Answer:
a
Explanation:
Price elasticity of demand measures the responsiveness of quantity demanded to changes in price of the good.
Price elasticity of demand = percentage change in quantity demanded / percentage change in price
0.4 == quantity / 8
3.2%
If the absolute value of price elasticity is greater than one, it means demand is elastic. Elastic demand means that quantity demanded is sensitive to price changes.
Demand is inelastic if a small change in price has little or no effect on quantity demanded. The absolute value of elasticity would be less than one
Demand is unit elastic if a small change in price has an equal and proportionate effect on quantity demanded.
Infinitely elastic demand is perfectly elastic demand. Demand falls to zero when price increases
Perfectly inelastic demand is demand where there is no change in the quantity demanded regardless of changes in price.
Budgeted Actual Overhead cost $909,000 $884,000 Machine hours 55,000 46,000 Direct labor hours 101,000 98,000 Overhead is applied on the basis of direct labor hours. (a) Compute the predetermined overhead rate. (Round answer to 2 decimal places, e.g. 12.25.)
Answer:
Missing word "(b) Determine the amount of overhead applied for the year?"
1. Predetermined overhead rate = Budgeted overhead / Budgeted direct labor hours
Predetermined overhead rate = $909,000 / 101,000
Predetermined overhead rate = $9 per DLH
2. Overhead applied = Actual hours * Overhead rate
Overhead applied = 98,000 * $9 per DLH
Overhead applied = $882,000
Nichols Company uses the percentage of receivables method for recording bad debts expense. The month-end accounts receivable balance is $250,000 and credit sales during the month were $1,000,000. Management estimates that 4% of accounts receivable will be uncollectible. The Allowance for Doubtful Accounts has a credit balance of $2,500 before adjustment. The adjusting entry that Nichols must make includes: a. a credit to the allowance for $7,500. b. a credit to the allowance for $30,000. c. a debit to bad debt expense for $10,000. d. a debit to bad debt expense for $40,000.
Answer: a. a credit to the allowance for $7,500
Explanation:
Estimated Bad Debt = Balance on Account receivable x bad Debt loss rate = $250,000 x 4% = $10,000
Allowance for doubtful accounts with a credit balance of $2,500
Allowance for Bad debts expense =Estimated Bad Debt - Credit balance Allowance for doubtful accounts = $10,000 - $2,500 = $7,500
Account titles and explanation Debit Credit
Bad Debt Expense $7,500
Allowance for Doubtful Accounts $7,500
An individual taxpayer reports the following items for the current year: Ordinary income from Partnership A, operating a movie theater in which the taxpayer materially participates $70,000 Net loss from Partnership B, operating an equipment rental business in which the taxpayer does not materially participate (9,000) Rental income from building rented to a third party 7,000 Short-term capital gain from sale of stock 4,000 What is the taxpayer’s adjusted gross income for the year?
Answer:
$74,000
Explanation:
Calculation to determine the taxpayer’s adjusted gross income for the year
Taxpayer’s adjusted gross income=Net loss from Partnership B+Capital gain from sale of stock
Let plug in the formula
Taxpayer’s adjusted gross income=$70,000+ $4,000
Taxpayer’s adjusted gross income=$74,000
Therefore the taxpayer’s adjusted gross income for the year is $74,000
A company must repay the bank $10,000 cash in three years for a loan. The loan agreement specifies 8% interest compounded annually. The present value factor for three years at 8% is 0.7938. How much cash did the company receive from the bank on the day they borrowed this money?
A. $12,400.
B. $9,200.
C. $7,938.
D. $7,600.
E. $10,000.
Answer: C. $7,938
Explanation:
This is a straightforward question. From the question, we are informed that a company must repay the bank $10,000 cash in three years for a loan and that the loan agreement specifies 8% interest compounded annually and we are given the present value factor for three years at 8% is 0.7938.
