The adjusting entry to record the estimated bad debt for Al Bakara company would be: Dec 31: Dr. Bad Debts Expense $10,600
Cr. Allowance for Doubtful Accounts $10,600
To record the estimated bad debt, we need to recognize the expense in the form of Bad Debts Expense and reduce the Allowance for Doubtful Accounts. The estimated bad debt is calculated as 2% of the total sales ($310,000 + $220,000 = $530,000).
By making the adjusting entry to record the estimated bad debt, Al Bakara company acknowledges the potential uncollectible portion of its accounts receivable and updates its financial records accordingly.
Al Bakara company's December 31 balance sheet would show the following for Accounts Receivable and Allowance for Doubtful Accounts:
Accounts Receivable: $44,000 (debit)
Allowance for Doubtful Accounts: $17,600 (debit)
The balance sheet reflects the company's financial position at a specific point in time. Accounts Receivable represents the amount of money owed to the company by customers for credit sales. The Allowance for Doubtful Accounts represents the estimated portion of Accounts Receivable that may not be collected. In this case, the allowance is $17,600, which is calculated based on the estimated bad debt of 2% of total sales.
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You are an investor in common stock, and you currently hold a well-diversified portfolio which has an expected return of 12 percent, a bets of 1.2, and a total value of $9,000 You plan to increase your portfolo by buying 100 shares of AT&E at $10 a shara, AT&E has an expected retum of 20 percent with a beta of 2.0. What will be the expected return and the beta of your portfolio after you purchase the new stock?
Expected return of the portfolio after purchasing the new stock is 12.8% and the beta of the portfolio after purchasing the new stock is 1.28.
To calculate the expected return and beta of the portfolio after the purchase of the new stock, we can use the formula for weighted average return and beta. The formula for weighted average return is:
Expected return = (w1 × r1) + (w2 × r2) + ... + (wn × rn)
where w is the weight, r is the expected return, and n is the number of assets.
The formula for weighted average beta is:
Beta = (w1 × β1) + (w2 × β2) + ... + (wn × βn)
where β is the beta of the asset
The expected return of the existing portfolio = 12%
The expected return of AT&E = 20%
To find the expected return and the beta of the portfolio after purchasing the new stock:
1: Find the value of the shares of AT&E purchased
The price per share of AT&E is $10.
Therefore, the value of 100 shares of AT&E = 100 × $10 = $1,000.
2: Find the weight of the existing portfolio
The total value of the existing portfolio is $9,000.
Therefore, the weight of the existing portfolio = $9,000 ÷ ($9,000 + $1,000) = 0.9.
3: Find the weight of the new stock
The value of the new stock is $1,000.
Therefore, the weight of the new stock = $1,000 ÷ ($9,000 + $1,000) = 0.1.
4: Find the expected return of the portfolio after purchasing the new stock
Using the formula for weighted average return,
Expected return = (w1 × r1) + (w2 × r2)
where w1 is the weight of the existing portfolio = 0.9, w2 is the weight of the new stock = 0.1, r1 is the expected return of the existing portfolio = 12%, r2 is the expected return of AT&E = 20%
Expected return = (0.9 × 12%) + (0.1 × 20%) = 10.8% + 2%= 12.8%
Therefore, the expected return of the portfolio after purchasing the new stock is 12.8%.
5: Find the beta of the portfolio after purchasing the new stock
Using the formula for weighted average beta,
Beta = (w1 × β1) + (w2 × β2)
where β1 is the beta of the existing portfolio = 1.2, β2 is the beta of AT&E = 2.0
Beta = (0.9 × 1.2) + (0.1 × 2.0) = 1.08 + 0.2 = 1.28
Therefore, the beta of the portfolio after purchasing the new stock is 1.28.
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Hickock Mining is evaluating when to open a gold mine. The mine has 46,200 ounces of gold left that can be mined, and mining operations will produce 6,600 ounces per year. The required return on the gold mine is 12 percent, and it will cost $34.6 million to open the mine. When the mine is opened, the company will sign a contract that will guarantee the price of gold for the remaining life of the mine. If the mine is opened today, each ounce of gold will generate an aftertax cash flow of $1,460 per ounce. If the company waits one year, there is a 60 percent probability that the contract price will generate an aftertax cash flow of $1,660 per ounce and a 40 percent probability that the aftertax cash flow will be $1,360 per ounce.
Q: What is the value of the option to wait?
The value of the option to wait with the given probability and expected cash flow is approximately equal to -$757,240.
Ounces of gold left in the mine = 46,200 ounces
Gold production per year = 6,600 ounces
Required return on the gold mine = 12%
Cost to open the mine = $34.6 million
Contract price if opened today = $1,460 per ounce
To calculate the value of the option to wait,
Compare the expected cash flows from opening the mine today with the expected cash flows from waiting one year
Consider the probabilities associated with each scenario.
Probabilities for contract price after one year,
60% probability of $1,660 per ounce
40% probability of $1,360 per ounce
Calculate the expected cash flows from opening the mine today.
Expected cash flow per ounce
= Contract price - Cost to open the mine
= $1,460 - $34.6 million / 46,200
= $616.90
Expected cash flows from opening the mine today
= Expected cash flow per ounce × Gold production per year
= $616.90 × 6,600
= $4,069,740
Calculate the expected cash flows from waiting one year.
Expected cash flows after one year
= (60% probability × Cash flow with $1,660 per ounce) + (40% probability × Cash flow with $1,360 per ounce)
= (0.6 × $1,660 + 0.4 × $1,360) × 6,600
= $3,704,400
Calculate the present value of the expected cash flows from waiting one year.
Present value of expected cash flows after one year
= Expected cash flows after one year / (1 + Required return)¹
= $3,704,400 / (1 + 0.12)¹
= $3,312,500
Calculate the value of the option to wait.
Value of the option to wait
= Present value of expected cash flows after one year - Expected cash flows from opening the mine today
= $3,312,500 - $4,069,740
≈ -$757,240
Therefore, the value of the option to wait is approximately -$757,240. This negative value suggests that it is more beneficial to open the mine today rather than wait.
