Question

Why is A

straight-one method Topic: Determining interest and amortization 51. For the issuer of 20-year bonds, the amount of amortization using the effective interest method would decrease each year if the bonds are sold at a: Discount No No Yes Yes Premium No Yes Yes No A. Option A B. Option B C. Option C D. Option D

Answer 1

A bond is sold at premium when the market interest rate is below the bond interest rate. The logic is that since the Bond pays higher return that the market, investors tend to pay more than its face value. On the same note, A bond A bond is sold at discount when the market interest rate is above the bond interest rate. The logic is that since the Bond pays lower return that the market, investors are willing to pay less less than its face value. A bond is sold at par when bond interest and market interest rates are the same.Thus sold at face value.

Now let me explain what is amortization. When bond is sold at premium or discount the difference is amortized over the period of bond, In this question they have asked about effective interest method of amortization. This is essentially the market interest rate. Under this model of accounting interest is calculated @ market rate on the actual value of the bond(not face value) and the difference between this calculated discount and interest on face value is amortized. I will be explaining the reason why amortization expense increases in both these cases along with my example.

I have prepared amortization schedule for a bond sold at premium and discount. My examples are prepared for bonds with a 10 years maturity, but the concept will hold true for bonds with any maturity.

Example 1. Bond Sold at premium (A bond is sold at premium when market interest rate is below the bond interest rate) 10,000 no.s 10%-bonds with a face value of $10 sold at a premium price of $11.34(rounded). Market interest rate is 8%. Thus cash paid annually will be = $10(FV) x 10,000 nos x 10% = 1,00,000 p.a

Closing value/ Carrying value of bond = Opening bond value + Interest expense - Cash paid

Amortization = Opening value of bond - Closing value of bond [Equation is different for both premium and discount bond as amortization will always be a positive value]

As you can see from the example below, Interest expense of the bond is always lower than the cash paid. Hence opening carrying value of the bond will always be greater than closing value of the bond. Thus Amortization expense which is difference between opening and closing carrying value will keep increasing each year.

Amortization shcedule premium bond Interest Date Interest expense (Carrying value x 8%) | Cash paid 1 million x 10% Amortization Carrying value of bond Carrying value = the Sales vale = $11.34 x 10,000 no.s $ 11,34,201.63 31-12-2000 90,736.13 $ 1,00,000.00 $ 9.263.87 $ 11.24.937.76 31-12-2001 89,995.02 $ 1,00,000.00 $ 10,004.98 $ 11,14,932.78 31-12-2002 89.194.62 $ 1,00,000.00 $ 10,805.38 $ 11,04,127.40 31-12-2003 88,330.19 $ 1,00,000.00 $ 11,669.81 $ 10,92,457.59 31-12-2004 87,396.61 $ 1,00,000.00 $ 12,603.39 $ 10,79,854.20 31-12-2005 86,388.34 $ 1,00,000.00 $ 13,611.66 $ 10,66,242.54 31-12-2006 85,299.40 $ 1,00,000.00 $ 14,700.60 $ 10,51,541.94 31-12-2007 84,123.36 $ 1,00,000.00 $ 15,876.64 $ 10,35,665.29 31-12-2008 82,853.22 $ 1,00,000.00 $ 17,146.78 $ 10,18,518.52 31-12-2009 81,481.48 $ 11,00,000.00 3.39 $

Example 2. Bond Sold at discount (A bond is sold at discount when market interest rate is above the bond interest rate) 10,000 no.s 10%-bonds with a face value of $10 sold at a premium price of $8.87(rounded). Market interest rate is 12%. Thus cash paid annually will be = $10(FV) x 10,000 nos x 10% = 1,00,000 p.a

Closing value/ Carrying value of bond = Opening bond value + Interest expense - Cash paid

Amortization = Closing value of bond - Opening value of bond [Equation is different for both premium and discount bond as amortization will always be a positive value]

As you can see from the example below, Interest expense of the bond is always higher than the cash paid. Hence closing carrying value of the bond will always be greater than opening value of the bond. Thus Amortization expense which is difference between opening and closing carrying value will keep increasing each year.

Amortization shcedule discount bond Interest Date Interest expense (Carrying value x 12%) Cash paid 1million x 10% Amortization Carrying value of bond Carrying value = the Sales vale = $8.87 x 10,000 no.s $ 8,86,995.54 31-12-2000 1,06,439.46 $ 1,00,000.00 $ 6,439.46 $ 8,93,435.00 31-12-2001 1,07,212.20 $ 1,00,000.00 $ 7.212.20 $ 9,00,647.20 31-12-2002 1,08,077.66 $ 1,00,000.00 $ 8,077.66 $ 9,08,724.87 31-12-2003 1,09,046.98 $ 1,00,000.00 $ 9,046.98 $ 9,17,771.85 31-12-2004 1,10,132.62 $ 1,00,000.00 $ 10,132.62 $ 9,27,904.48 31-12-2005 1,11,348.54 $ 1,00,000.00 $ 11,348.54 $ 9,39,253.01 31-12-2006 1,12,710.36 $ 1,00,000.00 $ 12,710.36 $ 9,51,963.37 31-12-2007 1,14,235.60 $ 1,00,000.00 $ 14,235.60 $ 9,66,198.98 31-12-2008 1,15,943.88 $ 1,00,000.00 $ 15,943.88 $ 9,82,142.86 31-12-2009 1,17,857.14 $ 11,00,000.00 $