Fixed Income Homework3 Hariharan Alavandan
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Finance
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Apr 3, 2024
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Hariharan Alavandan
alavanhn@mail.uc.edu
Class Number: 11660
Section 001
HOMEWORK 3: FIN7037 FIXED INCOME
FIN7037: Fixed Income Security Analysis
Homework 2
1.
a. Amortization schedule for the first 10 months
Amount $100,000
Periods 360
Rate
0.8333%
Payment
$877.57 Months
Beginning
Payment
Interest
Principal
Ending Balance
1
$100,000.00
$877.57 $833.33
$44.24 $99,955.76
2
$99,955.76
$877.57 $832.96
$44.61
$99,911.15
3
$99,911.15
$877.57 $832.59
$44.98
$99,866.18
4
$99,866.18
$877.57 $832.22
$45.35
$99,820.82
5
$99,820.82
$877.57 $831.84
$45.73
$99,775.09
6
$99,775.09
$877.57 $831.46
$46.11
$99,728.98
7
$99,728.98
$877.57 $831.07
$46.50
$99,682.48
8
$99,682.48
$877.57 $830.69
$46.88
$99,635.60
9
$99,635.60
$877.57 $830.30
$47.27
$99,588.32
10
$99,588.32
$877.57 $829.90
$47.67
$99,540.65
b
. As you can see from the amortization table for the last 3 months, mortgage
balance at the end of 360
th
month
assuming no prepayment is
0
c. Mortgage balance at
the end of month 270 assuming no prepayment
The remaining principle at the end of the month 270
is simply the present value of the remaining 90 months of payment
of Coupon = PMT= 877.57 in 360-month payment period.
So, PMT = -877.57, N = 90, I/Y = 0.8333%, FV = 0, We use financial calculator to compute PV = 55409.40. Mortgage balance at
the end of month 270 assuming no prepayment = 55409.40
Month
s
Beginning
Payment
Interest
Principa
l
Ending Balance
358
$2,589.44
$877.57 $21.58
$855.99
$1,733.45
359
$1,733.45
$877.57 $14.45
$863.13
$870.32
360
$870.32
$877.57 $7.25
$870.32
$0.00
(Note: - As explained in the partial answers, this can also be calculated by computing beginning balance for N = (90+ 1) and then subtracting respective interest from Principle payment and calculating the ending balance)
2.
1)
2-Bedroom condo in Boston. The price is $300,000. You
have a 30-year 3% APR mortgage with 20% down payment
N=360, I/Y= 3/12= 0.25, PV = 240,000, FV = 0, Calculating Monthly mortgage payment
using financial calculator PMT = 1011.849
Monthly mortgage payment = PMT = 1011.85
2) Annual investment return on rental Using financial calculator, N = 60 (semiannual 30 years), PV = - 60,000, FV = 300,000, PMT = 0, we compute semi-annual yield = 2.718%
Annual yield = Bond- equivalent yield = 2.718*2 = 5.437
3) Using financial calculator, N = 360, PV = - 60,000, PMT = 2000- 200- 1011.85= 788.15, FV = 390,000
Monthly yield = 1.3702%
Semi-annual yield = (1.013702) ^ 6 = 8.51%
Bond – equivalent yield = 8.51%*2 = 17.02%
3.
(
Calculated from excel) a)
CPR = 6%*(t/30) t < 30 months
CPR = 6% t > 30 months
Mont
h
100% PSA
70% PSA 320% PSA
(0.7*100% PSA)
(3.2*100% PSA)
1
0.002
0.0014
0.0064
4
0.008
0.0056
0.0256
9
0.018
0.0126
0.0576
27
0.054
0.0378
0.1728
40
0.06
0.042
0.192
b)
(From excel) SMM = (1- ((1-CPR) ^ (1/12))
Month
100% PSA
70% PSA 320% PSA CPR
SMM
CPR
SMM
CPR
SMM
1
0.002
0.01668%
0.001
4
0.01167%
0.006
4
0.05349%
4
0.008
0.06691%
0.005
6
0.04679%
0.025
6
0.21588%
9
0.018
0.15125%
0.012
6
0.10561%
0.057
6
0.49316%
27
0.054
0.46154%
0.037
8
0.32059%
0.172
8
1.56848%
40
0.060
0.51430%
0.042
0
0.35692%
0.192
0
1.76092%
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4.
