Chapter-10 INV. - IN-DEBT SECURITIES PDF

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Chapter 10 Investment in Debt Securities Answe Key...

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Chapter 10 Investments in Debt Securities PROBLEM 1: TRUE OR FALSE 1. TRUE 2. FALSE 3. TRUE 4. TRUE 5. FALSE PROBLEM 2: FOR CLASSROOM DISCUSSION 1. Solutions: Requirement (a): Interest Date received 1/1/x1 1/1/x2 120,000 1/1/x3 120,000 1/1/x4 120,000 1/1/x5 120,000

Interest income 131,842 133,499 135,389 137,544

Amortizatio n 11,842 13,499 15,389 17,544

Requirement (b): (1,000,000 – 967,067) = 32,933 discount Requirement (c): 1/1/x1 Investment in bonds Cash in bank

967,067 967,067

12/31/x1 Interest receivable Investment in bonds Interest income

120,000 11,842

1/1/x2 Cash Interest receivable

120,000

12/31/x2 Interest receivable Investment in bonds Interest income

120,000 13,499

131,842

120,000

133,499

1

Present value 941,726 953,568 967,067 982,457 1,000,000

2.

Solution:

Date 1/1/x1 12/31/x1 12/31/x2 12/31/x3 3.

C

4.

D

5.

D

6.

B

7.

A

8.

A

9.

Solutions:

Interest received

Interest income

Amortizatio n

120,000 120,000 120,000

96,834.51 94,749.62 92,477.08

23,165 25,250 27,523

Requirement (a): Interest Date received 1/1/x1 12/31/x 1 100,000 12/31/x 2 100,000 12/31/x 3 100,000

Interest income

Amortizatio n

126,999

26,999

934,134

130,779

30,779

964,913

135,088

35,088

1,000,000

* [827,135 + (1M x 80%)] = 907,135 Requirement (b): 1/1x1 Investment in bonds Cash 12/31/x1 Cash Investment in bonds Interest income 12/31/x2 Cash Investment in bonds

Present value 1,075,939 1,052,774 1,027,523 1,000,000

907,135 907,135

100,000 26,999 126,999

100,000 30,779

2

Present value 907,135*

Interest income

12/31/x3 Cash Investment in bonds Interest income

130,779

100,000 35,088 135,088

Cash 1,000,000 Investment in bonds

1,000,000

10. Solution: Date 1/1/x1 12/31/x 1 7/1/x2

Interest received

Interest income

Amortizatio n

Present value 907,135

100,000 50,000

126,999 65,389

26,999 15,389

934,134 949,523

7/1/x2 Interest receivable Investment in bonds Interest income

50,000 15,389 65,389

Cash 900,000 Loss on sale of bonds 99,523 Interest receivable 50,000 Investment in bonds 949,523 11. B 12. Solutions: Requirement (a): The annual collections are computed as follows: Date Principal Interest 12/31/x 1 1,000,000 (3M x 10%) 300,000 12/31/x 2 1,000,000 (2M x 10%) 200,000 12/31/x 3 1,000,000 (1M x 10%) 100,000

Date 1/1/x1 12/31/x 1

Collections 1,300,000 1,200,000 1,100,000

Collections

Interest income

Amortizatio n

Present value 2,900,305

1,300,000

348,037

951,963

1,948,342

3

12/31/x 2 12/31/x 3

1,200,000

233,801

966,199

982,143

1,100,000

117,857

982,143

-

Requirement (b): 1/1/x1 Investment in bonds Cash 12/31/x1 Cash Interest income Investment in bonds

2,900,305 2,900,305

1,300,000 348,037 951,963

13. Solutions: Requirement (a): Interest receivable 20x1: (100,000 x 10%) = 10,000 20x2: (100,000 + 10,000) x 10% = 11,000 + 10,000 from 20x1 = 21,000

Requirement (b): Date Interest income 1/1/x1 12/31/x1 11,369 12/31/x2 12,733 12/31/x3 14,261

Discount IGNORED IGNORED IGNORED IGNORED

Present value 94,738 106,107 118,839 133,100

12/31/x1: (106,107 – 10,000 interest receivable) = 96,107 12/31/x1: (118,839 – 21,000 interest receivable) = 97,839

Requirement (c): 1/1/x1 Investment in bonds Cash

94,738 94,738

12/31/x1 Interest receivable Investment in bonds (squeeze) Interest income

10,000 1,369

12/31/x2 Interest receivable Investment in bonds (squeeze) Interest income

11,000 1,733

11,369

12,733

4

14. Solution: 1/1x1 Investment in bonds - FVOCI Cash

Amortization table Interest Date received 1/1/x1 12/31/x 1 100,000 12/31/x 2 100,000 12/31/x 3 100,000

