Effective Interest Method PDF

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EFFECTIVE INTEREST METHODMarket price of bondsPFRS 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 rat...

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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 effective 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= 40,000 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.

Date Jan.1, 2020 June 30, 2020 Dec. 31, 2020 June 30, 2021 Dec. 31, 2021

Interest paid 40,000 40,000 40,000 40,000

Journal entries for 2020: 1/1/20 – Issuance of bonds

Interest expense 48,227 48,638 49,070 49,525

Discount amortization 8,227 8,638 9,070 9,525

Carrying amount 964,540 972,767 981,405 990,475 1,000,000

Cash Discount on bonds payable (1,000,000 – 964,540) Bonds payable (at face amount)

964,540 35,460 1,000,000

6/30/20 – Payment of semiannual interest and discount amortization for 6 months. Interest expense 48,227 Cash (1,000,000 x 8% x 6/12) 40,000 Discount on bonds payable (See table of amortization) 8,227 12/31/20 – Payment of semiannual interest and discount amortization for 6 months. Interest expense 48,638 Cash (1,000,000 x 8% x 6/12) 40,000 Discount on bonds payable (see table of amortization) 8,638 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 P1,000,000 for P1,049,740, a price which will yield a 10% effective interest cost per year. The interest is payable annually every December 31.

Date Jan. 1, 2020 Dec. 31, 2020 Dec. 31, 2021 Dec. 31, 2022

Interest paid 120,000 120,000 120,000

Interest expense

Premium amortization

104,974 103,471 101,815

Journal entries for 2020 and 2021: 1/1/20 – Issuance of bonds. Cash Premium on bonds payable Bonds payable (at face amount) 12/31/20 – Payment of annual interest.

15,026 16,529 18,185

1,049,740 49,740 1,000,000

Carrying amount 1,049,740 1,034,714 1,018,185 1,000,000

Interest expense Cash (1,000,000 x 12%)

120,000 120,000

12/31/20 - Premium amortization for 1 year. Premium on bonds payable (See table of amortization) Interest expense

15,026 15,026

12/31/21 – Payment of annual interest. Interest expense 120,000 Cash (1,000,000 x 12%) 120,000 12/31/21 – Premium amortization Premium on bonds payable (See table of amortization) 16,529 Interest expense 16,529 Note: The annual payment of interest and the premium amortization are recorded separately for 2020 and 2021. Another illustration On January 1, 2020, Wolf company issued 10% bonds in the face amount of P5,000,000, which mature on January 1, 2030. The bonds were issued for P5,675,000 to yield 8%, resulting in the premium of P675,000. The entity used the interest method of amortizing bond premium. Interest is payable annually on December 31. Required: 1. What is the balance of the premium on bonds payable on December 31, 2020? 2. What is the carrying amount of bonds payable on December 31, 2020? Answers: Interest Paid Date

Jan 1, 2020 Dec 31, 2020

500,000

Interest Expense

454,000

Premium amortizatio n

46,000

Carrying amount

5675000 5,629,000

1. Premium on bonds payable (5,675,000 – 5,000,000) Less: Premium amortization – 12/31/20 Balance of the premium on bonds payable – 12/31/20 2. Carrying amount of bonds payable on 12/31/20:

675,000 46,000 629,000 5,629,000

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 4,000,000 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 .7350 PV of an ordinary annuity of 1 at 8% for 4 periods 3.3121 Required: What is the market issue price of the bonds? Ans. 3,734,904 Answer: Present value of the principal (4,000,000 x .7350) Present value of annual interest payments (240,000 x 3.3121) Total Present value of the bonds

Date Jan. 1 , 2020 Dec. 31,2020 Dec. 31, 2021 Dec. 31, 2022 Dec. 31, 2023

Interest paid

Interest expense

240,000 240,000 240,000 240,000

298,793 303,496 308,575 314,233

Discount amortization 58,792 63,496 68,575 74,233

2,940,000 794,904 3,734,904 Carrying amount 3,734,904 3,793,696 3,857,192 3,925,767 4,000,000

Illustration 2: Interest is payable semiannually Face amount of bonds 5,000,000 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 .7462 PV of an ordinary annuity of 1 at 5% for 6 periods 5.0757 Required: What is the market issue price of the bonds? Ans. 5,253,710 Answer: PV of principal (5,000,000 x .7462) PV of interest payment (300,000 x 5.0757) Total present value of bonds

3,731,000 1,522,710 5,253,710

Note: The semiannual 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).