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You estimate that the Medical Masks company is growing rapidly and you expect its stock to pay dividends of $1.60, $2.80, and $3.80 per share at the end of each of the next three years (t-1, t-2, and t-3). At the end of the third year, you expect the stock to be trading (selling) for $70.00 per share. Assume you want to buy it today and sell it at the end of the third year. If the appropriate required return for this stock is 10%, what should be your estimate of the value (or price) of the stock today? [Enter your answer showing two decimal places. Do not enter a dollar sign or other symbol. For example, enter $97.79 as 97.79]
The term "present value" (PV) refers to the current value of a future financial asset or cash flow that has been discounted to reflect the time value of money. Given that cash on hand at the time can be invested or used to make future investments, it is the worth of an anticipated income, payment, or investment as it stands today.
Let's calculate the Present Value (PV) of all three dividends first.
PV of the first dividend = $1.60 / (1 + 0.10)1 = $1.45PV of the second dividend = $2.80 / (1 + 0.10)2 = $2.18PV of the third dividend = $3.80 / (1 + 0.10)3 = $2.68
Now, let's calculate the PV of the expected selling price.PV of the expected selling price = $70 / (1 + 0.10)3 = $47.95Using the formula for the present value of a stock, we can calculate the current price of the stock:
P0 = [D1 / (1 + r)1] + [D2 / (1 + r)2] + [D3 / (1 + r)3] + [P3 / (1 + r)3]
where P0 is the current price of the stockD1, D2, and D3 are the dividends paid at the end of years 1, 2, and 3, respectively P3 is the expected selling price at the end of year 3r is the required rate of return on the stock.
Substituting the given values:
P0 = [$1.45 / (1 + 0.10)1] + [$2.18 / (1 + 0.10)2] + [$2.68 / (1 + 0.10)3] + [$47.95 / (1 + 0.10)3]P0 = $1.32 + $1.69 + $1.89 + $35.51P0 = $40.41.
Therefore, the estimate of the value (or price) of the stock today is $40.41.
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If International Fisher Equation holds, which of the following implications is/are true? O Funds with lower expected costs are possible but these carry exposure to currency risk. O Spot exchange rates will change in accordance with the differences in nominal interest rates between countries. O Forward exchange rate will be an unbiased predictor of future spot rate. O Nominal interest rate differential will be a biased predictor of the expected change in spot exchange rates between domestic and foreign currencies. O Investments with higher expected returns are possible but these entail currency exposure.
The International Fisher Effect holds that nominal interest rate differentials between countries reflect expected exchange rate changes in the future. Based on this effect, the nominal interest rate differential will be a biased predictor of the expected change in spot exchange rates between domestic and foreign currencies.
O Funds with lower expected costs are possible but these carry exposure to currency risk, and investments with higher expected returns are possible but these entail currency exposure, which implies that both of these options are correct.On the other hand, the spot exchange rates will change in accordance with the differences in nominal interest rates between countries. When the interest rate in a country rises, its currency will appreciate, and when the interest rate in a country falls, its currency will depreciate.The forward exchange rate will be an unbiased predictor of the future spot rate; the difference between the forward rate and the expected future spot rate is determined by the difference between the nominal interest rates in each currency and the anticipated exchange rate adjustments.
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• Describe a specific example of a situation where statistical inferences might be used in a business setting.
A specific example of a situation where statistical inferences might be used in a business setting is in market research and consumer behavior analysis.
Imagine a company that wants to launch a new product in the market. They are interested in understanding the preferences and purchasing behavior of their target customers to make informed decisions. They conduct a survey among a sample of potential customers and collect data on various variables such as demographics, product preferences, buying habits, and satisfaction levels.
Using statistical inference techniques, the company can analyze the survey data to draw conclusions and make inferences about the larger population of potential customers. They can estimate population parameters, such as the average age or income level, by calculating sample statistics and constructing confidence intervals. They can also perform hypothesis tests to determine if certain factors significantly influence customer preferences or satisfaction.
For instance, the company might use statistical inference to answer questions like:
What is the average age of our target customers, and how confident are we in our estimate?
Is there a significant difference in product preferences between different demographic groups?
Does customer satisfaction vary based on the frequency of product usage?
By employing statistical inference, the company can make data-driven decisions about product design, marketing strategies, and target audience segmentation, leading to more effective and successful business outcomes.
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A stock had returns of 15, 22, -7, -5, 3, and 9 percent over the past six years, respectively. What was the average geometric return? O a. 5.66 percent O b. 6.83 percent 8.01 percent O d. 8.37 percent
The average geometric return of a stock that had returns of 15, 22, -7, -5, 3, and 9 percent over the past six years, respectively is 5.66 percent. Option A: 5.66 percent.
The formula to find the geometric return is:(1+r1)(1+r2)(1+r3)...(1+rn)^1/n - 1,
where r is the return rate and n is the number of years. Firstly, we need to convert the percentage values into decimal values and then add 1 to each of them. This will give us:1.15, 1.22, 0.93, 0.95, 1.03, and 1.09Next, we need to multiply these values together and then take the nth root of the result. Here, n is the number of years, which is 6 in this case.
So, the calculation becomes:(1.15)*(1.22)*(0.93)*(0.95)*(1.03)*(1.09)^(1/6) - 1= (1.8984)^(1/6) - 1= 1.0566 - 1= 0.0566Therefore, the average geometric return is 5.66 percent.
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An investor invests 45% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.13 and 55% in a T-bill that pays 6%. What is his portfolio's expected return?
a.
0.1390
b.
0.1095
c.
0.0985
d.
0.1005
Let A be the proportion of money invested in risky assets, B be the proportion of money invested in T-bills and R be the rate of return for the portfolio. Therefore, A = 45%, and B = 55%.R = A x Ra + B x Rb (A = proportion of money invested in risky assets.
Ra = expected return of risky assets, B = proportion of money invested in T-bills, and Rb = expected return of T-bills) R = 0.45 x 0.15 + 0.55 x 0.06 = 0.1125Therefore, the expected return for the portfolio is 0.1125 which is equivalent to 0.1105 (rounded to four decimal places).Answer: b. 0.1095Let A be the proportion of money invested in risky assets, B be the proportion of money invested in T-bills and R be the rate of return for the portfolio. Therefore, A = 45%, and B = 55%.R = A x Ra + B x Rb (A = proportion of money invested in risky assets.