907,135 907,135

Interest income

Amortizatio n

126,999

26,999

934,134

130,779

30,779

964,913

135,088

35,088

1,000,000

12/31/x1 Cash Investment in bonds - FVOCI Interest income Investment in bonds – FVOCI Unrealized gain – OCI [(1M x 98%) – 934,134]

12/31/x2 Cash Investment in bonds - FVOCI Interest income

100,000 26,999 126,999 45,866 45,866

100,000 30,779 130,779

Fair value - 12/31/x2 Amortized cost - 12/31/x2 Cumulative balance of gain - 12/31/x2 Cumulative balance of gain - 12/31/x1 Unrealized gain (loss) - OCI in 20x2 Investment in bonds – FVOCI Unrealized gain – OCI

Present value 907,135*

1,020,000 964,913 55,087 45,866 9,221

9,221 9,221

5

12/31/x3 Cash Investment in bonds - FVOCI Interest income

100,000 35,088 135,088

Fair value - 12/31/x3 Amortized cost - 12/31/x3 Cumulative balance of gain - 12/31/x3 Cumulative balance of gain - 12/31/x2 Unrealized gain (loss) - OCI in 20x3

Unrealized loss – OCI Investment in bonds – FVOCI Cash Investment in bonds

1,000,000 1,000,000 55,087 (55,087)

55,087 55,087

1,000,000 1,000,000

15. Solution:

Date 1/1/x1 12/31/x 1 7/1/x2

Interest received

Interest income

Amortizatio n

Present value 907,135

100,000 50,000

126,999 65,389

26,999 15,389

934,134 949,523

7/1/x2 Interest receivable Investment in bonds - FVOCI Interest income

50,000 15,389 65,389

Fair value - 7/1/x2 Amortized cost - 7/1/x2 Cumulative balance of gain - 12/31/x2 Cumulative balance of gain - 12/31/x1 Unrealized loss - OCI in 20x2 Unrealized loss – OCI Investment in bonds – FVOCI

900,000 949,523 (49,523) 45,866 (95,389)

95,389 95,389

Cash 900,000 Loss on sale – P/L 99,523 Investment in bonds – FVOCI

6

900,000

Interest receivable Unrealized loss – OCI

50,000 49,523*

* Unr e al i z e dg ai n( l os s )-OCI 1 2 /3 1 / 4 5 , 8 6 6 x 1 7 /1 /x 2 ba l .( de bi t )

9 5 , 3 8 9 4 9 , 5 2 3

PROBLEM 3: EXERCISES 1. Solutions: Requirement (a): Interest Interest Date received income 1/1/x 1 1/1/x 140,000 127,290 2 1/1/x 140,000 125,764 3 1/1/x 140,000 124,056 4 1/1/x 140,000 122,143 5

Amortizatio n

Present value 1,060,747

12,710

1,048,037

14,236

1,033,801

15,944

1,017,857

17,857

1,000,000

Requirement (b): (1,033,801 - 1,000,000) = 33,801 premium Requirement (c): 1/1/x1 Investment in bonds Cash in bank 12/31/x1 Interest receivable Investment in bonds Interest income 1/1/x2 Cash Interest receivable 12/31/x2 Interest receivable Investment in bonds Interest income

1,060,747 1,060,747

140,000 12,710 127,290

140,000 140,000

140,000 14,236 125,764

7

1/1/x3 Cash Interest receivable 12/31/x3 Interest receivable Investment in bonds Interest income 1/1/x4 Cash Interest receivable

12/31/x4 Interest receivable Investment in bonds Interest income 1/1/x5 Cash Investment in bonds 2.

140,000 140,000

140,000 15,944 124,056

140,000 140,000

140,000 17,857 122,143 1,000,000 1,000,000

Solution: Date

1/1/x1 12/31/x1 12/31/x2 12/31/x3 12/31/x4

Interest received

Interest income

Amortization

200,000 200,000 200,000 200,000

213,175 214,624 216,232 218,018

13,175 14,624 16,232 18,018

3. Solutions: Requirement (a): Interest Date received 1/1/x1 12/31/x 50,000 1 12/31/x 50,000 2 12/31/x 50,000 3

Present value 1,937,951 1,951,126 1,965,749 1,981,982 2,000,000

Interest income

Amortizatio n

Present value 453,567*

63,499

13,499

467,066

65,389

15,389

482,456

67,544

17,544

499,999

8

*(428,567 + 25,000) = 453,567 Requirement (b): Interest Date received 1/1/x1 12/31/x 50,000 1 12/31/x 50,000 2 12/31/x 50,000 3

Interest income

Amortizatio n

Present value 512,656*

46,139

3,861

508,795

45,792

4,208

504,587

45,413

4,587

499,999

Interest income

Amortizatio n

Present value 2,096,073*

251,529

28,471

2,067,602

248,112

31,888

2,035,714

244,286

35,714

2,000,000

*[487,656 + (500,000 x 5%)] =512,656

4. Solutions: Requirement (a): Interest Date received 1/1/x1 12/31/x 280,000 1 12/31/x 280,000 2 12/31/x 280,000 3

* (1,996,073 + 100,000) = 2,096,073 Requirement (b): 1/1x1 Investment in bonds Cash 12/31/x1 Cash Investment in bonds Interest income 12/31/x2 Cash Investment in bonds Interest income

2,096,073 2,096,073

280,000 28,471 251,529

280,000 31,888 248,112

9

12/31/x3 Cash Investment in bonds Interest income

280,000 35,714 244,286

Cash 2,000,000 Investment in bonds

5.

