Ruiz Jacqueline_FIN7570-800_Module 3 Test
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Date
Feb 20, 2024
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Uploaded by GeneralFire9814
Jacqueline Ruiz
Investment Policy, Ethics, and Portfolio Management
William Paterson University
Professor Malindretos
FIN7570-800
Module 3 Assignment
YOU OUGHT TO DO THE FIRST 4 PROBLEMS. MOREOVER, YOU SHOULD DO 3 ADDITIONAL QUESTIONS FROM EITHER PROBLEMS OR ESSAYS. TOTALLY, YOU HAVE TO DO SEVEN QUESTIONS. EACH IS WORTH
14 POINTS.
A. PROBLEMS:
1. The Z score is 1.7. The values of X1, X2, X3, X4 and X5 are respectively .1, .3, .25, .2 and you have to compute the last one. Explicate the meaning of the different determinants of the Z score. Will this company default? A yes or no answer does not suffice.
Z
−
score
=
1.2
X
1
+
1.4
X
2
+
3.3
X
3
+
0.6
X
4
+
X
5
X
5
=
Z
−
1.2
X
1
−
1.4
X
2
−
3.3
X
3
−
0.6
X
4
X
5
=
1.7
−
1.2
(
0.1
)
−
1.4
(
0.3
)
−
3.3
(
0.25
)
−
0.6
(
0.2
)
=
1.7
−
0.12
−
0.42
−
0.825
−
0.12
=
0.215
The determinants of the Z-score are:
1.
X
1
= Working Capital divided by Total Assets which measures the ability of a company to cover its short-term liabilities with its short-term assets.
2.
X
2
= Retained Earnings divided by Total Assets which reflects the profitability of the company and its ability to reinvest earnings for growth.
3.
X
3
= Earnings Before Interest and Taxes divided by Total Assets which indicates the operational efficiency of the company in generating profits relative to its total assets.
4.
X
4
= Market Value of Equity divided by Total Liabilities which reflects the market perception of the company's financial health relative to its debt obligations.
5.
X
5
= Sales divided by Total Assets which measures the efficiency of asset utilization in generating sales revenue.
Whether the company will default depends on its Z-score. If the calculated Z-score is below 1.81, it suggests that the company is at risk of financial distress and potential bankruptcy. However, without knowing the industry average or historical data for comparison, it's difficult to conclusively determine if the company will default based solely on the Z-score provided in the question.
2. Compute the duration of a 30-year 9% bond if yields to maturity are 6% presently. What if rates drop by 2%. Ascertain that you compute both the exact price, via the bond valuation formulas, and the approximate price by using duration.
Exact Price
=
P
=
∑
t
=
1
n
C
(
1
+
r
)
t
+
¿
F
(
1
+
r
)
n
=
∑
t
=
1
30
90
(
1
+
0.06
)
t
+
¿
1090
(
1
+
0.06
)
30
=
$
1
,
428.61
¿¿
3. There are 3 explanations of the shape of the yield curve (term structure of interest rates.) The shape of the yield curve represents the relationship between the yield and the time to maturity of debt securities and provides insight into the market's potential regarding future interest rates and financial conditions. The yield curves are a tool for investors, policymakers, and economists. The three common explanations for the shape of the yield curve are the normal yield curve, the inverted yield curve, and the flat or humped yield curve.
The normal yield curve is the most common shape where longer-term bonds have higher yields than shorter-term bonds. This shape implies that investors can expect financial growth and rising inflation in the future. Investors demand higher yields for locking in their money for longer periods due to the increased uncertainty overtime. The inverted yield curve occurs when short-term interest rates are higher than long-term rates. It is often understood as a sign of an impending financial recession. Investors may expect interest rates to fall in the future due to deflationary difficulties leading them to want to lock in longer-term yields while they are still relatively high. The flat yield curve occurs when the yields on short-term and long-term bonds are similar while the humped yield curve is a variation of the flat curve where yields in the middle of the maturity range are higher than both the short-term and long-term yields. This shape may show uncertainty about future financial conditions.
Each yield curve shape offers valuable views on interest rate determination but a combination of factors more likely influence interest rates in practice, with central bank policies, market expectations, and liquidity considerations playing significant roles.
4. There is a bond, which has a duration of 7 and a convexity of 40. Compute exact and approximate prices.
∆ P
exact
=−
D
∗
∆ y
∗
P
+
1
2
∗
C
∗
(
∆ y
)
2
∗
P
∆ P
¿
=−
D
∗
∆ y
∗
P
a) If the bond increases by 3%, what will its price alter by?
∆ y
=
0.03
∆ P
exact
=−
7
∗
0.03
∗
P
+
1
2
∗
40
∗
(
0.03
)
2
∗
P
=−
0.21
P
+
0.018
P
=−
0.192
P
∆ P
¿
=−
7
∗
0.03
∗
P
=−
0.21
P
b) If it decreases by 3%, what will the alteration of price be?
∆ y
=−
0.03
∆ P
exact
=−
7
∗−
0.03
∗
P
+
1
2
∗
40
∗
(
−
0.03
)
2
∗
P
=
0.21
P
+
0.018
P
=
0.228
P
∆ P
¿
=−
7
∗−
0.03
∗
P
=
0.21
P
c) Discuss without derivations. Are the true results symmetric in the 2 cases?
The exact results are not perfectly symmetric in both cases. The exact price change due to an increase in
yield is approximately $0.192P while the exact price change due to a decrease in yield is approximately $0.228P. Both are relatively close to each other, but they are not the same. When yields increase, convexity causes the bond price to decrease by a slightly larger amount than when yields decrease by the same percentage.