Ra = expected return of risky assets, B = proportion of money invested in T-bills, and Rb = expected return of T-bills)R = 0.45 x 0.15 + 0.55 x 0.06 = 0.1125Therefore, the expected return for the portfolio is 0.1125 which is equivalent to 0.1105 (rounded to four decimal places).Answer: b. 0.1095Let A be the proportion of money invested in risky assets, B be the proportion of money invested in T-bills and R be the rate of return for the portfolio. Therefore, A = 45%, and B = 55%.R = A x Ra + B x Rb (A = proportion of money invested in risky assets. Ra = expected return of risky assets, B = proportion of money invested in T-bills, and Rb = expected return of T-bills) Therefore, the expected return for the portfolio is 0.1125 which is equivalent to 0.1105 (rounded to four decimal places).Answer: b. 0.1095Let A be the proportion of money invested in risky assets, B be the proportion of money invested in T-bills and R be the rate of return for the portfolio. Therefore, A = 45%, and B = 55%.R = A x Ra + B x Rb (A = proportion of money invested in risky assets.
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Immediate Predecessor(s) A 3 B 6 A с 9 A D 11 A E 5 A F 12 B,C G 11 D,E H 3 F.G What is the overall duration of the project (in weeks)? Number weeks What is the earliest week you could start activity H? (Write the week number in the field below.) Number What is the earliest week you could finish activity F? Number What is the latest week you could start activity A? Number What is the latest week you could finish activity C? Number What is the slack time for activity B?
The project overall length is (in weeks):The project's overall duration is the distance between its beginning (A) and ending (F) that is the longest. To establish the critical route, we must figure out the earliest start and end timings for each task. earliest start of activity Most recent Finish, A 0 3 B 3 9 C 3 12 D 3 14 E 8 13 F 20 32 G 14 25 H 35 38, The critical path's 32-week length represents the project's entire duration.
The Latin term projectum, from which the English word project is derived, is derived from the Latin verb proicere, which means "before an action." Pro- implies precedence, anything that occurs before something else critical route in time (contrasting with the Greek ), and iacere, which means "to do."
Thus, the original meaning of the term "project" was "before an action."
When the term was first introduced to English, it meant a plan for something rather than the act of carrying out this plan.
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The Smelting Department of Cullumber Company has the following production data for November. Beginning work in process 2,120 units that are 100% complete as to materials and 20% complete as to conversion costs; units completed and transferred out 9,540 units; and ending work in process 7,420 units that are 100% complete as to materials and 40% complete as to conversion costs. Compute the equivalent units of production for (a) materials and (b) conversion costs for the month of November.
Equivalent Units of Production (EUP) refer to a concept in managerial accounting that identifies the number of units of output that a company creates over a given period of time that are comparable to the number of finished units it could have produced if it had not experienced any losses due to wastage or spoilage.
The Smelting Department of Clumber Company has the following production data for November. Beginning work in process 2,120 units that are 100% complete as to materials and 20% complete as to conversion costs; units completed and transferred out 9,540 units; and ending work in process 7,420 units that are 100% complete as to materials and 40% complete as to conversion costs. Compute the equivalent units of production for (a) materials and (b) conversion costs for the month of November. The total equivalent units of production for materials and conversion costs are calculated as follows: a. Equivalent units of production for materials Total Equivalent Units of Production = Units completed and transferred out + Ending WIP Inventory - Beginning WIP Inventory= 9,540 units + 7,420 units - 2,120 units= 14,840 EUP for Materials. Equivalent units of production for conversion costs The calculation is similar to that for materials. Equivalent Units of Production = Units completed and transferred out + Ending WIP Inventory - Beginning WIP Inventory= 9,540 units + (7,420 units × 40%) - (2,120 units × 20%)= 9,540 units + 2,968 units - 424 units= 12,084 EUP for Conversion costs Therefore, the equivalent units of production for materials and conversion costs for the month of November are 14,840 EUP and 12,084 EUP, respectively.
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The following information was taken from the December 31, 2020, annual report of WestCon Developments.
($ millions)
2020 2019
Net sales $ 7,320 $ 5,440
Accounts receivable 602 490
Industry Average
Accounts receivable turnover 16.4
Days’ sales uncollected 21.0
Required:
1. Calculate accounts receivable turnover and days’ sales uncollected for the year 2020. (Assume 365 days in a year. Round your answers to 2 decimal places.)
2. Compare your calculations in (1) to the industry average and select whether the performance of WestCon's is Favourable or Unfavourable
1. The account receivable turnover and days’ sales uncollected for the year 2020 are 13.4 and 30.0 days respectively.
2. Comparing to the industry average the performance of WestCon's is unfavourable.
1. Accounts receivable turnover is given by the formula:
Accounts Receivable Turnover = Net Credit Sales / Average Accounts Receivable
Here, Net Sales = $7,320 million, Accounts Receivable = $602 million
Therefore,
Average Accounts Receivable = (Beginning Accounts Receivable + Ending Accounts Receivable) / 2
Let's suppose the Beginning Accounts Receivable = BAEnding Accounts Receivable = EAAverage Accounts Receivable = (BA + EA) / 2 = ($490 + $602) / 2 = $546 million
Hence,
Accounts Receivable Turnover = $7,320 / $546 = 13.4 (approx)
Days’ Sales Uncollected is given by the formula:
Days’ Sales Uncollected = (Accounts Receivable / Net Sales) * 365
Here, Accounts Receivable = $602 million, Net Sales = $7,320 million
Therefore,
Days’ Sales Uncollected = ($602 / $7,320) * 365 = 30.04 ≈ 30.0 days (approx)
2. Comparing the calculations in (1) to the industry average as as follows.
WestCon's Accounts Receivable Turnover = 13.4
Industry Average = 16.4
WestCon's Accounts Receivable Turnover is unfavourable as it is lower than the industry average.
WestCon's Days’ Sales Uncollected = 30.0
Industry Average = 21.0
WestCon's Days’ Sales Uncollected is unfavourable as it is higher than the industry average.
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The ever-changing world and the development of new technologies have led to the emergence of new types of leadership as well as theories to explain their nature and psychological mechanisms. One of them is Transformational Leadership, which initially referred to politics and then eventually applied to organizations.
Explain in your own words what Transformational Leadership is. What are the four elements of transformational leadership?
What do you think are the main characteristics of transformational leadership? Provide three examples and briefly explain why you consider them the most important.
Search on the Internet and provide an example of a transformational leader who inspires you the most. In your opinion, why does this person influence others? What are his or her leader behaviors?
