This document contains the solutions to four questions regarding bond valuation and analysis for a financial modeling course. It includes the valuations of four bonds using various inputs like maturity, coupon rate, yield to maturity, etc. It also includes the calculations of convexity for each of the four bonds.

1. CASE-2
FIN455: Financial Modelling using Excel
Submitted to: Farhana Zahir (FZH)
Senior Lecturer, Department of Accounting and Finance, School of Business and Economics
North South University.
Submitted by:
Section: 1
Date: 08 April 2019
Aymaan Hossain 153-1434-030
Juhair Karim 151-0379-030
Sadat Ahmed Nabil 151-0945-030

2. Answer1.i)
Bond 1
Maturity in
Years
15
YTM 10%
Couponrate 9%
Frequency 2
Face Value 1000
CF 45
N 30
BondValue $923.14
Bond 2
Maturity in
Years
17
YTM 8%
Couponrate 10%
Frequency 2
Face Value 1000
CF 50
N 34
Bond Value $1,184.11
Bond 3
Maturity in
Years
15
YTM 7.80%
Couponrate 13%
Frequency 1
Face Value 1500
CF 195
Bond Value $2,175.87
Bond 4
Maturity in
Years
15
YTM 6.50%
Couponrate 15%
Frequency 4
Face Value 1200
CF 45
N 60
Bond Value $2,172.67

3. Answer1.ii)
Bond 1
Maturity in Years 15
YTM 10%
Couponrate 9%
Frequency 2
Face Value 1000
CF 45
N $30.00
Bond Value 923.1377
SettlementDate 30-Mar-19
Maturity Date 30-Mar-34
Duration 8.244219
ModifiedDuration 7.851637
Bond 2
Maturity in Years 17
YTM 8%
Couponrate 10%
Frequency 2
Face Value 1000
Bond Value $1,184.11
SettlementDate 30-Mar-19
Maturity Date 30-Mar-36
Duration 9.160605
ModifiedDuration 8.808274
Bond 3
Maturity in Years 15
YTM 7.80%
Couponrate 13%
Frequency 1
Face Value 1500
Bond Value $2,175.87
SettlementDate 30-Mar-19
Maturity Date 30-Mar-34
Duration 8.497863
ModifiedDuration 7.88299
Bond 4
Maturity in Years 15
YTM 6.5
Couponrate 15%
Frequency 4
Face Value 1200
Bond Value $2,172.67
SettlementDate 30-Mar-19
Maturity Date 30-Mar-34
Duration 0.4038462
ModifiedDuration 0.1538462

4. Answer1.iii)
Convexityof Bond1:
53.17
Periods
Time CF PV Weight Time*pv Timesq*pv
1 0.5 45 $43.06 $0.04 $21.53 $21.53
2 1 45 $41.21 $0.04 $41.21 $61.81
3 1.5 45 $39.43 $0.04 $59.15 $118.30
4 2 45 $37.74 $0.04 $75.47 $188.68
5 2.5 45 $36.11 $0.04 $90.28 $270.83
6 3 45 $34.56 $0.03 $103.67 $362.83
7 3.5 45 $33.07 $0.03 $115.74 $462.94
8 4 45 $31.64 $0.03 $126.57 $569.58
9 4.5 45 $30.28 $0.03 $136.26 $681.32
10 5 45 $28.98 $0.03 $144.88 $796.86
11 5.5 45 $27.73 $0.03 $152.51 $915.06
12 6 45 $26.53 $0.03 $159.21 $1,034.86
13 6.5 45 $25.39 $0.03 $165.05 $1,155.35
14 7 45 $24.30 $0.02 $170.09 $1,275.69
15 7.5 45 $23.25 $0.02 $174.39 $1,395.15
16 8 45 $22.25 $0.02 $178.01 $1,513.08
17 8.5 45 $21.29 $0.02 $180.99 $1,628.91
18 9 45 $20.38 $0.02 $183.38 $1,742.15
19 9.5 45 $19.50 $0.02 $185.24 $1,852.37
20 10 45 $18.66 $0.02 $186.59 $1,959.19
21 10.5 45 $17.86 $0.02 $187.48 $2,062.30
22 11 45 $17.09 $0.02 $187.95 $2,161.45
23 11.5 45 $16.35 $0.02 $188.03 $2,256.40
24 12 45 $15.65 $0.02 $187.76 $2,347.00
25 12.5 45 $14.97 $0.01 $187.16 $2,433.09
26 13 45 $14.33 $0.01 $186.27 $2,514.58
27 13.5 45 $13.71 $0.01 $185.10 $2,591.40
28 14 45 $13.12 $0.01 $183.69 $2,663.50
29 14.5 45 $12.56 $0.01 $182.06 $2,730.86
30 15 45 $12.02 $0.01 $180.23 $2,793.49
SUM $733.00 $0.73 4,505.94 42,560.53

