{Interest time period}\\ =\$750,000,000\times 5\%\times \frac{1}{2}\\ =\$18,750,000\end{array}$

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

Particulars	Amount
Interest payment (a)	$18,750,000
PV factor at annual market interest rate of 2% for 20 periods (b)	16.35143
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$306,589,313

Table (1)

Note: The present value factor for 20periods at 2% interest would be 16.35143 (Refer Appendix E (Table E.2) in the book for present value factor).

Step 3: Calculate the present value of single principal payment of $750,000,000 (principal amount) at 2% for 20 periods.

Particulars	Amount
Single principal payment (a)	$750,000,000
PV factor at annual market interest rate of 2% for 20 periods (b)	0.67297
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$504,727,500

Table (2)

Note: The present value factor for 20periods at 2% interest would be 0.67297 (Refer Appendix E (Table E.1) in the book for present value factor).

Step 4: Calculate the issue price of the bonds.

$\begin{array}{c}\text{Issue price of the bonds }=\left(\begin{array}{c}\text{Present value of interest payment} \\ +\text{ Present value of single principal payment}\end{array}\right)\\ =\left(\begin{array}{l}\text{\$306,589,313}\left(\text{from table 1}\right)\\ +\text{\$504,727,500}\left(\text{from table 2}\right)\end{array}\right)\\ =\text{\$811,316,813}\end{array}$

Conclusion

Hence, The issuance price of the bondson January 1 of this Year is $811,316,813.

2.

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.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\left(\text{issue price}\right)\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$811,316,813}\times 4\%\times \frac{1}{2}\\ =\$16,226,336\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on June 30 of this year is $16,226,336.

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.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= }\left(\$811,316,813-\left(\$18,750,000-\$16,226,336\right)\right)\times 4\%\times \frac{1}{2}\\ =\$16,175,863\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31 of this year is $16,175,863.

3.

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 on June 30 of this year.

$\begin{array}{c}\text{Cash paid}=\text{Face value}\times \text{Coupon rate}\times \text{Interest time period}\\ =\$750,000,000\times 5\%\times \frac{1}{2}\\ =\$18,750,000\end{array}$

Conclusion

Hence, amount of cash that should be paid on June 30 of this year is $18,750,000.

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.

$\begin{array}{c}\text{Cash paid}=\text{Face value}\times \text{Coupon rate}\times \text{Interest time period}\\ =\$750,000,000\times 5\%\times \frac{1}{2}\\ =\$18,750,000\end{array}$

Conclusion

Hence, amount of cash that should be paid on December 31 of this year is $18,750,000.

4.

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.

$\begin{array}{c}\text{Book value of bond on June 30 =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ -\text{Premium amortized on June 30}\end{array}\right)\\ =\left(\$811,316,813-\left(\$18,750,000-\$16,226,336\right)\right)\\ =\$808,793,149\end{array}$

Conclusion

Hence, the book value of the bonds on June 30 of this year is $808,793,149.

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.

$\begin{array}{c}\text{Book value of bond on December 31 =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ -\text{Premium amortized on June 30}\\ -\text{Premium amortized on December 31}\end{array}\right)\\ =\left(\begin{array}{l}\left(\begin{array}{l}\$811,316,813\\ -\left(\$18,750,000-\$16,226,336\right)\end{array}\right)\\ -\left(\$18,750,000-\$16,175,863\right)\end{array}\right)\\ =\$806,219,012\end{array}$

Conclusion

Hence, the book value of the bonds on December 31 of this year is $806,219,012.