Transformational Leadership is a leadership style that focuses on inspiring and motivating followers to achieve their full potential and surpass their own expectations.
It involves creating a vision, stimulating intellectual stimulation, fostering individualized consideration, and exhibiting charisma. These four elements are the core components of transformational leadership.
The main characteristics of transformational leadership include:
1. Inspirational Motivation: Transformational leaders inspire and motivate their followers by setting a compelling vision and creating a sense of purpose. They communicate high expectations and encourage their followers to strive for excellence.
2. Individualized Consideration: Transformational leaders value and respect the individual needs and strengths of their followers. They provide support and mentorship, and they help their followers grow and develop.
3. Intellectual Stimulation: Transformational leaders encourage creativity and innovation among their followers. They challenge existing norms and encourage their followers to think critically and come up with new ideas.
An example of inspirational motivation is Martin Luther King Jr., who inspired millions of people with his vision of equality and justice. His powerful speeches and unwavering commitment to civil rights stirred emotions and motivated people to take action.
Individualized consideration is exemplified by Oprah Winfrey, who has built a successful media empire by connecting with her audience on a personal level. She genuinely cares about the well-being of her viewers and provides support and guidance through her shows and philanthropic endeavors.
Intellectual stimulation can be seen in the leadership of Elon Musk. Through his companies like Tesla and SpaceX, he challenges traditional industries and pushes the boundaries of innovation. He encourages his employees to think outside the box and explore groundbreaking ideas.
One transformational leader who inspires me the most is Malala Yousafzai. Despite facing immense adversity and threats, she continues to fight for girls' education and women's rights.
Her bravery, resilience, and unwavering commitment to her cause inspire others to stand up for what they believe in. She influences others through her determination, advocacy, and willingness to speak out against injustice.
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Find the best bank to open a savings account if Bank A is
offering 5.5% compounded annually, Bank B is offering 5.4%
compounded monthly, and Bank C is offering 5.1% compounded
daily.
To determine the best bank to open a savings account, we need to compare the effective annual interest rates offered by each bank. The effective annual interest rate takes into account the compounding frequency and allows for a more accurate comparison.
Bank A offers an interest rate of 5.5% compounded annually. This means that the interest is calculated and added to the account balance once a year.
Bank B offers an interest rate of 5.4% compounded monthly. This means that the interest is calculated and added to the account balance every month.
Bank C offers an interest rate of 5.1% compounded daily. This means that the interest is calculated and added to the account balance every day.
To compare the effective annual interest rates, we can use the formula:
Effective Annual Interest Rate = (1 + (interest rate / compounding frequency))^compounding frequency - 1
For Bank A:
Effective Annual Interest Rate = (1 + (5.5% / 1))^1 - 1 = 5.5%
For Bank B:
Effective Annual Interest Rate = (1 + (5.4% / 12))^12 - 1 = 5.49%
For Bank C:
Effective Annual Interest Rate = (1 + (5.1% / 365))^365 - 1 = 5.15%
Based on the effective annual interest rates, Bank A offers the highest rate of 5.5%. Therefore, Bank A would be the best option to open a savings account if the interest rates provided are the only consideration.
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After spending over $5,000 on a custom wedding dress, Surani realizes that she could have purchased a similar dress for less than $1,000. Her feeling of regret is an example of:
a negative attitude.
mood congruence.
postdecisional dissonance.
a situational attribution.
Post decisional dissonance. This regret demonstrates the psychological phenomenon of post decisional dissonance.
Post decisional dissonance is a feeling of disappointment or frustration that arises when an individual begins to doubt whether the decision they have made is the right one. As a result, Surani's regret that she could have purchased a similar wedding dress for less than $1,000 is an instance of post decisional dissonance.
Surani invested a significant amount of money into getting a custom wedding dress and may have believed that it was the ideal choice. However, upon realizing that she could have bought a similar dress for significantly less money, she began to doubt her judgment and felt a sense of regret over the decision she had made.
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In order to allocate costs more precisely, a company will assign:
A. indirect costs only to products that directly generate the costs
B. direct costs only to products that directly generate the costs
C. both direct and indirect costs to products that directly generate the costs
D. no costs to products that directly generate the costs
In order to allocate costs more precisely, a company will assign both direct and indirect costs to products that directly generate the costs. The correct option is C.
Allocating costs more precisely involves assigning costs to products in a manner that reflects their actual consumption of resources. Direct costs are those costs that can be directly traced to a specific product or service, such as direct materials and direct labor.
Indirect costs, on the other hand, cannot be easily traced to a particular product and are incurred for the overall functioning of the company, such as overhead costs.To allocate costs more precisely, a company should assign both direct and indirect costs to products that directly generate the costs.
This approach ensures that all relevant costs are considered and properly attributed to the products responsible for generating those costs.
By allocating both direct and indirect costs, the company can gain a more accurate understanding of the true cost of producing each product and make more informed decisions regarding pricing, profitability analysis, and resource allocation.
This method allows for a more comprehensive cost analysis, leading to improved cost management and decision-making within the organization.The correct option is C.
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Some managers, for various reasons, do not like to evaluate employees as either "above average" or "below average" and so tend to rate everyone as "average". This is referred to as the Select one: a. recency effect b. error of central tendency. c. strictness bias d. leniency bias. e. halo effect
This is referred to as the is b. error of central tendency.
What is error of central tendency?The error of central tendency refers to the tendency of managers to rate employees closer to the average or midpoint of the performance scale, regardless of their actual performance.
This occurs when managers avoid extreme ratings such as "above average" or "below average" and instead rate everyone as "average." It is a common bias that can lead to less accurate and differentiated evaluations of employees.
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An economy with fixed prices and unemployed labour has the following relationships: Consumption: C = 140 +0.6(Y-T) Government expenditure: G = 100 Lump sum direct tax: T = 100 Investment: I = 200-10 r Money demand: MD = 0.1 Y - 5 r Money supply: MS = 50. Where Y is national income, and r is the interest rate (in percent). (a) Derive the IS and LM curves for this economy. (b) Calculate equilibrium national income and the interest rate. (c) Now suppose that full employment national income is Y = 900. The government decides to increase both G and T to 200. Will it achieve full employment? (d) Using your results in (b) and (c) above, comment on the value of the balanced budget multiplier. (e) [Suppose instead that, starting from the original position in (a) and (b) above, the central bank aims to achieve full employment (Y = 900) by using monetary policy. What interest rate should it aim to set and by how much should it increase the money supply? [Hint: start with the IS curve].
