Answer: d. 20
Explanation:
The Money multiplier is the number that new deposits are multiplied with to find out their total effect on the banking system.
It is calculated by dividing 1 by the required reserve ratio.
Required reserve ratio = 0.5/10
= 5%
Money Multiplier = 1/5%
= 20
A 10 percent decrease in the price of a Pepsi decreases the demand for a Coca-Cola by 50 percent. The cross elasticity of demand between a Pepsi and Coca-Cola is ?
Answer:
the cross elasticity of demand between a Pepsi and Coca-Cola is 5
Explanation:
The computation of the cross elasticity of demand is shown below:
= Percentage change in quantity demanded of one product ÷ percentage change in the price of other product
= -50 ÷ -10
= 5
Hence, the cross elasticity of demand between a Pepsi and Coca-Cola is 5
We simply applied the above formula so that the correct value could come
And, the same is to be considered
Which stage of an industry's growth cycle offers the greatest opportunity for an investor who is seeking capital gains?
a. initial development
b. mature growth
c. stability or decline
d. rapid expansion
Answer:
d. rapid expansion
Explanation:
The main objective of an investor is to invest his capital in an industry that generates profits. Therefore, analyzing the above question, it is correct to say that an organization that is expanding its business quickly, is achieving success in the market in which it operates, so this alternative is ideal for an investor seeking capital gains.
Initial development would be an alternative that does not have a real return for the investor, mature growth is also not the most profitable option, and the stability or decline option does not present a profitable and reliable alternative for an investor.
XYZ, Inc. just paid an annual per share dividend of $3.50. Dividends are expected to grow at a rate of 3% per year from here on out. If the risk-free rate is 2.5%, the expected return on the market is 7% and the beta of the stock is 2, what is the most that you should be willing to pay for a share of this stock today?
Answer:
P0 = $42.4117 rounded off to $41.41
Explanation:
Using the constant growth model of dividend discount model, we can calculate the price of the stock today. The DDM values a stock based on the present value of the expected future dividends from the stock. The formula for price today under this model is,
P0 = D0 * (1+g) / (r - g)
Where,
D0 is the dividend paid recentl
D0 * (1+g) is dividend expected for the next period /year
g is the growth rate
r is the required rate of return or cost of equity
First we need to calculate the required rate of return on this stock using CAPM.
Using the CAPM, we can calculate the required rate of return on a stock. This is the minimum return required by the investors to invest in a stock based on its systematic risk, the market's risk premium and the risk free rate.
The formula for required rate of return under CAPM is,
r = rRF + Beta * (rM - rRF)
Where,
rRF is the risk free rate
rpM is the market return
r = 0.025 + 2 * (0.07 - 0.025)
r = 0.115 or 11.5%
Using the constant growth of dividend formula,
P0 = 3.5 * (1+0.03) / (0.115 - 0.03)
P0 = $42.4117 rounded off to $41.41
Match each situation with the term that best describes it. Use each term only once.
a. Personal power
b. Legitimate power
c. Reward power
d. Coercive power
e. Expert power
f. Informational power
g. Referent power
h. Persuasive power
1. One of your subordinates only seems to respond to threats of punishment. What type of power should you use to motivate him?
2. You manage a difficult subordinate who only cooperates when she feels that youhave the formal authority to ask her to do something. What type of power shouldyou use to motivate her?
3. One of your subordinates looks up to you as a role model. What type of powershould you use to motivate her?
Answer:
1. One of your subordinates only seems to respond to threats of punishment. What type of power should you use to motivate him?
h. Persuasive power
2. You manage a difficult subordinate who only cooperates when she feels that you have the formal authority to ask her to do something. What type of power should you use to motivate her?
b. Legitimate power
3. One of your subordinates looks up to you as a role model. What type of power should you use to motivate her?
a. Personal power
Explanation:
In any given situations there are different incidents that would require someone to apply different power in-order to manage the situation. This could be in form of motivation or deterrent method during the application of the power.
