Answer:
industrial products
Explanation:
A company that does this and mostly favors a push strategy is usually selling industrial products. That is because a push strategy focuses on taking the product to the potential customer and showing them how it works as well as how it can benefit them, therefore pushing the product on them. Industrial Products are great for such a strategy since they require actual demonstration and can easily show the potential customer the actual value that the product can provide.
Chuck has $2,500 invested in a bank that pays 4% annually. The length of time it will take for his funds to double is closest to:
Answer:
The answer is 17.67 years.
Explanation:
Present value is $2,500
Future value of the money to be double of the present value. This means the future value will be $5,000($2,500 x 2)
Interest rate is 4%
Number of years or periods to reach this $5,000 is unknown. So we are looking for this.
To compute this number of periods, lets use Financial calculator.
I/Y = 4; PV= -2,500; FV= 5,000; CPT N= 17.67 years.
Therefore, the number of years to accumulate to $5,000 is 17.67 years
Downtown Bancshares has 40,000 shares of $8 par common stock outstanding. Suppose Downtown declares and distributes a 16% stock dividend when the market value of its stock is $20 per share.
1. Journalize Downtown's declaration and distribution of the stock dividend on May 11. An explanation is not required.
2. What was the overall effect of the stock dividend on Downtown's total assets? On total liabilities?
Answer and Explanation:
1. The journal entry is shown below:
Retained earnings Dr (40,000 shares × 16% × $20) $128,000
To Common stock (40,000 shares × 16% × $8) $51,200
To Paid in capital in excess of par value - common stock $76,800
(Being the declaration and the stock distribution is recorded)
2. Since the retained earnings is debited which reduced the equity by $128,000 but at the same time it also increased the equity via common stock and paid in capital by $128,000 so the overall effect should be NIL or zero
Also the assets and liabilities remains unaffected
A project has cash flows of -152,000, 60,800, 62300, and 75000 for years 0 to 3 respectively. The required rate of return is 13 years percent. Based on the internal rate of return of__________percent, you should________the project.
Answer:
Based on the IRR of 14.05 percent, you should be accept the project
Explanation:
Internal rate of Return is the discount rate of that equates the present value of cash inflows to the initial cost. It is the maximum cost of capital that can be used to evaluate a project without causing harm to the shareholders.
It is calculated as follows:
IRR = a% + ( NPVa/(NPVa + NPVb)× (b-a)%
NPV = PV of cash inflows - initial cost
Step 1: NPVa at 13% discount rate
PV of cash inflow = 60,800× 1.13^(-1) + 62300 ×1.13^(-2) + 75000 ×1.13^(-3)
= 154,574.11
NPVa = 154,574.11 - 152000 = 2,574.11
Step 2: NPVb at 20%
PV of cash inflow = 60,800× 1.20^(-1) + 62300 ×1.20^(-2) + 75000 ×1.20^(-3) = 137,333.33
NPVb = 137,333.33 - 152,000 = (14,666.67)
Step 3: IRR
IRR = 13% + ( 2,574.11 /(2,574.11 + 14,666.67) )× (20-13)%
IRR = 14.05%
Based on the IRR of 14.05%, the project you should be accept the project
Since the IRR (14.05%) is greater than the required rate rate (13%) , the project should be accepted. An IRR which is higher than the hurdle rate implies that the project would increase the wealth of the shareholders
Colorado experiences a record snowfall during the winter season. What impact will this have on the market for snowmobiles?
Answer:
The demand curve for snowmobiles will increase and the price of snowmobiles will rise.
Explanation:
Demand is defined as the quantity of a good that is requested by a customer at a given price and time.
In the given instance there was heavy snowfall during the winter season that will result in more people wanting to go out on the snow.
When there is a change in demand as a result of a factor apart from price demand shifts.
In this case demand will shift to the right (increase).
Demand will increase at an increased price.
This is illustrated in the attached diagram.
