Answer:
Instructions are below.
Explanation:
Giving the following information:
Direct materials 5.50 pounds $ 2.50 per pound.
Actual:
1. 10,600 were purchased for $2.40 per pound.
2. The company produced only 1,060 units, using 9,540 pounds of material.
To calculate the direct material price and quantity variance, we need to use the following formulas:
Direct material price variance= (standard price - actual price)*actual quantity
Direct material price variance= (2.5 - 2.4)*10,600
Direct material price variance= $1,060 favorable
Direct material quantity variance= (standard quantity - actual quantity)*standard price
standard quantity= 1,060*5.5= 5,830
Direct material quantity variance= (5,830 - 9,540)*2.5
Direct material quantity variance= $9,275 unfavorable
At an output level of 53,000 units, you calculate that the degree of operating leverage is 3.21. If output rises to 57,000 units, what will the percentage change in operating cash flow be? Suppose fixed costs are $175,000. What is the operating cash flow at 46,000 units? The degree of operating leverage? that the degree of operating
Answer:
If output rises to 57,000 units, what will the percentage change in operating cash flow be?
24.23%What is the operating cash flow at 46,000 units?
$45,613.84The degree of operating leverage (at 46,000 units)?
4.84Explanation:
degree of operating leverage = [quantity x (price - variable costs)] / {[quantity x (price - variable costs)] - fixed costs}
degree of operating leverage x {[quantity x (price - variable costs)] - fixed costs} = [quantity x (price - variable costs)]
3.21 x {[53000 x (contribution margin)] - fixed costs} = [53000 x (contribution margin)]
(3.21 x 53000 x contribution margin) - (3.21 x 175000) = 53000 x contribution margin
let C = contribution margin
170130C - 561750 = 53000C
117130C = 561750
C = 561750 / 117130 = 4.795953
operating cash flow (at 53,000) = (53,000 x $4.795953) - $175,000 = $79,185.52
operating cash flow (at 57,000) = (57,000 x $4.795953) - $175,000 = $98,369.32
% change = ($98,369.32 - $79,185.52) / $79,185.52 = 24.23%
operating cash flow (at 46,000) = (46,000 x $4.795953) - $175,000 = $45,613.84
% change in operating cash flows = ($45,613.84 - $79,185.52) / $79,185.52 = -43.4%
% change in sales = (46,000 - 53,000) / 53,000 = -13.21
degree of operating leverage = $220,613.84 / $45,613.74 = 4.84
Two investment advisors are comparing performance. Advisor A averaged a 20% return with a portfolio beta of 1.5 and Advisor B averaged a 15% return with a portfolio beta of 1.2. If the T-bill rate was 5% and the market return during the period was 13%, which advisor was the better stock picker?
Answer:
Advisor A
Explanation:
t bill rate = 0.05
market rate = 0.13
the beta of the market is always 1
the rate of return= 0.05 + (0.13 - 0.05) x 1
= 0.13
which is 13%
this is for advisor A.
with a return of 20% and 1.5 beta
0.05 + ( 0.20 - 0.05) x 1.5
= 27.5% for advisor b
when the return is 15% and beta is 1.2
0.05 + (0.15 - 0.05) x 1.2
= 17%
Therefore advisor a is better
Discount-Mart issues $18 million in bonds on January 1, 2021. The bonds have a eight-year term and pay interest semiannually on June 30 and December 31 each year. Below is a partial bond amortization schedule for the bonds: Date Cash Paid Interest Expense Increase in Carrying Value Carrying Value 01/01/2021 $ 16,180,939 06/30/2021 $ 900,000 $ 970,856 $ 70,856 16,251,795 12/31/2021 900,000 975,108 75,108 16,326,903 06/30/2022 900,000 979,614 79,614 16,406,517 12/31/2022 900,000 984,391 84,391 16,490,908 What is the carrying value of the bonds as of December 31, 2022
Answer:
Discount-Mart
The carrying value of the bonds as of December 31, 2022 is:
$16,490,908
Explanation:
a) Data and Calculations:
Bonds issued = $18 million
Date of issue = Jan. 1, 2021
Bond term = 8 years
Interest payable on June 30 and December 31 each year.
