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Effective Interest Method
Accounting
University of Manila
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EFFECTIVE INTEREST METHOD
Market price of bonds
PFRS 9 requires that discount on bonds payable, premium on bonds payable and bond issue cost shall be amortized using the effective interest method.
This method distinguishes two kinds of interest rates, namely: 1. Nominal rate is the coupon or stated rate 2. Effective rate is yield or market rate
The e ffective rate is the rate that exactly discounts estimated cash future payments through the expected life of the bonds payable or when appropriate, a shorter period to the net carrying amount of the bonds payable.
When bonds are sold at a premium , the effective rate is lower than the nominal rate.
When bonds are sold at a discount, the effective rate is higher than the nominal rate.
Effective interest method
Under the effective interest method, the effective interest expense is determined by multiplying the effective rate by the carrying amount of the bonds. The carrying amount of the bonds changes every year as the amount of premium or discount is amortized periodically.
Discount amortization = Effective interest - Nominal interest Interest paid = Face amount x nominal rate Interest expense = Carrying amount x effective rate Discount amortization = Interest expense – interest paid Carrying amount = preceding carrying amount + discount amortization
Illustration: Effective amortization of discount 1,000,000 x 8% x 6/12= 40, On January 1, 2020, an entity issued two-year 8% bonds with face amount of P1,000,000 for P964,540, a price which will yield a 10% effective interest cost per year. Interest is payable semiannually on June 30 and December 31.
Interest Interest Discount Carrying Date paid expense amortization amount Jan, 2020 964, June 30, 2020 40,000 48,227 8,227 972, Dec. 31, 2020 40,000 48,638 8,638 981, June 30, 2021 40,000 49,070 9,070 990, Dec. 31, 2021 40,000 49,525 9,525 1,000, Journal entries for 2020: 1/1/20 – Issuance of bonds
Cash 964, Discount on bonds payable (1,000,000 – 964,540) 35, Bonds payable (at face amount) 1,000,
6/30/20 – Payment of semiannual interest and discount amortization for 6 months. Interest expense 48, Cash (1,000,000 x 8% x 6/12) 40, Discount on bonds payable (See table of amortization) 8,
12/31/20 – Payment of semiannual interest and discount amortization for 6 months. Interest expense 48, Cash (1,000,000 x 8% x 6/12) 40, Discount on bonds payable (see table of amortization) 8,
Note: Payment of semiannual interest and the periodic amortization of the discount are compounded in one entry. This items can be recorded separately.
Effective amortization of premium Premium amortization = Nominal interest – Effective interest Interest paid = Face amount x nominal rate Interest expense = Carrying amount x effective rate Premium amortization = Interest paid – interest expense Carrying amount = Preceding carrying amount – premium amortization
Illustration: Effective amortization of premium On January 1, 2020, an entity issued three-year 12% bonds with face amount of P1,000, for P1,049,740, a price which will yield a 10% effective interest cost per year. The interest is payable annually every December 31.
Interest Interest Premium Carrying Date paid expense amortization amount Jan. 1, 2020 1,049, Dec. 31, 2020 120,000 104,974 15,026 1,034, Dec. 31, 2021 120,000 103,471 16,529 1,018, Dec. 31, 2022 120,000 101,815 18,185 1,000,
Journal entries for 2020 and 2021: 1/1/20 – Issuance of bonds. Cash 1,049, Premium on bonds payable 49, Bonds payable (at face amount) 1,000,
12/31/20 – Payment of annual interest.
Market price or issue price of bonds payable
The market price or issue price of bonds payable is equal to the present value of the principal bond liability plus the present value of the future interest payments using the effective or market rate of interest. The present value of the principal bond liability is equal to the face amount of the bond multiplied by the present value of 1 factor at the effective rate for a number of interest periods. The present value of the future interest payments is equal to the periodic nominal interest multiplied by the present value of an ordinary annuity of 1 factor at the effective rate for a number of interest periods.
In other words, the market price of bonds payable is equal to the sum of the following: a. Present value of bonds payable (face amount of bonds x PV of 1 factor) b. Present value of the total interest payments (Periodic nominal interest x PV of an ordinary annuity of 1 factor)
Illustration 1: Interest is payable annually Face amount of bonds 4,000, Nominal rate 6% Effective rate 8% The bonds are issued on January 1, 2020 and mature in four years on January 1, 2024. The interest is payable annually every December 31. PV of 1 at 8% for 4 periods. PV of an ordinary annuity of 1 at 8% for 4 periods 3. Required: What is the market issue price of the bonds? Ans. 3,734,
Answer: Present value of the principal (4,000,000 x .7350) 2,940, Present value of annual interest payments (240,000 x 3) 794, Total Present value of the bonds 3,734,
Interest Interest Discount Carrying Date paid expense amortization amount Jan. 1 , 2020 3,734, Dec. 31,2020 240,000 298,793 58,792 3,793, Dec. 31, 2021 240,000 303,496 63,496 3,857, Dec. 31, 2022 240,000 308,575 68,575 3,925, Dec. 31, 2023 240,000 314,233 74,233 4,000,
Illustration 2: Interest is payable semiannually Face amount of bonds 5,000, Nominal rate 12% Effective rate 10% The bonds are issued on January 1, 2020 and mature in 3 years on January 1, 2023. The interest is payable semiannually. The PV factors using the semiannual effective rate are: PV of 1 at 5% for 6 periods. PV of an ordinary annuity of 1 at 5% for 6 periods 5. Required : What is the market issue price of the bonds? Ans. 5,253,
Answer : PV of principal (5,000,000 x .7462) 3,731, PV of interest payment (300,000 x 5) 1,522, Total present value of bonds 5,253,
Note: The s emiannual interest payment of P300,000 is computed by multiplying the face amount of P5,000,000 by the semiannual nominal rate of 6% (12% / 2).