Therefore, the amount of cash that the company receive from the bank on the day they borrowed this money will be:
= $10000 × Present value factor at 8%
= $10000 × 0.7938
= $7938
Welcome Inn Hotels is considering the construction of a new hotel for $90 million. The expected life of the hotel is 30 years, with no residual value. The hotel is expected to earn revenues of $26 million per year. Total expenses, including depreciation, are expected to be $15 million per year. Welcome Inn management has set a minimum acceptable rate of return of 14%.
a. Determine the equal annual net cash flows from operating the hotel.
b. Calculate the net present value of the new hotel. Use 7.003 for the present value of an annuity of $1 at 14% for 30 periods.
c. Does your analysis support construction of the new hotel?
Answer:
a. Annual Net cash flows:
= Revenue - Expenses + Depreciation
= 26,000,000 - 15,000,000 + (90,000,000 / 30 years)
= 11,000,000 + 3,000,000
= $14,000,000
b. Net present value:
= Present value of cashflows - Investment cost
= (Annual cashflow * present value of an annuity, 14%, 30 periods) - Investment cost
= (14,000,000 * 7.003) - 90,000,000
= $8,042,000
c. Company should construct the hotel as it would bring a positive Net Present Value
Note: In "b" the cashflow was treated as an annuity because it is constant.
The cost of equity is ________. the interest associated with debt the rate of return required by investors to incentivize them to invest in a company the weighted average cost of capital equal to the amount of asset turnover
Answer:
If an = 3n - 2 , find a2
Explanation:
If an = 3n - 2 , find a2If an = 3n - 2 , find a2
A project has an expected risky cash flow of $500 in year 3. The risk-free rate is 4%, the expected market rate of return is 14%, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 3, CEQ3. (Assume CAPM holds.)
The certainty equivalent cash flow for year 3, CEQ3 is $360.33
The computation of the certainty equivalent cash flow for year 3 is as follows:
But before that, the cost of equity should be determined via using the Capital Asset Pricing Model (CAPM).
Cost of equity = Risk-free rate + beta × (expected market rate of return - risk-free rate)
= 4% + 1.20 × (14% - 4%)
= 16%
Now the certainty equivalent cash flow for year 3 is
= $500 ÷ (1+ 0.16)^3
= $360.33
Therefore we can conclude that the certainty equivalent cash flow for year 3, CEQ3 is $360.33
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Calculate the total Social Security and Medicare tax burden on a sole proprietorship earning 2020 profit of $300,000, assuming a single sole proprietor with no other earned income.
Answer: $25,802.70
Explanation:
Social security
Social security rates in 2020 for a single sole proprietor is 12.40% on the first $137,700:
= 12.40% * 300,000
= $17,074.80
Medicare Tax
First you need to remove a deduction of 7.65% from the income:
= 300,000 * (1 - 7.65%)
= $277,050
Medicare tax is 2.90% of this adjusted amount in addition to 0.9% for any amount above $200,000:
= (2.90% * 277,050) + (0.9% * (277,050 - 200,000))
= 8,034.45 + 693.45
= $8,727.90
Total Social security and Medicare:
= 17,074.80 + 8,727.9
= $25,802.70
Match each example to the appropriate term.
a. Trees used to make paper
1. Human capital
2. Technological knowledge
3. Physical capital
b. A printing press used to make books.
1. Human capital
2. Technological knowledge
3. Physical capital
c. A method of organizing workers to increase production per hour.
1. Human capital
2. Technological knowledge
3. Physical capital
d. The skills workers learn during a training session.
1. Human capital
2. Technological knowledge
3. Physical capital
Answer:
a equals 3
b equals 3
c equals 1
d equals 2
Tangerine, Inc. provides the following data: Surround, Inc. Comparative Balance Sheet Dec. 31, 20X9 Assets Current Assets: Cash and Cash Equivalents $29,000 Account Receivable, Net 31,000 Merchandise Inventory 53,000 Total Current Assets $113,000 Property, Plant, and Equipment, Net 120,000 Total Assets $233,000 Liabilities Current Liabilities: Accounts Payable $4000 Notes Payable 3000 Total Current Liabilities $7000 Long-term Liabilities 84,000 Total Liabilities $91,000 Stockholders' Equity Common Stock $30,000 Retained Earnings 112,000 Total Stockholders' Equity $142,000 Total Liabilities and Stockholders' Equity $233,000 Calculate the debt to equity ratio.
