## Effective Interest Rate

### Learning Outcomes

• Discuss the effective interest rate method of amortizing bond premium and discount

Rather than using the straight line method of amortizing discounts or premiums, the preferable approach to recording amortization is the effective-interest method that uses a constant percentage of the carrying value, rather than an equal dollar amount each year, similar to the double-declining balance method of depreciation or fixed assets.

The amount of amortization is the difference between the cash paid for interest and the calculated amount of bond interest expense, and at the end of the bond carrying period, the unamortized discount or premium would be zero.

Let’s take a look at the concept of effective interest rate from the bond investor’s point of view.

For instance, on March 5, 2014, Tesla Inc. (TSLA) issued $1.2 billion in fixed-rate bonds ($1,000 face value each, so 1.2 million bonds) with a maturity date of March 01, 2021, and a fixed coupon rate of 1.25%, payable semi-annually. The debt received an S&P rating of B- when it was issued. So each bond of $1,000 pays$12.50 per year, but the average investor may be looking for something like 7%, or 10%, depending on what else is available in the market, so let’s say the investor paid $625 for one of the$1000 bonds. The $12.50 per year in interest on a$625 investment is still only a 2% return, but when (if) the bond matures 7 years later, the investor also gains an additional $375 over what was paid for the bond. In this case, the effective rate would be a 7% ROI on the difference between the investment and the maturity value, plus the 2% coupon rate, for a combined yield of 9%. To find the ROI on the investment, divide the maturity value by the purchase price (1000/625 = 1.6). Find a future value table of$1. On that table, find the row for n=7 (7 years). Look for a factor close to 1.6 (you should find it in the column for 7% annual return.)  You could check this mathematically by taking 625 * 1.077 which would give you the future value of 625 invested for 7 years at 7% compounded annually (it comes to $1,003.61 which is close enough for this purpose). Assume that Premium Corp. issues 100, five-year, semi-annual,$1,000 bonds with an 8% coupon. Premium Corp. receives $108,530 because the market rate is 6% (the bonds sold at a premium because the coupon rate was higher than the market rate). Instead of just dividing the premium by five to get the annual amortization (or by 10 to get the semi-annual adjustment), Premium Corp. uses the effective interest method to amortize the premium. For the first payment, we multiply the carrying amount of$108,530 by 6% and then divide that by two (or multiply by half) = $3,255.90. The coupon payment is$4,000 (cash disbursement) but the interest expense is only $3,255.90. Therefore the premium amortization is$744.10 ($4,000 –$3,255.90). The premium amortization reduces the net book value of the debt to $107,785.90 ($108,530 – $744.10). This new balance would then be used to calculate the effective interest for the next period. This process would be repeated each period, as shown in the following table: Period ending Book Value Interest expense at 6%, semi-annual Coupon Payment Premium Amortization Book Value, end of period 6/30/X1 108,530.00 3,255.90 4,000.00 (744.10) 107,785.90 12/31/X1 107,785.90 3,233.58 4,000.00 (766.42) 107,019.48 6/30/X2 107,019.48 3,210.58 4,000.00 (789.42) 106,230.06 12/31/X2 106,230.06 3,186.90 4,000.00 (813.10) 105,416.96 6/30/X3 105,416.96 3,162.51 4,000.00 (837.49) 104,579.47 12/31/X3 104,579.47 3,137.38 4,000.00 (862.62) 103,716.86 6/30/X4 103,716.86 3,111.51 4,000.00 (888.49) 102,828.36 12/31/X4 102,828.36 3,084.85 4,000.00 (915.15) 101,913.21 6/30/X5 101,913.21 3,057.40 4,000.00 (942.60) 100,970.61 12/31/X5 100,970.61 3,029.12 4,000.00 (970.61) 100,000.00 Note that the last amortization amount was adjusted slightly to fully amortize the premium. Period ending Premium Premium Amortization Unamortized Premium 6/30/X1 8,530.00 (744.10) 7,785.90 >12/31/X1 7,785.90 (766.42) 7,019.48 6/30/X2 7,019.48 (789.42) 6,230.06 12/31/X2 6,230.06 (813.10) 5,416.96 6/30/X3 5,416.96 (837.49) 4,579.47 12/31/X3 4,579.47 (862.62) 3,716.86 6/30/X4 3,716.86 (888.49) 2,828.36 12/31/X4 2,828.36 (915.15) 1,913.21 6/30/X5 1,913.21 (942.60) 970.61 12/31/X5 970.61 (970.61) (0.00) The initial journal entry to record the issuance of the bonds and the final journal entry to record repayment at maturity would be identical to those demonstrated for the straight line method. However, each journal entry to record the periodic interest expense recognition would vary and can be determined by reference to the preceding amortization table. For instance, the following entry would record interest on June 30, 20X3: Date Description Post. Ref. 20X3 Interest expense 3,162.51 Premium on bonds payable 837.49 Checking Account 4,000.00 To record coupon payment on bonds Assume that Discount Corp. issues 100, five-year, semi-annual,$1,000 bonds with an 8% coupon during a period of time when the market rate is 10% and so receives \$92,278 because the coupon rate is lower than the market rate.

Period ending Book Value Interest expense at 10%, semi-annual Coupon Payment Discount Amortization Book Value, end of period
6/30/X1 92,278.00 4,613.90 4,000.00 613.90 92,891.90
12/31/X1 92,891.90 4,644.60 4,000.00 644.60 93,536.50
6/30/X2 93,536.50 4,676.82 4,000.00 676.82 94,213.32
12/31/X2 94,213.32 4,710.67 4,000.00 710.67 94,923.99
6/30/X3 94,923.99 4,746.20 4,000.00 746.20 95,670.19
12/31/X3 95,670.19 4,783.51 4,000.00 783.51 96,453.69
6/30/X4 96,453.69 4,822.68 4,000.00 822.68 97,276.38
12/31/X4 97,276.38 4,863.82 4,000.00 863.82 98,140.20
6/30/X5 98,140.20 4,907.01 4,000.00 907.01 99,047.21
12/31/X5 99,047.21 4,952.36 4,000.00 952.79 100,000.00
Period ending Discount Discount Amortization Unamortized Discount
6/30/X1 7,722.00 613.90 7,108.10
12/31/X1 7,108.10 644.60 6,463.51
6/30/X2 6,463.51 676.82 5,786.68
12/31/X2 5,786.68 710.67 5,076.01
6/30/X3 5,076.01 746.20 4,329.81
12/31/X3 4,329.81 783.51 3,546.31
6/30/X4 3,546.31 822.68 2,723.62
12/31/X4 2,723.62 863.82 1,859.80
6/30/X5 1,859.80 907.01 952.79
12/31/X5 952.79 952.79 0.00

Each journal entry to record the periodic interest expense recognition would vary, and can be determined by reference to the preceding amortization table. For instance, the following entry would record interest on June 30, 20X3:

Date Description Post. Ref. 20X3 Interest expense 4,746.20 Discount on bonds payable 746.20 Checking Account 4,000.00 To record coupon payment on bonds

Now that you understand the effective interest rate method of amortizing bond premiums and discounts we’ll move on to other long-term liabilities.