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Bond Concepts: Bond Pricing
It is important for prospective bond buyers to know how to determine the price of a bond because it will indicate the yield received should the bond be purchased. In this section, we will run through some bond price calculations for various types of bond instruments. Bonds can be priced at a premium, discount, or at par. If the bond's price is higher than its par value, it will sell at a premium because its interest rate is higher than current prevailing rates. If the bond's price is lower than its par value, the bond will sell at a discount because its interest rate is lower than current prevailing interest rates. When you calculate the price of a bond, you are
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1.Calculate Invoice price for bond maturing Nov. 15, 2012 (in Excel). Assume today’s date is 1/15/2009
2. Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 10%.
3. A) A zero-coupon bond with face value $1,000 and maturity of 6 years sells for $887.25. What is its yield to maturity?
B) What will happen to its YTM if the price goes up to $899.99?
4. Why do bond prices go down when interest rates go up? Don’t investors like high interest rates?
5. A) ABC bond has a 3.5 coupon and 9 years till maturity
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Centre for Foundation Studies, UTAR
Bond energies, bond lengths & bond
Drawing Lewis structure and calculate the
Forms of Chemical Bonds
1) Intramolecular bond – forces hold the
atoms _______ a molecule
• Ionic / Electrovalent Bond
• Covalent Bond
• Metallic Bond
2) Intermolecular bond – forces ________ the
• Hydrogen bonding
• Van der Waals
3) Co-ordinate / Dative Bond
FHSC1114 Physical Chemistry
Electrovalent / ionic bonding
Co-ordinate / dative covalent bonding
Intermolecular bonding (including
hydrogen bonding, Van der Waals
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Q1. What is risk premium? How is it measured? When there is an increase in the default risk on corporate bonds (due to bad economic conditions), what will happen to risk premium. Will it shrink or widen? Why?
(See pages 120-22 3rd edition) (see page 114-115 4th edition)
Default risk occurs when the issuer of a bond is unable or unwilling to make interest payments when promised or pay off the face value when bond matures. This could happen to a corporation suffering high losses due to bad economic conditions. Canadian Government bonds are considered to have no default risk, as its backed by the taxation power. These bonds are called default free bonds. The spread between the interest
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may emerge as the mainstay of the credit and capital markets. (Sumon Kumar Bhaumik&SuchismitaBose, 2001)
Bond market link having long-term financing needs with investors willing to place funds in long-term interest bearing securities (UN, TW; 2001). When a corporation (or government) wishes toborrow money from the public on a long term basis, itusually does so by issuing or selling debt securities. Theyare generally called bonds (Ross, 1998).A corporate bond is security representing a long-term promise to pay a certain sum of money at certain time over the course of the loan with fixed rate of interest payable to holder of the bond. And the debenture is the bond backed or secured only by
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On 31-Dec-14 we made the following entry:
Interest Expense $27.36
Discount on Bond Payable ($2.83*5/6) $2.36
Interest Payable ($30*5/6) $25.00
This transaction was made when the share price was $6, but James had not elected to receive common stock as opposed to his usual $25.00 cash coupon. Now that Kat’s common stock price has jumped above $6 per share, James now elects to receive 5 shares of Kat common stock. This does not change the fact that there is a discount to amortize (i.e. the discount must be present as $960 was paid for the face value of $1000) Therefore we must continue to credit discount on bond payable according to the amortization table provided (1/6 now). Now
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Running Head: Yield to Maturity
Yield to Maturity
Von Stanley Gossi
University of Phoenix
May 10, 2010
Yield to Maturity
What is yield to maturity?
The rate of return anticipated on a bond if it is held until the maturity date. YTM is considered a long-term bond yield expressed as an annual rate. The calculation of YTM takes into account the current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupons are reinvested at the same rate. Sometimes this is simply referred to as "yield" for short (Investopedia, 2010, para. 1).