b) Partial bond amortization schedule for the bonds:
Date Cash Paid Interest Expense Increase in Carrying Value
Carrying Value
01/01/2021 $ 16,180,939
06/30/2021 $ 900,000 $ 970,856 $ 70,856 16,251,795
12/31/2021 900,000 975,108 75,108 16,326,903
06/30/2022 900,000 979,614 79,614 16,406,517
12/31/2022 900,000 984,391 84,391 16,490,908
b) The carrying value of the bond is the net amount between the par value of $18 million and the unamortized premium or discount. It is this value that is reported on the balance sheet.
An investment offers a total return of 12.0 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 6.0 percent. What does Janice believe the inflation rate will be over the next year?
Answer:
inflation rate= 0.06= 6%
Explanation:
Giving the following information:
Interest rate= 12%
Real rate of return= 6%
The inflation rate is counterproductive to the interest rate. The inflation rate reduces the purchasing price, therefore it decreases the interest rate effect on nominal money.
Real interest rate= interest rate - inflation rate
0.06 = 0.12 - inflation rate
inflation rate= 0.12 - 0.06
inflation rate= 0.06= 6%
The simple rate of return is also called all of the following except ________. annual rate of return unadjusted rate of return accounting rate of return
Answer: annual rate of return
Explanation:
The simple rate of return is also called the unadjusted rate of return or the accounting rate of return.
The simple rate of return is calculated when the incremental net operating income for the year is taken and then divided by the initial investment.
It should be noted that it's not called the annual rate of return.
If the price that determined where marginal revenue equaled marginal cost were below the bottom of the average variable cost curve, then the profit-maximizing, monopolistically competitive firm would
Answer: c. shut down because it would cost more to produce and sell output than it would to shut down and lose all fixed costs.
Explanation:
The profit maximizing, monopolistically competitive firm maximises profit at the point where marginal revenue equals marginal costs.
If this point is below Average variable costs then that means that the company is not making enough to cover its variable costs. Should this be the case then the company should shutdown operations because variable costs are only there when the company is producing. If they shutdown then they will no longer incur them which would be the cheaper option.
They would take losses on the fixed costs but these have already been incurred so it would be better to lose the fixed costs than continue to make losses on variable costs.
Mr. Dow bought 100 shares of stock at $17 per share. Three years later, he sold the stock for $23 per share. What is his annual rate of return
Answer:
10.60%
Explanation:
The compound annual growth rate formula stated below can be used to determine the annual rate of return on the stock investment.
CAGR=(future value/present value)^(1/n)-1
future value is the future worth of the stock after three years i.e100*$23=$2300
Present value is the initial cost of the stock which is 100*$17=$1700
n is the number of years the stocks have been owned
CAGR=($2300/$1700)^(1/3)-1=10.60%
The before-trade domestic price of tomatoes in the United States is $500 per ton. The world price of tomatoes is $400 per ton. The U.S. is a price-taker in the tomatoes market.
If trade in tomatoes is allowed, the United States:______
a) will experience increases in both consumer surplus and producer surplus.
b) may become either an importer or an exporter of tomatoes, but this cannot be determined.
c) will become an exporter of tomatoes.
d) will become an importer of tomatoes.
Answer:
d) will become an importer of tomatoes.
Explanation:
Consumer surplus would increase because the price at which they buy tomatoes would reduce while producer surplus would reduce because the price of tomatoes would reduce as a result of international trade.
Consumer surplus is the difference between the willingness to pay of a consumer and the price of the good.Because the price of tomatoes in the US is greater than the price of tomatoes in the world, when the US begins international trade, it would import tomatoes because it is inefficient in the production of tomatoes.
Producer surplus is the difference between the price of a good and the least price the seller is willing to sell the product
the fair value of Blossom is estimated to be $820,800. The carrying value of Blossom’s net identifiable assets, including the goodwill, at year-end is $855,000. Prepare Cullumber’s journal entry, if necessary, to record impairment of goodwill.