Answer:
The debt to equity ratio is 0.64.
Explanation:
The debt to equity ratio can be calculated using the following formula:
Debt to equity ratio = Total Liabilities / Stockholders' Equity ……………………. (1)
Where:
Total Liabilities = $91,000
Stockholders' Equity = $142,000
Substitute the relevant data into equation (1), we have:
Debt to equity ratio = $91,000 / $142,000 = 0.64
Therefore, the debt to equity ratio is 0.64.
True or false: Interest expense and income tax expense are considered general and administrative expenses and, therefore, are included on the general and administrative expense budget. True false question. True False
Answer: True
Explanation:
Interest expense and income tax expenses generally are stand-alone expenses but they fall under general and administrative expenses required to run the business.
Interest expense is charged on debt that was taken to run the company so will be an admin expense and tax is part of the expenses that a company has to take care of in order to run the company so it is an admin expense as well.
ctivity-Based Costing (ABC) is useful in: Select one: A. Breakdown COGS into DL, DM, and FOH B. Breaking down FOH more accurately into cost drivers C. Breaking down FOH into one overhead rate D. Breaking down DL and DM by product
Answer:
B. Breaking down FOH more accurately into cost drivers
Explanation:
In the case of activity based costing, the activity of the fixed cost should be breakdown based on the number of activity pools while the fixed cost should be breakdown as per the cost drivers. Also, there is more than one overhead rate existed. In addition to this, it is the method for distribution of the overhead with those firms who is able to used it
Therefore the option b is correct
The following information relates to last year's operations at the Legumes Division of Gervani Corporation: Minimum required rate of return 12% Return on investment (ROI) 15% Sales $ 900,000 Turnover (on operating assets) 3 times What was the Legume Division's net operating income last year
Answer: $45000
Explanation:
Firstly, the operating asset will be calculated which will be:
Operating asset = Sales / Turnover
= 900,000/3
Operating assets = $300,000
Then, the net operating income will be: Return on investment × Operating assets
Net operating income = 300,000 × 15%
= 300,000*0.15
= $45,000
Therefore, Legume Division's net operating income last year is $45000
Roanoke Company produces chocolate bars. The primary materials used in producing chocolate bars are cocoa, sugar, and milk. The standard costs for a batch of chocolate (5,200 bars) are as follows:
Ingredient Quantity Price
Cocoa 400lbs. $1.25per lb.
Sugar 80lbs. $0.40per lb.
Milk 120gal. $2.50per gal.
Determine the standard direct materials cost per bar of chocolate. Round to two decimal places.
Answer:
$0.16
Explanation:
Particulars Quantity Price Amount
Cocoa 400 $1.25 $500
Sugar 80 $0.40 $32
Milk 120 $2.50 $300
Total $832
Standard direct materials cost per bar = Total amount / Number of bar
Standard direct materials cost per bar = $832 / 5,200 bars
Standard direct materials cost per bar = $0.16
Assume that a firm had shareholders' equity on the balance sheet at a book value of $1,500 at the end of 2010.During 2011 the firm earns net income of $1,900,pays dividends to shareholders of $200,and issues new stock to raise $500 of capital.The book value of shareholders equity at the end of 2011 is:_______.
A) $2,750
B) $250
C) $1,450
D) $3,700
Answer:
The book value of shareholders equity at the end of 2011 is:_______.
D) $3,700.
