Question

Prepare an​ effective-interest amortization table for the bonds through the first three interest payments.

Answer 1

Interest expense is a constant percentage of the bond’s carrying value, rather than an equal dollar amount each year. The theoretical merit rests on the fact that the interest calculation aligns with the basis on which the bond was priced.Interest expense is calculated as the effective-interest rate times the bond’s carrying value for each period. The amount of amortization is the difference between the cash paid for interest and the calculated amount of bond interest expense.

Let's start first with a scenario in which a company issues bonds at a discount.

Suppose a company sells $100,000 in 10-year bonds with an annual coupon of 9% at a discount to face value. Investors demand a 10% annual return to buy the bond, and thus will only pay $93,855.43 for the bonds.

I calculated this with a finance calculator with the following inputs:

• Future value: $100,000
• Number of periods: 10
• Payment: $9,000
• Rate: 10%

Solve for present value to get $93,855.43, or the amount investors will pay for these bonds if they want a 10% annual return, also known as a yield to maturity.

Accounting for this bond in the first year takes a few more steps.

In the first period, we record $93,855.43 as the carrying amount of the bond. To calculate total interest expense for the first year, we take the carrying amount of the bond and multiply it by investors' required return of 10%.

$93,582.34 X 10% = $9,385.54.

This figure is the interest expense for year one.

The cash interest is calculated by taking the coupon rate of the bond (9%) and multiplying it by the bond's face value ($100,000), resulting in $9,000 of cash interest.

You can find the amount of discount amortization by taking the interest expense we calculated ($9,385.54) and subtracting the cash interest ($9,000), resulting in $385.54 of discount amortization in year one.

Each year, we add the amortization to the carrying value and repeat these steps to find the next year's interest expense and discount amortization. Under the effective interest method, a company's interest expense and amortization amount will change every single year.

The table below shows how the bond would amortize over the full 10-year period.

Effective Interest Discount Amortization Cash Interest Interest Expense Amortization Carrying Amount N/A Time N/A N/A $93,855.43 $9,000.00 $9,385.54 -$385.54 $94,240.98 $94,665.07 1 $9,000.00 $9,424.10 -$424.10 2 $9,000.00 $9,466.51 -$466.51 $95,131.58 3 $9,000.00 $9,513.16 -$513.16 $95,644.74 4 $9,000.00 $9,564.47 -$564.47 $96,209.21 5 $9,000.00 $9,620.92 -$620.92 $96,830.13 $9,000.00 $9,683.01 -$683.01 $97,513.15 7 $9,000.00 $9,751.31 $9,826.45 -$751.31 -$826.45 -$909.09 $98,264.46 $9,000.00 $99,090.91 $9,000.00 $9,909.09 $100,000.00 10

Effective interest amortization of premiums
Premiums are amortized in similar fashion to discounts under the effective interest method. Suppose a company issues $100,000 in 10-year, 9% coupon bonds at a premium to face value. Investors only demand an 8% return for owning the bond, and thus pay the company $106,710.08 for the bonds.

I calculated this with the help of a finance calculator, using the following inputs:

• Future value: $100,000
• Number of periods: 10
• Payment: $9,000
• Rate: 8%

Solve for present value to get $106,710.08, or the amount investors will pay for these bonds assuming they want an annual return of 8%, also known as a yield to maturity.

To calculate interest expense for the first period, we multiply the carrying value of the bonds ($106,710.08) by investors' required return (8%) to get interest expense of $8,536.81.

To calculate cash interest, we multiply the face value of the bonds ($100,000) by the coupon rate (9%) to get $9,000.

To calculate premium amortization, we take the amount of cash interest ($9,000) and subtract the interest expense ($8,536.81) to get premium amortization of $463.19.

Each year the amortization is subtracted from the carrying amount, and the new carrying amount is used to calculate interest expense and amortization for the next year.

The table below shows how this example bond would be accounted for over the full 10-year period. Note that the only static figure is the amount of cash interest -- interest expense and amortization are different in every single year. Over time, the carrying amount of the bonds is slowly reduced to $100,000 due to the amortization of the premium each year.

Effective Interest Premium Amortization Cash Interest Interest Expense Amortization Carrying Amount N/A Time N/A N/A $106,710.08 0 $9,000.00 $8,536.81 $463.19 $106,246.89 1 $9,000.00 $8,499.75 $500.25 $105,746.64 2 $9,000.00 $8,459.73 $540.27 $583.49 $105,206.37 3 $9,000.00 $9,000.00 $8,416.51 $104,622.88 $8,369.83 $630.17 $103,992.71 5 $9,000.00 $8,319.42 $680.58 $103,312.13 6 $9,000.00 $8,264.97 $735.03 $102,577.10 7 $9,000.00 $8,206.17 $793.83 $101,783.26 8 $9,000.00 $8,142.66 $857.34 $925.93 $100,925.93 9 $9,000.00 $8,074.07 $100,000.00 10