Easiest way to understand yield to maturity…
A perfect example to understand
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1. Discount = Par value - Issue price = $90,000 - $85,431 = $4,569
2. Total bond interest expense over the life of the bonds
|Amount repaid | |
| Six payments of $3,600 |$ 21,600 |
| Par value at maturity | 90,000 |
| Total repaid |111,600 |
|Less amount borrowed | (85,431) |
|Total bond interest expense
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Euro bonds and International bonds
Debt investments that are issued in a country by a non-domestic entity. International bonds are issued in countries outside the United States, in their native country's currency. They pay interest at specific intervals, and pay the principal amount back to the bond's buyer at maturity.
International bonds include eurobonds, foreign bonds and global bonds. A different type of international bond is the Brady bond, which is issued in U.S. currency. Brady bonds are issued in order to help developing countries better manage their international debt. International bonds are also private corporate bonds issued by companies in foreign countries, and many mutual
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1. Three Functions of Money
A) Measure of value
B) Store of purchasing power
C) Store of purchasing power
D) Store of purchasing power
E) Means of exchange
F) Store of purchasing power
4. Bond Price Changes
A) A bond worth $10 000 initially and has an interest rate
of 4 percent, annual interest rates would be $400.
A drop in interest rate to 2 percent means that the price of
this bond rises to $20 000. (.02 x $20 000 = $400).
B) A rise in interest rate to 6 percent causes the price
of this bond to decline to $6667 (.06 x $6667 = $400).
5. Hudson Bank
A) Desired reserves are .05 x $10 million =$500 000.
Actual reserves are $600 000, it has $100 000 in excess
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E10-18 Hrabik Corporation issued $600,000, 9%, 10-year bonds on January 1, 2011, for
$562,613.This price resulted in an effective-interest rate of 10% on the bonds. Interest is payable
semiannually on July 1 and January 1. Hrabik uses the effective-interest method to amortize
bond premium or discount.
Prepare the journal entries to record the following. (Round to the nearest dollar.)
(a) The issuance of the bonds.
Jan.1 Cash 562,613, Discount on Bonds Payable 37,387, Bonds Payable 600,000 (To record sale of bonds at discount)
(b) The payment of interest and the discount amortization on July 1, 2011, assuming that interest
was not accrued on June 30. Jul.1,Bond Interest Expense
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1.) Explain how futures contracts could be used to hedge a bond portfolio against the risk of rising interest rates. Then explain how futures could be used by exporters and by importers to hedge against their foreign-exchange exposures.
Someone with a large bond oprtfolio may want to hedge against future interest rate movements. When interest rates rise, bond prices decline. The use of futures can be used to hedge against the likelihood of rising interest rates. When the hedging is balanced, the gains/losses in the cash holdings will be offset by gains/losses in futures account. Hedging bond portfolios with futures contracts, will be done by holding short positions.