Original balance: $100,000,000
Pass-through rate: 9.0%
WAM: 360 months
WAC: 9.65%
A WAM of 360 months means that the mortgages were newly originated.
CPR = 6% *(1/30) = 0.2% at 100% PSA
For month 1, at 165% PSA
1) To compute SMM, we start with CPR = 0.0033 (=1.65*0.2%)
SMM = (1- (1 - CPR) ^ (1/12) = 0.00027542
2) N = 360; I/Y = 9.65/12; PV = -100,000,000; FV=0
Mortgage payment = PMT = 851,820
3) Interest payment of the MBS = (Beg. Balance * Pass through/12)
100,000,000* 9% /12 = 750,000
4) Interest payment of the mortgage = (WAC*outstanding mortgage balance/12) 9.65%*100,000,000/12 = 804,167
Scheduled Principal payment = 851820 – 804167 = 47,653
5) Prepayment = SMM*(100,000,000 – scheduled payment) = 27,528
6) Total Principal payment = Scheduled Principal payment + Prepayment = 75,181
7) Cash flow to MBS investor = Interest Payment of the MBS + Total Principal payment
= 825,181
For month 2, at 165% PSA
CPR = 6% *(2/30) = 0.4% at 100% PSA
At 165 PSA, CPR = 1.65*0.4% = 0.0066
1)
To compute SMM, SMM = (1- (1 - CPR) ^ (1/12) = 0.055167% = 0.00055167
2)
N = 359; I/Y = 9.65/12; PV = -999,248,19; FV=0
3)
Mortgage payment = PMT = 851,585
4)
Interest payment of the MBS = 999,248,19* 9% /12 = 749,436
5)
Interest payment of the mortgage = 9.65%*99,924,819/12=803,562
Scheduled Principal payment = 851,585 – 803,562 = 48,023
6)
Prepayment = SMM*(99,924,819 – scheduled payment) = 55,099
7)
Total Principal payment = Scheduled Principal payment + Prepayment = 103,122
8)
Cash flow to MBS investor = Interest Payment of the MBS + Total Principal payment= 749,436 + 103122
= 852,558
Tabulating in excel,
Mont
h
Balance SMM Mortgag
e
Payment
Interes
t Schedule
d
Principal
Prepaymen
t Total
Principa
l
Cash
Flow
1
$100,000,00
0
0.0002754
2
851,820
750,00
0
47,653
27,528
75181
825,18
1
2 $ 0.0005516
851,585
749,43
48,023
55099
103122
852,55
99,924,819
7
6
8
5.
“Nobel Economics Prize Is Awarded to
U.S.-Based Trio” The Nobel Prize in Economic Sciences was awarded to David Card, Joshua D. Angrist and
Guido W. Imbens for their work on natural experiments, in particular their contributions to better
understanding how the job market works
. Their research has substantially improved the ability
to answer key causal questions, which has been of great benefit to society. In one paper, Mr. Card and his co-author, Alan Krueger, looked at an increase in New Jersey’s
minimum wage to $5.05 an hour from $4.25
. The two economists compared restaurants in the
state and in neighboring eastern Pennsylvania and found that there was no fall in employment
in
the New Jersey restaurants subject to the higher minimum wage. In another experiment, Mr.
Angrist compared the employment history of people who had been drafted to serve in the
Vietnam War
with those who had not and found that those who had been randomly selected to
serve earned less in the years after their service
than those who hadn’t. Mr. Imbens has
studied whether people who win the lottery are more likely to stop working than those who
don’t
.
