Question

compare and contrast the amortization of discounts/premiums using the effective interest and straight line methods. In 200 worlds.

Answer 1

Straight Line Method

Premium/discout of the bond is amortized equally over the life of the bond.

Example for a discount on the bond-

Let's say, a firm issues $100,000 of 10-year bonds that pay an 7% annual coupon. The bonds are sold at a discount. Hence, the company only receives $90,000 in proceeds from the sale. The $10,000 difference between the face value and the market value of the bonds would be amortized over 10 years.

Eevery year, the company will have to pay $7,000 in cash interest (coupon rate of 7% X $100,000 of face value). Also, it will book the amortization of the discount. This annual amortization amount is the discount on the bonds ($10,000) divided by the 10-year life of the bond, or $1,000 per year. Thus, the firm needs to book $8,000 of interest expense, of which $7,000 is cash and $1,000 is the amortization of the discount.

Effective Interest Method

Let's say a firm 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.

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

If we solve to calculate the present value of the bonds, we get $93,855.43, or the amount investors will pay for these bonds if they want a 10% annual return.

In the first period, the firm will book $93,855.43 as the carrying amount of the bond. To find out the total interest expense for the first year=

$93,582.34(carrying amount) X 10%(annual return) = $9,385.54 (Yearly interest expense booked by the firm)

The cash interest is 9%(coupn rate) *100,000 (face value) = $9000

Now, the amount of discount amortization= $9,385.54 (interest expense) - $9,000 (cash interest)= $385.54

Conclusion

Straigt line is simple but effective interest is complex in calclation. However, effective interest method is widely used because it factors in the present value of bonds.