For example, in the case of the subordinate looking up to you as a role model, you should apply personal power in-order to motivate the person. the personal power will help you to build personal relationship between the subordinate and you.
According to the condition, the following matches are as follows:
One of your employees appears to react to threats of punishment solely. This condition is a Persuasive type of power you should use to motivate him. Thus, the correct matches are 1-h, 2-b, 3-a.
A persuasive individual may persuade others to make intelligent judgments, as well as convince others to make foolish decisions.
Thus, it is beneficial for the organization when that individual has expertise as well as the judgment to recognize when they should seek the opinion of someone else.
You manage a tough subordinate who only cooperates when she believes you have the official power to request something of her. The Legitimate type of power is used to motivate.
One of your subordinates regards you as a mentor. The Personal type of power is used here.
Therefore, the correct option is 1-h, 2-b, 3-a.
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Four years ago your firm issued a $1,000 par bond with a 4% semi-annual coupon and 20 years to maturity. The bond is now priced at $860. What is the current yield to maturity of the bond?
Answer:
the current yield to maturity of the bond is 5.31%
Explanation:
The computation of the yield to maturity is shown below:
Given that
Future value = $1,000
Present value = $860
NPER = (20 - 4) × 2 = 16
PMT = $1,000 × 4% ÷ 2 = $20
The formula is shown below:
= RATE(NPER;PMT;-PV;FV;TYPE)
The present values comes in negative
After applying the above formula, the yield to maturity is
= 2.6548% × 2
= 5.31%
Hence, the current yield to maturity of the bond is 5.31%
Bolt Corp. acquires equipment valued at $81,630 by signing a 3-year noninterest-bearing note payable for $100,000. Calculate the implicit interest rate on the note.
Answer:
7%
Explanation:
Calculation for the implicit interest rate on the note
First step is to calculate the PV factor
PV factor=$81,630/100,000
PV factor = 0.81630
Last Step is to find the implicit interest rate by using the PV table for 3 years to find the factor that matches the PV factor of 0.81630
Hence the factor that matches the PV factor of 0.81630 can be found or see in the 7% column which means that the implicit interest rate will be 7%
Therefore the implicit interest rate on the note will be 7%
YCD, Inc., has sales of $5,783, total assets of $2,604, and a debt-equity ratio of 0.75. If its return on equity is 11 percent, what is its net income?
Answer:Net income=$164
Explanation:
Equity multiplier = 1 + Debt-equity ratio
Equity multiplier = 1 + 0.75
Equity multiplier = 1.75
And the total asset turnover is:
Total asset turnover = Sales / Total assets
Total asset turnover = $5,783 / $2,604
Total asset turnover = 2.22 times
ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
0.11 = (Profit margin)(2.22)(1.75)
Profit margin = 0.14/3.885 =0.0283
Rearranging we can find the net income as
Profit margin = Net income / Sales
Net income = profit margin x Sales
Net income =0.0283 x $5,783,= $163.6589 = $164
please help its due in 2 hours time will give all my points
"Explain how the development of money over time has helped to improve the way in which monetary transactions are conducted" 6 MARK QUESTION
Explanation:
First money ever made was just coins and it differed in worth compared to today. In the present, money is not only a physical object but it also an imaginary value on our bank accounts and cards. Having in mind that monetary transactions are all-in-all deposits, withdrawals and exchanges, its way easier to conduct those with not having to give and recieve money in physical form, but being, able to do it all while just transfering the numbers from one to another account. Bankers have less responsibility due to not having to stock all the money in safes and secure boxes, but just checking if all the numbers are adding up. So, shall we say, the development of money over time has improved the way in which monetary transactions are conducted because this way, it's safer, faster and much more trustworthy.
Which of the following is an example of an effective persuasive speech topic for a group of elementary school children?
a.
the origins of Santa Claus in different cultures around the world
b.
abstinence: the best protection
c.
read at least 20 minutes a day
d.
staying in school is cool
Answer: d. staying in school is cool
Explanation:
An elementary school has children who have grown past childhood but have not yet reached teenagerhood. Persuasive topics for them would therefore have to be tailored to their level of understanding.