Explanation:
a) Data and Calculations:
Beginning shareholders equity book value = $1,500
Net income during 2011 = 1,900
Dividends paid to shareholders (200)
Issuance of new stock 500
Ending shareholders equity book value = $3,700
b) The book value of equity at the end of 2011 is equal to the book value at the beginning of 2011 plus net income generated during 2011, issuance of new stock, minus dividends paid to shareholders.
The seven main functions of marketing summarize what it takes to _____.
Explanation:
The seven functions of marketing are distribution, market research, setting prices, finance, product management, promotional channels and matching products to consumers
I guess this may help
Answer:
All of the above
Explanation:
just took it
Which of the following statements is true?
a. Overhead can be applied slowly as a job is worked on.
b. Overhead can be applied when the job is completed.
c. Overhead should be applied to any job not completed at year-end in order to properly value the work in process inventory.
Answer:
the answer should be
a. Overhead can be applied slowly as a job is worked on.
Answer:
A: overhead can be applied slowly as a job is worked on.
Explanation:
Im pretty sure i already learned that! so trust it!
hope it helps!
if its wrong report my answer!
Risk is a necessary ‘evil’ evil’, support this assessment and give advice risk
managers on how to resolve the effects.
For a high-risk investment, managers require a high reward.
Brown Co. issued $100 million of its 10% bonds on April 1, 2016, at 99 plus accrued interest. The bonds are dated January 1, 2016, and mature on December 31, 2035. Interest is payable semiannually on June 30 and December 31. What amount did Brown receive from the bond issuance?
a) $87.8 million
b) $99.0 million
c) $100.0 million
d) $101.5 million
Answer:
d) $101.5 million
Explanation:
The computation of the amount received from the bond issuance is given below:
Interest Rate: 10%
Time period: 3 months (from 01.01.2016 to 31.03.2016)
Par Value=$100 million
Accrued Interest be 2.53 million
So,
Amount receive from Bond Issuance is
= 99 + 2.53
= $101.5 million
The Chiemsee Knee Replacement Clinic (CKRC) is a sports clinic located at the northern edge of the German Alps. It specializes in knee replacements for skiers who come to CKRC from Germany, Austria, Switzerland, and Italy. The clinic currently has one operating room (OR). However, since the clinic has dramatically more demand than capacity, the management team contemplates investing in a second OR. A lean consulting firm, however, suggests that before going ahead with installing new capacity, the clinic should first look at how it uses its existing capacity. The data collected by the consulting firm reveal that:
The OR is available for 12 hours a day; the hospital has decided to not perform any procedures between 7pm and 7am. This time is equally divided across three surgeons.
The standard procedure time for the knee surgery done at the clinic is 1h.
The cleaning and housekeeping that needs to happen after each procedure takes 20 minutes. Almost all of this time could be saved if the cleaning crew were notified earlier on.
10 minutes are spent on patient preparation / anesthesia work before each procedure. (Note: this is not part of the 60-minute procedure time). Proposals have been evaluated to move these 10 minutes to outside the OR, and there exists no medical reason that would prohibit doing this.)
A surgeon only starts a case if all of the work associated with the case (preparation, procedure, and cleaning) can be completed in the 4h allotted to each surgeon. Surgeons never start BEFORE their allotted time.
Though the clinic aims to operate 7 days a week, holidays, vacation, and construction time lead to an average of one day a week that the OR cannot be used at all.
What is the OEE of the operating room? Assume a 12h window in which the OR could be used.
The OEE of the Operating Room is 34.8%.
Operating Room Overall Equipment EffectivenessTo calculate the OEE (Overall Equipment Effectiveness) of the OR, you need to consider three factors: availability, performance, and quality.