Answer:
Cullumber Company
Journal Entry:
Debit Loss on Goodwill Impairment $34,200
Credit Goodwill $34,200
To record the loss on goodwill impairment.
Explanation:
a) Data and Calculation:
Fair value = $820,800
Carrying value of net identifiable assets, including goodwill = $855,000
Goodwill impairment = $34,200 ($855,000 - $820,800)
b) Cullumber, which acquired Blossom is expected to check for the impairment of goodwill yearly. The impairment occurs when the carrying value of the net identifiable assets of Blossom is more than the fair value of Blossom. Generally Accepted Accounting Standards require the annual review of the fair value of goodwill to check for its impairment. By the above entry, the goodwill will be reduced by $34,200 and a loss debited in Cullumber's accounts.
Activity-Based Costing: Selling and Administrative Expenses Jungle Junior Company manufactures and sells outdoor play equipment. Jungle Junior uses activity-based costing to determine the cost of the sales order processing and the customer return activity. The sales order processing activity has an activity rate of $20 per sales order, and the customer return activity has an activity rate of $100 per return. Jungle Junior sold 2,500 swing sets, which consisted of 750 orders and 80 returns.
Required:
a. Determine the total sales order processing and customer return activity cost for swing sets.
b. Determine the per-unit sales order processing and customer return activity cost for swing sets. Round your answer to the nearest cent.
Answer: 1}ToTAL Activity cost =$23,000
2a) Sales order Processing Activity per unit sale=$6.00
2b)customer return activity per unit sale=$3.20
Explanation:
a. total sales order processing and customer return activity cost for swing sets
Sales order Processing Activity =Number of orders x rate per sales order
=750 x 20 = $15,000
customer return activity = Number of returns x rate per return
= 80 x 100= $8,000
ToTAL Activity cost = Sales order Processing Activity +customer return activity= $15,000 + $8000 = $23,000
b)per-unit sales order processing and customer return activity cost for swing sets
Cost of Sale order processing = $15,000
Number of swing set sold = 2,500
Therefore Sales order Processing Activity per unit sale = Cost of Sale order processing/ Number of swing set sold = $15,000/ 2,500= $6.00
customer return activity cost = $8,000
Number of swing set sold = 2,500
Therefore customer return activity per unit sale= customer return activity cost / Number of swing set sold = $8,000/ 2,500= $3.20
ToTAL Activity cost per unit sale = Sales order Processing Activity cost per unit +customer return activity cost per unit = $6.00 + $3.20 = $9.20
Which statement thanks respondent for their participation, describes how incentives are received, and reassures them of the confidentiality of their responses
Answer:
Closing statement
Explanation:
Hope it helped
What is the present value of a perpetuity that pays you annual, end-of-year payments of $950? Use a nominal rate (monthly compounding) of 7.50%.
Answer:
The present value of the perpetuity is $12,242.27.
Explanation:
A perpetuity is an annuity that provide cash flow for an infinite period .Examples are Non -redeemable Preference Share.
Present Value (perpetuity) = Payments ÷ Required Rate
But, first change the 7.50 % nominal rate to Annual Effective Rate to match the period of Cash flow.
Effective Rate = (1 + r / m)^m - 1
= ( 1 + 0.0750 / 12) ^12 -1
= 7.76%
Therefore, Present Value (perpetuity) = $950 ÷ 7.76%
= $12,242.27
At the certain interest rate, present value (PV) is the current value of a future sum of money or stream of cash flows.
The discount rate determines the present value of the cash flows, and the higher the discount rate, the lower the current value of future cash flows.
The present value of the perpetuity is $12,242.27.
A perpetuity is an annuity that payments out during an indefinite period of time. Non-redeemable Preference Share is an example.
Present Value (perpetuity) = [tex]\frac{\text{Payments}}{\text{Required Rate}}[/tex]
However, to match the Working capital period, change a 7.50 percent nominal rate to a Yearly Effective Tax rate.
