2012136 Ankit Garg FIS Assignment

FIS Ankit Garg(2012136)

Fix income security

Question1:

How do we complete the conversion from Money Market Actual/365 to Bond Market 30E/360?

Answer: Conversion of bond interest payment into money market payment: R(BM)= R(MM)*D(MM)*B(BM) / B(MM)*D(BM)Where:R(BM)= Interest rate in bond market.R(MM)= Interest rate in money market.D(MM)= Number of days per year, Money market.B(MM)= Basis of term calculation, Money market.D(BM)= Number of days per year, Bond market.B(BM)= Basis of term calculation, Bond market. Question 2: CFA Questions


1. Compute the value of a 5-year 7.4% coupon bond that pays interest annually assuming that the appropriate discount rate is 5.6%.

Answer:

Coupon Rate 7.40% Year Cash Flows df Pv

Yield 5.60% 1 7.4 0.9469697 7.00757576

Face (Assumption) 100 2 7.4 0.89675161 6.63596189

N 5 years 3 7.4 0.8491966 6.28405482

4 7.4 0.80416344 5.95080949

5 107.4 0.76151841 81.7870776

Total 107.66548

2. A 5-year amortizing security with a par value of $100,000 and a coupon rate of 6.4% has an

expected cash flow of $23,998.55 per year assuming no prepayments. The annual cash flow includes interest and principal payment. What is the value of this amortizing security assuming no principal prepayments and a discount rate of 7.8%.

Answer:


Yield 7.80% 1 23998.55 0.92764378 22262.1058

Face $ 1,00,000.00 2 23998.55 0.86052299 20651.304

N 5 years 3 23998.55 0.7982588 19157.0538

Annuity $ 23,998.55 4 23998.55 0.74049982 17770.9219

5 23998.55 0.68692005 16485.0853

Total 96326.4708

3. Assuming annual interest payments, what is the value of a 5-year 6.2% coupon bond when the discount rate is (i) 4.5%, (ii) 6.2%, and (iii)7.3%?

Answer:

Coupon Rate 6.20% Yield 4.5%

Yield 1 4.50% Year Cash Flows df Pv

Yield 2 6.20% 1 6.2 0.9569378 5.93301435

Yield 3 7.30% 2 6.2 0.91572995 5.6775257

Face (Assumption) 100 3 6.2 0.8762966 5.43303895

N 5 years 4 6.2 0.83856134 5.19908033

5 106.2 0.80245105 85.2203011

Total 107.46296

Yield 6.2% Yield 7.3%

Cash Flows df Pv Cash Flows df Pv

6.2 0.941619586 5.83804143 6.2 0.93196645 5.77819199

6.2 0.886647444 5.49721415 6.2 0.86856146 5.38508107

6.2 0.834884599 5.17628451 6.2 0.80947014 5.01871488

6.2 0.78614369 4.87409088 6.2 0.75439901 4.67727389


106.2 0.740248296 78.614369 106.2 0.70307457 74.6665194

100 95.5257812

4. A 4-year 5.8% coupon bond is selling to yield 7%. The bond pays interest annually. One year later interest rates decrease from 7% to 6.2%.a. What is the price of the 4-year 5.8% coupon bond selling to yield 7%?b. What is the price of this bond one year later assuming the yield is unchanged at 7%?c. What is the price of this bond one year later if instead of the yield being unchanged the yield decreases to 6.2%?

Answer: a.


Yield 7.00% 1 5.8 0.93457944 5.42056075

Face (Assumption) 100 2 5.8 0.87343873 5.06594462

N 4 years 3 5.8 0.81629788 4.73452769

4 105.8 0.76289521 80.7143134

Total 95.9353465

b.


Yield 7.00% 1 5.8 0.93457944 5.42056075

Face (Assumption) 100 2 5.8 0.87343873 5.06594462

N 3 years 3 105.8 0.81629788 86.3643154

Total 96.8508207

c.