Based on the options, the best would be to teach them to stay in school. The origins of Santa Claus is for their juniors and abstinence is for their seniors as well as reading 20 minutes a day. Staying in school is great for their age as it instils the values of education at a time they can understand it.
Susmel Inc. is considering a project that has the following cash flow data. What is the project's payback
Answer: 2.5 years
Explanation:
The payback period of a project as the term implies, is the amount of time it takes for a project's cashflows to pay off its original outlay.
The formula is;
= Year before payback + Amount remaining/ Cashflow in year of Payback
Year 1 + 2 = 150 + 200 = $350
Amount remaining = 500 - 350 = $150
Payback period = 2 + 150/300
= 2.5 years
For which of the following businesses would a job costing system be appropriate?
Root beer producer.
Drug manufacturer.
Auto repair shop.
Crude oil refinery.
Answer:
Auto repair shop.
Explanation:
A job costing system involves accounting for the expenses as per a specific production or service job. Accumulation of expenses is in relation to a certain job or production for a particular good. An Auto repair shop will be best suited to use the job costing system. Expenses can be attached to the repair of a specific car. The costs of repairing each vehicle can be identified with ease.
The other options would require process costing.
The FOURX Corp. has purchased $50,000 of experimental equipment. The anticipated salvage value is $5500 at the end of its 5-year depreciable life. This profitable corporation is considering two methods of depreciation: straight-line and double declining balance. If it uses 10% interest in its comparison, which method do you recommend?
a. NPW(SL): $37,908; NPW(DDB): $37,068; Recommendation: SL
b. NPW(SL): $33,738; NPW(DDB): $37,068; Recommendation: DDB
c. NPW(SL): $33,738; NPW(DDB): $26,551; Recommendation: SL
d. NPW(SL): $33,738; NPW(DDB): $38,069; Recommendation: DDB
Answer:
b. NPW(SL): $33,738; NPW(DDB): $37,068; Recommendation: DDB
Explanation:
The computation is shown below:
As we know that
Present value is
= [Cash Flow ÷ (1 + Rate of Interest)^Year]
where,
Rate of Interest = 10%
Under Straight-line depreciation:
Beginning book value = $50,000
Salvage value = $5,500
So, the depreciationper year is
= [($50,000 - $5,500) ÷ 5]
= $8,900
Year Beginning Depreciation End Present value
book value book value of depreciation
1 $50,000 $8,900 $41,100 $8,090.91
2 $41,100 $8,900 $32,200 $7,355.37
3 $32,200 $8,900 $23,300 $6,686.70
4 $23,300 $8,900 $14,400 $6,078.82
5 $14,400 $8,900 $5,500 $5,526.20
$33,738.00
Under Double declining depreciation:
Depreciation rate per year = (1 ÷ Useful Life) × 100
= 1 ÷ 5 × 100
= 20%
Now for double-declining, the rate is doubled
So,
= 20% × 2
= 40%
Year Beginning Depreciation End Present value
book value book value of depreciation
1 $50,000 $20,000 $30,000 $18,181.82
2 $30,000 $12,000 $18,000 $9,917.36
3 $18,000 $7,200 $10,800 $5,409.47
4 $10,800 $4,320 $6,480 $2,950.62
5 $6,480 $980 $5,500 $608.50
$37,068
A portfolio has 70 shares of Stock A that sell for $30 per share and 125 shares of Stock B that sell for $17 per share. (a) What is the portfolio weight of Stock A?(b) What is the portfolio weight of Stock B?