[tex]\text{Effective Rate} = (1 + \frac{r}{m} )^m - 1= [1 + \frac{0.0750}{12}]^{12} -1= 7.76\%[/tex]
Therefore, Present Value (perpetuity)= [tex]\frac{\$950}{7.76\%} = $12,242.27[/tex]
To know more about the calculations of the present value, refer to the link below:
https://brainly.com/question/15036500
Jock and Kyla decide to wager, in violation of a state statute, on the outcome of a football game. They each deposit money with Len, who agrees to pay the winner of the bet. Before the game begins, Kyla tells Len that she changed her mind about the bet. Kyla can recover Group of answer choices
Answer:
The amount of her bet only
Explanation:
A wager is a gamble on a particular outcome of a situation. In this case the outcome of a football match.
However wagering in such a manner is a violation of state staute. So this is an illegal activity.
Jock and Kyla deposit funds for the wager with Len. Before the bet of Kyla changes her mind she can recover the money she deposited.
Len will not be able to withhold he deposit because she can sue and claim this is an illegal activity that she does not want to be part of. Len will be forced.to return at least her own money.
Sam has contracted with Dave to purchase Dave's racing bike, with payment and delivery of the bicycle to be made 10 days after the contract was made. Three days later Sam hears that Dave is going to sell the bike to Gene in three days at a higher price. If Sam really wants the bike, what should he do? Multiple Choice Immediately seek injunctive relief. Immediately sue for specific performance. Immediately sue for compensatory damages. Immediately sue for consequential damages.
Answer: Immediately seek injunctive relief.
Explanation:
An injunctive relief is an order by the court stopping an action from taking place. From the question, we are told that Sam has contracted with Dave to buy Dave's racing bike, with payment and delivery of the bicycle to be made 10 days after the contract was made.
We are further told that three days later Sam hears that Dave is going to sell the bike to Gene in three days at a higher price. If Sam really wants the bike, he should seek injunctive relief. By doing so, the court will stop Dave from selling the bike to Gene.
Evaluate the Ritz-Carlton business model and associate key quality characteristics in the operations of a hotel set-up process.
Answer:
Ritz Carlton is luxury hotel chain of America. The company has 101 luxury hotel in more than 30 countries of the world. The success of Ritz Carlton is mainly because they keep the comfort of their guests as their highest priority. Their mission statement clearly states that comfort and genuine care of their guests is utmost important to them.
Explanation:
Their business model focuses entirely on their customers. Ritz Carlton has created its leading brand by providing great ambiance to the visitors and its guest. One can dream of staying at such luxury hotel. They are famous for their hospitality of their guests. The hotel management believes on total quality management. It has set highest standard for themselves and strive to meet them by providing better and better service to its guests.
The risk-free rate of return is 3.2 percent and the market risk premium is 4.6 percent. What is the expected rate of return on a stock with a beta of 2.12
Answer:
12.95%
Explanation:
The risk free rate of return is 3.2%
The market risk premium is 4.6%
The beta is 2.12
Therefore, the expected rate of return on a stock can be calculated as follows
= 3.2% + (2.12×4.6%)
= 3.2% + 9.752
= 12.95%
Hence the expected rate of return on a stock is 12.95%
If a bank that faces a 10% reserve ratio received a deposit of $50,000 and makes a loan to a customer for $5,000, what is the consequence if the bank then deposits the rest of the funds at the Federal Reserve?
Answer:
Excess reserve increases by $40,000
Required reserve increases by $5,000
Explanation:
In order to calculate the reserve, we need to multiply the Deposit received by a required reserve ratio.
DATA
Reserve ratio = 10%
Deposit received = $50,000
Loan to customer = $5,000
Solution
Reserve = Deposit x Required reserve ratio
Reserve = $50,000 x 10%
Reserve = $5,000
After providing a $5,000 loan to the customer and keeping $5,000 as a reserve remaining $40,000 would be deposited in the Federal Reserve.