Yield 6.20% 1 5.8 0.94161959 5.4613936

Face (Assumption) 100 2 5.8 0.88664744 5.14255518

N 3 years 3 105.8 0.8348846 88.3307906

Total 98.9347393

5. What is the value of a 5-year 5.8% annual coupon bond if the appropriatediscount rate for discounting each cash flow is as follows:Year Discount rate1 5.90%2 6.40%3 6.60%4 6.90%5 7.30

Answer:

Year Cash Flows Yield df Pv

1 5.8 5.90% 0.94428706 5.47686497

2 5.8 6.40% 0.88331732 5.12324043

3 5.8 6.60% 0.82552149 4.78802467

4 5.8 6.90% 0.76575383 4.44137223


5 105.8 7.30% 0.70307457 74.3852895

Total 94.2147918

6. What is the value of a 5-year 7.4% coupon bond selling to yield 5.6% assuming the coupon payments are made semi-annually?

Answer:

Coupon Rate 7.40% Period Cash Flows df Pv

Yield 5.60% 1 3.7 0.97276265 3.59922179

Face (Assumption) 100 2 3.7 0.94626717 3.50118851

N 5 years 3 3.7 0.92049335 3.4058254

Frequency 2 4 3.7 0.89542155 3.31305973

Semiannual Yield 2.80% 5 3.7 0.87103263 3.22282075

Semiannual Coupon 3.70% 6 3.7 0.84730801 3.13503964

7 3.7 0.82422958 3.04964945

8 3.7 0.80177975 2.96658507

9 3.7 0.77994139 2.88578314

10 103.7 0.75869785 78.6769671

Total 107.756141

7. What is the value of a zero-coupon bond paying semiannually that matures in 20 years, has a maturity of $1 million, and is selling to yield 7.6%.

Answer:

Coupon Rate 0.00% Value

Yield 7.60% $ 2,24,960.29

Face $ 10,00,000.00

N 20 years

Frequency 2

Semiannual Yield 3.80%

Semiannual Coupon 0.00%

8. Suppose that a bond is purchased between coupon periods. The days between the settlement date and the next coupon period is 115. There are 183 days in the coupon period. Suppose that the bond purchased has a coupon rate of 7.4% and there are 10 semiannual coupon payments remaining.a. What is the dirty price for this bond if a 5.6% discount rate is used?b. What is the accrued interest for this bond?c. What is the clean price?

Answer:

Coupon Rate 7.40%

Days in Coupon period 183

Days between Settlement and coupon payment 115

0.628415301

Yield 5.60%

Semiannual Yield 2.80%

Semiannual Coupon 3.70%

Face (Assumption) 100

Period Cash Flows df Pv


1 3.7 0.98279592 3.63634489

2 3.7 0.95602716 3.53730048

3 3.7 0.92998751 3.44095377

4 3.7 0.90465711 3.3472313

5 3.7 0.88001664 3.25606157

6 3.7 0.85604732 3.16737507

7 3.7 0.83273085 3.08110415

8 3.7 0.81004947 2.99718303

9 3.7 0.78798586 2.91554769

10 103.7 0.76652321 79.4884572

Dirty Price 108.867559

b. Accrued Interest= 3.7*(1-(115/183)) = 1.3748c. Clean Price= Dirty Price – Accrued Interest= 108.8676 – 1.3748= 107.492696

Question 3: Fixed Income Valuation Cases

1. A) The yield to maturity at the time of issuance is 4.750%. (it will remain same as coupon rate is equal to yield rate)Yield to maturity when bond is priced at 99 is 4.879%(price decreased so yield increased) and when bond is

priced at 101 Yield to maturity is 4.623%(price increased yield decreased)

B) If the yield is dropped to 3% then bonds should be sell at 112.2844613.

2. A) The Prices for each of them are given below:

Bond A: 1040.55448

Bond B: 1000

Bond C: 456.3869.(this is done taking semiannually coupon rate =4% so could be different from others).

Please find calculations in attached excel.