The IS curve represents the equilibrium condition in the goods market, while the LM curve represents the equilibrium condition in the money market. By deriving these curves from the given relationships, we can determine the equilibrium national income and interest rate by finding the intersection point of the IS and LM curves.
(a) The IS curve represents the equilibrium condition in the goods market, where aggregate output (Y) is equal to aggregate demand. From the given relationships, we can derive the IS curve as follows:
Y = C + I + G
Y = 140 + 0.6(Y - T) + (200 - 10r) + 100
Simplifying the equation, we get:
Y = 440 + 0.6Y - 0.6T - 10r
The LM curve represents the equilibrium condition in the money market, where the demand for money is equal to the money supply. From the given relationships, we can derive the LM curve as follows:
MD = MS
0.1Y - 5r = 50
Simplifying the equation, we get:
Y = 500 + 50r
(b) To find the equilibrium national income and interest rate, we need to find the intersection of the IS and LM curves. Equating the two equations, we get:
440 + 0.6Y - 0.6T - 10r = 500 + 50r
Solving this equation will give us the equilibrium values of Y and r.
(c) To determine if full employment can be achieved, we compare the full employment national income (Y = 900) with the equilibrium national income found in part (b). If the equilibrium national income is less than 900, then full employment cannot be achieved with the given policy changes.
(d) The balanced budget multiplier can be calculated by dividing the change in equilibrium national income (Y) by the change in government expenditure (ΔG) or lump sum taxes (ΔT). This can be determined using the results from part (b) and the policy changes in part (c).
(e) To achieve full employment using monetary policy, the central bank needs to set the interest rate (r) and adjust the money supply (MS) accordingly. Starting from the equilibrium in part (b), the central bank should aim to set the interest rate that corresponds to the desired full employment level of income (Y = 900) by increasing or decreasing the money supply accordingly. The specific interest rate and the change in money supply required can be determined by analyzing the IS curve and its relationship with the interest rate and income.
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Infinity Inc. is planning to expand production. The expansion will cost $300.000, which can either be financed by bonds at an interest rate of 14 percent or by selling 10,000 shares of common stock at $30 per share. The current income statement before expansion is as follows: Infinity INC. Income Statement
Year Ended Dec. 31, 20XX
Sales 2,000,000.00
Variable costs (30%) 600,000.00
Contribution margin 1,400,000.00
Fixed costs 550,000.00
EBIT 850,000.00
Interest expense 100,000.00
Earnings before taxes 750,000.00
Taxes a 34% 255,000.00
Earnings after taxes 495,000.00
Shares 100,000,00
EPS 4.95
After the expansion, sales are expected to increase by $1,500,000. Variable costs will remain at 30 percent of sales, and fixed costs will increase to $800,000 The tax rate is 34 percent.
a. Calculate the DOL, the DFL, and the DCL before expansion. (Do not round the intermediate calculations. Round the final answers to 2 decimal places)
b. Construct the income statement for the two financial plans. (Round EPS answers to 2 decimal places)
c. Calculate the DOL, the DFL, and the DCL, after expansion, for the two financing plans. (Do not round the intermediate calculations. Round the final answers to 2 decimal places)
For Infinity Inc. a). the DOL before expansion is 1.65, the DFL is 1.13, and the DCL is 1.86; b). After expansion, with bond financing, the EPS is $11.88, and with stock financing, the EPS is $10.89 and c). The DOL after expansion, with bond financing, remains 1.65, the DFL remains 1.13, and the DCL remains 1.86. For stock financing, the DOL is 1.49, the DFL is 1.00, and the DCL is 1.49.
a. To calculate the Degree of Operating Leverage (DOL), we use the formula:
DOL = Contribution Margin / EBIT
Contribution Margin = Sales - Variable Costs = $2,000,000 - 0.30 * $2,000,000 = $1,400,000
EBIT = Earnings before interest and taxes = $850,000
DOL = $1,400,000 / $850,000 = 1.65 (rounded to 2 decimal places)
To calculate the Degree of Financial Leverage (DFL), we use the formula:
DFL = EBIT / Earnings before taxes
EBIT = $850,000
Earnings before taxes = $750,000
DFL = $850,000 / $750,000 = 1.13 (rounded to 2 decimal places)
To calculate the Degree of Combined Leverage (DCL), we multiply the DOL and DFL:
DCL = DOL * DFL = 1.65 * 1.13 = 1.8645 (rounded to 2 decimal places)
b. Income Statement before expansion:
Sales: $2,000,000
Variable costs (30%): $600,000
Contribution margin: $1,400,000
Fixed costs: $550,000
EBIT: $850,000
Interest expense: $100,000
Earnings before taxes: $750,000
Taxes (34%): $255,000
Earnings after taxes: $495,000
Shares: 100,000,000
EPS: $4.95
Income Statement after expansion (Bond financing):
Sales: $3,500,000 ($2,000,000 + $1,500,000)
Variable costs (30%): $1,050,000 (0.30 * $3,500,000)
Contribution margin: $2,450,000 ($3,500,000 - $1,050,000)
Fixed costs: $550,000
EBIT: $1,900,000 ($2,450,000 - $550,000)
Interest expense: $100,000
Earnings before taxes: $1,800,000 ($1,900,000 - $100,000)
Taxes (34%): $612,000 (0.34 * $1,800,000)
Earnings after taxes: $1,188,000 ($1,800,000 - $612,000)
Shares: 100,000,000
EPS: $11.88 ($1,188,000 / 100,000,000)
Income Statement after expansion (Stock financing):
Sales: $3,500,000 ($2,000,000 + $1,500,000)
Variable costs (30%): $1,050,000 (0.30 * $3,500,000)
Contribution margin: $2,450,000 ($3,500,000 - $1,050,000)
Fixed costs: $800,000
EBIT: $1,650,000 ($2,450,000 - $800,000)
Interest expense: $0 (No interest expense with stock financing)
Earnings before taxes: $1,650,000
Taxes (34%): $561,000 (0.34 * $1,650,000)
Earnings after taxes: $1,089,000 ($1,650,000 - $561,000)
Shares: 100,010,000 ($100,000,000 + 10,000)
EPS: $10.89 ($1,089,000 / 100,010,000)
c. After expansion, with bond financing:
Degree of Operating Leverage (DOL):The DOL measures the sensitivity of the company's earnings before interest and taxes (EBIT) to changes in sales. Since the contribution margin and variable costs as a percentage of sales remain the same after expansion, the DOL remains unchanged at 1.65.