HighLife Corporation has the following information: Average demand = 30 units per day Average lead time = 40 days Item unit cost = $45 for orders of less than 400 units Item unit cost = $40 for orders of 400 units or more Ordering cost = $50 Inventory carrying cost = 15 percent The business year is 300 days. Standard deviation of demand during lead time = 90 Desired service level = 95 percent What is the EOQ if HighLife pays $45/unit? Due to possible differences in rounding, choose the closest answer.\
Answer:
365.15 units
Explanation:
The computation of the economic order quantity is shown below:
[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]
where,
Annual demand is
= 30 units × 300 days
= 90,000 units
ordering cost is $50
Carrying cost is
= $45 × 15%
= $6.75
Now placing these values to the above formula
So, the economic order quantity is
[tex]= \sqrt{\frac{2\times \text{90,000}\times \text{\$50}}{\text{\$6.75}}}[/tex]
= 365.15 units
We simply applied the above formula so that the EOQ could come
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.
Despite the theoretical elegance of this hypothesis, empirical studies have come to the opposite conclusion. Despite the favorable effect of international diversification of cash flows, bankruptcy risk was only about the same for MNEs as for domestic firms. However, MNEs faced higher costs for each of the following EXCEPT:
A) agency costs.
B) political risk.
C) asymmetric information.
D) In fact, each of these costs were higher for the MNE than for the domestic firm.
Answer:
D) In fact, each of these costs were higher for the MNE than for the domestic firm.
Explanation:
It has been concluded through empirical studies, that Multinational Enterprises, MNEs encounters various factors leading to lower debt ratios and a higher cost of long-term debt, such as greater agency costs, political risk, asymmetric information, and foreign exchange risk,
Hence, given the question above, the right answer is option D "In fact, each of these costs was higher for the MNE than for the domestic firm."
Instruments had retained earnings of at December 31, . Net income for totaled , and dividends declared for were . How much retained earnings should report at December 31, ?
Answer:
B. $ 490,000
Explanation:
According to the given situation, the computation of retained earning in the year end is shown below:-
Ending retained earning = Beginning Retained Earnings + Net Income for the year - Dividend
= $360,000 + $180,000 - $50,000
= $490,000
Therefore for computing the ending retained earning we simply applied the above formula.
On July 1, 20X1, James and Short formed a partnership. James contributed cash. Short, previously a sole proprietor, contributed property other than cash, including realty subject to a mortgage, which the partnership assumed. Short’s capital account on July 1, 20X1, should be recorded at
Answer:
James and Short LLC
Short's capital account on July 1, 20X1 should be recorded at the fair value of contributed property minus the mortgage liability, which the partnership assumed.
Explanation:
The fair value of contributed property is the current market value of the contributed property by Short. It is the market value that will determine how the contributed property can be valued. The market value assumes that the contributed property is being sold in pieces and not as a whole. This is why the value is considered a fair basis for recognizing the capital contribution of Short into the partnership.
The Sprint vs. Verizon ads that compare the features and pricing of the two networks are examples of competitive advertising. True False
Answer:
True
Explanation:
They are trying to win over customers by comparing each others features in a competition
Competitive advertising is demonstrated by the Sprint vs. Verizon adverts, which compare the functionality and pricing of the two networks. So, it is a true statement.
What is competitive advertising?Competitive advertising is the act of showcasing or promoting one's product in comparison to the product of another company.
This form of marketing can be used to target customers who are devoted to the other brand, prompting them to reassess their purchasing patterns.
The three types of competitive advertising are:
ComparativeReminderReinforcementFor more information about competitive advertising, refer below
https://brainly.com/question/3463451
A one-month summary of manufacturing costs for Rapid Routers Company follows.
Direct materials $40,000
Direct labour 20,000
Material handling costs 1,500
Product inspection and rework 2,000
Materials purchasing and inspection 500
Routine maintenance and equipment servicing 1,200
Repair of equipment 300
Required:
Classify each cost as value-added or non-value-added
Answer:
Cost Classification
Direct materials Value added
Direct labor Value added
Material handling costs Non-value added
Product inspection and rework Non-value added
Materials purchasing and inspection Value added
Routine maintenance and equipment Non-value added
servicing
Repair of equipment Non-value added
The smartest thing a firm involved in an oligopoly market could do is to cut their prices and capture more of the market share from their competitors.
a) We learned in class that the best move would be to raise prices.
b) We also learned that cutting prices on an elastic demand curve will be a smart way of getting more revenues.
c) Cutting prices is no gaurantee of success. Indeed if the firm does capture more market share and customers, then their costs will go up and it will be harder for them because they will have lower profit margins - if they can earn any profit at all.
d) Both A and C are correct.