Answer:
Portfolio weight of Stock A=49.70%
Portfolio weight of Stock A=50.29%
Explanation:
Calculation for the portfolio weight of Stock A and Stock B
First step is to calculate the total amount invested in both portfolio weight of Stock A and Stock B
Stock A and Stock B Total amount invested=
(A 70 shares*$30 per share)+ (B 125 shares*$17 per share)
Stock A and Stock B Total amount invested=$2,100+$2,125
Stock A and Stock B Total amount invested=$4,225
Now let calculate the PORTFOLIO WEIGHT OF STOCK A
Using this formula
Portfolio weight of Stock A=Stock A/Stock A and Stock B Total amount invested
Let plug in the formula
Portfolio weight of Stock A=(70 shares*$30 per share)/$4,225
Portfolio weight of Stock A=$2,100/$4,225
Portfolio weight of Stock A=0.4970*100
Portfolio weight of Stock A=49.70%
Therefore the Portfolio weight of Stock A
will be 49.70%
Calculation for PORTFOLIO WEIGHT OF STOCK B
Using this formula
Portfolio weight of Stock B=Stock B/Stock A and Stock B Total amount invested
Let plug in the formula
Portfolio weight of Stock B=(125 shares*$17 per share)/$4,225
Portfolio weight of Stock B=$2,125/$4,225
Portfolio weight of Stock B=0.5029*100
Portfolio weight of Stock B=50.29%
Therefore the Portfolio weight of Stock will be 50.29%
Ajax Corp's sales last year were $460,000, its operating costs were $362,500, and its interest charges were $12,500. What was the firm's times-interest-earned (TIE) ratio? Group of answer choices
Answer:
the times interest ratio is 7.80
Explanation:
The computation of the times-interest earned ratio is shown below:
As we know that
Times-interest-earned (TIE) ratio is
= Earnings Before Interest and Taxes ( EBIT) ÷ Interest expense
= ($460,000 - $362,500) ÷ $12,500
= 7.80
Hence, the times interest ratio is 7.80
We simply applied the above formula so that the correct value could come
And, the same is to be considered
Naomi complains to Andy that he "hasn’t been here – until now, when we’re in crisis mode." Based on this statement, Andy is most likely viewed as a(n) ________ leader by Naomi.
a. passive management by exception
b. active management by exception
c. transformational
d. laissez-faire
e. contingent reward
Answer: a. passive management by exception
Explanation:
Even though this might sound like it is laissez-faire leadership, it is not.
This is a passive management by exception leadership style and a leader that does this is usually inactive and absent from their duties unless mistakes are being made or crisis are popping up that need to be fixed. They will then spring into action to mitigate the adverse effects of their absence.
This is different from laissez-faire leadership because in laissez-faire, the leader is simply absent even during crisis.
Based on the given statement, it is the passive management by exception that leader by Naomi.
The following information should be considered related to the passive management by exception :
In this, the leader is not active also it is absent from the duties until the mistakes should be made or the crisis should be popping up the requirement to be fixed. After this, there is the transformation of the spring into action for decreasing the opposite impacts.Therefore we can conclude that the correct option is a.
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If the yield to maturity (the market rate of return) of a bond is less than its coupon rate, the bond should be:_______.a. selling at a discount; i.e., the bond's market price should be less than its face (maturity) value.
b. selling at a premium; i.e., the bond's market price should be greater than its face value.
c. selling at par; i.e., the bond's market price should be the same as its face value.
d. purchased because it is a good deal.
Answer:
b. selling at a premium; i.e., the bond's market price should be greater than its face value.
Explanation:
In the case when the market rate of return or yield to maturity is lower than the coupon rate this represents that the bond sells at a premium i.e. the market price of the bond is more than the face value
Let us suppose the market price of the bond is $1,050
And, the face value is $1,000
So the bond is sold at a premium
hence, the correct option is b.
The combination of debt financing and equity financing that maximizes a firm's value is known as its:
Answer:
optimal capital structure
Explanation:
optimal capital structure can be regarded as a combination of
of debt and equity financing which brings about maximization of amarket value in a firm. It should be noted that optimal capital structure is the combination of debt financing and equity financing that maximizes a firm's value.
A snack manufacturer discovers that they must increase the salt content of chips by 14 milligrams before about 50 percent of their consumers notice the change. A clever intern points out that this is an example of:
Answer:
difference threshold
Explanation:
Difference threshold is use by businesses or effectively reduce cost without affecting their profit margin .
It is the minimum amount of change that is required to make consumers of a product to notice the change 50% of the time.