Demand shifts from D1 to D2 and price increases from P1 to P2
What is the value of a zero-coupon bond with a par value of $1,000 and a yield to maturity of 6.60%? The bond has 19 years to maturity.
Answer:
$296.90
Explanation:
For computing the value of the zero coupon bond we need to apply the present value formula i.e to be shown in the attachment below:
Given that,
Future value = $1,000
Rate of interest = 6.60%
NPER = 19 years
PMT = $0
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
So, after applying the above formula, the value of zero coupon bond is would be $296.90
Choose three organizations that you believe have had the greatest impact on the current state of safety and health programs in the United States. Summarize the purpose of each organization, and discuss how you believe you can use these organizations to improve your ability to perform your duties as a safety and health professional.
The correct answer to this open question is the following.
The three organizations would be OSHA, NIOSH, and NACOSH.
OSHA stands for Occupational Safety and Health Administration. It tries to ensure that the workers labor under the proper safety and health conditions in their workplace.
NIOSH stands for the National Instituto for Occupational Safety and Health. This organization basically is dedicated to researching to know the working conditions of workers in America and make recommendations.
NACOSH stands for the National Advisory Committee on Occupational Safety and Health. It functions as an adviser or counselor to the Department of Labor on safety and security issues.
These three can definitely be used to improve my ability to perform my duties as a safety and health professional in that they include a series of recommendations, programs, and educational tips to be applied in the workplace and diminish the possibility of accidents or how to react in case of one.
Jordan is the marketing head of Hastings Comprehensive Systems. He usually strives for long-term improvement rather than short-term profit, regardless of the economic environment. In the context of Deming's 14 points of quality, this is an example of
Answer:
Create constancy of purpose
Explanation:
Deming 14 points of quality are recommended management strategy to transform business effectiveness.
Deming postulated that by increasing quality one is able to reduce cost and increase efficiency of a business.
The first of his 14 points is to create a constancy of purpose. This is achieved by striving for long-term improvement rather than short-term profit, as is done by Jordan in the given scenario.
The 14 points of Deming are given below:
Create a constancy of purpose
Adopt the new philosophy
Stop depending on inspections
Using a single supplier for one item
Improve constantly and forever
Use training on the job
Implement leadership
Eliminate fear
Breakdown barriers between departments
Get rid of unclear slogans
Eliminate management by objectives
Remove barriers to pride of workmanship
Implement education and self improvement
Make transformation everyone's job
The operating margin measures tells you that for every dollar of sales XXXX dollars makes it to the net income line on the income statement.
A. True
B. False
Answer:
A. True
Explanation:
The Operating Margin is the profit obtained for every dollar of sale and this is the sames as saying a certain amount of sales makes it to the net income line on the income statement.
Lead time for one of your fastest-moving products is 24 days. Demand during this period averages 110 units per day. a) What would be an appropriate reorder point? nothing units (enter your response as a whole number). b) How does your answer change if demand during lead time doubles? nothing units (enter your response as a whole number). c) How does your answer change if demand during lead time drops in half? nothing units (enter your response as a whole number).
Answer:
a.) reorder point = 2,640 units
b.) reorder point = 5,280 units (reorder point doubles)
c.) reorder point = 1,320 units (reorder point drops in half)
Explanation:
Reorder point is the inventory level (point) at which action is taken (order placed) to replenish the stocked item. It is calculated as follows:
Reorder point = (Lead time × average daily sales) + safety stock
Lead time = 24 days
average daily sales = 110 units
safety stock = 0 (not given)
a.) reorder point = (Lead time × average daily sales) + safety stock
reorder point = (24 × 110) + 0 = 2,640 units
b.) if demand during lead time doubles:
lead time = 24 days
average daily sales = (110 × 2) = 220
∴ reorder point = 220 × 24 = 5,280 units
Therefore the reorder point doubles
c.) if demand during lead time drops in half:
lead time = 24 days
average daily demand = (110 ÷ 2) = 55 units
∴ reorder point = 24 × 55 = 1,320 units
Therefore the reorder point drops in half.