5. Convexityof Bond2 :
61.60
Periods
Time CF PV Weight Time*pv Timesq*pv
1 0.5 50 $47.62 $0.05 $23.81 23.809524
2 1 50 $45.35 $0.05 $45.35 $68.03
3 1.5 50 $43.19 $0.04 $64.79 $129.58
4 2 50 $41.14 $0.04 $82.27 $205.68
5 2.5 50 $39.18 $0.04 $97.94 $293.82
6 3 50 $37.31 $0.04 $111.93 $391.76
7 3.5 50 $35.53 $0.04 $124.37 $497.48
8 4 50 $33.84 $0.03 $135.37 $609.16
9 4.5 50 $32.23 $0.03 $145.04 $725.19
10 5 50 $30.70 $0.03 $153.48 $844.13
11 5.5 50 $29.23 $0.03 $160.79 $964.72
12 6 50 $27.84 $0.03 $167.05 $1,085.83
13 6.5 50 $26.52 $0.03 $172.35 $1,206.48
14 7 50 $25.25 $0.03 $176.77 $1,325.80
15 7.5 50 $24.05 $0.02 $180.38 $1,443.05
16 8 50 $22.91 $0.02 $183.24 $1,557.58
17 8.5 50 $21.81 $0.02 $185.43 $1,668.83
18 9 50 $20.78 $0.02 $186.98 $1,776.35
19 9.5 50 $19.79 $0.02 $187.97 $1,879.74
20 10 50 $18.84 $0.02 $188.44 $1,978.67
21 10.5 50 $17.95 $0.02 $188.44 $2,072.89
22 11 50 $17.09 $0.02 $188.02 $2,162.20
23 11.5 50 $16.28 $0.02 $187.20 $2,246.44
24 12 50 $15.50 $0.02 $186.04 $2,325.51
25 12.5 50 $14.77 $0.01 $184.56 $2,399.34
26 13 50 $14.06 $0.01 $182.81 $2,467.89
27 13.5 50 $13.39 $0.01 $180.80 $2,531.17
28 14 50 $12.75 $0.01 $178.57 $2,589.20
29 14.5 50 $12.15 $0.01 $176.14 $2,642.04
30 15 50 $11.57 $0.01 $173.53 $2,689.76
31 15.5 50 $11.02 $0.01 $170.78 $2,732.46
32 16 50 $10.49 $0.01 $167.89 $2,770.23
33 16.5 50 $9.99 $0.01 $164.89 $2,803.21
34 17 50 $9.52 $0.01 $161.80 $2,831.53
SUM $809.65 $0.81 5,265.24 53,939.55