In the given scenario the snack manufacturer discovers that they must increase the salt content of chips by 14 milligrams before about 50 percent of their consumers notice the change.
The present value of a 10-year annuity-immediate with level annual payments and interest rate i is X. The present value of a 20-year annuity immediate with the same payments and interest rate is 1.5X. Find i.a. 7.2%. b. 7.0% c. 6.8% d. 6.6% e. 6.4%
Answer:
what is this?
Explanation:
g A monopoly may exist because Question 21 options: a) government has refused to grant a public franchise. b) one firm has the exclusive ownership of a necessary resource. c) the firm is so large and is currently experiencing such vast diseconomies of scale that it can out-compete all newcomers. d) a and b e) a, b, and c
Answer:
B. one firm has the exclusive ownership of a scarce resource.
Explanation:
Monopoly can be regarded as market structure whereby a single seller thrives, this is a structure whereby the seller sells a unique product in the market. As far as monopoly market is concerned, no competition is been encontered by the manufacturer , because he is the only one selling goods with no close substitute. As a result of this there is restrictions of the entry of other sellers in the market.
It should be noted that monopoly may exist because one firm has the exclusive ownership of a scarce resource.
Answer:
b) one firm has the exclusive ownership of a necessary resource
Explanation:
A monopoly is a situation where a single supplier of a commodity.
This gives the supplier the benefit of fixing a price that maximises profit for them. Consumers have no alternative so they pay the high price for the commodity.
There is no substitute good so there is no competition from other firms. Price is usually set at a high level so that the monopoly enjoys profit high above its marginal cost.
Monopolies exist because one firm has the exclusive ownership of a necessary resource not available to other firms.
A methods and measurements analyst needs to develop a time standard for a certain task. In a preliminary study, he observed one of his workers perform this task five times, with the following results:
Observation --- 1 --- 2 --- 3 --- 4 --- 5
Time(seconds) 84 ---76 - -80 --84 --76
How many observations should be made if the analyst wants to be 99.74 percent confident that the maximum error in the observed time is two seconds?
a. 25
b. 6
c. 49
d. 5
e. 36
Answer:
e. 36
Explanation:
Number of observations needed, n = (z *s / h) ^2
Where, z = number of standard deviation needed for desired confidence level of 99.74% = 3, s = Standard Deviation of task = 4 seconds, h = maximum error in the observed time = 2 seconds.
n = (3*4/ 2) ^2
n = (12/2) ^2
n = 6^2
n = 36 observations
Thus, the number of observations needed in the task is 36 observations
UPS has a beta of 1.5 and FedEx has a beta of 0.9. The risk-free rate is 4% and the market risk premium is 7%. If the portfolio comprised of these two stocks has a beta equal to 1.08, what are the portfolio weights of UPS and FedEx
Answer and Explanation:
The computation of the portfolio weighted of UPS and FedEx is shown below:
Let us assume the weight of UPS be x
And, the weight of FedEx be (1 - x)
As we know that
Portfolio beta = Respective beta × Respective weight
1.08 = (x × 1.5) + (1 - x) × 0.9
1.08 = 1.5x + 0.9 - 0.9x
x = (1.08 - 0.9) ÷ (1.5 - 0.9)
x = 0.30 or 30%
= UPS weight
And, the weight of FedEx is
= 1 - x
= 1 - 0.30
= 0.70
Admire County Bank agrees to lend Sheffield Brick Company $614000 on January 1. Sheffield Brick Company signs a $614000, 8%, 9-month note. The entry made by Sheffield Brick Company on January 1 to record the proceeds and issuance of the note is:______________.
Answer:
January 1
Cash 614000 Dr
Notes Payable 614000 Cr
Explanation:
The Sheffield Brick Company has borrowed from the Admire county bank which means the note payable is a liability in the books of the Sheffield Brick company. As liability is increased or recorded, it is credited. The amount of liability is $614000 on the day of the issuance of note. Thus, Sheffield will credit Note payable by $614000.
