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A company issues $25750000, 7.8%, 20-year bonds to yield 8% on January 1, 2016. Interest is...

A company issues $25750000, 7.8%, 20-year bonds to yield 8% on January 1, 2016. Interest is paid on June 30 and December 31. The proceeds from the bonds are $25240330. Using straight-line amortization, what is the carrying value of the bonds on December 31, 2018?

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Expert Solution

A company issues $25750000, 7.8%, 20-year bonds to yield 8% on January 1, 2016. Interest is paid on June 30 and December 31. The proceeds from the bonds are $25240330. Using straight-line amortization,

what is the carrying value of the bonds on December 31, 2018?  = $25316780.50

**Straight line amortization of discount is the easiest method to account for discounts on bonds. Under the straight line method, the discount on the bond is amortized in equal amounts over the life of the bond.

**Straight line amortization of discounts results in the same amount of interest expense, amortization, and cash interest in every single year until the bond is repaid. Each year the carrying value will increase the same amount of amortization.

**for this purpose here, we need to calculate the amortization of each year ( each year is same under straight line )

Amortization = Discount on bond / number of interest payment period

Where,

Discount on bond = Par value - Current selling price

Par value = $25750000

Current selling price = proceeds from the bonds = $25240330

Discount on bond = 25750000 - 25240330 = $509670

number of interest payment period = 20 years interest are paid semi annually = 20 * 2 = 40

Amortization = $509670 / 40 = $12741.75

carrying value of the bonds on December 31, 2018

issue price

$25240330

Add amortized discount (12741.75 * 6)

$76450.50

= Carrying value of bonds

$25316780.50

**Between jan 1, 2016 and dec 31, 2018, there is 6 semi annual periods of interest payment, so we add 6 periods amortized discount to its carrying value on jan 1, 2016

The schedule of bond amount interest payments are look like this ( for your better understanding)

Date

Cash interest

Interest expenses

Amortization

Carrying value

January 1, 2016

N/A

N/A

N/A

$25240330

June 30, 2016

$1004250

$1016991.75

$12741.75

$2,52,53,071.75

December31, 2016

$1004250

$1016991.75

$12741.75

$2,52,65,813.50

June 30, 2017

$1004250

$1016991.75

$12741.75

$2,52,78,555.25

December31, 2017

$1004250

$1016991.75

$12741.75

$2,52,91,297.00

June 30, 2018

$1004250

$1016991.75

$12741.75

$2,53,04,038.75

December31, 2018

$1004250

$1016991.75

$12741.75

$2,53,16,780.50

*cash interest = par * semi annual interest rate

cash interest = 25750000  * 7.8 / 2 = $1004250

*Interest expenses = cash interest + Amortization

Interest expenses = $1004250 + $12741.75 = $1016991.75

*Carrying value: each period the amortized discount is added to Carrying value until it reach the par value amount


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