Question

On December 31, 2012, a company issued a 3-year, 10% annual coupon bond with a face value of $100,000. Calculate the book value of the bond at year-end 2012, 2013, and 2014, and the interest expense for 2013, 2014, and 2015, assuming the bond was issued at a market rate of interest of (A) 10%, (B) 9%, and (C) 11%.

Answer 1

A) Face value = $100000, Annual coupon rate = 10%, Period of bond = 3 years, interest rate = 10%

Coupon = annual coupon rate x face value = 10% x 100000 = 10000

First we will find the selling price of bond on December 31, 2012 using pv function in excel

Formula to be used in excel: =pv(rate,nper,-pmt,-fv)

Using pv function in excel, we get price of bond at end of 2012 = 100000

Hence Book value at end of 2012 = 100000

Since the bond has been issued at par and interest rate = coupon rate, therefore there will not be any amortization of discount or premium. Therefore book value bond will be equal to par value of bond at all coupon dates

Hence book value of bond at end of 2013 = book value of bond at end of 2014 = 100000

Year	Ending Book value
2012	100000
2013	100000
2014	100000

Interest expense for a year = Interest rate x book value at beginning of year

Interest expense for 2013 = 10% x book value at beginning of 2013 or end of 2012 = 10% x 100000 = 10000

Interest expense for 2014 = 10% x book value at beginning of 2014 or end of 2013 = 10% x 100000 = 10000

Interest expense for 2015 = 10% x book value at beginning of 2015 or end of 2014 = 10% x 100000 = 10000

Year	Interest Expense
2013	10000
2014	10000
2015	10000

B) Face value = $100000, Annual coupon rate = 10%, Period of bond = 3 years, interest rate = 9%

Coupon = annual coupon rate x face value = 10% x 100000 = 10000

First we will find the selling price of bond on December 31, 2012 using pv function in excel

Formula to be used in excel: =pv(rate,nper,-pmt,-fv)

Using pv function in excel, we get price of bond at end 2012 = 102531.29

Book value of bond at end of 2012 = 102531.29

Since the bond has been issued at premium, therefore there will be amortization of bond premium

We know that Interest expense for a year = Book value at beginning of year x interest rate

Amortization of bond premium for a year = Coupon - interest expense for year

Ending book value for a year = Beginning book value - Amortization of bond premium

Beginning book value for a year = Ending book value for previous year

For year 2013

Interest expense for 2013 = Beginning book value of 2013 or ending book value of 2012 x interest rate = 102531.29 x 9% = 9227.82

Bond premium amortization for 2013 = 10000 - 9227.82 = 772.18

Ending book value for 2013 = 102531.29 - 772.18 = 101759.11

Now beginning book value of 2014 = Ending book value of 2013 = 101759.11

Similarly values can be found out for other years,we get the following table

Year	Beginning Book value	Interest Expense	Coupon	Bond Premium Amortization	Ending Book Value
2013	102531.29	9227.82	10000.00	772.18	101759.11
2014	101759.11	9158.32	10000.00	841.68	100917.43
2015	100917.43	9082.57	10000.00	917.43	100000.00

Hence we get following book value

Year	Ending Book value
2012	102531.29
2013	101759.11
2014	100917.43

We get following interest expense

Year	Interest Expense
2013	9227.82
2014	9158.32
2015	9082.57

C) Face value = $100000, Annual coupon rate = 10%, Period of bond = 3 years, interest rate = 11%

Coupon = annual coupon rate x face value = 10% x 100000 = 10000

First we will find the selling price of bond on December 31, 2012 using pv function in excel

Formula to be used in excel: =pv(rate,nper,-pmt,-fv)

Using pv function in excel, we get price of bond at end 2012 = 97556.29

Book value of bond at end of 2012 = 97556.29

Since the bond has been issued at discount, therefore there will be amortization of bond discount

We know that Interest expense for a year = Book value at beginning of year x interest rate

Amortization of bond discount for a year = interest expense for year - coupon

Ending book value for a year = Beginning book value + Amortization of bond discount

Beginning book value for a year = Ending book value for previous year

For year 2013

Interest for 2013 = Beginning book value of 2013 or ending book value of 2012 x interest rate = 97556.29 x 11% = 10731.19

Bond discount amortization for 2013 = 10731.19 - 10000 = 731.19

Ending book value for 2013 = 97556.29 + 731.19= 98287.48

Now beginning book value of 2014 = Ending book value of 2013 = 98287.48

Similarly values can be found out for other years,we get the following table

Year	Beginning Book value	Interest Expense	Coupon	Bond discount Amortization	Ending Book Value
2013	97556.29	10731.19	10000.00	731.19	98287.48
2014	98287.48	10811.62	10000.00	811.62	99099.10
2015	99099.10	10900.90	10000.00	900.90	100000.00

Hence we get following end of year book values

Year	Ending Book value
2012	97556.29
2013	98287.48
2014	99099.10

We get following interest expense

Year	Interest Expense
2013	10731.19
2014	10811.62
2015	10900.90