Natural experiments
differ from the laboratory experiments that physical scientist use to test
their theories in that economists can’t choose the subjects that take part
. The Royal Swedish
Academy of Sciences said Messrs. Angrist and Imbens had advanced the understanding of the
conditions under which natural experiments can help to establish
causal links
. They showed it
is possible to estimate a well-defined causal effect of an intervention, even when the researcher
cannot control who takes part in the intervention. Ratings
Last Sale
Issuer Name
Symbol
Callable
Sub-Product Type
Coupon
Maturity
Moody'
s
S&P
Price
Yield
TESL
A INC
TSLA4474416
Corporate Bond
2.38
3/15/2022
BB
1150
-206.495
TESL
A INC
TSLA4530906
Yes
Corporate Bond
5.30
8/15/2025
B3
NR
102.66
3.885
TESL
A INC
TSLA4830349
Corporate Bond
2.00
5/15/2024
BB
1430
-80.623
TESL
A INC
TSLA4103350
Corporate Bond
0.25
3/1/2019
NR
99.13
105.438
TESL
A INC
TSLA4103351
Corporate Bond
1.25
3/1/2021
NR
1039.24
-3612.92
TESL
A INC
TSLA4530907
Corporate Bond
5.30
8/15/2025
102.68
6.
Ratings for bonds issued by Tesla from Finra Market Data
Yield of the first bond Issuer Name
Symbol
Yield
TESLA INC
TSLA4474416
-206.5
Price chart
Yield chart
Price of the bond increases
from 100 in 2017 to 1150 in 2021 as on 04/10/2021
Yield of the bond decreases from 2.38% to -206.495% in 2021 as on 04/10/2021
As yield decreased, price of the bond increased
.
Negative yields happened
after 2019-20 due to low interest rates
, many large
institutional investors were willing to pay a little over face value for high-quality bonds.
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They accepted a negative return on their investment for the safety and liquidity
that
high-quality government and corporate bonds offer.
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fx
A
1.
Amortization schedule
2.
3.
Loan amount to be repaid (PV)
$30,000.00
Interest rate (r)
4.
Length of loan (in years)
8.00%
6.
7.
a. Setting up amortization table
Formula
8.
Calculation of loan payment
#N/A
6.
Repayment of
Principal
10
Year
Beginning Balance
Payment
Interest
Remaining Balance
11
1
12
13
3
14
15 b. Calculating % of Payment Representing Interest and Principal for Each Year
Payment %
Representing
Payment %
Representing
Principal
Check: Total =
16
Year
Interest
100%
17
1
18
19
20
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Consider the following loan information.
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180
loan B
180
months
amt $375,000
$375,000
rate 6.0%
7.0%
points
3%
1%
prepay
2%
1%
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8
Create a spreadsheet & chart which compares the effective cost of borrowing (EBC) under Loan A
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STEP 1:
STEP 2:
Step 1:
Step 2:
Step 3:
Step 4:
Answer:
Step 1:
Step 2:
Step 3:
Step 4:
Answer:
4
9
$20,600
4
8
PV:
Payment:
Annual Interest Rate:
Deferral period:
Payment period:
Compounded:
Amount
159295
Amount
159295
Facts
+/-
CPT
+/-
CPT
$20,600
4%
8 year(s)
9 year(s)
Annually
Keystroke
I/Y
N
PMT
PV
Keystroke
I/Y
N
FV
PV
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K
Que
Show Transcribed Text
Que
Que
Determine the nominal annual rate of interest of the following ordinary general annuity.
Que
Present
Value
$4600
solve this question view how to solve this question from second image thankyou...
Que
The nominal annual rate of interest is % compounded quarterly
(Round to two decimal places as needed.)
BA II PLUS Solution Process
Periodic
Payment
$59.94
280
The nominal annual rate of interest of an ordinary general
annuity with a present value of $270, a periodic payment of
$86, a payment interval of 1 year, a term of 4 years, and
interest converted quarterly
("END" mode)
Set P/Y=1, C/Y=4
The solution process, using the BA II PLUS financial calculator and rounding the
answer to two decimal places, is given below.
4
270
CPT
Payment
Interval
1 month
86
CLR TVM
FV
PV
Term
PMT
I/Y
Ans: 10.06
8 years
Conversion
Period
quarterly
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Author:KEOWN, Arthur J., Martin, John D., PETTY, J. William
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Fundamentals of Financial Management (MindTap Cou...
Finance
ISBN:9781337395250
Author:Eugene F. Brigham, Joel F. Houston
Publisher:Cengage Learning

Corporate Finance (The Mcgraw-hill/Irwin Series i...
Finance
ISBN:9780077861759
Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:McGraw-Hill Education
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