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Answers | Mathematics and Statistics for Financial Risk Management
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Answers
CHAPTER 1
1.
a. y
= 5
a.
y
= ln(1) – ln(
e
) = 0 – 1 = –1
b.
y
= ln(10) + ln(
e
) = ln(10) + 1 = 3.3026
2.
Annual rate = 5.12%; semiannual rate = 5.05%; continuous rate = 4.99%.
3.
4.
5.
6.
7.
8.
ln(ln(10)) = 0.8340.
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Answers | Mathematics and Statistics for Financial Risk Management
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9.
10.
11.
The bond will pay 10 coupons of $2, starting in a year's time. In addi-
tion, the notional value of the bond will be returned with the final coupon
payment in 10 years. The present value, V, is then:
We start by evaluating the summation, using a discount factor of δ
=
1/1.05 ≈
0.95:
Inserting this result into the initial equation we obtain our final result:
Note that the present value of the bond, $78.83, is less than the notional
value of the bond, $100. This is what we would expect, given that there is
no risk of default, and the coupon rate is less than the discount rate.
CHAPTER 2
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1.
Probability that both generate positive returns = 60% × 70% = 42%.
Probability that both funds lose money = (1 – 60%) × (1 – 70%) = 40% ×
30% = 12%.
2.
88%. The sum of all three events—upgrade, downgrade, and no change
—must sum to one. There is no other possible outcome. 88% + 8% + 4% =
100%.
3.
50%. The outcomes are mutually exclusive; therefore, 20% + 30% =
50%.
4.
5.
6.
32.14%. By applying Bayes’ theorem, we can calculate the result:
Even though the model is 90% accurate, 95% of the bonds don't default
and it predicts that 10% of them will. Within the bond portfolio, the mod-
el identifies 9.5% of the bonds as likely to default, even though they won’t.
Of the 5% of bonds that actually default, the model correctly identifies
90%, or 4.5% of the portfolio. This 4.5% correctly identified is over-
whelmed by the 9.5% incorrectly identified.
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7.
Given the density function, we can find c
by noting that the sum of
probabilities must be equal to one:
8.
First we check that this is a valid CDF, by calculating the value of the
CDF for the minimum and maximum values of x
:
Next we calculate the PDF by taking the first derivative of the CDF:
9.
We first calculate the CDF by integrating the PDF:
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We first try to find c
using the fact that the CDF is zero at the minimum
value of x
, x
= 0.
As it turns out, any value of c
will satisfy this constraint, and we cannot
use this to determine c
.
If we use the fact that the CDF is 1 for the maximum value of x
, x
= e
, we
find that c
= 1:
The CDF can then be expressed simply as:
10.
P
(both bonds default) = 9%.
P
(one defaults) = 42%.
P
(neither defaults) = 49%.
11.
We can start by summing across the first row to get W
:
In a similar fashion, we can find X
by summing across the second row:
To calculate Y
, we can sum down the first column, using our previously
calculated value for W
:
Using this result, we can sum across the third row to get Z
:
10/23/23, 1:31 PM
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The completed probability matrix is:
The last part of the question asks us to find the conditional probability,
which we can express as:
We can solve this by taking values from the completed probability matrix.
The equity underperforms in 40% of scenarios. The equity underper-
forms and the bonds are downgraded in 15% of scenarios. Dividing, we
get our final answer, 37.5%.
12.
The probability that a B-rated bond defaults over one year is 2%. This
can be read directly from the last column of the second row of the ratings
transition matrix.
The probability of default over two years is 4.8%. During the first year, a
B-rated bond can either be upgraded to an A rating, stay at B, be down-
graded to C, or default. From the transition matrix, we know that the
probability of these events is 10%, 80%, 8%, and 2%, respectively. If the
bond is upgraded to A, then there is zero probability of default in the sec-
ond year (the last column of the first row of the matrix is 0%). If it re-
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December 31, 2014 and 2013
Dec. 31, 2014
Dec. 31, 2013
Assets
bloe
Current assets:
Cash.
