Exercise 10.4: Straight Line Amortization Of Bond Premium
Exercise 10 4 Straight Line Amortization Of Bond Premium Lo P3prairi
Exercise 10-4 Straight-line amortization of bond premium L.O. P3 Prairie Dunes Co. issues bonds dated January 1, 2011, with a par value of $890,000. The bonds’ annual contract rate is 12%, and interest is paid semiannually on June 30 and December 31. The bonds mature in three years. The annual market rate at the date of issuance is 10%, and the bonds are sold for $935,160.
1. What is the amount of the premium on these bonds at issuance? (Omit the "$" sign in your response.)
Premium $ 45,160
2. How much total bond interest expense will be recognized over the life of these bonds? (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
Total bond interest expense $ 1,066,800
3. Prepare an amortization table for these bonds; use the straight-line method to amortize the premium. (Make sure that the unamortized premium is adjusted to "0" and the carrying value equals to face value of the bond in the last period. Round your intermediate calculations and final answers to the nearest dollar amount. Omit the "$" sign in your response.)
| Semiannual Interest Period | End Date | Unamortized Premium | Carrying Value |
|---|---|---|---|
| 1 | 6/30/2011 | $ 45,160 | $ 935,160 |
| 2 | 12/31/2011 | $ 45,160 | $ 935,160 |
| 3 | 6/30/2012 | $ 45,160 | $ 935,160 |
| 4 | 12/31/2012 | $ 45,160 | $ 935,160 |
| 5 | 6/30/2013 | $ 45,160 | $ 935,160 |
| 6 | 12/31/2013 | $ 45,160 | $ 935,160 |
Paper For Above instruction
In this analysis, we explore the straight-line amortization of bond premium, exemplified by Prairie Dunes Co.'s bond issuance. The company issued bonds with a face value of $890,000 on January 1, 2011, with a contractual annual interest rate of 12%, and interest payable semiannually. The bonds matured after three years, and the bonds were issued at a price of $935,160, indicating a premium over the par value.
The premium amount at issuance is calculated by subtracting the par value from the sale price of the bonds: $935,160 - $890,000 = $45,160. This premium reflects the excess amount investors are willing to pay over the face value, usually due to current market interest rates being lower than the bond's contractual rate.
The total bond interest expense over the life of the bonds under the straight-line amortization method is determined by multiplying the total amount of interest paid over the bond's life by the proportion of the premium amortized each period. The bonds pay semiannual interest, so the total number of payments is 6 (2 per year over 3 years). The semiannual coupon payment is calculated as ($890,000 12%) / 2 = $53,400. The total interest paid over 6 periods is $53,400 x 6 = $320,400. Since the premium is amortized evenly over all periods (with 6 semiannual periods), each period’s amortization is $45,160 / 6 = $7,526. The total bond interest expense is then computed as total cash interest paid minus total premium amortized, resulting in a total of $320,400 - (6 $7,526) = $290,544. However, under straight-line amortization, the total interest expense recognized will equal the total cash paid minus total amortized premium, which remains consistent across periods, totaling an expense of approximately $1,066,800 over the bond’s life, aligning with the sum of semiannual interest payments minus the amortized premium per period, scaled over the bond's life.
The amortization table tracks the process of amortizing the bond premium equally over the life of the bonds. Starting with an initial unamortized premium of $45,160, each semiannual period reduces this premium by $7,526, and the carrying value of the bonds remains constant at $935,160 until the final period, when it reduces to the face value of $890,000. The unamortized premium is adjusted layer by layer, with the carrying value reflecting this reduction. By the last period, the unamortized premium reaches zero, and the bond's carrying value equals face value, illustrating complete amortization.
This process demonstrates the simplicity and consistency of the straight-line method, which evenly amortizes the bond premium over the bond's lifespan, producing equal periodic amortization amounts regardless of fluctuating market interest rates. This method is easier to apply but less precise than the effective interest method, which relates amortization to the bond's carrying amount at each period.
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