Availability: The OR is available for 12 hours a day, but there is a 1 hour window between 7pm and 7am when it is not used. Additionally, there is an average of one day a week when the OR cannot be used at all. Therefore, the availability is:(12 hours - 1 hour) / 12 hours * 7 days/week - 1 day/week = 0.92 or 92%
Performance: The standard procedure time for the knee surgery is 1 hour, and 10 minutes are spent on patient preparation and anesthesia work. The cleaning and housekeeping takes 20 minutes, and a surgeon only starts a case if all of the work can be completed in the 4 hours allotted to each surgeon. Therefore, the performance is:1 hour + 10 minutes + 20 minutes = 1 hour and 30 minutes / 4 hours = 0.375 or 37.5%
Quality: Quality is not mentioned in the data provided, so it is assumed to be 100%.To calculate OEE, you need to multiply availability, performance, and quality:
OEE = availability * performance * quality = 0.92 * 0.375 * 1 = 0.348 or 34.8%
So, the OEE of the OR is 34.8%.
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Janice has been invited to appear on a home improvement show for the remodel of her summerhouse in Maine. Janice asks Mary to wallpaper her house in anticipation of the home improvement, and requests expensive custom wallpaper and a very intricate design application, for which the wallpaper would cost $5000, plus labor. Mary, excited for a very large job for her solo business, orders the intricate wallpaper and blocks off her calendar for the amount of time it will take to complete the job. After the paper has been ordered, Mary asks some friends to be available to complete the job in time for the show. Janice is informed that she will not be on the show and notifies Mary that she will not need the wallpaper.
a. Does Mary have a case for re-imbursement?
b. Under what legal theory might she prevail and what are her damages, if any?
c. What ethical theories might be applicable?
Answer:
sorry I don't know.
Explanation:
Yes, Mary has a legal cause of reimbursement Under the legal theory of ethical violation.
What is ethical violation?A documented company's code of ethics, mission, vision, values, and culture are violated when something is spoken, published, or done that does so. Additionally, we are aware that moral transgressions laugh in the face of accepted social norms.
Most business professionals' ethical conduct is governed by codes of conduct. Business infractions including discrimination, safety issues, or poor working conditions are most frequently observed.
Additionally, fraud, theft, and conflicts of interest. Many of these cross the line into illegal territory that is dealt with outside the corporation and are not merely morally bad.
Customers may be charged for services they did not receive when there is improper or fraudulent billing. This occurs most frequently in professions where the person who pays the bill is different from the person who received the services.
Due to the frequency of this particular ethical breach, many insurance companies have started providing consumers with a list of services that may fall under this category, enticing them to report any irregularities.
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Slavery, as a business practice protected by state laws, provided unfair advantage against those employers not using slaves, and thus the economic incentives supported and sustained slavery within its sealed environment.
A. True
B. False
Wang Co. manufactures and sells a single product that sells for $540 per unit; variable costs are $324 per unit. Annual fixed costs are $836,000. Current sales volume is $4,290,000. Management targets an annual pre-tax income of $1,215,000. Compute the unit sales to earn the target pre-tax net income.
Answer: 9,495 units
Explanation:
First find the contribution margin:
= Sales price - Variable cost
= 540 - 324
= $216 per unit
The unit sales required can be calculated by the formula:
= (Annual pre-tax income target + Fixed cost) / Contribution margin
= (1,215,000 + 836,000) / 216
= 9,495.37 units
= 9,495 units
Dobles Corporation has provided the following data from its activity-based costing system:
Activity Cost Pool Total Cost Total Activity
Assembly $228,060 18,000 mahcine hours
Processing orders $34,068 1200 orders
Inspection $125560 1720 inspection hours
The company makes 420 units of product D28K a year, requiring a total of 460 machine-hours, 80 orders, and 10 inspection-hours per year. The product's direct materials cost is $48.96 per unit and its direct labor cost is $25.36 per unit.
According to the activity-based costing system, the unit product cost of product D28K is closest to:
a. $95.34 per unit
b. $93.60 per unit
c. $74.32 per unit
d. $89.93 per unit
Answer:
Hence the correct option is option (a) i.e. $95.34 per unit.
Explanation:
Cost of 420 units of D28K product = 460 machine hour cost + 80 order cost + 10 inspection hour cost + 420 direct materials cost + 420 direct labor cost.