Marketable securities
$ 500,000
$ 400,000
1,000,000
1,010,000
Accounts receivable (net)...
740,000
510,000
Inventories
1,190,000
950,000
000. Prepaid expenses.
250,000
229,000
Total current assets.
$3,690,000
$3,089,000
Long-term investments...
2,350,000
2,300,000
1
Property, plant, and equipment (net)
Total assets
3,740,000
3,366,000
$9,780,000
$8,755,000
Liabilities
Current liabilities
$ 900,000
$ 880,000
Long-term liabilities:
$ 200,000
Mortgage note payable, 8%, due 2019.
Bonds payable, 10%,…
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Changes in Current Operating Assets and Liabilities-Indirect Method
Covington Corporation's comparative balance sheet for current assets and liabilities was as follows:
Dec. 31, 20Y2
Dec. 31, 20Y1
Accounts receivable
$15,300
Inventory
66,500
67,200
Accounts payable
20,100
0098
Dividends payable
000'
Adjust net income of $84,200 for changes in operating assets and liabilities to arrive at net cash flow from operating activities.
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Crane Corporation reports the following adjusted account balances, shown in alphabetical order, at the end of its fiscal year, February
28, 2021:
Accounts payable
12,600
Income tax payable
4,700
Accounts receivable
27,100
Insurance expense
3,400
Accumulated depreciation-equipment
5,400
Prepaid insurance
2,900
Cash
17,600
Rent expense
5,800
Common shares
10,100
Retained earnings
20,100
Depreciation expense
4,400
Salaries expense…
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Bonita Corporation reports the following adjusted account balances, shown in alphabetical order, at the end of its fiscal year, February
28, 2021:
Accounts payable
12,700
Income tax payable
$
4,400
Accounts receivable
28,300
Insurance expense
3,600
Accumulated depreciation-equipment
5,200
Prepaid insurance
2,600
Cash
17,400
Rent expense
5,700
Common shares
19,900
Retained earnings
21,300
Depreciation expense
4,100
Salaries expense…
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Changes in Current Operating Assets and Liabilities
Paneous Corporation's comparative balance sheet for current assets and liabilities was as follows:
Dec. 31, Year 2 Dec. 31, Year 1
Accounts receivable
$39,490
$31,590
Inventory
76,340
65,150
Accounts payable
60,750
45,410
Dividends payable
18,000
24,000
Adjust net income of $351,000 for changes in operating assets and liabilities to arrive at net cash flows from operating activities.
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Van Occupanther is the bookkeeper for Roscoe Company. Van has been trying to get the balance sheet of Roscoe Company to balance.
Roscoe's balance sheet is as follows.
ROSCOE COMPANY
Balance Sheet
December 31, 2022
Assets
Liabilities
Cash
$ 9,400
Accounts payable
$25,000
Supplies
7,100
Accounts receivable
(19,500)
Equipment
45,000
Common stock
40,000
Dividends
9,200
Retained earnings
25,200
Total assets
$70,700
Total liabilities and stockholders' equity
$70,700
Prepare a correct balance sheet. (List Assets in order of liquidity.)
ROSCOE COMPANY
Balance Sheet
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O (Current assets stock) Current liabilities.
O Current assets: (Current liabilities - bank overdraft).
Frev Cueston
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1. Slater Company uses the cash basis of accounting. Slater Company collected $950,000
from its customers during 2019. Customers owed Slater $150,000 of accounts receivable
at the beginning of 2019, and $190,000 of accounts receivable at the end of 2019. What is
Slater's sales revenue for 2019 under the accrual basis of accounting?
2. Merry Company uses the cash basis of accounting. Merry Company made $600,000 in
payments to its suppliers during the year. Merry's beginning inventory was $20,000, and
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XYZ Company had the following information for the year:
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Proceeds from Notes Payable
On January 26, Bella Co. borrowed cash from Conrad Bank by issuing a 30-day note with a face amount of $48,000. Assume a 360-day year.
a. Determine the proceeds of the note, assuming the note carries an interest rate of 6%.