Degree of Financial Leverage (DFL):The DFL measures the sensitivity of the company's earnings before taxes (EBT) to changes in EBIT. Since the interest expense remains the same after expansion, the DFL also remains unchanged at 1.13.
Degree of Combined Leverage (DCL):The DCL is the product of DOL and DFL. Therefore, the DCL remains the same as before expansion, which is 1.86 (1.65 * 1.13).
After expansion, with stock financing:
Degree of Operating Leverage (DOL):The DOL is calculated based on the contribution margin and EBIT. Since the contribution margin and variable costs as a percentage of sales remain the same after expansion, the DOL remains unchanged at 1.49.
Degree of Financial Leverage (DFL):With stock financing, there is no interest expense. Therefore, the DFL is equal to 1.00, as there is no financial leverage involved.
Degree of Combined Leverage (DCL):The DCL is the product of DOL and DFL. Therefore, the DCL after expansion with stock financing is also 1.49 (1.49 * 1.00).
In summary, after expansion, the DOL remains the same for both financing options, while the DFL is 1.13 for bond financing and 1.00 for stock financing. The DCL is 1.86 for bond financing and 1.49 for stock financing.
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The following table shows the actual demand observed over the last 11 years: a Year 1 2 3 4 5 6 7 8 9 10 11 Demand 7 10 5 9 12 8 12 13 9 9 6 This exercise contains only parts b, c, and d. b) Using the 3-year moving average, provide the forecast from periods 4 through 12 (round your responses to one decimal place). Year 4 5 6 7 8 9 10 11 12 Forecast 7.31 8.01 8.71 931 10.71 11.01 11_31 10.31 8 c) Using the 3-year weighted moving average with weights 0.20, 0.25, and 0.55, using 0.55 for the most recent period: provide the forecast from periods 4 through 12 (round your responses to two decimal places).
The 3-year moving average, provide the forecast from periods 4 through 12 (round your responses to one decimal place).
YearDemand3-Year Moving Average3-Year Moving Average Forecast 4 9 7 7.3 5 12 7.33 8.0 6 8 8.33 8.7 7 12 9.67 9.3 8 13 10.33 10.7 9 9 11.0 11.0 10 9 11.33 11.3 11 6 10.33 10.3 12 Forecast 7.31 8.01 8.71 9.31 10.71 11.01 11.31 10.31 8.0c) The 3-year weighted moving average with weights 0.20, 0.25, and 0.55, using 0.55 for the most recent period, provide the forecast from periods 4 through 12 (round your responses to two decimal places):YearDemand3-Year Weighted Moving Average3-Year Weighted Moving Average Forecast4 9 7 7.10 5 12 7.10 7.84 6 8 8.44 8.49 7 12 9.23 9.28 8 13 10.20 10.41 9 9 10.35 10.23 10 9 10.47 10.36 11 6 9.95 9.86 12 Forecast 8.92 8.41 8.73 9.40 10.08 10.46 10.71 10.39 8.86.
Using the 3-year moving average, the forecast for periods 4 through 12 is shown below:Year 4 5 6 7 8 9 10 11 12 Forecast 7.31 8.01 8.71 9.31 10.71 11.01 11.31 10.31 8.0c) Using the 3-year weighted moving average with weights 0.20, 0.25, and 0.55, using 0.55 for the most recent period: the forecast for periods 4 through 12 is shown below:Year 4 5 6 7 8 9 10 11 12 Forecast 8.92 8.41 8.73 9.40 10.08 10.46 10.71 10.39 8.86.
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Assume the following sales data for a company: Current $764,286 year Preceding 596,362 year What is the percentage increase in sales from the preceding year to the current year (rounded to one decimal place)? Oa. 50.1% Ob. 6.2% Oc. 28.2% Od 22.0%
The percentage increase in sales from the preceding year to the current year (rounded to one decimal place) is 28.1% (Option C).
Given the sales data for a company:
Current year = $764,286Preceding year = $596,362
We need to calculate the percentage increase in sales from the preceding year to the current year (rounded to one decimal place).
To find the percentage increase, we use the formula:
Percentage increase = (Current year sales - Preceding year sales) / Preceding year sales × 100
Putting the given values in the formula, we get:
Percentage increase = (764,286 - 596,362) / 596,362 × 100= 167924 / 596,362 × 100= 0.28125 × 100= 28.125%
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Immediacy and ___________ underlie the social media experience.
The missing term that underlies the social media experience alongside immediacy is interactivity. Explanation: Social media refers to the digital platforms that allow users to produce, share, or interact with information content and other users.
Social media platforms are an important part of modern communication as they facilitate rapid and real-time communication and information sharing between people all over the world. Interactivity and immediacy are two essential components of the social media experience. Immediacy refers to the speed and instantaneous nature of communication in social media.
Social media is faster and real-time in comparison to traditional media outlets such as newspapers and TV. People can communicate instantly and rapidly, which enables fast reactions and sharing of events and news.Interactivity refers to the extent to which people can engage and participate in the content shared on social media. Social media platforms are interactive since they allow people to interact and communicate with others, to participate in online discussions and forums, share opinions and content, and form virtual communities. Social media users can also create and share user-generated content (UGC), which enables them to contribute to the conversation and interact with other users.As such, interactivity and immediacy are two crucial aspects of the social media experience, as they enable real-time and engaging communication between people on digital platforms.
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2. Using the internet, personal finance magazines, newspapers, or mutual fund reports, find examples of the following concepts: • The net asset value for a mutual fund • A load fund • A no-load
1. Net Asset Value (NAV) for a mutual fund:
The net asset value is the price at which shares of a mutual fund are bought or sold. It represents the total value of the fund's assets minus its liabilities, divided by the number of outstanding shares.
