Question

Computing Amounts under Effective Interest and Straight-Line Interest Methods For the following separate bond issues, assume that the bonds are sold on January 1, 2020, interest is paid semiannually on July 1 and December 31, and the bond term is 5 years. Complete the following schedule by measuring the bond selling price on January 1, 2020, and interest expense and interest paid for 2020. • Note: Round your answers to the nearest whole dollar. S Face Value Stated Market Amortization Bond Selling Case of Bonds Rate Rate Method Price $5,000 596 6% creclive interest $ 3,906 X 20,000 49 5 % Crective interest 65,000 5% 4% Straight-line 250,000 0% 7% Straight-line 40,000 7% 6% Cllective interest OX 50,000 6% 8% Straight-line Interest interest Revenue 2020 Paid 2020 50 XS 800 x 800 3.250 x 3.250 250 2,800 3,000 Ox 0 x Check

Answer 1

Case Face Value of Bond Stated Rate $5,000 5.00% $20,000 4.00% $65,000 5.00% $2,50,000 0.00% $40,000 7.00% $50,000 6.00% Market Rate Amortisation Method Bond Selling Price Interest Expense 2020 Interest Paid 6.00% Effective Interest $4,786 $288 5.00% Effective Interest $19,125 $958 4.00% Straight Line $67,920 $2,666 7.00% Straight Line $1,77,230 $14,554 6.00% Effective Interest $41,706 $2,498 8.00% Straight Line $45,944 $3,811 $250 $800 $3,250 $0 $2,800 $3,000 The effective interest rate is also called as market rate. It is the investor's yield maturity. When the effective interest rate is higher/lower as compared bond coupon rate then, the bonds were issued at a discount/premium. The Discount/premium is then amortised over the period of bond by using effective interest rate method. Under this method, interest expense is derived by multiplying the bond carrying value with the effective interest rate applicable when the bonds were issued. The difference between the interest expense and actual interest paid is the discount/(premium) which will be amortised. In straight line amortization, the premium received or discount given on issue of bond is amortized over the bond period maturity on straight line basis. Formula is (Discount / Premium Amount) divided by bond period.

Note (1) Case Calculation of issue price of bond 5 Face Value Stated Rate Coupon Payment Market Rate Maturity Period $5,000 5.00% Semiannually 6.00% 2 $20,000 4.00% Semiannually 5.00% $65,000 5.00% Semiannually 4.00% 4 $2,50,000 0.00% Semiannually 7.00% $40,000 7.00% Semiannually 6.00% $50,000 6.00% Semiannually 8.00% $0 10 10 Coupon payment frequency Coupon Rate consider for calculation 2.50% 2.00% 2.50% 0.00% 3.50% 3.00% [5%/2] [4%/2] [5%/2] [0%/2] [7%/2] [6%/2] Coupon Payment $125 $400 $1,625 $1,400 $1,500 [$5000 x 2.5%] ($20000 x 2%] ($65000 x 2.5%] ($250000 x 0%] [$40000 x 3.5%] [$50000 x 3%] Market Rate Consider for Calculation 3.00% 2.50% 2.00% 3.50% 3.00% 4.00% [6%/2] [5%/2] [4%/2] [7%/2] [6%/2] [8%/2] Period 10 10 10 10 [5 x 2] [5 x 2] [5 x 2] (5 x 2] [5 x 2] [5 x 2] Present Value of Coupon Payments Present Value of Annuity of $1 period 10 8.530203 8.752064 8.982585 8.316605/ 8.530203 8.110896 Present Value of Coupon Payments (A) $1,066 $3,501 $14,597 $11,942 $12,166 ($125 x 8.530203] [$400 x 8.752064] [$1625 x 8.982585] [$0 X 8.316605] ($1400 x 8.530203] | [$1500 x 8.110896] Present Value of Maturity Value Present Value of $1 period 10 0.74409 0.78120 0.82035 0.70892 0.74409 0.67556 Present Value of Maturity Value (B) $3,720 $15,624 $53,323 $1,77,230 $29,764 $33,778 [$5000 x 0.744094] [$20000 x 0.781198] [$65000 x 0.820348] [$250000 x 0.708919] [$40000 x 0.744094] [$50000 x 0.675564] Present Value of Bond = Present Value of Coupon Payment + Present Value of Maturity Present Value of Bond [(A) + (B)] $4,786 $19,125 $67,920 $1,77,230 $41,706 $45,944 Issue price of the Bond $4,786 $19,125 $67,920 $1,77,230 $41,706 $45,944 Premium/(Discount) ($214) ($875) $2,920 ($72,770) $1,706 ($4,056) $0

Date Carrying Value Discount Amortisation (D) = (B)-(C) Case 1 Amortisation schedule (Effective Interest Method) Opening book Cash paid for Interest Expense Balance interest (A) (B) (C) = (A) x 3% Jan 1, 2020 July 1,2020 $4,786 $125 $144 Dec 31, 2020 $4,805 $125 $144 $250 $288 (A)+(C)-(B) $4,786 $4,805 $4,824 ($19) ($19) Case 2 Amortisation schedule (Effective Interest Method) Opening book Cash paid for Date Balance interest Interest Expense Carrying Value Discount Amortisation (D) = (B)-(C) (A) (B) (C) = (A) x 2.50% Jan 1, 2020 July 1,2020 Dec 31, 2020 (A)+(C)-(B) $19,125 $19,203 $19,283 $19,125 $19,203 $400 $400 $800 $478 $480 $958 ($78) ($80) ($158) Interest Expense Carrying Value Premium Amortisation (C) = $2920/10 (D) = (B) - © Case 3 Amortisation schedule ( Straight Line Method) Opening book Cash paid for Date Balance interest (A) (B) Jan 1, 2020 July 1,2020 $67,920 $1,625 Dec 31, 2020 $67,628 $1,625 $3,250 (A)+(D)-(B) $67,920 $67,628 $67,336 $292 $292 $584 $1,333 $1,333 $2,666

Interest Expense Carrying Value Case 4 Amortisation schedule ( Straight Line Method) Opening book Cash paid for Date Balance interest (A) (B) Jan 1, 2020 July 1,2020 $1,77,230 Dec 31, 2020 $1,84,507 (C) = $72770/10 (A)+(C)-(B) $1,77,230 $1,84,507 $1,91,784 SO 50 $7,277 $7,277 $14,554 $0 Interest Expense Amortisation Carrying Value (C) = (A) x 3% (D) = (B)-(C) Case 5 Amortisation schedule (Effective Interest Method) Opening book Cash paid for Date Balance interest (A) (B) Jan 1, 2020 July 1,2020 $41,706 $1,400 Dec 31, 2020 $41,557 $1,400 $2,800 (A)+(C)-(B) $41,706 $41,557 $41,404 $1,251 $1,247 $2,498 $149 $153 Interest Expense Discount Amortisation (C) = $4056/10 Case 6 Amortisation schedule ( Straight Line Method) Opening book Cash paid for Date Balance interest (B) Jan 1, 2020 July 1,2020 $45,944 $1,500 Dec 31, 2020 $46,350 $1,500 $3,000 (A) (D) = (B) + (C) Carrying Value (A)+(D)-(B) $45,944 $46,350 $46,755 $406 $406 $811 $1,906 $1,906 $3,811