Use effective-interest method of bond amortization. Interest Periods Interest to

Question

Use effective-interest method of bond amortization.

Interest Periods

Interest to Be Paid

Interest Expense to Be Recorded

Discount Amortization

Unamortized Discount

Bond Carrying Value

Issue date

$38,609

$961,391

1

$45,000

$48,070

$3,070

35,539

964,461

2

45,000

48,223

3,223

32,316

967,684

Instructions

Interest Periods

Interest to Be Paid

Interest Expense to Be Recorded

Discount Amortization

Unamortized Discount

Bond Carrying Value

Issue date

$38,609

$961,391

1

$45,000

$48,070

$3,070

35,539

964,461

2

45,000

48,223

3,223

32,316

967,684

Explanation / Answer

To begin with, note that the bonds are issued at 7.8% coupon and the market rate is 8%. This means the bonds will sell at a discount. The sale proceeds are: $19,604,145 (if they had sold at par the proceeds would have been $20m). Recall that at maturity, the company will owe $20m in principal, so the effective interest rate method essentially accounts for the amortization of the discount, as the bonds "pull toward par" as they approach maturity. The effective interest rate method takes the market interest rate (at which the bonds sold) and applies it to the proceeds garnered at sale. The rate is divided by two to reflect semi-annual bond payments. In the first 6 month period you "accrue" at the effective interest rate: 19,604,145 * 0.04 = 784,165.80, but only the coupon is actually paid out in cash, so the difference (784,165.80 - coupon($20m*0.078/2=) 780,000 = $4,165.80

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