B) The yield to maturity of the Nationaliste Eurobond is 8.15%. The yield to maturity of the previous bond is 8% which means the price of Nationaliste Eurobond will be less than the bond with 8% yield as yield to maturity and price are inversely related. So Ms Alumm should invest in the Nationaliste Eurobond which has a higher yield.

3. A)

Interest Rate 9%

Pre-tax payment 25000

Time 20

Mortgage amount 228213.6417

1st Year Interest 20539.22776

Total Interest 271786.3583

Principal paid in 1st year 4460.772245

Amortization Schedule

Payment Period Payment Interest Interest Amount Principal Repaid Balance


Rate

0 9% 228213.6417

1 25000 9% 20539.2278 4460.7722 223752.8695

2 25000 9% 20137.7583 4862.2417 218890.6277

3 25000 9% 19700.1565 5299.8435 213590.7842

4 25000 9% 19223.1706 5776.8294 207813.9548

5 25000 9% 18703.2559 6296.7441 201517.2107

6 25000 9% 18136.5490 6863.4510 194653.7597

7 25000 9% 17518.8384 7481.1616 187172.5980

8 25000 9% 16845.5338 8154.4662 179018.1319

9 25000 9% 16111.6319 8888.3681 170129.7637

10 25000 9% 15311.6787 9688.3213 160441.4425

11 25000 9% 14439.7298 10560.2702 149881.1723

12 25000 9% 13489.3055 11510.6945 138370.4778

13 25000 9% 12453.3430 12546.6570 125823.8208

14 25000 9% 11324.1439 13675.8561 112147.9647

15 25000 9% 10093.3168 14906.6832 97241.2815

16 25000 9% 8751.7153 16248.2847 80992.9968

17 25000 9% 7289.3697 17710.6303 63282.3665

18 25000 9% 5695.4130 19304.5870 43977.7795

19 25000 9% 3958.0002 21041.9998 22935.7797

20 25000 9% 2064.2202 22935.7798 -0.0002

The amount of interest payment in the 20th year is 2064.2202 and principal amount is 22935.7798

B) When the cash flow differ from year to year, we at first find the discount rate for each year and then multiply it with the cash flows i.e 25000 for first 5 years, 30000 for second 5 years, 35000 for third 5 years and 40000 for last 5 years.

Time Period (years)

Discount factor(1/1.09^Time Period) Cash Flow Mortgage Amount

1 0.91743119322935.779

8 273301.8398

2 0.84167999321041.999

8

3 0.77218348 19304.587

4 0.70842521117710.630

3

5 0.64993138616248.284

7

6 0.59626732717888.019

8

7 0.54703424516411.027

3

8 0.5018662815055.988

4

9 0.4604277813812.833

4

10 0.42241080712672.324

2

11 0.3875328513563.649

8

12 0.35553472512443.715

4


13 0.32617864711416.252

6

14 0.29924646510473.626

3

15 0.2745380419608.8314

5

16 0.25186976310074.790

5

17 0.2310731779242.9270

7

18 0.211993748479.7496

1

19 0.194489677779.5867

9

20 0.178430897137.2355

9

The total mortage amount is 273301.8398

4. A, B) The effective annual yield to maturity and the final amount that Consolidated Chemical will make after 15 years on each bond is given below:

Pru Johntower Tom Paine

Time to maturity 15 Time to maturity 15

Coupon Rate 10% Coupon Rate 9.7200%

Face value 10000000 Face value 10000000

Quoted price 10000000 Quoted price 10000000

Final Amount 41772481.69 Final Amount 42721909.3

Effective YTM 10.00% Effective YTM 10.165%

C) The reason for insurance companies demanding a higher effective annual yield for coupon bonds is the reinvestment risk. The risk is that the insurance companies may not be able to reinvest the coupon payments at the prevailing interest rates. The companies expect the interest rates to drop. To cover this risk, the insurance companies ask for higher effective yields for coupon yielding bonds.