Futures could be
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JOURNAL OF ECONOMICS AND FINANCE EDUCATION Volume 9 Number 2 Winter 2010
Using Microsoft Corporation to Demonstrate the Optimal Capital Structure Trade-off Theory
John C. Gardner, Carl B. McGowan Jr., and Susan E. Moeller1 ABSTRACT
In this paper, we apply the trade-off theory of capital structure to Microsoft. We use data for bond ratings, bond risk premiums, and levered CAPM betas to compute the cost of equity and the weighted average cost of capital for Microsoft at different debt levels. This study shows the impact of increasing financial leverage on WACC. As financial leverage increases, the WACC decreases until the optimal debt ratio is reached, after which, the WACC
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BOND MARKET OF BANGLADESH
Prapared for : Mohammad shahidul Islam
Director, MBA Program
Prepared by : A. M. Shahed Chowdhury
Batch No. 27
ID No. 09435020
SOB, RMBA, UITS
Date of Submission: 21-01-2011
Institution: University of Information Technology& Sciences
BOND MARKET OF BANGLADESH
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tell which is the cis and which the trans form just by looking at them. All you really have to remember is that trans means "across" (as in transatlantic or transcontinental) and that cis is the opposite. It is a simple and visual way of telling the two isomers apart. So why do we need another system?There are problems as compounds get more complicated. For example, could you name these two isomers using cis and trans?Because everything attached to the carbon-carbon double bond is different, there aren't any obvious things which you can think of as being "cis" or "trans" to each other. The E-Z system gets around this problem completely - but unfortunately makes things slightly more difficult
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ECON530: Money and Banking Homework 3 Due: Feb. 12th Instructions: Provide concise answers to the following questions. Credit given is based on the accuracy and completeness of your answers. Show all the necessary calculations. 1. Explain why you would be more or less willing to buy a share of Microsoft stock in the following situations: a) Your wealth falls. b) You expect the stock to appreciate in value. c) The bond market becomes more liquid. d) You expect gold to appreciate in value. e) Prices in the bond market become more volatile. 2. Explain why you would be more or less willing to buy long-term AT&T bonds under the following circumstances: a) Trading in these bonds increases, making
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CDS (Credit Default Swap) is designed to transfer risk from bond holders to CDS issuers. Bond holders buy bonds from a company and buy CDS from insurance company at the same time to make sure even the company default; the bond holders can get the par value back from insurance company. We will look at the CDS spread of Delphi for this question. After we plotted in the data, we find out that the overall CDS spread are abnormally large during the year of 2005 and 2008. The high CDS spreads indicates the unsuccessful operation of Delphi at that time and investors perceiving the possibility of Delphi defaulting on its bond payment.
Delph is one of the world's largest automotive
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| | |
| |If inflationary expectations increase, the yield to maturity (required rate of return) will increase. This |
| |will mean a lower bond price. |
| | |
|10-5. |Why is the remaining time to maturity an important factor in evaluating the impact of a change in yield to |
| |maturity on bond prices
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JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY
Kenya School of Monetary Studies
DETERMINANTS OF MORTGAGE INTEREST RATES IN KENYA
* MBURU LEONARD GATHUNGU HD336-040-0040-2012
* TAYARI AMOS MATANGA HD336-040-0043-2012
* KIBET JOSHUA HD336-040-0044-2012
* DR. NYAMONGO
This paper provides an analysis of the determinants of mortgage rates in Kenya. The study was restricted to the period 2006-2012 quarterly data. During the analysis, mortgage rates were regressed against the CBR rate, inflation, bond rate and Household income for the period under study
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Homework Assignment – Week 2
1. Write down the formula that is used to calculate the yield to maturity on a 20-year 10% coupon bond with $1,000 face value that sells for $2,000. Assume yearly coupons.
$2000 $100/(1 i) $100/(1 i)2 $100/(1 i)20 $1000/(1 i)20
2. If there is a decline in interest rates, which would you rather be holding, long-term bonds or short-term bonds? Why? Which type of bond has the greater interest-rate risk?
You would rather be holding long-term bonds because their price would increase more than the price of the short-term bonds, giving them a higher return.
3. A financial advisor has just given you the following advice
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branches of American banks.
REPURCHASE AGREEMENTS (REPOS) – are short-term sales of government securities with an agreement to repurchase the securities at a higher price.
FEDERAL FUNDS – are funds in the accounts of commercial banks at the Federal Reserve Bank.
LIBOR – lending rate among banks in the London market.
TREAURY NOTES OR BONDS – debt obligations of the federal government with original maturities of one year or more.
MUNICIPAL BONDS – tax-exempt bonds issued by state and local governments.
CORPORATE BONDS – long-term debt issued by private corporations typically paying semi-annual coupons and returning the face value of the bond at maturity.
COMMON STOCKS – ownership shares
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income (EBIT) of $1,000,000. The company's depreciation expense is $200,000. Moore is 100% equity financed, and it faces a 35% tax rate.
a) What is the company’s net income?
b) What is the company’s net cash flow?