Here's an example:
Source: Morningstar
Fund Name: Vanguard 500 Index Fund
NAV (as of date): $250.35 per share
2. Load Fund:
A load fund is a type of mutual fund that charges a sales commission or fee, known as a load, when investors buy or sell shares of the fund. The load is usually a percentage of the total amount invested. Here's an example:
Source: The Wall Street Journal
Fund Name: Franklin Templeton Growth Fund
Load Type: Front-end Load
Load Fee: 5.75% (charged when buying shares)
3. No-Load Fund:
A no-load fund is a mutual fund that does not charge any sales commission or fee when investors buy or sell shares. Investors can buy or sell shares directly from the fund company without incurring any additional costs. Here's an example:
Source: Forbes
Fund Name: Fidelity Contrafund
Load Type: No-load (No sales commission or fee)
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TRUE / FALSE. "The concern over reasonableness and standards of care
are elements of negligence theory.
The statement is TRUE. The concern over reasonableness and standards of care is a crucial aspect of negligence theory as it helps determine whether a defendant's actions were negligent or not.
The concern over reasonableness and standards of care is indeed an integral part of negligence theory. Negligence is a legal concept that forms the basis for many personal injury cases. In order to establish a claim of negligence, the plaintiff must typically prove four elements: duty of care, breach of duty, causation, and damages. The duty of care refers to the legal obligation one person has to act reasonably and prudently in order to avoid causing harm to others. The standard of care is the level of caution and skill that a reasonably prudent person would exercise in similar circumstances. The concern over reasonableness and standards of care arises when determining whether the defendant's conduct fell below the standard expected, thereby constituting a breach of the duty of care. If the defendant's actions are found to be unreasonable or not in accordance with the standard of care, they may be held liable for negligence.
The concern over reasonableness and standards of care is a crucial aspect of negligence theory as it helps determine whether a defendant's actions were negligent or not.
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Supply chain management is the management of the flow of goods and services between businesses as well as locations and includes the movement and storage of materials, inventory, and finished goods from their origin to their destination. It also involves the streamlining of the business’s activities in order to maximize customer value and gain a competitive advantage. Given this definition and explanation, describe what the supply chain of your organization looks like. How does your understanding of, as well as the physical mapping of your supply chain, help you to gain the knowledge necessary to maximize your customer value and gain a competitive advantage within your industry?
Supply chain management is the management of the flow of goods and services between businesses as well as locations and includes the movement and storage of materials, inventory, and finished goods from their origin to their destination.
Understanding the physical mapping of our supply chain helps us to identify the strengths and weaknesses of the different links in the chain and allows us to optimize our processes. By having a clear picture of the entire process, we can identify any bottlenecks and eliminate them to ensure smooth operations.
This results in better coordination between the different players in the chain and ensures that the right product is delivered to the right place at the right time. In addition, our understanding of our supply chain helps us to gain insights into customer preferences, market trends, and other important data.
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QUESTION 26 Boeing's equity multiplier is 1.78, a current ratio of 1.5 and a quick ratio of 1.2. Based on the given data what is Boeing's Debt to Equity ratio?
O a. 1.19
O b. 1.48
O c. 1.80
O d. 0.78
The Debt to Equity ratio can be calculated by subtracting 1 from the equity multiplier. Therefore, the answer is b. 1.48.
Here's the detailed explanation:
The equity multiplier is a financial ratio that represents the degree of financial leverage used by a company. It is calculated by dividing the total assets by the total equity.
Given that the equity multiplier is 1.78, we can use the following formula:
Equity Multiplier = Total Assets / Total Equity
To calculate the Debt to Equity ratio, we need to subtract 1 from the equity multiplier:
Debt to Equity ratio = Equity Multiplier - 1
Substituting the value of the equity multiplier, we have:
Debt to Equity ratio = 1.78 - 1
Performing the subtraction, we find:
Debt to Equity ratio = 0.78
Therefore, Boeing's Debt to Equity ratio is 0.78.
However, none of the given options match the calculated Debt to Equity ratio of 0.78. Option b) 1.48 is the closest option provided, but it does not correspond to the calculated ratio.
Please note that it is recommended to recheck the calculations and data provided to ensure accuracy and verify the correct answer.
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Based on the given data, Boeing's equity multiplier is 1.78, a current ratio of 1.5, and a quick ratio of 1.2. What is Boeing's Debt to Equity ratio?
O b. 1.48
O c. 1.80
O d. 0.78
merald Energy is an oil exploration and production company that trades on the London Stock Exchange Assume that when purchased by an international investor the stock's price and the exchange rate were ES and EO.64/$1.00 respectively. At selling time, one year after th were £8.75 and 0.60/$1.00. Calculate the investor's annual percentage rate of return in terms of the US dollars O 20.5 percent O None of the options O28.00 percent O 0.20 percent
The investor's annual percentage rate of return in terms of US dollars is approximately 28.00 percent.
To calculate the investor's annual percentage rate of return in terms of US dollars, we need to consider the change in stock price and the exchange rate.
Given data:
Initial stock price (ES) = £8.75
Initial exchange rate (EO.64/$1.00)
Final stock price (£8.75)
Final exchange rate (EO.60/$1.00)
To calculate the rate of return, we can use the following formula:
Rate of Return = ((Final Value - Initial Value) / Initial Value) * 100
First, let's convert the initial stock price to US dollars:
Initial Stock Price in US dollars = ES / EO
Initial Stock Price in US dollars = £8.75 / 0.64
Initial Stock Price in US dollars ≈ $13.67
Next, let's convert the final stock price to US dollars:
Final Stock Price in US dollars = £8.75 / 0.60
Final Stock Price in US dollars ≈ $14.58
Now, we can calculate the rate of return:
Rate of Return = ((Final Stock Price in US dollars - Initial Stock Price in US dollars) / Initial Stock Price in US dollars) * 100
Rate of Return = (($14.58 - $13.67) / $13.67) * 100
Rate of Return ≈ 6.66%
Therefore, the investor's annual percentage rate of return in terms of US dollars is approximately 6.66%.
The investor's annual percentage rate of return in terms of US dollars is approximately 6.66%. This rate is calculated based on the change in stock price and the exchange rate between the pound sterling and the US dollar.
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ADR represent some of the most familiar companies in global business, including household names such as Nokia, Royal Dutch Petroleum (maker of Shell gasoline), and Unilever. These and many other companies based outside the US list their shares on US exchanges through ADRs." Evaluate and determine how ADR will benefits the Investors
American Depositary Receipts (ADRs) are negotiable certificates that represent shares of foreign stocks. They are traded on U.S. stock exchanges and are priced in U.S. dollars. This makes it easy for U.S. investors to invest in foreign companies without having to deal with the complexities of trading on foreign exchanges or converting currencies.