Assume that interest rates on 20-year Treasury and 20-year corporate bonds are as follows T-bond = 3.72% AAA = 4.12% A = 4.64% BB = 5.18% The differences in these rates were probably caused primarily by:
Answer: Default risk differences.
Explanation:
The Default risk is the inherent risk a lender faces that a borrower will not pay them back the debt they want to borrow. The lender will therefore charger a high return to cater for this risk. The higher the risk, the higher the return charged.
T-bonds have no default risk because they are guaranteed by the US Government which is why it's rate is the lowest. For the other bonds, there is something called a Credit rating. Bonds are usually rated on how risky it will be to lend to the company borrowing with AAA being of the lowest risk. Therefore as one goes up from AAA, the bonds will have higher default risks.
An exchange-rate policy in which the government usually allows the exchange rate to be set by the market, but sometimes intervenes is called a __________________ exchange rate system.
Answer: Managed Float
Explanation:
Also called "Dirty Float", the Managed float is an exchange rate system that allows for the currency of a country to be set by the forces of demand and supply in the market.
However, unlike in a clean float, the Central bank will occasionally intervene in the market to influence the how fast the currency is changing value or to control the direction it is going.
This is usually done to protect the domestic economy from sudden shocks in the global economy.
Job Searching in the Digital Age(Part II) Which of the following are job boards?
A. Open Post
B. College Grad
C. Big Careers
Users of ________ are increasingly using the sites to prospect for jobs.
Which of the following is an advantage to using networks and referral in the hidden job market?
A. Between 50 and 80 percent of all jobs are found there
B. Since there are fewer jobs in the hidden job market, a more targeted search can be conducted
C. It includes all jobs posted on job boards
Which of the following is an example of a way to search for jobs on the open job market?
A. Newspapers
B. Social networks
C. Personal networking
D. Referrals
E. Job boards
Which of the following will help protect you when posting to online job boards?
A. Include references
B. Only use sites where you publicly post
C. Only use sites where you pay to post
D. Remove your posted résumés when your job search is over
Answer and Explanation:
1. B. College Grad: college grad is a job board used by millions for their job search. Other popular job boards include: Monster, Indeed and career builder
2. Social networking:social networking sites are increasingly used today in job search. A popular example is LinkedIn which is used for professional connections and networking.
3. B. Since there are fewer jobs in the hidden job market, a more targeted search can be conducted : the hidden job market consisting of personal networking and referrals has fewer jobs but is very effective in selecting the right people for a job
4.A. Newspapers E. Job boards: open job markets consist Jon's listed publicly in newspapers, Jon boards and websites for all qualified candidates to apply. It is different from the hidden job market which is usually referral based such as in personal network and social network, former colleagues or former schoolmates and alumni groups.
5. D. Remove your posted résumés when your job search is over: use reputable sites in your job search and don't post private data. Don't jump on every job post. Endeavor to remove your resume from the site when your search is over
Often management is "under the gun" and want to solve problems and meet deliverables before logically assessing the situation. This problem is related to:________
a. Odecisive leadership
b. stakeholder framing.
c. misguided leadership
d. perceptual defense
e. identifying opportunities.
Answer:
decisive leadership
Explanation:
Decisive leadership is the leadership in which the leaders have to decide quickly for a particular thing. It is basically a capability for deciding with the speed and clarity of the things happen.
Also the quick decision result in a bad situation without knowing the impact of that decision
Therefore according to the given scenario, the "under the gun" represents the decisive leadership
A project with an initial cost of $27,250 is expected to generate cash flows of $6,600, $8,700, $9,100, $8,000, and $7,400 over each of the next five years, respectively. What is the project's payback period?
Answer:
It will take 4 years and 130 days to recover for the initial investment.
