OS Environmental provides cost-effective solutions for managing regulatory requirements and environmental needs specific to the airline industry. Assume that on July 1 the company issues a one-year note for the amount of $5.2 million. Interest is payable at maturity. Determine the amount of interest expense that should be recorded in a year-end adjusting entry under each of the following independent assumptions:

Interest rate Fiscal year-end Interest expense
12% December 31
10% September 30
9% October 31
6% January 31

In accrual basis accounting, expenses are recorded in the period when their matching revenues are obtained.

In this case, even if the full interest will be paid at maturity, interest expense will still be recorded in each period according to the information that we are given in the question.

Interest expense to be recorded by December 31

5,200,000 * 0.12 = 624,000 / 2 = 312,000

Interest expense to be recorded by September 30

5,200,000 * 0.10 = 520,000 * 3/12 = 130,000

Interest expense to be recorded by October 31

5,200,000 * 0.09 = 468,000 * 4/12 = 156,000

Interest expense to be recorded by January 31

5,200,000 * 0.06 = 312,000 * 7/12 = 182,000

Miller-bond:

today:            $  1,167.68

after 1-year:   $  1,157.74

after 3 year:  $  1,136.03

after 7-year:  $ 1,084.25

after 11-year: $  1,018.87

at maturity:   $ 1,000.00

Modigliani-bond:

today:            $    847.53

after 1-year:   $    855.49

after 3 year:  $     873.41

after 7-year:  $     918.89

after 11-year: $       981.14

at maturity:   $  1,000.00

Explanation:

We need to solve for the present value of the coupon payment and maturity of each bonds:

Miller:

C80.000

time12

rate0.06

PV$670.7075

Maturity   1,000.00

time   12.00

rate  0.06

PV   496.97

PV c$670.7075

PV m  $496.9694

Total$1,167.6769

In few years ahead we can capitalize the bod and subtract the coupon payment

after a year:

1.167.669 x (1.06) - 80 = $1,157.7375

after three-year:

1,157.74 x 1.06^2 - 80*1.06 - 80 = 1136.033855

If we are far away then, it is better to re do the main formula

after 7-years:

C80.000

time5

rate0.06

PV$336.9891

Maturity   1,000.00

time   5.00

rate  0.06

PV $747.26

PV c$336.9891

PV m  $747.2582

Total$1,084.2473

1 year before maturity:

last coupon payment + maturity

1,080 /1.06 =  1.018,8679 = 1,018.87

For the Modigliani bond, we repeat the same procedure.

PV

C30.000

time24

rate0.04

PV$457.4089

Maturity   1,000.00

time   24.00

rate  0.04

PV   390.12

PV c$457.4089

PV m  $390.1215

Total$847.5304

And we repeat the procedure for other years