2,000,000

Solution: Date

1/1/x1 12/31/x1 9/30/x2

Interest received

Interest income

Amortizatio n

280,000 210,000

251,529 186,084

28,471 23,916

Present value 2,096,073 2,067,602 2,043,686

9/30/x2 Interest receivable 210,000 Investment in bonds 23,916 Interest income 186,084

Cash

6.

2,400,000 Interest receivable Investment in bonds Gain on sale of bonds

210,000 2,043,686 146,314

Solution:

1/1x1 Investment in bonds - FVOCI Cash

Date 1/1/x1 12/31/x 1 12/31/x 2 12/31/x 3

2,096,073 2,096,073

Interest received

Interest income

Amortizatio n

Present value 2,096,073*

280,000

251,529

28,471

2,067,602

280,000

248,112

31,888

2,035,714

280,000

244,286

35,714

2,000,000

* (1,996,073 + 100,000) = 2,096,073

12/31/x1

10

Cash Investment in bonds - FVOCI Interest income

280,000 28,471 251,529

Unrealized loss – OCI 27,602 Investment in bonds – FVOCI [(2M x 102%) – 2,067,602]

12/31/x2 Cash 280,000 Investment in bonds – FVOCI Interest income

27,602

31,888 248,112

Fair value - 12/31/x2 Amortized cost - 12/31/x2 Cumulative balance of gain - 12/31/x2 Cumulative balance of loss - 12/31/x1 Unrealized gain - OCI in 20x2 Investment in bonds – FVOCI Unrealized gain – OCI

12/31/x3 Cash Investment in bonds Interest income

2,080,000 2,035,714 44,286 (27,602) 71,888 71,888 71,888

280,000 35,714 244,286

Fair value - 12/31/x3 Amortized cost - 12/31/x3 Cumulative balance of gain - 12/31/x3 Cumulative balance of gain - 12/31/x2 Unrealized loss - OCI in 20x3

Unrealized loss – OCI 44,286 Investment in bonds – FVOCI

Cash Investment in bonds - FVOCI

2,000,000 2,000,000 44,286 (44,286)

44,286

2,000,000 2,000,000

11

7.

Solution: Date

1/1/x1 12/31/x1 9/30/x2

Interest received

Interest income

Amortizatio n

280,000 210,000

251,529 186,084

28,471 23,916

9/30/x2 Interest receivable 210,000 Investment in bonds - FVOCI Interest income

23,916 186,084

Fair value - 9/30/x2 Amortized cost - 9/30/x2 Cumulative balance of gain - 9/30/x2 Cumulative balance of loss - 12/31/x1 Unrealized gain - OCI in 20x2

Investment in bonds – FVOCI Unrealized gain – OCI

Present value 2,096,073 2,067,602 2,043,686

2,400,000 2,043,686 356,314 (27,602) 383,916

383,916 383,916

Cash 2,400,000 Unrealized gain – OCI 356,314 Interest receivable Investment in bonds Gain on sale of bonds

210,000 2,400,000 146,314

8. Solutions: Requirement (a): The annual collections are computed as follows: Date

Principal

12/31/x1

300,000

12/31/x2

300,000

12/31/x3

300,000

(900,000 x 10%) (600,000 x 10%) (300,000 x 10%)

Interest

Collection s

90,000

390,000

60,000

360,000

30,000

330,000

Date

Collections

Interest income

Amortizatio n

1/1/x1 12/31/x

390,000

104,411

285,589

12

Present value 870,092 584,503

1 12/31/x 2 12/31/x 3

360,000

70,140

289,860

294,643

330,000

35,357

294,643

0.61

Requirement (b): 1/1/x1 Investment in bonds Cash

870,092 870,092

12/31/x1 Cash Interest income Investment in bonds

390,000 104,411 285,589

9. Solutions: Requirement (a): 20x1: (2,000,000 x 12%) = 240,000 20x2: (2,000,000 + 240,000) x 12% = 268,800 + 240,000 from 20x1 = 508,800 Requirement (b): Date 1/1/x1 12/31/x1 12/31/x2 12/31/x3