5. We are considering investing in one of the following two bonds. The one is a 2 year, 7% versus one, which is 25 year, 3% bond. Which shall we choose, if we predict that market rates will rise from 10% to 12 % in the future one year? Compute the exact amount more we shall make by investing in the right one. 2-year 7% Bond 10% Current Rate:
Exact Price
=
P
=
∑
t
=
1
n
C
(
1
+
r
)
t
+
¿
F
(
1
+
r
)
n
=
∑
t
=
1
2
70
(
1
+
0.10
)
t
+
¿
1070
(
1
+
0.10
)
2
=
$
1,005.79
¿¿
2-year 7% Bond 12% Future Rate:
Exact Price
=
P
=
∑
t
=
1
n
C
(
1
+
r
)
t
+
¿
F
(
1
+
r
)
n
=
∑
t
=
1
2
70
(
1
+
0.12
)
t
+
¿
1070
(
1
+
0.12
)
2
=
$
971.30
¿¿
Change
=
Future – Current
=
$
971.30
−
$
1,005.79
=−
$
34.49
25-year 3% Bond 10% Current Rate:
Exact Price
=
P
=
∑
t
=
1
n
C
(
1
+
r
)
t
+
¿
F
(
1
+
r
)
n
=
∑
t
=
1
25
30
(
1
+
0.10
)
t
+
¿
1030
(
1
+
0.10
)
25
=
$
367.38
¿¿
25-year 3% Bond 12% Future Rate:
Exact Price
=
P
=
∑
t
=
1
n
C
(
1
+
r
)
t
+
¿
F
(
1
+
r
)
n
=
∑
t
=
1
25
30
(
1
+
0.12
)
t
+
¿
1030
(
1
+
0.12
)
25
=
$
295.88
¿¿
Change
=
Future – Current
=
$
295.88
−
$
367.38
=−
$
71.50
We can see that the price of the 2-year 7% bond decreases by a smaller amount compared to the 25-
year 3% bond. If market rates rise from 10% to 12% in the future one year, investing in the 2-year 7% bond would result in a smaller loss in bond value compared to investing in the 25-year 3% bond. Therefore, based on the comparison of price changes, the better investment option would be the 2-year 7% bond.
6. We have the following information. The debt to assets, average collection period, ITO, net profit margin and return on equity are .70, 60 days, 2 times, 9% and 18% respectively for a company, while they are .45, 30 days, 6 times, 5% and 11% for the industry. Evaluate the company’s prospects.
Company
Industry
Debt to Assets
0.70
0.45
Average Collection Period
60 days
30 days
ITO
2 times
6 times
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Net Profit Margin
9%
5%
Return on Equity
18%
11%
The company has a higher debt to assets ratio compared to the industry, showing that a larger portion of its assets is financed by debt. The company takes longer to collect its accounts receivable compared to the industry average. This shows issues with credit policies or customer payment behaviors. The company's inventory turnover rate is lower than the industry average, indicating less efficient management of inventory or potential overstocking issues. The company's net profit margin is higher than the industry average, showing better profitability in terms of converting revenue into profit. The company's return on equity is higher than the industry average, implying better utilization of shareholder equity to generate profits. While the company shows profitability and good return metrics, it needs to focus on improving operational efficiency and managing its financial leverage to ensure sustained growth and competitiveness in the industry.
B. ESSAYS:
7. Essay #5. Describe the covenants of bonds. How do they affect default probability?
Bond covenants are legally binding clauses, and if breached will trigger compensatory or other legal action. In simpler terms, a bond covenant is a written promise in a bond document stating that the bond
issuer will or will not do something, for example borrow more than a particular amount of money. Bond covenants exist to protect the bondholders. Bond covenants are utilized to restrict the borrowing firm from making decisions which will deteriorate its financial health from the time of borrowing. There are both affirmative and negative covenants. Affirmative covenants require the issuer to take certain actions or meet specific requirements. Examples include maintaining certain financial ratios, providing financial statements regularly, or maintaining insurance coverage. Negative covenants restrict the issuer from taking certain actions that could negatively impact bondholders' interests. Examples include restrictions on issuing additional debt, making certain investments, or paying dividends beyond a
certain threshold.
Covenants requiring the issuer to maintain certain financial ratios or provide regular financial statements enable bondholders to monitor the issuer's financial health. If the issuer fails to meet these requirements, it could signal financial distress, increasing the likelihood of default. Negative covenants that limit the issuer's ability to take on additional debt help mitigate default risk by preventing the issuer
from becoming overly leveraged. This reduces the likelihood of default due to an unsustainable debt burden. By protecting assets and limiting risky behavior, these covenants reduce the likelihood of default by ensuring the issuer maintains sufficient collateral or resources to meet its obligations. Covenants may require the issuer to maintain certain levels of cash flow or liquidity, ensuring it has the resources to make interest and principal payments on the bonds. Adequate cash flow management reduces the risk of default due to cash shortages.
In summary, covenants play a significant role in influencing default probability by imposing restrictions, monitoring requirements, and financial safeguards on the issuer. By aligning the interests of bondholders and issuers and promoting responsible economic management, covenants help mitigate default risk.
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2 Return Rate
3 Investment Duration in Years
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Bark and Bliss Limited is a pet supply company headquartered in Edmonton, Alberta. They have four different lines
of business. Here is an excerpt of their financial statements for the December 31, 2020 fiscal
year:
Dog Walking
Brick &
Division
Online Shop
Pet Training
& Pet Care
Mortar Stores
Sales
$1
22,500,000
13,980,000
27,630,500
5,407,000
Net operating income
$4
1,250,000
1,840,000
2,845,200
1,134,750
Average operating assets
$1
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8,275,000
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Bark and Bliss Limited has a policy that all investments must have a rate of return of at least
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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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