Chapter 10, Problem 6AP

1.

To determine

Calculate the issuance price of the bonds on January 1, 2014.

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 issue price of the bonds on January 1, 2014.

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)	$360,000
PV factor at annual market interest rate of 6% for 5 periods (b)	4.2124
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$1,516,464

Table (1)

Note: The present value factor for 5 periods at 6% interest would be 4.2124 (Refer Appendix A (Table A.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)	0.7473
Present value $\left(\text{a}\right)\times \left(\text{b}\right)$	$2,989,200

Table (2)

Note: The present value factor for 5 periods at 6% interest would be 0.7473 (Refer Appendix E (Table E.1) in the book for present value factor).

Step 4: Calculate the issue price of the bonds.

$\begin{array}{c}\text{Issue price of the bonds }=\left(\begin{array}{c}\text{Present value of interest payment} \\ +\text{ Present value of single principal payment}\end{array}\right)\\ =\left(\begin{array}{l}\text{\$1,516,464}\left(\text{from table 1}\right)\\ +\text{\$2,989,200}\left(\text{from table 2}\right)\end{array}\right)\\ =\text{\$4,505,664}\end{array}$

Conclusion

Hence, the issue price of the bonds on January 1, 2014 is $4,505,664.

2.

a.

To determine

Calculate the amount of interest expense that should be recorded on December 31, 2014.

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, 2014.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\left(\text{issue price}\right)\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= \$4,505,664}\times 6\%\times 1\\ =\$270,340\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31, 2014 is $270,340.

b.

To determine

Calculate the amount of interest expense that should be recorded on December 31, 2015.

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.

$\begin{array}{c}\text{Interest expense}=\left(\begin{array}{l}\text{Book value of bond }\times \text{Market interest rate}\\ \times \text{Interest}\text{time period}\end{array}\right)\\ \text{= }\left(\$4,505,664-\left(\$360,000-\$270,340\right)\right)\times 6\%\times 1\\ =\$264,960\end{array}$

Conclusion

Hence, amount of interest expense that should be recorded on December 31, 2015 is $264,960.

3.

a.

To determine

Calculate the amount of cash that should be paid on December 31, 2014.

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, 2014.

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

Conclusion

Hence, amount of cash that should be paid on December 31, 2014 is $360,000.

b.

To determine

Calculate the amount of cash that should be paid on December 31, 2015.

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, 2015.

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

Conclusion

Hence, amount of cash that should be paid on December 31, 2015 is $360,000.

4.

a.

To determine

Calculate the book value of the bonds on December 31, 2014.

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, 2014.

$\begin{array}{c}\begin{array}{l}\text{Book value of bond on }\\ \text{December 31, 2014}\end{array})\text{ =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ -\text{Premium amortized on December 31, 2014}\end{array}\right)\\ =\left(\$4,505,664-\left(\$360,000-\$270,340\right)\right)\\ =\$4,416,004\end{array}$

Conclusion

Hence, the book value of the bonds on December 31, 2014 is $4,416,004.

b.

To determine

Calculate the book value of the bonds on December 31, 2015.

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, 2015.

$\begin{array}{c}\begin{array}{l}\text{Book value of bond on }\\ \text{December 31, 2015}\end{array})\text{ =}\left(\begin{array}{l}\text{Beginning book value of bonds}\\ -\text{Premium amortized on December 31, 2014}\\ -\text{Premium amortized on December 31, 2015}\end{array}\right)\\ =\left(\begin{array}{l}\$4,505,664-\left(\$360,000-\$270,340\right)\\ -\left(\$360,000-\$264,960\right)\end{array}\right)\\ =\$4,320,764\end{array}$

Conclusion

Hence, the book value of the bonds on December 31, 2015 is $4,320,764.