3) A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 10%. Assume that the liquidity premium on the corporate bond is 0.4%. What is the default risk premium on the corporate bond? Round your answer to two decimal places.
4) Find the present value of $700 due in the future under each of the following conditions. Round your answers to the nearest cent.
a) 4% nominal rate, semiannual compounding, discounted back
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bill has 135 days remaining until maturity. Compute the quoted yield. (100-98.235)/100 * (360/135) = 4.71%
Compute the BEY on the above referenced T-bill. (100 – 98.235)/98.235 * (365/135) = 4.86%
A negotiable CD has a quoted interest rate equal to 2.35%. Compute the yield on bond equivalent basis. – 2.35 * (365/360) = 2.38
A “bond equivalent yield” as presented in class is an “annual percentage rate” or APR.
Consider the two bonds with 10 years to maturity & identical risk characteristics.
Coupon 5% 6%
Price $1,000 $1,200
YTM 5% ?
Compute the quoted yield to maturity for bond B assuming it pays semi-annual coupons.
PV = -1200 , PMT = 30 , FV
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a. 1. redox reactions means the transfer of electrons . In a redox reaction, the loss of electrons
from one substance is called oxidation, and the addition of electrons to another substance is known as reduction.
In photosynthesis, the reaction is
Water is split, and electrons are transferred along with hydrogen ions from the water to carbon dioxide, reducing it to sugar.
Because the electrons increase in potential energy as they move from water(H-O bond) to sugar(C-H bond), this process requires energy—in other words is endergonic. This energy boost is provided by light.
In cellular respiration, the summary equation is
Glucose loss electrons and become oxidized, oxygen
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debt by borrowing the money to family members instead of the strangers.
4. The nominal interest rate=2%+6%=8%.
At the end of one year, I will have $1080 in account ($1000*1.08).
At that time, the stereo will sell for $1050*1.06=$1113. I don’t have enough money to buy it. I still need $33 ($1113-1180=$33) in order to buy it.
Years Cash payment PV OF CP Weights Weighted maturity
1 60 56.07 5.76 0.06
2 60 52.41 5.38 0.11
3 1060 865.28 88.86 2.67
973.73 Duration 2.83
The expected price changes if interest rate drops to 6.75%:
%△P = -2.83*(-0.0025/1+0.07)=0.0066=0.66%
6. It will increase the interest rates if prices in the bond market become volatile,. Since the price
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prices of several corporate bonds with face values of $1000 are summarized in the following table:
|Corporate Bond |Price |Trading Status |
|IGA |$1,090.75 |? Premium Bond |
|CISCO |$976.50 |? Discounted Bond |
| BMB |$1,000 |? Par Bond |
|TNN |$858.25 |? Discounted Bond |
For each bond, state whether it trades at a discount, at par
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The bond market is a less known in the financial world than the share market, but it doesn’t mean that it is not as important as the share one in terms of volumes. The main reason may be that the Governments are a big part of this market. Because unlike a share, a bond is a debt contract not a proportion of capital.
Usually, the international bond market is divided in three entities: the domestic bonds, the foreign bonds and the Eurobonds. The Eurobonds segment of the international market is, according to David. L. Scott and almost all dictionaries “a type of foreign bond issued and traded in countries other than the one in which the bond is denominated.”
This paper is going to focused on
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In finance, the net present value (NPV) or net present worth (NPW) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows of the same entity.