Interest Interest Premium Carrying Date paid expense amortization amount Jan. 1 2020 5,253, June 30, 2020 300,000 262,686 37,314 5,216, Dec. 31, 2020 300,000 260,820 39,180 5,177, June 30, 2021 300,000 258,861 41,139 5,136, Dec. 31, 2021 300,000 256,804 43,196 5,092, June 30, 2022 300,000 254,644 45,356 5,047, Dec. 31, 2022 300,000 252,475 47,525 5,000,
Illustration 3: Serial bonds Face amount of bonds 3,000, Nominal rate 12% Effective rate 10% Date of issue January 1, Annual payment every December 31 1,000, Interest is payable annually December 31 Present value of 1 at 10%: One period 0. Two periods 0. Three periods 0.
Required: What is the market price of the serial bonds? Ans. 3,102,
Cash 1,000,
Effective interest method – bond issue cost PFRS 9 provides that transaction costs that are directly attributable to the issue of financial liability shall be included in the initial measurement of financial liability. Transaction costs are fees and commissions paid to agents, advisers, brokers and dealers, levies by regulatory agencies and security exchange, and transfer taxes and duties. Transaction costs include bond issue costs. These bond issue costs will increase discount on bonds payable and will decrease premium on bonds payable. Under the effective interest method, bond issue cost must be “lumped” with the discount on bonds payable and “netted” against the premium on bonds payable
Illustration 1: Discount and bond issue cost On January 1, 2020, an entity issued three-year bonds with face amount of P10,000,000 and 9% stated rate. The bonds mature on January 1, 2023 and interest is payable annually on December 31. The bonds are issued at P9,751,210 with an effective yield of 10% before considering the bond issue cost. The entity paid bond issue cost of P239,880.
Face amount 10,000, Discount on bonds payable 248, Issue price 9,751, Bond issue cost 239, Net proceeds 9,511,
Note: The effective rate is 10% but because of the bond issue cost, the effective rate must be higher than 10%. The problem is to find an effective rate that will equate the present value of the cash outflows for the bonds payable to the net proceeds of P9,511,330.
The effective rate cannot be computed algebraically but by means of trial and error or the interpolation process. By trial and error, using a new effective rate of 11%: Present value of 1 for 3 periods is -. Present value of an ordinary annuity of 1 is – 2. The present value of the bonds payable using an interest rate of 11% is computed as follows: PV of principal (10,000,000 x .7312) 7,312, PV of interest payments (900,000 x 2) 2,199, Total present value of bonds 9,511,
Journal entries for 2020:
1/1/2020 – Issuance of bonds. Cash (10,000,000 – 248,790 – 239,880) 9,511, Discount on bonds payable (248,790 + 239,880) 488, Bonds payable (at face amount) 10,000, 12/31/20 – Payment of annual interest and discount amortization using effective interest method. Interest expense (10,000,000 x 9%) 900, Cash 900, Interest expense 146, Discount on bonds payable (9,511,330 x11%) - (10,000,000 x 9%) 146,
Illustration 2: Discount (with no effective rate) and bond issue cost On January 1, 2020, an entity issued 5-year bonds with face amount of P10,000,000 at 95. The nominal rate is 10% and the interest is payable annually on December 31. The bonds mature on January 1, 2025. The entity paid bond issue cost of P200,000.
Face amount 10,000, Discount on bonds payable 500, Issue price (10,000,000 x .95) 9,500, Bond issue cost 200, Net proceeds 9,300,
Again, the problem is to find an effective rate applicable to the proceeds of P9,300,000. Since, the bonds are issued at a discount, the effective rate must be higher than nominal rate of 10%. By interpolation, using a rate of 11%, the PV of 1 for 5 periods is .5935 and the PV of an ordinary annuity of 1 is 3. The total present value of bonds would be P9,630,900.
The net proceeds of P9,300,000 are lower than the present value of bonds payable of P9,630,900 using 11% interest rate. This means that the effective rate must be higher than 11%. So, another interpolation is made using the rate of 12%. The PV of 1 for 5 periods at 12% is. 5674. The PV of an ordinary annuity of 1 for 5 periods at 12% is 3. Thus, the total present value of bonds would be P9,278,800. This time, the net proceeds of P9,300,000 are higher than the present value of bonds payable of P9,278,800 using 12% interest rate. This means that the effective rate must be lower than 12%. In conclusion, the effective interest rate must be between 11% and 12%. The difference between 11% and 12% is interpolated as follows: Let X as the unknown effective interest rate (X – 11%) / (12% - 11%) (9,300,000 – 9,630,900) / (9,278,800 – 9,630,900)
Effective Interest Method
Course: Accounting
University: University of Manila
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