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Changes in Current Operating Assets and Liabilities
Jasneet Corporation's comparative balance sheet for current assets and liabilities was as follows:
Dec. 31, Year 2 Dec. 31, Year 1
Accounts receivable
$20,200
$22,900
Inventory
13,000
10,700
Accounts payable
10,900
9,400
Dividends payable
25,100
30,700
Adjust net income of $185,000 for changes in operating assets and liabilities to arrive at net cash flows from operating activities.
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Once you have calculated the changes in the current operating assets and liabilities determine what impact those changes would
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If accounts payable has decreased does that mean the company has more cash or less cash?
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of 4
EXERCISES
For questions number 1 to 7, given the accounting transaction, indicate
whether the asset, liability or owner's equity has increase or decrease or
has no effect by circling the appropriate answer.
1 The owner invests personal cash in the business. (Example)
Asset
Increase
Decrease
No Effect
Liability
Increase
Decrease
No Effect
Owner's Equity
Increase
Decrease
No Effect
2 The owner withdraws cash from the business for personal use.
Asset
Increase
Decrease
No Effect
Liability
Increase
Decrease
No Effect
Owner's Equity
Increase
Decrease
No Effect
3 The company receives cash from a bank loan
Asset
Increase
Decrease
No Effect
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Question 7
Using the stylized balance sheet below, please 1) finish the balance sheet, and 2)
use that information to answer the following question, entering your answer in the
place provided.
Avg.
Interest
Amount
Avg.
Interest
Amount
Demand
Vault Cash
$1,262
$1,408
Deposits
US Treas.
Savings
5.51%
2,372
3.46%
9,071
Securities
Deposits
Consumer/Bus.
5.76%
12,678
CD's
2.34%
????
Loans
Mortgage
6.08%
7,692
Borrowings
5.12%
1,600
Loans
Property
Equipment
Total Assets
986
Equity
Total Liab.&
????
Equity
3,433
????
What is the net interest margin the this bank? (Please enter the answer without the %
sign-so
- so for instance is the answer is 5.67%, then enter just 5.67)
1.565
er
3.13 margin of error +/- 0.05
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4. Problem 3.02 (Income Statement)
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Byron Books Inc. recently reported $14 million of net income. Its EBIT was $26.6 million, and its tax rate was 30%. What was its interest expense? (Hint: Write out the headings for an income
statement, and then
in the known values. Then divide $14 million of net income by (1 - T) = 0.7 to find the pretax income. The difference
EBIT and taxable income must be interest
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Final Exam
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Exam
What is the interest earned in a savings
account after 12 months on a balance of
$1000 if the interest rate is 1% APY
compounded yearly?
interest = $[?]
Round your answer to the nearest hundredth.
Enter
EX
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wo ahttps//altemativet
4 SQUCOFFEE - Goog. B BCOM2911-Busines. D Sultan Caboos Univ. G Trading Platform C.
MIC)
E-LEARNING SERVICES SQU LIBRARIES -
Accounting C
SQU PORTAL ATTENDANCE
gerial Accounting - Spring21
murses / ACCT2121_yasserg Spring21 / Midterm Exam One / Midterm Exam One
Time left 1:51:50
A Company uses a job order costing system and allocates its manufacturing overhead costs based on direct labor costs. The Company's
production costs for the year were: direct labor, $80,000; direct materials, $40,000; and factory overhead applied $20,000. The
predetermined overhead rate was:
O a. 4%.
O b. 50%.
Oc 200%.
O d. 25%.
O e. 400.%.
XYZ Co. has provided the following data for the month of June. There were no beginning inventories; consequently, the direct
materials, direct labor, and manufacturing overhead applied listed below are all for the current month.
Work In
Finished Goods
Cost of Goods Sold
Process
OMR 8,450 OMR
61,880
Direct materials
OMR 3,440…
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Section V: SCF-Question 5
Identify the most significant cash inflow and outflow activity from Financing activities
for the current year.
Description of Activity
Amount
Cash inflow:
Click here to enter
text.
Cash outflow: (Note: cash dividends paid are reported here.)
Click here to enter
text.
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