Answer:
Correct Answer:
c) Cutting prices is no gaurantee of success. Indeed if the firm does capture more market share and customers, then their costs will go up and it will be harder for them because they will have lower profit margins - if they can earn any profit at all.
Explanation:
An oligopoly market is a market form wherein a market or industry is dominated by a small group of large sellers. A pure monopoly maximizes profits by producing that quantity where marginal revenue = marginal cost. however, it is much more difficult for an oligopoly to determine at what output it can maximize its profit.
Refer to the following lease amortization schedule. The five payments are made annually starting with the inception of the lease. A $2,000 bargin purchase option is exercisable at the end of the five-year lease. The asset has an expected economic life of eight years.
Lease Payment Cash Payment Effective Interest Decrease in Balance Balance
34,600
1 8,000 ?? ?? 26,600
2 8,000 2,660 5,340 21,260
3 8,000 2,126 5,874 15,386
4 8,000 1,539 6,461 8,925
5 8,000 ?? ?? ??
6 2,000 182 1,818 0
What is the effective annual inerest rate?
A. 9%
B. 10%
C. 11%
D. 20%
Answer:
B. 10%
Explanation:
The computation of the effective annual interest rate is shown below:-
Effective annual interest rate = Lease payment third effective interest ÷ Lease payment second balance × 100
= $2,126 ÷ $21,260 × 100
= 10%
Therefore for computing the effective annual interest rate we simply applied the above formula.
Hence the correct option is B.
Explain how you would value a stock. Provide an example of a valuation of a stock based on retrieved real data. Include evidence of the retrieved data in your answer. Compare your valuation with the actual price of the stock at the designated time for your valuation.
Answer with Explanation:
There are numerous stock valuing models but here, I will use Dividend Valuation Model which is based on finding the intrinsic value of Stock which is the present value of the stock at a required rate of return. The formula to calculate Intrinsic value of stock is given as under:
P0= D0 * (1 + g) / (ke - g)
Here
P0 is the intrinsic value of the stock
D0 is the dividend just paid
g is the growth rate
ke is the investor's required rate of return
The model doesn't holds if the company doesn't pays Dividend.
Now suppose that the Dividend just paid by Apple is $20 per stock. The anticipated growth rate of dividend is 10% and the required rate of return is at 15%.
By putting values in the above equation, we have:
P0= $20 * (1 + 10%) / (15% - 10%)
= $20 / (15% - 10%)
= $400 per share
The value of stock of Apple is $400 per share which must be its fair market value as per the Dividend Valuation Model.
As per the model, if the value of stock is higher as per dividend valuation model then we must purchase the stock as it will generate higher value and vice versa. The inherent limitation of the model is that it assumes that the dividend is growing at constant rate and is consistently paid. The main disadvantage of Dividend valuation model is that it doesn't account for political factors, economical factors, evolving business risks, technological factors, etc.
Terrance needs to comminicate with managers in several different locations regarding a sensitive complex topic. Therefore he should choose the communication medium highest in information richness which would be a:______
a. Voice mail message.
b. Group email.
c. Videoconference.
d. Recorded presentation.
You purchased 1,000 shares of stock in Natural Chicken Wings, Inc., at a price of $43.37 per share. Since you purchased the stock, you have received dividends of $.95 per share. Today, you sold your stock at a price of $46.62 per share. What was your total percentage return on this investment?
Answer:
9.68%
Explanation:
Percent Return on Investment is calculated as Net Profit / Cost of Investment x 100
Net Profit= $46,620 (1,000 x $46.62 per share) + $950 (1,000 x $.95 per share) - $43,370 (1,000 x $43.37 per share) = $4,200
Cost of Investment= $43,370 (1,000 x $43.37 per share)
Percent Return on Investment= $4,200 / $43,370 x 100 = 9.68%
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.