Explanation:
Giving the following information:
A project with an initial cost of $27,250 is expected to generate cash flows of $6,600, $8,700, $9,100, $8,000, and $7,400
The payback period is the time required to recover for the initial investment:
Year 1= 6,600 - 27,250= -20,650
Year 2= 8,700 - 20,650= -11,950
Year 3= 9,100 - 11,950= -2,850
Year 4= 8,000 - 2,850= 5,150
To be more accurate:
(2,850/8,000)*365= 130
It will take 4 years and 130 days to recover for the initial investment.
When a job analyst watches employees directly or reviews films of workers on the job, which analysis method is being used?
Answer:
Observation method
Explanation:
Through observation, this analyst collects data by watching the employees directly. This is participatory because the analyst has to involve himself in the work environment where this employees are in other to collect data. This method would allow the analyst to have more reliable insights. He would get data based on what the employees do rather than what the Employees tell him that they do.
At the end of the current accounting period, account balances were as follows: Cash, $26,000; Accounts Receivable, $42,000; Common Stock, $18,000; Retained Earnings, $12,000. Liabilities for the period were:
Answer: Liabilities =$38,000
Explanation: An asset whether tangible or intangible is a source of value to a company examples are Cash, investments, accounts receivables etc
Liabilities are referred to the debts owed to a company or buisness at a particular period eg bank debts, tax owed, wages owed etc.
Equity is the measure of value of a company"s asset eg Common stock, retained earnings, , preferred stock etc.
The three above are related using the equation below
Assets = Liabilities + Equity.
Total Liabilities = Assets - Equity
Total asset = Cash + Account receivables = 26,000+42,000=68,000
Total equity = Common stock + retained earnings = 18,000+12000=30,000
Total liabilities =Total asset -total equity
= 68,000-30,000
= $38,000
A sales tax of $1 per unit of output is placed on one firm whose current equilibrium price is $5 and current equilibrium quantity is 100 units. If you know that the elasticity of demand is -1 and the elasticity of supply is (infinity), then after the tax:
a. pb=6, ps=5, and QT=unknown but less than 100
b. pb=4, ps=5, and QT=unknown but less than 100
c. pb=6, ps=5, and QT=100
d. pb=4, ps=5, and QT=100
Answer:
B
Explanation:
B is the correct answer
Given a stock index with a value of $1,200, an anticipated dividend of $45, and a risk-free rate of 6%, what should be the value of one futures contract on the index
Answer: $1,227
Explanation:
The value of the futures contract should be calculated by the formula;
= Stock Index Value * ( 1 + risk free rate ) - dividends
= 1,200 * ( 1 + 0.06) - 45
= $1,227
McKerley Corp. has preferred stock outstanding that will pay an annual dividend of $3.70 per share with the first dividend exactly 14 years from today. If the required return is 3.6 percent, what is the current price of the stock?
Answer:
$64.89
Explanation:
Calculation for the current price of the stock
First step is to find the preference stock value at end of 13 years
Using this formula
P13= Annual dividend/Required return
Let plug in the formula
P13=$3.70/.036
P13= $102.78
The second step is to calculate for the current price of the stock
Using this formula
P0= P13/(1+Required return)^Dividend years
Let plug in the formula
P0= $102.78/(1 + .036)^13
P0=$102.78/(1.036)^13
P0=$102.78/1.5837
P0=$64.89
Therefore the current price of the stock will be $64.89
Digby's balance sheet has $99,131,000 in equity. Further, the company is expecting net income of 3,000,000 next year, and also expecting to issue $4,000,000 in new stock. If there are no dividends paid what will beDigby's book value
Answer:
Book Value = $106,131,000
Explanation:
DATA
Equity = $99,131,000
Expected Net Income = $3,000,000
New stock issued = $4,000,000
Solution:
We can calculate Digby's Book value by adding Equity, Expected Net Income and New Stock issued.