The Sheffield company has received cash by signing note. As cash is an asset and it is increasing, the Sheffield company will debit cash by 614000 against the notes payable.
Who is the founder of royal crown hotel ??
Charging off the cost of a wastebasket with an estimated useful life of 10 years as an expense of the period when purchased is an example of the application of the
Answer:
E. materiality concept
Explanation:
The materiality concept refers to a concept in which it impacts the decisions of the user if there is any small impact. In other words, any small impact could change the user decisions with respect to the financial statement i.e. relevant and useful
Therefore according to the given situation, the Option E is correct
And all the other options are incorrect
1. Which generally accepted accounting principle (GAAP) requires the use of depreciation for assets that have useful lives beyond one year
Answer:
matching principle
Explanation:
The matching principle in accounting basically states that you must record expenses or costs in the same period as you record revenues associated to them. I.e. the use of assets generates revenue, therefore, you must expense that use at the same time when you record revenues.
US GAAP accepts 4 depreciation methods:
Straight line method Declining balance method Units of production method Sum of years' digitsHayden Company currently sells widgets for $160 per unit. The variable cost is $60 per unit and total fixed costs equal $240,000 per year. Sales are currently 40,000 units annually, and the income tax rate is 40 percent. Required: a. Calculate the contribution margin per unit. b. Calculate break-even in units. c. Calculate break-even in sales dollars d. Calculate the current after-tax net income. e. The company is considering a 10% drop in the selling price that it believes will raise units sold by 15%. Assuming all costs stay the same, what is the impact on income if this change is made? f. How many units need to be sold to earn a pre-tax operating income of $100,000?
Answer:
a. $100
b. 2,400 units
c. $380,952
d. $2,256,000
e. 15.90 %
f. 3,400 units
Explanation:
Contribution margin per unit
Contribution margin per unit = Sales per unit less Variable Cost per unit
Therefore,
Contribution margin per unit = $160 - $60
= $100
Break-even in units
The Breakeven units is the level of activity where a firm makes neither a profit nor a loss.
Break-even in units = Fixed Cost ÷ Contribution margin per unit
Therefore,
Break-even in units = $240,000 ÷ $100
= 2,400 units
Break-even in sales dollars
Break-even in sales dollars = Fixed Cost ÷ Contribution margin ratio
Where,
Contribution margin ratio = Contribution margin ÷ Sales
= $100 ÷ $160
= 0.63
Therefore,
Break-even in sales dollars = $240,000 ÷ 0.63
= $380,952
After-tax net income
Contribution ( $100 × 40,000 ) $4,000,000
Less Fixed Cost ($240,000)
Next Income Before Tax $3,760,000
Less Income tax at 40 % ($1,504,000)
Net Income After Tax $2,256,000
Effect of the Change on Income
First, calculate the Degree of Operating Leverage (DOL).
The DOL shows the times Net Income Before Interest and Tax will change as a result of a change in sales contribution.
Degree of Operating Leverage (DOL) = Contribution ÷ Net Income
Therefore,
Degree of Operating Leverage (DOL) = $4,000,000 ÷ $3,760,000
= 1.06
Effect on Income using the DOL = 1.06 × 15% = 15.90 %
Therefore Net Income would also increase by 15.90 %.
Units to be sold to earn an income of $100,000
Units to Earn a Target Profit = (Fixed Costs + Target Profit) ÷ Contribution margin per unit
Therefore,
Units to be sold to earn an income of $100,000 = ($100,000 + $240,000) ÷ $100
= 3,400 units
If a person deposits $1,000 now into a savings account for 10 years, the amount of money required in year 10 to account for a 6% per year inflation and earn a real 8% per year interest rate is closest to what?
