Question

PowerTap Utilities is planning to issue bonds with a face value of $1,500,000 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. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.) 1. What was the issue price on January 1 of this year? (Round your final answer to whole dollars.) 2. What amount of interest expense should be recorded on June 30 and December 31 of this year? 3. What amount of cash should be paid to investors June 30 and December 31 of this year?4. What is the book value of the bonds on June 30 and December 31 of this year?

Answer 1

The issue price of bond is equal to present value of coupon payment plus present value of face value
Face value	1500000
Semi annual coupon rate	5%	10%/2
Semi annual coupon amount	75000	1500000*5%
Semi annual interest rate	6%	12%/2
Number of payments	20	10*2
Formula to calculate issue price of bond
Issue price of bond	Coupon amount*PVA (n=20,i=6%) + Face value*PV(n=20,i=6%)
Calculation of issue price of bond
Issue price of bond	75000*11.46992 + 1500000*0.311805
Issue price of bond	$1,327,951
PVA(n=20,i=6%)	(1-(1.06^-20))/0.06
PVA(n=20,i=6%)	11.46992
PV(n=20,i=6%)	1/(1.06^20)
PV(n=20,i=6%)	0.311804727
Issue price of bond is $1,327,951
Calculation of interest expense and cash paid on 30th June
Interest expense = Book (issue) price of bond*Interest rate
Interest expense	1327951*6%
Interest expense on 30th June	$79,677
Cash (coupon paid) = Face value*Coupon rate
Cash (coupon paid)	1500000*5%
Cash (coupon paid) on 30th June	$75,000
The bonds are issued at below face value which means they are issued at discount and therefore the discount will have to be amortized and also the book value of bond would increase
Increase in book value of bond (79677-75000)	$4,677
Book value of bond as on 30th June	$1,332,628	(1327951+4677)
Calculation of interest expense and cash paid on 31st December
Interest expense = Book (issue) price of bond*Interest rate
Interest expense	1332628*6%
Interest expense on 31st December	$79,958
Cash (coupon paid) = Face value*Coupon rate
Cash (coupon paid)	1500000*5%
Cash (coupon paid) on 31st December	$75,000
The bonds are issued at below face value which means they are issued at discount and therefore the discount will have to be amortized and also the book value of bond would increase
Increase in book value of bond (79958-75000)	$4,958
Book value of bond as on 31st December	$1,337,586	(1332628+4958)