5. A)

Total Amount $150 million

Issued at par value 100

Interest rate 6.625%

Tax rate 35.000%

Period (in years) 10

Quoted price -100 The yield to maturity for McDonalds is 6.625% and the effective after-tax-cost is :

6.625*(1-0.35)= 4.3063%

B)

Year Tax savings

1 6459375

2 6459375

3 6459375

4 6459375


5 6459375

6 6459375

7 6459375

8 6459375

9 6459375

10 6459375

PV 51601622.13

The tax saving for each year is calculated and added. It has then been discounted at 4.3063% to arrive at the present value figure.

6. A) If Weyerhauser’s were to issue bonds of equivalent maturity and risk as the IRBs but do so as a direct obligation of its own, the interest paid on them would not be exempted from taxation whereas for IRB’s there would be tax exemption. Hence the effective annual yield would be lower for IRBs, and price will be higher.

B) Present value of the savings is 286.80. The cash flow for all the years at 7.25% semi-annually on 1000 is calculated along with the discount factor where yield to maturity is 9%. The tax saving for each year is 13 which is then discounted using the discount factor to arrive at the present value.

year CF df df x CF Tax

PV(tax savings)

1 36.250.96 34.69 13 12.14

2 36.250.92 33.20 13 11.62

3 36.250.88 31.77 13 11.12

4 36.250.84 30.40 13 10.64

5 36.250.80 29.09 13 10.18

6 36.250.77 27.84 13 9.74

7 36.250.73 26.64 13 9.32

8 36.250.70 25.49 13 8.92

9 36.250.67 24.39 13 8.54

10 36.250.64 23.34 13 8.17

11 36.250.62 22.34 13 7.82

12 36.250.59 21.38 13 7.48

13 36.250.56 20.45 13 7.16

14 36.250.54 19.57 13 6.85

15 36.250.52 18.73 13 6.56

16 36.250.49 17.92 13 6.27

17 36.250.47 17.15 13 6.00

18 36.250.45 16.41 13 5.74

19 36.25 0.4 15.71 13 5.50


3

20 36.250.41 15.03 13 5.26

21 36.250.40 14.38 13 5.03

22 36.250.38 13.76 13 4.82

23 36.250.36 13.17 13 4.61

24 36.250.35 12.60 13 4.41

25 36.250.33 12.06 13 4.22

26 36.250.32 11.54 13 4.04

27 36.250.30 11.05 13 3.87

28 36.250.29 10.57 13 3.70

29 36.250.28 10.11 13 3.54

30 36.250.27 9.68 13 3.39

31 36.250.26 9.26 13 3.24

32 36.250.24 8.86 13 3.10

33 36.250.23 8.48 13 2.97

34 36.250.22 8.12 13 2.84

35 36.250.21 7.77 13 2.72

36 36.250.21 7.43 13 2.60

37 36.250.20 7.11 13 2.49

38 36.250.19 6.81 13 2.38

39 36.250.18 6.51 13 2.28

40 36.250.17 6.23 13 2.18

41 36.250.16 5.96 13 2.09

42 36.250.16 5.71 13 2.00

43 36.250.15 5.46 13 1.91

44 36.250.14 5.23 13 1.83

45 36.250.14 5.00 13 1.75

46 36.250.13 4.79 13 1.68

47 36.250.13 4.58 13 1.60

48 36.250.12 4.38 13 1.53

49 36.250.12 4.19 13 1.47

50 36.250.11 4.01 13 1.40

51 36.250.11 3.84 13 1.34


52 36.250.10 3.68 13 1.29

53 36.250.10 3.52 13 1.23

54 36.250.09 3.37 13 1.18

55 36.250.09 3.22 13 1.13

56 36.250.09 3.08 13 1.08

57 36.250.08 2.95 13 1.03

58 36.250.08 2.82 13 0.99

59 36.250.07 2.70 13 0.95

60 1036.250.07 74 363 25.86

819 286.80

Documents

2012136 Ankit Garg FIS Assignment