In the case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV is a central tool in discounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects. Used for capital budgeting and widely used throughout economics, finance, and
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Continental Carriers Inc. Case Analysis
Continental Carriers, IncContinental Carriers, Inc is a regulated general commodities motor carrier who had shipping routes up and down the Pacific Coast andto parts of the Midwest. They sought to acquire Midland Freight, Incto expand its operations and were deliberating about which methodto finance the acquisition. The purchase of Midland Freight, Incwould cost $50 million in cash. CCI would gain $8.4 million to itsearnings before interest and tax. There were three options that theboard of directors debated over: issuing new common stock, issuingpreferred stock or selling bonds. As Ms. Thorp, evaluate the impact of the bond issue and of
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before a note or bond can be issued. Long-term debts have covenants that are meant to protect lenders and borrowers. Long term debts have indentures or agreements that have all information about the debt. Companies disclose the features of the indenture within the body of its financial statements so that end users can have a precise understanding of the company’s financial positioning and its operations results.
Bonds and Notes Payable
According to Kiesco, the main purpose of bonds is to borrow for the long term when the amount of capital needed is too large for one lender to supply (2007, p. 673). Bonds allow more than one lender to partake in a company’s debt. When reporting
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ensure proper application of requirements, an explanation is given. Loan covenants or restrictions usually come with long-term debt to protect both lenders and borrowers (Kieso, Weygandt, and Warfield, 2007). The information included in the loan covenant is the amount authorized to be issued, interest rate, due dates, call provisions, property pledged as security, sinking fund requirements, working capital, or any other restrictions. All of this information should be included in the body of the financial statements or the notes for a complete understanding of the financial position of the company (Kieso, et al., 2007).
Companies should report long-term bond liabilities at
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certain friends over others no matter what happens. Another level of love is that of siblings and other family members. Even though we do things to our family members, and sometimes we don't like some of our family, that bond is still there. It's this family bond level of love that brought about the phrase, blood is thicker than water. We will do things for our brothers, sisters, mothers, fathers, and children before we would even consider doing them for anyone else. Many wars have been started because of this family level, brother avenging brother or father, father protecting his wife and children, or even vice versa. This simple family bond can even extend to include our pets, amazingly enough
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improved your performance over the two-day period?
The market-maker’s objective is to make money on the bid-ask spread, by buying stock at a lower price than the price at which they sell it, or selling the stock at a higher price than they buy it back. To improve performance over the two day period, I could have avoided completing a full buy order on the 1st day to avoid the short balance.
Topic 2: Performance Measures
2. Suppose a 5-year zero-coupon Treasury bond with face value $1000 has a 5% yield (annually compounded).
(a) What price does this bond sell for?
FV = $1000
t = 5 years
r = 5%
PV= FV / (1 + r)^t = $1000 / (1.05)^5 = $783.53
(b) Suppose another zero-coupon
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sweating about this right now), whilst people will want to lend/save money because the returns are good. If more people want to borrow money than people want to lend/save (demand>supply), it is going to be tough to get a loan, so people will be willing to pay a higher interest rate to secure their loan (increase in interest rates). If more people have excess money that they want to lend/save and fewer people want to borrow money (supply>demand), then they will be willing to accept a lower interest rate, just so they can get some return on their money (decrease in interest rates). Interest rates change until demand is equal to supply.
5. Describe how a bond is like a loan.
A bond is a debt
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= $1,500,000 THIS IS FV TVM - INVESTING CONTD. SOLUTIONS STEP 2: WE ARE SOLVING FOR I/Y P/Y =12 NOTE: since you are saving MONTHLY, you must set P/Y to 12 N = 15 X 12 = 180 PV = -100000 PMT = -500 FV = 1500000 SOLVE FOR I/Y = 16.20%
12. USING BOND SPREADSHEET (covered later in course). You want to buy an A rated bond that matures in 15 years. The coupon rate is 8%. The yield on A rated bonds in the same maturity range is 7.5%. What price would you pay for this bond? Corporate bonds mature at PAR. Par = $1000
• Corporate bonds pay interest coupons SEMIANNUALLY. P/Y = 2
• The stated interest rate on the bond is fixed for the life of the bond. This is called the
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Maese Industries Inc. has warrants outstanding that permit the holders to purchase 1 share of stock per warrant at a price of $25.