Answer:
$3,707.22
Explanation:
the nominal interest rate that this person wants = real interest rate + inflation rate = 8% + 6% = 14%
this means that his/her account needs to earn 14% per year in order to gain an 8% real interest rate with a 6% inflation rate:
future value = present value x (1 + r)ⁿ
present value = $1,000r =14%n = 10future value = $1,000 x (1 + 14%)¹⁰ = $3,707.22
Derst Inc. sells a particular textbook for $27. Variable expenses are $20 per book. At the current volume of 43,000 books sold per year the company is just breaking even. Given these data, the annual fixed expenses associated with the textbook total:___________
a) $860,000
b) $1,161,000
c) $1,462,000
d) $301,000
Answer:
d. 301,000
Explanation:
Given that the cost per textbook is $27, we know that the addition of variable and fixed Cost gives total cost.
We will multiply variable cost per textbook of $20 with current volume of book sold per year 43,000, which gives a total variable cost of $860,000.
Also, total cost would be 43,000 multiplied with $27 , which is $1,161,000 minus the total variable cost of $860,000 equals $301,000 which is the associated fixed cost.
Suppose you have the following three zero-coupon bond (ZCB) available: a 1-year ZCB that costs $97, a 2-year ZCB that costs $95, and a 3-year ZCB that costs $92. Assume that the par values are $100.
a. What must the price of a 3-year coupon bond with at 8% coupon rate?
b. How would you make an arbitrage profit if the coupon bond was trading at $100?
c. How much arbitrage profit would you make per $100 of the 3-year coupon bond trade?
Answer:
Bond price = Par value / (1 + 1 year spot rate)1
$97 = $100 / (1 + 1 year spot rate)^1
(1 + 1 year spot rate)^1 = $100 / $97
(1 + 1 year spot rate) = 1.030928
1 year spot rate = 3.0928%
Bond price = Par value / (1 + 2 year spot rate)^2
$95 = $100 / (1 + 2 year spot rate)^2
(1 + 2 year spot rate)^2 = $100 / $95
(1 + 2 year spot rate)^2 = 1.052632
(1 + 2 year spot rate) = (1.052632)(1 / 2)
(1 + 2 year spot rate) = 1.025978
2 year spot rate = 2.5978%
Bond price = Par value / (1 + 3 year spot rate)^3
$92 = $100 / (1 + 3 year spot rate)^3
(1 + 3 year spot rate)^3 = $100 / $92
(1 + 3 year spot rate)^3 = 1.086957
(1 + 3 year spot rate) = (1.086957)(1 / 3)
(1 + 3 year spot rate) = 1.028184
3 year spot rate = 2.8184%
Coupon per period = (Coupon rate / No of coupon payments per year) * Par value
Coupon per period = (8% / 1) * $100
Coupon per period = $8
a) Bond price = Coupon / (1 + 1 year spot rate)^1 + Coupon / (1 + 2 year spot rate)^2 + (Coupon + Par value) / (1 + 3 year spot rate)^3
Bond price = $8 / (1 + 3.0928%)^1 + $8 / (1 + 2.5978%)^2 + ($8 + $100) / (1 + 2.8184%)^3
Bond price based on spot rates = $114.7199
b. Bond price based on spot rates is greater than traded bond price to exploit this arbitrage the following strategy must be implemented
The 3 year 8% coupon bond should be bought at $100.
Portfolio = -$100
1 year zero coupon bond with face value $8 must be sold
Portfolio = (Price of 1 year zero coupon bond / Face value) * Amount of Face value to be Sold
Portfolio = ($97 / $100) * $8
Portfolio = $7.76
2 year zero coupon bond with face value $8 must be sold
Portfolio = Price of 2 year zero coupon bond / Face value) * Amount of Face value to be Sold
Portfolio = ($95 / $100) * $8
Portfolio = $7.6
3 year zero coupon bond with face value $108 must be sold
Portfolio = Price of 3 year zero coupon bond / Face value) * Amount of Face value to be Sold
Portfolio = ($92 / $100) * $108
Portfolio = $99.36
Arbitrage profit = -$100 + $7.76 + $7.6 + $99.36
Arbitrage profit = $14.72
c) Arbitrage profit = Bond price based on spot rates - Traded Bond price
Arbitrage profit = $114.72 - $100
Arbitrage profit = $14.72
Arbitrage profit would you make per $100 = $14.72