Date Jan. 1 2020 June 30, 2020 Dec. 31, 2020 June 30, 2021 Dec. 31, 2021 June 30, 2022 Dec. 31, 2022

Interest paid 300,000 300,000 300,000 300,000 300,000 300,000

Interest expense 262,686 260,820 258,861 256,804 254,644 252,475

Illustration 3: Serial bonds Face amount of bonds Nominal rate Effective rate Date of issue Annual payment every December 31 Interest is payable annually Present value of 1 at 10%: One period Two periods Three periods

Premium amortization 37,314 39,180 41,139 43,196 45,356 47,525

Carrying amount 5,253,710 5,216,396 5,177,216 5,136,077 5,092,881 5,047,525 5,000,000

3,000,000 12% 10% January 1,2020 1,000,000 December 31 0.9091 0.8264 0.7513

Required: What is the market price of the serial bonds?Ans. 3,102,568

Answer: Principal Interest Date payment payment 12/31/20 1,000,000 360,000 12/31/21 1,000,000 240,000 12/31/22 1,000,000 120,000 Total present value of serial bonds Less: Face amount Premium on bonds payable

Date 1/1/2020 12/31/2020 12/31/2021 12/31/2022

Interest paid 360,000 240,000 120,000

Interest expense 310,257 205,282 101,893

(a) Total payment 1,360,000 1,240,000 1,120,000

Premium amortization 49,743 34,718 18,107

(b) PV factor 0.9091 0.8264 0.7513

Principal payment 1,000,000 1,000,000 1,000,000

(a x b) Present value 1,236,376 1,024,736 841,456 3,102,568 3,000,000 102,568

Carrying amount 3,102,568 2,052,825 1,018,107 0

Journal entries for 2020 and 2021: 1/1/2020 – Issuance of bonds. Cash 3,102,568 Premium on bonds payable 102,568 Bonds payable (at face amount) 3,000,000 12/31/20 – Payment of annual interest. Interest expense 360,000 Cash (3,000,000 x 12%) 360,000 12/31/20 – Amortization of premium for 2020. Premium on bonds payable (See table of amortization) 49,743 Interest expense 49,743 12/31/20 – First annual payment of principal. Bonds payable 1,000,000 Cash 1,000,000 12/31/21 – Payment of annual interest. Interest expense 240,000 Cash (2,000,000 x 12%) 240,000 12/31/21 – Amortization of premium for 2021and second annual payment of principal. Premium on bonds payable (See table or amortization) 34,718 Interest expense 34,718 Bonds payable 1,000,000

Cash

1,000,000

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 Discount on bonds payable Issue price Bond issue cost Net proceeds

10,000,000 248,790 9,751,210 239,880 9,511,330

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 .7312 Present value of an ordinary annuity of 1 is – 2.4437 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) 7,312,000 PV of interest payments (900,000 x 2.4437) 2,199,330 Total present value of bonds 9,511,330 Journal entries for 2020:

1/1/2020 – Issuance of bonds. Cash (10,000,000 – 248,790 – 239,880) 9,511,330 Discount on bonds payable (248,790 + 239,880) 488,670 Bonds payable (at face amount) 10,000,000 12/31/20 – Payment of annual interest and discount amortization using effective interest method. Interest expense (10,000,000 x 9%) 900,000 Cash 900,000 Interest expense 146,246 Discount on bonds payable (9,511,330 x11%) - (10,000,000 x 9%) 146,246

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 Discount on bonds payable Issue price (10,000,000 x .95) Bond issue cost Net proceeds

10,000,000 500,000 9,500,000 200,000 9,300,000

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 3.6959. 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 3.6048. 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)

330,900 / 352,100 = 0.94 This difference of .94 between 11% and 12% is added to 11% to get an effective rate of 11.94%. Thus, the PV of 1 for 5 periods at 11.94 % effective rate is .56895 and the PV of an ordinary annuity of 1 for 5 periods at 11.94% effective rate is 3.61014. The present value of bonds is computed as follows: PV of principal (10,000,000 x .56895) 5,689,500 PV of interest payments (1,000,000 x 3.61014) 3,610,140 Total present value of bonds 9,299,840 or 9,300,000

Illustration : Retirement of bonds Nixon Company reported 10% bonds payable with carrying amount of P5,700,000 on January 1, 2020. The bonds had a face amount of P6,000,000 and were issued to yield 12%. The interest method of amortization is used. Interest was paid on January 1 and July 1 of each year On July 1, 2020, the entity retired the bonds at 102. The interest payment on July 1, 2020 was made as scheduled. Required: 1.What is the carrying amount of bonds payable on July 1, 2020? 2. What amount should be recorded as loss on the early extinguishment of the bonds? Answers: 1. Interest expense (5,700,000 x 12% x 6/12) Interest paid (6,000,000 x 10% x 6/12) Discount amortization – 7/1/2020 Add: carrying amount – 1/1/2020 Carrying amount of bonds payable – 7/1/2020 2. Carrying amount of bonds payable -7/1/2020 Less; Retirement price (6,000,000 x 1.02) Loss on the early retirement of bonds

342,000 300,000 42,000 5,700,000 5,742,000 5,742,000 6,120,000 378,000...