A. Calculate the exercise value of the firms warrants if the common sells at each of the following prices:
1. $20 -$ 25 = $5
2. $25 - $25 = $0
3. $25 - $30 = $5
4. $100 - $25 = $75
B. Assume the firms stock now sells for $20 per share. The company wants to sell some 20-year, $1,000 par value bonds with interest paid annually. Each bond will have attached 50 warrants, each exercisable into 1 share of stock at an exercise price of $25. The firm’s straight bonds yield 12%. Assume that each warrant will have a market value of $3
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Third year premium=0.013289*5000000/1.03=64510
Probability of losses exceeds 200million =15.87%
Since the interest rates fall 2% and the equity price is flat.
So the bond price will increase, so the pension plan price will increase.
Suppose the salary of final year is X
Tax is paid as though the investor owned the mutual fund investments
If the mutual fund realizes capital gains or dividends during a year, the investor has to pay taxes on the amount realized
The investor’s basis (i.e., the
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Exam I AC202
Name Anthony Edwards
Multiple Choice: Chose the one best answer for each of the following (2 points each)
1. Which of the following does not impact the calculation of the cash interest payments to be made to bondholders?
a. Face value of the bond
b. Stated interest rate
c. Market interest rate
d. The length of time between payments
2. Which of the following is false when a bond is issued at a premium?
a. The bond will issue for an amount above its face value
b. Interest expense will exceed the cash interest payments
c. The market interest rate is lower than the stated interest rate
d. The issue price will be
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the image of the flea, which is made to seem insignificant throughout the poem, the flea goes through a “sex” journey without even knowing it. The poem maintains one speaker until the end, but has two significant characters: the speaker and his lover. While he is trying to convince his female lover to see that her virginity isn’t all that it’s hyped to be, he compares a flea to sex in the process, “It suck'd me first, and now sucks thee, And in this flea our two bloods mingled be” (line 3), this quote suggests that the flea has united the two into one. Ultimately by comparing the flea to the bond between his lover and himself, the bond that “is you and I, and this Our marriage bed, and
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six theories try to explain the source of child abuse. These theories use two main methods to explain child abuse the first one is adorning ones action, and the second one is copying ones behavior (Champe, 2012).
Research shows that children who are abused grow up to be abusive because of copying ones behavior and they grow with it into adulthood. Children who abused grow up to be criminals and end up in prisons. These theories try to explain how parents and children should relate in their families (Champe, 2012).
The first theory is the attachment theory it explains how children turn up to be in future as a result of the relationship they had with their guards. The bond
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, management needs to use capital budgeting techniques to determine which projects will yield the most return over an applicable period of time.
Popular methods of capital budgeting include net present value (NPV), internal rate of return (IRR), discounted cash flow (DCF) and payback period.
6)Convertible preferred stock vs. convertible debt: Malavika
As the name implies, convertible debts (both preferred stock and debt), or converts, give the holder the option to exchange the bond for a predetermined number of shares in the issuing company. When first issued, they act just like regular corporate bonds, albeit with a slightly lower interest rate. Because convertibles can be changed into
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Greek CDS drama holds lessons for investors
It’s over. The long-running drama over Greek credit default swaps finally came to end with a $2.5bn pay-out for those who had bought protection against default by Athens. Yet, while market disorder was avoided, there remain concerns that CDS are flawed.
Market participants insist lessons need to be learned from the Greek debt restructuring deal and bond exchange, or these insurance-like instruments, untested in a sovereign restructuring before Greece and which are used as a protection against losses on bonds, could lose their appeal.
An auction held by 14 banks set a market-wide payout of $2.5bn, or 78.5 per cent of the $3.2bn of net
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would be the stock market, as these change drastically and often based on new announcements.
Primary market: This is a part of the financial market where new security issues are initially bought and sold. One great example would be Companies, governments or public sector institutions that funding through the direct purchase of a new stock or bond.