6. Convexityof Bond3:
55.76
Periods
CF PV Weight Time*pv Timesq*pv
1 195 $172.57 $0.12 $172.57 $345.13
2 195 $152.71 $0.10 $305.43 $916.28
3 195 $135.14 $0.09 $405.43 $1,621.74
4 195 $119.60 $0.08 $478.39 $2,391.94
5 195 $105.84 $0.07 $529.19 $3,175.15
6 195 $93.66 $0.06 $561.97 $3,933.81
7 195 $82.89 $0.06 $580.21 $4,641.66
8 195 $73.35 $0.05 $586.81 $5,281.28
9 195 $64.91 $0.04 $584.21 $5,842.13
10 195 $57.44 $0.04 $574.45 $6,318.92
11 195 $50.84 $0.03 $559.20 $6,710.36
12 195 $44.99 $0.03 $539.85 $7,018.07
13 195 $39.81 $0.03 $517.56 $7,245.80
14 195 $35.23 $0.02 $493.25 $7,398.70
15 195 $31.18 $0.02 $467.68 $7,482.89
SUM 1,260.16 0.84 7,356.19 70,323.87

7. Convexityof Bond4:
36.13
Periods
Time CF PV Weight Time*pv Timesq*pv
1 0.25 45 $43.37 0.04 $10.84 $5.42
2 0.5 45 $41.81 0.03 $20.90 $15.68
3 0.75 45 $40.29 0.03 $30.22 $30.22
4 1 45 $38.84 0.03 $38.84 $48.55
5 1.25 45 $37.43 0.03 $46.79 $70.19
6 1.5 45 $36.08 0.03 $54.12 $94.71
7 1.75 45 $34.78 0.03 $60.86 $121.72
8 2 45 $33.52 0.03 $67.04 $150.84
9 2.25 45 $32.31 0.03 $72.69 $181.74
10 2.5 45 $31.14 0.03 $77.85 $214.09
11 2.75 45 $30.02 0.03 $82.54 $247.63
12 3 45 $28.93 0.02 $86.79 $282.07
13 3.25 45 $27.88 0.02 $90.63 $317.19
14 3.5 45 $26.88 0.02 $94.07 $352.76
15 3.75 45 $25.91 0.02 $97.15 $388.58
16 4 45 $24.97 0.02 $99.88 $424.47
17 4.25 45 $24.07 0.02 $102.28 $460.27
18 4.5 45 $23.20 0.02 $104.39 $495.83
19 4.75 45 $22.36 0.02 $106.20 $531.01
20 5 45 $21.55 0.02 $107.75 $565.69
21 5.25 45 $20.77 0.02 $109.05 $599.77
22 5.5 45 $20.02 0.02 $110.11 $633.15
23 5.75 45 $19.30 0.02 $110.96 $665.74
24 6 45 $18.60 0.02 $111.60 $697.48
25 6.25 45 $17.93 0.01 $112.04 $728.29
26 6.5 45 $17.28 0.01 $112.31 $758.12
27 6.75 45 $16.65 0.01 $112.42 $786.93
28 7 45 $16.05 0.01 $112.37 $814.67
29 7.25 45 $15.47 0.01 $112.17 $841.31
30 7.5 45 $14.91 0.01 $111.85 $866.83
31 7.75 45 $14.37 0.01 $111.40 $891.20
32 8 45 $13.85 0.01 $110.84 $914.40
33 8.25 45 $13.35 0.01 $110.17 $936.44
34 8.5 45 $12.87 0.01 $109.40 $957.29
35 8.75 45 $12.41 0.01 $108.55 $976.97
36 9 45 $11.96 0.01 $107.62 $995.46
37 9.25 45 $11.53 0.01 $106.61 $1,012.79
38 9.5 45 $11.11 0.01 $105.53 $1,028.95

