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How to Calculate Accretion and Amortization on the Series 7 Exam

The Series 7 exam will ask you questions about calculating accretion and amortization. You use accretion and amortization when figuring out taxes on bonds; you simply adjust the cost of the bond toward par in the time that the bond matures.

Accretion

When investors purchase bonds at a discount, the discount must be accreted over the life of the bond. Accretion, which involves adjusting the cost basis (price paid) of the bond toward par each year that the bond is held, increases both the cost basis of the bond and the reported interest income.

To determine the annual accretion, find the difference between the cost of the bond and par value; divide the result by the original number of years to maturity.

The following question tests your understanding of accretion.

Mr. Dancer purchases a 5-percent corporate bond with 10 years to maturity at 80. What would Mr. Dancer’s annual reported income on this bond be?

(A)    $20
(B)    $30
(C)    $50
(D)    $70

The right answer is Choice (D). Mr. Dancer purchased the bond at 80 ($800), and you can assume that it matures at $1,000 (par) in 10 years (you can always assume $1,000 par unless otherwise stated). You need to take the $200 difference and divide it by 10 years to get $20. Mr. Dancer’s reported income would be $70 ($50 interest plus $20 accretion).

Be prepared to answer questions about the annual accretion and yearly reported income and to calculate the capital gain or loss the investor would incur if selling the bond before maturity.

The following question tests your ability to figure out the capital gain or loss on a bond purchased at a discount.

Ms. Jones purchased a 7-percent DEF corporate bond at 80 with ten years to maturity. Six years later, Ms. Jones sold the bond at 85. What is the gain or loss?

(A)    $50 gain
(B)    $70 loss
(C)    $150 loss
(D)    None of the above

The answer you’re looking for is Choice (B). First, adjust the cost basis of the bond in the time the bond matures:

image0.jpg

The bond was purchased at $800 (80 percent of $1,000 par) and matures at $1,000 par in ten years. Next, take that $200 difference and divide it by the ten years to maturity:

image1.jpg

Then take the $20 per year accretion and multiply it by the number of years that the investor held the bond:

image2.jpg

Next, add the total accretion to the purchase price of the bond to determine the investor’s adjusted cost basis:

image3.jpg

After that, compare the adjusted cost basis to the selling price to determine the gain or loss:

image4.jpg

Ms. Jones incurred a $70 capital loss on her sale of the DEF bond, which she can use to offset capital gains on other investments.

All discount bonds, except municipal bonds purchased in the secondary market, are accreted. If a municipal bond is purchased as an original issue discount, the accretion is treated as part of the tax-free interest. If an investor purchases a municipal bond in the secondary market at a discount, the bond is not accreted, but the difference between the purchase price and the selling price is treated as a capital gain.

Amortization

When bonds are purchased at a premium, the premium can be amortized over the life of the bond. You amortize the bond by adjusting the cost basis of the bond towards par each year that the bond is held; amortization decreases the cost basis of the bond and decreases the reported interest income.

To find the yearly amortization, divide the difference between the purchase price and par value by the original number of years to maturity.

The following question involves annual amortization:

Mrs. Sheppard purchases a 7-percent corporate bond with 20 years to maturity at 110. If Mrs. Sheppard decides to amortize the bond, what is the annual reported income?

(A)    $5
(B)    $65
(C)    $70
(D)    $75

The correct answer is Choice (B). Because Mrs. Sheppard purchased the bond at 110 ($1,100) and you can assume that it matures at $1,000 (par) in 20 years, you need to take the $100 difference and divide it by 20 years to get $5. Mrs. Sheppard’s reported income would be $65 ($70 interest minus $5 amortization).

Corporate bondholders can elect to amortize their premium bonds or not; however, all municipal bondholders must amortize their premium bonds, whether they were purchased as a new issue or in the secondary market (used).

You can use the same formula that you use for accretion to determine the gain or loss on an amortization problem. Only the first couple steps change. You still take the difference between the purchase price and par value and divide it by the number of years until maturity, which gives you the annual amortization. You multiply the annual amortization by the number of years the investor held the bond.

At this point, you need to subtract that amount from the purchase price instead of adding it to the purchase price to get the adjusted cost basis. Then, as you do with accretion problems, you compare the adjusted cost basis to the selling price to determine the gain or loss.

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