Calculation:
Book Value = Equity + expected net income + Bew stock issued
Book Value = $99,131,000+ $3,000,000+$4,000,000
Book Value = $106,131,000
erekes Manufacturing Corporation has prepared the following overhead budget for next month. Activity level 3,200 machine-hours Variable overhead costs: Supplies $ 16,640 Indirect labor 29,120 Fixed overhead costs: Supervision 15,400 Utilities 6,600 Depreciation 7,600 Total overhead cost $ 75,360 The company's variable overhead costs are driven by machine-hours. What would be the total budgeted overhead cost for next month if the activity level is 3,100 machine-hours rather than 3,200 machine-hours
Answer:
Variable overhead= $44,330
Fixed overhead= $29,600
Total overhead= $73,930
Explanation:
Giving the following information:
Total variable overhead= $45,760
Total fixed overhead= $29,600
Total overhead cost= $75,360
First, we need to calculate the variable predetermined overhead rate:
Variable predetermined overhead rate= 45,760/3,200= $14.3 per machine hour
Now, for 3,100 hours:
Variable overhead= 14.3*3,100= $44,330
Fixed overhead= $29,600
Total overhead= $73,930
Suppose that the income tax rate is reduced by the federal government and simultaneously a recession hits causing the economy to move below its potential output, this will:
Answer:
Raise both the cyclical and structural deficits
Explanation:
During economic downturn the cyclical deficit will rise, leading to rise in already structural deficit of federal government. The Structural deficit arises when government continue to spend more than its revenue, and thus cyclical deficit will add upward pressure in structural deficit.
Therefore there will be Raise in both the cyclical and structural deficits
On January 31, 2016, Danvers Logistics, Inc., issued five-year, 7% bonds payable with a face value of $10,000,000. The bonds were issued at 96 and pay interest on January 31 and July 31. Danvers Logistics, Inc., amortizes bond discount by the straight-line method.
Record:
a. Issuance of the bonds on January 31, 2016.
b. The semiannual interest payment and amortization of bond discount on July 31, 2016.
c. The interest accrual and discount amortization on December 31, 2016.
Answer:
Journal entries are given below
Explanation:
Journal Entries
Requirement A: Issuance of the bonds on January 31, 2016.
Debit Credit
Cash (w) $9,600,000
Discount on bonds payable $400,000
Bonds payable $10,000,000
Working
Cash = 10,000,000*0.96 = $9,600,000
Discount on bonds payable = 10,000,000*0.04 = $400,000
Requirement B: The semiannual interest payment and amortization of bond discount on July 31, 2016.
Debit Credit
Interest expense $390,000
Cash (w) $350,000
Discount on bonds payable (w) $40,000
Working
Cash = 10,000,000x 0.07 x 6/12 = $350,000
Discount on bonds payable = 400000/(5months*2) = $40,000
Requirement C: The interest accrual and discount amortization on December 31, 2016.
Debit Credit
Interest expense $325,000
Cash (w) $291,666.67
Discount on bonds payable (w) $33333.33
Working
Cash = 10,000,000x 0.07 x 5months/12months = 291,666.67
Discount on bonds payable = 400,000/(5*2)*5/6 = 33,333.33
Concord Corporation has 8,800 shares of common stock outstanding. It declares a $3 per share cash dividend on November 1 to stockholders of record on December 1. The dividend is paid on December 31. Prepare the entries on the appropriate dates to record the declaration and payment of the cash dividend
Answer:
Declaration date:
Dr retained earnings $26400
Cr dividends payable $26400
Payment date:
Dr dividends payable $26400
Cr Cash $26400
Explanation:
Total dividend declared is the number of shares multiplied by cash dividend per share
total dividend=$3*8,800=$26400
On the record date no entries are required since record date, is just about verifying the bonafide shareholders.
On declaration date,dividends payable would be credited with $26,400 while retained earnings is debited.