Secondary market: This is a financial market where previously issued securities such as stocks and bonds are bought and sold. A great example of this would be after the bank is issued stocks and bonds, they are then sold to consumers and customers at the bank.
Risk: Risk is a possibility for investments. Shareholders, investors, business owners
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significantly hirer beta of 1.2, given the recent volatility of Nike's stock. Ms. Cohen used the 20-year rate which I think is less then risk free. While there is no such thing as a risk free rate, a 3-month treasury bond is as close as it gets. Conversely, while unlikely there is the possibility in 20 years the U.S. could default on its debt. Finally, Ms. Cohen used 2.7 as the cost of debt which I feel is to low, especially given the historical rates range of 2.5- 3.5. I would have taken the median of 3.0%. With these adjustments the cost of capital would be 10% which I would more comfortable with.
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Chief Business Officer
Dear Mr. Xiang Fu Liu,
I am proud to introduce the expansion project of Happy Patty and would like to take this time to introduce the company and its business to you. Established in Texas 2013, our company takes pride in exceeding the standard to give our customers the best food and services possible. We strongly believe in creating an enjoyable long-term bond with customers to sustain long term profitability. We are currently licensed to operate in China in which our staff is fully prepared to start working.
Both our local and extended team has taken the time to revise the menu making sure to abide by your
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®-295 UV Backfill
Pre-treated Window Pane
Fig. 122 Examples of one of the many decorative glazing applications inside a luxury liner
Fig. 124 Typical construction of a window with outer UV protection
Fig. 123 (a, b & c) Examples of adhesively bonded organic glazing using Sikaflex®-295 UV in conjunction with UV Shielding Tape
Marine Application Guide
Procedure for Bonding and Sealing Organic Windows
Lightly abrade the gelcoat of the contact
area with a very fine sanding pad
Abrade the bond area with abrasive paper
or very fine abrasive pad. Abrade
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In its simplest form, the Black–Scholes(–Merton) model involves only two underlying assets, a
riskless asset Cash Bond and a risky asset Stock.3 The asset Cash Bond appreciates at the
short rate, or riskless rate of return rt , which (at least for now) is assumed to be nonrandom,
although possibly time–varying. Thus, the price Bt of the Cash Bond at time t is assumed to
satisfy the diﬀerential equation
= rt Bt ,
whose unique solution for the value B0 = 1 is (as the reader will now check)
rs ds .
Bt = exp
The share price St of the risky asset Stock at time t is assumed to follow a stochastic diﬀerential
equation (SDE) of the form
dSt = µt
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) hydrogen bonding
E) ionic bonding
Page Ref: Sec. 25.2
5) Hydrocarbons containing carbon-carbon triple bonds are called __________.
B) aromatic hydrocarbons
Page Ref: Sec. 25.2
6) Alkynes always contain a __________.
B) C≡C bond
C) C-C bond
D) C-H bond
E) C≡H bond
Page Ref: Sec. 25.2
7) Alkenes always contain a __________.
B) C≡C bond
C) C-C bond
E) C≡H bond
Page Ref: Sec. 25.2
8) Hybridization of the carbon atom indicated by (*) in [pic], [pic] , and [pic] is __________, __________, and __________, respectively.
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the rate at which they can borrow (especially if the bank debt is old.)
• Solution 1: Assume that the private firm can borrow at the same rate as similar firms (in terms of size) in the industry.
Cost of Debt for Private firm = Cost of Debt for similar firms in the industry
• Solution 2: Estimate an appropriate bond rating for the company, based upon financial ratios, and use the interest rate estimated bond rating.
Cost of Debt for Private firm = Interest Rate based upon estimated bond rating for private firm
Note: If the beta is calculated based upon the assumption that the firm will move to its optimal debt ratio, use the corresponding bond rating.
• Solution 3: If the