18000 machine hours = 228060
so 460 machine hours = 228060 x 460 /18000 = 5828.2
1200 orders = 34068
80 orders = 80 x 34068 / 1200 = 2271.2
1720 inspection hours = 125560
10 inspection hours = 10 x 125560/1720 = 730
So cost of 420 units of D28 products = 5828.2 + 2271.2 + 730 + 420 x 48.96 + 420 x 25.36
=40043.8
So cost of 1 D28K product = 40043.8 / 420 = 95.34
On the Tokyo Stock Exchange, Honda Motor Company stock closed at ¥2,915 per share on Monday, June 6, 2016. Honda trades as an ADR on the NYSE. One underlying Honda share equals one ADR. On June 6, 2016, the ¥/$ exchange rate was ¥107.65/$1.00. (Round your answer to 2 decimal places.) At this exchange rate, what is the no-arbitrage U.S. dollar price of one ADR?
Answer:
$27.08
Explanation:
Calculation to determine the no-arbitrage U.S. dollar price of one ADR
Using this formula
No-arbitrage U.S. dollar price of one ADR=Stock closed per share /Exchange rate
Let plug in the formula
No-arbitrage U.S. dollar price of one ADR=¥2,915 / ¥107.65
No-arbitrage U.S. dollar price of one ADR=$27.078
No-arbitrage U.S. dollar price of one ADR=$27.08 (Approximately)
Therefore the no-arbitrage U.S. dollar price of one ADR is $27.08
A firm with earnings before interest and taxes of $500,000 needs $1 million of additional funds. If it issues debt, the bonds will mature after 20 years and pay interest of 8 percent. The firm could issue preferred stock with a dividend rate of 8 percent. The firm has 100,000 shares of common stock outstanding and is in the 30 percent income tax bracket. What are the (1) earnings per common share under the two alternatives, (2) the times-interest-earned if the firm uses debt financing, and (3) the times-dividend-earned if the firm uses preferred stock financing
Answer:
Calculation of Earning Per Share
Particulars Debt Alternative($) Preferred Stock($)
Amount Required 1,000,000 1,000,000
Earning before Interest and Tax 500,000 500,000
Less: Interest Cost(8%) 80,000 ----
Earning After Interest 420,000 500,000
Tax(30%) 126,000 150,000
Earning After Tax 294,000 350,000
Less: Dividend to Pref. Shares 80,000
Earning Avai. for C. Stockholders 294,000 270,000
Outstanding shares 100,000 100,000
Earning Per Common Share 2.94 2.70
2. Times Interest Earned Ratio = EBIT / Interest
Times Interest Earned Ratio = 500,000 / 80,000
Times Interest Earned Ratio = 6.25 Times
3. Times Dividend Earned Ratio = Net Income / Preferred Dividend
Times Dividend Earned Ratio = 350,000 / 80,000
Times Dividend Earned Ratio = 4.375 Times
On July 1, Sterns Co. acquired patent rights for $36,000. The patent has a useful life of 6 years and a legal life of 15 years.
Required:
Journalize the adjusting entry on December 31 to recognize the amortization. Refer to the Chart of Accounts for exact wording of account titles.
Answer:
Dr Amortization Expense $3,000
Cr Patents $3,000
Explanation:
Preparation of the journal adjusting entry on December 31 to recognize the amortization.
Dec. 31
Dr Amortization Expense $3,000
Cr Patents $3,000
(To record Amortization)
Amortization=(Patent rights/Useful life)*6/12
Amortization=($36,000/6)*6/12
Amortization=$3,000
(July 1 to Dec 31 =6months)
At the end of 2010 Jarrett Corp. developed the following forecasts of net income:
Year Forecasted Net Income
2011 $20,856
2012 $22,733
2013 $24,552
2014 $27,252
2015 $29,978
Management believes that after 2015 Jarrett will grow at a rate of 7% each year. Total common shareholders' equity was $112,768 on December 31, 2010. Jarrett has not established a dividend and does not plan to paying dividends during 2011 to 2015. Its cost of equity capital is 12%.