On payment date,dividends payable is debited and cash credited
Hoosier Manufacturing operates a production shop that is designed to have the lowest unit production cost at an output rate of 145 units per hour. In the month of July, the company operated the production line for a total of 265 hours and produced 30,400 units of output.What was its capacity utilization rate for the month?
Answer:
79.1%
Explanation:
Hoosier manufacturing operates a production shop that is modelled to have the lowest unit of production
The output rate is 145 units per hour
In the month of July the company operated the production line for 265 hours
30,400 units of output were produced
Therefore, the capacity utilization rate can be calculated as follows
= 30,400 units/265 hours ×145
= 30,400/38,425
= 0.791×100
= 79.1%
Hence the capacity utilization rate for the month is 79.1%
A company’s common stock has a market value of $63.18 per share and its next dividend is expected to be $3.26 per share. The stock’s beta is 1.2, the tax rate is 35%, and the market risk premium is 6.1% per year. The yield to maturity for the company’s long-term debt is 6.4% per year. If the riskiness of the company’s equity requires that it provide a risk premium of 3.2% per year over the yield on its long-term debt, what is the company’s annual cost of internal equity financing?
Answer:
Cost of equity = 9.6%
Explanation:
The cost of equity is the return a firm theoretically pays to its equity investors, In order to calculate the cost of equity here we need to add up the yield to maturity for the company's long term debt and the risk premium per year over the yield on its long term debt.
Solution
Cost of equity = Yield to maturity + Risk premium
Cost of equity = 6.4% + 3.2%
Cost of equity = 9.6%
You have an annuity which pays $1,200 every two years. The first payment is two years from now and the last payment is ten years from now. You can trade that annuity for another annuity of equivalent present value, which pays $180 per quarter starting today. The interest rate for both annuities is 4% per annum convertible quarterly. If you took the second annuity, how many quarterly payments would you receive? The last payment may be less than $180 but not more than $180.
Answer:
31 payments
Explanation:
the present value of the first annuity is:
$1,200 / (1 + 1%)⁸ + $1,200 / (1 + 1%)¹⁶ + $1,200 / (1 + 1%)²⁴ + $1,200 / (1 + 1%)³² + $1,200 / (1 + 1%)⁴⁰ = $1,108.18 + $1,023.39 + $945.08 + $872.76 + $805.98 = $4,755.39
to determine the length of the second annuity:
PV = annuity payment x annuity factor
annuity factor = PV / annuity payment = $4,755.39 / $180 = 26.4188333
using an annuity table we must look for a present value annuity factor that corresponds to 1% interest rate and is close to 26.4188333
the annuity factor is between 30 and 31 payments. Since the final payment has to be less or equal to $180, we have to choose 31 payments.
In Sammy's fast food restaurant, she produces sandwiches, soups, and other items for customers in her town. Which of the following is a fixed input for the production function at Sammy's restaurant?
a) the employees hired to help make the food.
b) the loaves of bread used to make sandwiches.
c) the cans of tomato sauce used to make soups.
d) the dining room where customers eat their meals
Answer:
d) the dining room where customers eat their meals
Explanation:
In the given situation, since it is mentioned there is a Sammy's fast food restaurant that generates the sandwiches, soups, and other items for customers
So based on the options given, the last option should be considered as a fixed input for the production function as the dining room is a fixed plus non-movable item so the same is to be considered
hence, the correct option is d.
Answer:
D
Explanation:
I would say D because you want to give a good impression on your customers so they want to come back and know that you will take good care of them.
Hawley company makes decorative wedding cakes. The company is considering buying the cakes rather than baking them, which will allow it to concentrate on decorating. The company averages 100 wedding cakes per year and incurs the following costs from baking wedding cakes.