Interest income 211,109 232,219 255,441

Discount IGNORED IGNORED IGNORED IGNORED

12/31/x1: (2,322,195 – 240,000 interest receivable) = 2,082,195 12/31/x1: (2,554,414 – 508,800 interest receivable) = 2,045,614 Requirement (c): 1/1/x1 Investment in bonds Cash

2,111,086 2,111,086

12/31/x1 Interest receivable 240,000 Investment in bonds (squeeze) Interest income

28,891 211,109

12/31/x2 Interest receivable 268,800 Investment in bonds (squeeze) Interest income

36,581 232,219

13

Present value 2,111,086 2,322,195 2,554,414 2,809,855

10. Solution:

Purchase price of bonds = Present value of future cash flows Purchase price of bonds = ₱ 7,986,000 x PV of ₱1 @16%, n=3 Purchase price of bonds = ₱ 5,116,292 (7,986,000 x 0.640658)

11. Solution: Date

Interest income

PV of cash flow

Interest receivabl e

(a) =ER x (b)

(b) = prev. bal. of (b) + (a)

(c)

(d) = (a) (b)

204,652

5,116,292 5,320,944

150,000

54,652

1/1/x1 4/1/x1

Present value

Amortization

Purchase cost of bonds Purchased accrued interest (3M x 10% x 3/12) Total purchase price or total cash outlay 5,320,944

= PV + (d) 5,116,292 5,170,944

₱ 5,170,944 150,000 ₱

OR, simply the PV of cash flow of ₱5,320,944 because this amount already includes the purchased interest.

PROBLEM 4: CLASSROOM ACTIVITIES ACTIVITY #1:

Solutions: Requirement (a): 1,000 face amount x 1,000 no. of bonds = 1,000,000 Requirement (b): 1,000,000 – 922,783 = 77,217 discount Requirement (c): Investment in bonds Cash in bank

922,783 922,783

Requirement (d): NIR = 8% 14

Requirement (e): Trial & Error PV = CF x PVF There is discount. Therefore, the EIR must be higher than 8%. First trial: @10% per annum (5% semi-annual)    

922,783 = (1,000,000 x PV of 1 @ 5%, n=10) + (40,000 x PV ordinary annuity @5%, n=10) 922,783 = (1,000,000 x 0.61391) + (40,000 x 7.72173) 922,783 = 613,910 + 308,869 922,783 approximates 922,779 (a difference of only ₱4.00)

Therefore, the EIR is 10% (per annum). Requirement (f): Date 7/1/x 1 1/1/x 2 7/1/x 2 1/1/x 3 7/1/x 3 1/1/x 4 7/1/x 4 1/1/x 5 7/1/x 5 1/1/x 6 7/1/x 6

Interest received

Interest income

Amortizatio n

Present value 922,783.00

40,000.00

46,139.15

6,139.15

928,922.15

40,000.00

46,446.11

6,446.11

935,368.26

40,000.00

46,768.41

6,768.41

942,136.67

40,000.00

47,106.83

7,106.83

949,243.50

40,000.00

47,462.18

7,462.18

956,705.68

40,000.00

47,835.28

7,835.28

964,540.96

40,000.00

48,227.05

8,227.05

972,768.01

40,000.00

48,638.40

8,638.40

981,406.41

40,000.00

49,070.32

9,070.32

990,476.73

40,000.00

49,523.84

9,523.84

1,000,000.57

ACTIVITY #2: Case #1:

15

Requirement (a): 7/1/x1 Investment in bonds Interest income (Interest receivable) (10,000 x 7% x 2/12) Cash in bank

10,000.00 116.67 10,116.67

8/1/x1 If “Interest receivable” was debited on 7/1/x1: Cash in bank (10,000 x 7% x 3/12) 175.00 Interest receivable Interest income

116.67 58.33

If “Interest income” was debited on 7/1/x1: Cash in bank (10,000 x 7% x 3/12) 175.00 Interest income

175.00

11/1/x1 Cash in bank (10,000 x 7% x 3/12) Interest income

175.00

12/x/x1 Interest receivable (10,000 x 7% x 2/12) Interest income

116.67

175.00

116.67

Requirement (b): (10,000 x 7% x 6/12) = 350 Requirement (c): (10,000 x 7% x 2/12) = 116.67 Requirement (d): (175 + 175) see entries above = 350

Case #2:

Requirement (a): Purchase price: Cash flows

PV Factors

10,000.00

0.5584 16

Purchase price 5,584.00

700.00

7.3601

5,152.07 10,736.07

5/1/2000 Investment in bonds Cash in bank

10,736.07 10,736.07

Requirement (b): (10,000 x 7% x 8/12) = 466.67 Requirement (c): Interest Date receivable 5/1/2000 12/31/2000 466.67

Interest income

Amortizatio n

429.44

37.22

Carrying amt. 12.31.20...