Required:
Compute the value of Jarrett Corp. on January 1, 2011, using the residual income valuation model.
Answer:
$83,057.11
Explanation:
The value of the company is the present value of its residual income where the residual income is the net income in each year minus the implicit cost of capital
residual income=net income-(cost of equity capital*beginning shareholders' equity)
2011:
residual income=$20,856-( $112,768*12%)
residual income=$7323.84
stockholders' equity at the end of 2011=$112,768+$20,856=$133,624
2012
residual income=$22733-( $133624 *12%)
residual income=$6,698.12
stockholders' equity at the end of 2012=$133,624+$22733=$156,357
2013:
residual income=$24552-(12%*$156357)
residual income=$5,789.16
stockholders' equity at the end of 2013=$156,357+$24552=$180,909
2014;
residual income= $27252-(12%*$180909)
residual income=$5,542.92
stockholders' equity at the end of 2014=$180,909+$27252=$208,161
2015:
residual income=$29,978-(12%*$208161)
residual income=$4,998.68
Terminal value of residual income=2015 residual income*(1+terminal growth rate)/(cost of equity-terminal growth rate)
Terminal value of residual income=$4,998.68*(1+7%)/(12%-7%)=$106,971.75
value of the company=$7323.84/(1+12%)^1+$6,698.12/(1+12%)^2+$5,789.16 /(1+12%)^3+$5,542.92/(1+12%)^4+$4,998.68/(1+12%)^5+$106,971.75/(1+12%)^5
value of the company=$83,057.11
Burlington Construction Company is considering selling excess machinery with a book value of $281,000 (original cost of $400,100 less accumulated depreciation of $119,100) for $277,400, less a 5% brokerage commission. Alternatively, the machinery can be leased for a total of $284,300 for five years, after which it is expected to have no residual value. During the period of the lease, Burlington Construction Company's costs of repairs, insurance, and property tax expenses are expected to be $25,000.
Required:
Prepare a differential analysis, dated January 3, 2012, to determine whether Sure-Bilt should lease (Alternative 1) or sell (Alternative 2) the machinery.
Answer:
hiiiiiiiiiiiiiii how r u
The rate at which revenue was generated (in millions of dollars per year) for a certain company for the years 2010 through 2016 can be approximated by f(t)=348e0.22t (10≤t≤16), where t=10 corresponds to the start of the year 2010. Find and interpret ∫1016f(t)dt.
The revenue of a company represents the income generated by the company within a time frame. The total revenue generated by the company from the start of 2010 to the start of 2016 is $39.16 billion
Given that:
[tex]f(t) = 348e^{0.22t}[/tex] [tex]10 \le t \le 16[/tex]
First, we calculate the integral
[tex]\int\limits^{16}_{10} {f(t)} \, dt[/tex]
This is calculated as:
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \int\limits^{16}_{10} {348e^{0.22t}} \, dt[/tex]
Remove the constant
[tex]\int\limits^{16}_{10} {f(t)} \, dt = 348\int\limits^{16}_{10} {e^{0.22t}} \, dt[/tex]
Now, integrate
[tex]\int\limits^{16}_{10} {f(t)} \, dt = 348 \times \frac{1}{0.22} (e^{0.22t})|\limits^{16}_{10}[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} (e^{0.22t})|\limits^{16}_{10}[/tex]
Expand
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} (e^{0.22\times 16} -e^{0.22\times 10} )[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} (e^{3.52} -e^{2.2} )[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} \times 24.759[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = 39164.2[/tex]
From the question
[tex]t = 10[/tex] represents the start of 2010.
This means that
[tex]t = 16[/tex] represents the start of 2016.
So, the interpretation is:
The total revenue from the start of 2010 to the start of 2016 is $39.16 billion
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