Direct materials $550
Direct labor 950
Variable manufacturing overhead 150
Fixed manufacturing overhead 1,125
Total manufacturing cost $2,775
Number of cakes / 100
Cost per cake $28
Fixed costs are primarily the depreciation on kitchen equipment such as ovens and mixers. Hawley expects to retain the equipment. Hawley can buy the cakes for 28$.
1. Should Hawley make the cakes or buy them? Why?
2. If Hawley decides to buy the cakes, what are some qualitative factors that Hawley should also consider?
1. Should Hawley make the cakes or buy them? Why? (For the Difference column, use a minus sign or parentheses only when the cost of outsourcing exceeds the cost of making the cakes in-house.)
Make Outsource Difference
Cake costs cakes cakes (make—outsource)
Variable costs:
Direct materials
Direct labor
Variable manufacturing overhead
Purchase cost
Total differential cost of cakes
Hawley (should, should not) continue to make the cakes. Outsourcing will (decrease, increase) profits.
2. If Hawley decides to buy the cakes, what are some qualitative factors that Hawley should also consider?
A. Qualitative factors include considering sunk costs andmanager's opinions.
B. Qualitative factors include separating fixed and variable costs.
C. Qualitative factors include quality and on-time delivery.
D. Qualitative factors include contribution margins of the various products produced.
Answer:
1. Continue to Make the Cakes. Because the Cost of Outsourcing is greater that the cost of making by $1,150.
2. C. Qualitative factors include quality and on-time delivery.
Explanation:
Analysis of the Make or Buy Decision
Make Outsource Difference
Cake costs cakes cakes
Variable costs:
Direct materials $550 $0 $550
Direct labor $950 $0 $950
Variable manufacturing overhead $150 $0 $150
Fixed manufacturing overhead $1,125 $1,125 $0
Purchase cost $0 $2,800 ($2,800)
Total differential cost of cakes $2,275 $3,925 ($1,150)
Qualitative Factors.
Are non-monetary factors that need to be considered in decision making.
Company ABC is required to pay their customers $20,000 after 3 years. Based on an annual effective interest rate of 4%, Andy, the company’s actuary, uses full immunization strategy to construct a portfolio of assets using a 2-year zero-coupon bond and a 4-year zero-coupon bond. Calculate the par amount for the 2-year zero-coupon bond assuming full immunization is met.
Answer:
Par amount = $9,615.39
Explanation:
The condition that must hold in order to meet full immunization are as follows:
Condition 1: PV(assets) = PV(liabilities)
Condition 2: MD(assets) = MD(liabilities) or P'assets = P'liabilities
Condition 3: There is one asset cash inflow before the liability cash outflow, and there is also one asset cash inflow after the liability cash outflow.
Where PV denotes Present Value and MD denotes Macaulay Duration.
PV(liabilities) = Amount required to pay / (1 + i)^n ............ (1)
Where;
Amount required to pay = $20,000
i = interest rate = 4%
n = number of years after = 3 years
Substituting the values into equation (1), we have:
PV(liabilities) = $20,000 / (1 + 4%)^3 = 17,779.93
Let;
A = Weight of two-year-zero-coupon bond in the portfolio
n = Macaulay Duration of n-year-zero-coupon bond
Therefore, we can construct a portfolio of assets using a 2-year zero-coupon bond and a 4-year zero-coupon bond as follows:
A(2) + (1 – A)(4) = 3
2A + 4 – 4A = 3
2A – 4A = 3 – 4
-2A = - 1
A = -1/-2
A = 0.5
We can now calculate the par amount as follows:
Par amount = PV(liabilities) * A * (1 + i)^t .............. (2)
Where t = 2 as the duration of the bond
Substituting the values into equation (2), we have:
Par amount = 17,779.93 * 0.5 * (1 + 4%)^2
Par amount = 17,779.93 * 0.5 * 1.04^2
Par amount = 17,779.93 * 0.5 * 1.0816
Par amount = $9,615.39
Therefore, the par amount for the 2-year zero-coupon bond assuming full immunization is met is $9,615.39.