8. 39 9.75 45 $10.71 0.01 $104.40 $1,043.95
40 10 45 $10.32 0.01 $103.20 $1,057.82
41 10.25 45 $9.95 0.01 $101.96 $1,070.57
42 10.5 45 $9.59 0.01 $100.67 $1,082.21
43 10.75 45 $9.24 0.01 $99.34 $1,092.76
44 11 45 $8.91 0.01 $97.98 $1,102.25
45 11.25 45 $8.59 0.01 $96.58 $1,110.70
46 11.5 45 $8.27 0.01 $95.16 $1,118.14
47 11.75 45 $7.98 0.01 $93.72 $1,124.58
48 12 45 $7.69 0.01 $92.25 $1,130.06
49 12.25 45 $7.41 0.01 $90.77 $1,134.60
50 12.5 45 $7.14 0.01 $89.27 $1,138.22
51 12.75 45 $6.88 0.01 $87.77 $1,140.97
52 13 45 $6.63 0.01 $86.25 $1,142.85
53 13.25 45 $6.40 0.01 $84.73 $1,143.91
54 13.5 45 $6.16 0.01 $83.21 $1,144.17
55 13.75 45 $5.94 0.00 $81.69 $1,143.66
56 14 45 $5.73 0.00 $80.17 $1,142.41
57 14.25 45 $5.52 0.00 $78.65 $1,140.44
58 14.5 45 $5.32 0.00 $77.14 $1,137.79
59 14.75 45 $5.13 0.00 $75.63 $1,134.48
60 15 45 $4.94 0.00 $74.13 $1,130.54
SUM 1068.21 0.89 5411.52 44711.53

9. Answer2)
YTM YTM change
Dur
change Dur price Bond val Error
Adjust
Convexity
New
price
8% 0% 0 1184.112 $1,184.11 $0.00 $0.00 1184.112
9% -1%
-
108.47182 1075.6402 $1,086.23 $10.59 $3.65 1079.287
10% -2%
-
216.94364 967.16833 $1,000.00 $32.83 $14.59 981.7554
11% -3%
-
325.41546 858.69651 $923.81 $65.12 $32.82 891.5175
12% -4%
-
433.88729 750.22469 $856.32 $106.09 $58.35 808.5731
13% -5%
-
542.35911 641.75287 $796.35 $154.60 $91.17 732.9222
14% -6%
-
650.83093 533.28105 $742.92 $209.64 $131.28 664.5649
15% -7%
-
759.30275 424.80923 $695.18 $270.37 $178.69 603.5011
0
200
400
600
800
1000
1200
1400
8% 9% 10% 11% 12% 13% 14% 15%
YTM
Duration and Actual PriceChange

10. Answer3)
Discount Factor 10%
LiabilityCash
Flows
$
1 340
2 8274
3 7126
4 3601
5 4673
6 3874
7 7533
8 1846
9 4809
10 6777
11 9962
12 8716
13 7106
14 1625
15 3282
16 5602
17 3280
18 4253
19 9816
20 9088
21 1430
22 2087
23 587
24 7104
25 9794
26 2459
27 5767
28 2993
29 2298
30 4526
NPV $47,955.97 %
Change
Absolute
Value
NPV+100 $44,131.82 -7.97% 0.079742855
NPV-100 $52,351.20 9.17% 0.091651505
Effective Duration 8.57
SettlementDate 30-Mar-19

11. Answer3)
The prime and foremost risks in investing in Bonds are Interest rate risk and Maturity risk. As a
rationally risk taking investors we will formulate our portfolio in such a combination whereby
the bonds with low duration will carry the most weight compared to the ones with higher
duration. The risks are hedged as the cash flows committed to the bonds are recovered. We have
implemented the Low Bond duration strategy to structurally reduce the interest rate risk.
One Major drawback of such strategy is that there is a cringe in the Yield and Expected Return.
Interest rates are speculated to rise systematically and this mechanism is incorporated in the
yield curve. Therefore, investors are generally entitled to certain level of premiums, if they
purchase long-term dated bonds. But however, when we hedge duration, we have forgo this
premium and hence the expected return and risk reduces.
Expiry Bond Coupon Yield Par Maturity Freq Qty Dur Convex Value Income
30-Mar-34 15yr 9% 10% 1000 15 2 5 7.851637 53.17 923.1377 $450.00
30-Mar-36 17yr 10% 8% 1000 17 2 4 8.808274 61.60 1184.112 $400.00
30-Mar-34 15yr 13% 7.80% 1500 15 1 5 7.925402 55.76 2175.87 $975.00
30-Mar-34 15yr 15% 0.065 1200 15 4 10 8.094358 36.13 2538.936 $1,800.00