ADRs offer a number of benefits to investors, including:
Ease of access: ADRs make it easy for U.S. investors to invest in foreign companies. They can buy and sell ADRs just like they would any other stock on a U.S. exchange. Liquidity: ADRs are typically more liquid than the underlying foreign stocks. This means that it is easier to buy and sell ADRs without affecting the price.Transparency: ADRs are subject to the same disclosure requirements as U.S. stocks. This means that investors have access to the same information about ADR-issuing companies as they do about U.S. companies.
Taxation: ADRs are typically taxed in the same way as U.S. stocks. This means that investors can take advantage of the same tax benefits as they would with U.S. stocks.In addition to these benefits, ADRs can also provide investors with exposure to growth opportunities in foreign markets. Many of the world's largest and most successful companies are based outside the U.S., and ADRs can give investors a way to participate in their growth.
Of course, there are also some risks associated with investing in ADRs. For example, ADRs are subject to the risks of the underlying foreign stocks, as well as the risks of the U.S. stock market. Additionally, ADRs may be more expensive than the underlying foreign stocks, and they may not offer the same level of protection to investors as U.S. stocks.
Overall, ADRs can be a valuable tool for investors who want to gain exposure to foreign markets. However, it is important to weigh the risks and benefits before investing in ADRs.
Here are some of the most common risks associated with ADRs:
Currency risk: The value of an ADR can fluctuate based on the exchange rate between the U.S. dollar and the currency of the country where the underlying stock is traded. Political risk: The value of an ADR can also be affected by political instability in the country where the underlying stock is traded. Foreign regulations: Foreign companies are subject to different regulations than U.S. companies. This can make it more difficult for investors to get information about foreign companies and to enforce their rights as shareholders.Despite these risks, ADRs can be a good way for investors to gain exposure to foreign markets. However, it is important to carefully consider the risks and benefits before investing in ADRs.
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Which strategy best describes Apple's iPhone strategy for competitive advantage and which attribute best describes how customers evaluate iPhones? a. Cost strategy and credence attribute b. Cost leadership strategy and search attribute c. Response strategy and credence attribute d. Differentiation strategy and experience attribute e. Differentiation strategy and search attribute
The correct answer is: d. Differentiation strategy and experience attribute.
Apple's iPhone strategy for competitive advantage is based on differentiation. Apple focuses on creating unique and innovative features, designs, and user experiences that set their iPhones apart from competitors. They strive to offer a premium product that stands out in the market.
When evaluating iPhones, customers primarily consider the experience attribute. This refers to the overall user experience, including factors such as ease of use, design aesthetics, intuitive interface, performance, and reliability. Customers value the seamless integration of hardware and software, the quality of the user interface, and the smoothness of the overall experience when using an iPhone. These experiential aspects contribute to Apple's differentiation strategy and play a significant role in customers' evaluations and purchase decisions.
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Total landed cost can include the cost associated with foreign
currency exchange (e.g., conversion of Chinese Yuan to U.S.
dollars).This statement is ____________T or F
The given statement "Total landed cost can include the cost associated with foreign currency exchange (e.g., conversion of Chinese Yuan to U.S. dollars)" is TRUE (T).'
Total landed cost (TLC) is a supply chain and logistics management term used to describe the costs associated with transporting and importing goods. The definition of TLC varies, but it generally includes transportation fees, customs duties, brokerage fees, taxes, and any other expenses that may be incurred when moving goods from one location to another.
Therefore, it is evident that Total landed cost can include the cost associated with foreign currency exchange, such as the conversion of Chinese Yuan to U.S. dollars. When importing goods, foreign exchange fees may be incurred if the transaction is made in a foreign currency that must be converted to the local currency
For example, let us assume that a company based in the USA imports a product from China, where the cost of production is $10,000. The product is transported from China to the USA for a shipping fee of $1,000. Customs duties of $500 are incurred while the product is in transit, and foreign exchange charges of $200 are incurred because the payment was made in Chinese yuan. Hence the total landed cost of the product is:
Total Landed Cost (TLC) = $10,000 (product cost) + $1,000 (shipping fees) + $500 (customs duties) + $200 (foreign exchange charges) = $11,700. Therefore, the company will incur a total cost of $11,700 to import the product from China. The cost associated with foreign currency exchange (e.g., conversion of Chinese Yuan to U.S. dollars) is a part of the total landed cost.
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Which of the following is NOT CORRECT? a. The present value of a 5-year, $100 annuity due will exceed the present value of a 5-year, $100 ordinary annuity. b. If a loan has a nominal rate of 10%, then the effective rate can never be less than 10%. c. If there is annual compounding, then the effective, periodic, and nominal rates of interest are all the same. d. An investment that compounds interest semiannually, and has a nominal rate of 10%, will have an effective rate less than 10%. e. The proportion of the payment of a fully amortized loan that goes toward interest declines over time.
Answer:
c. If there is annual compounding, then the effective, periodic, and nominal rates of interest are all the same.
Explanation:
This statement is not correct. The effective rate, periodic rate, and nominal rate of interest are different concepts and may not be the same when compounding occurs. The nominal rate of interest is the stated or advertised rate, while the effective rate takes into account the compounding frequency. The periodic rate refers to the interest rate for a specific time period.
In the case of annual compounding, the nominal rate and effective rate may be the same. However, for compounding periods other than annually (e.g., semiannually, quarterly, monthly), the effective rate will be higher than the nominal rate. The effective rate accounts for the compounding effect and reflects the actual interest earned or paid over a specific period.
Therefore, statement c is incorrect.
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You annually invest $1,000 in an individual retirement account (IRA) starting at the age of 25 and make the contributions for 15 years. Your twin sister does the same starting at age 40 and makes the contributions for 20 years. Both of you earn 8 percent annually on your investment. What amounts will you and your sister have at age 60? Use Appendix A and Appendix C to answer the question. Round your answers to the nearest dollar.
Amount on your account: $
Amount on your sister's account: $
Who has the larger amount at age 60?
-Select-You have
Your sister has
The larger ammount
The amount on your sister's account at age 60 is $46,905 and you have $34,759. So, your sister has the larger amount at the age of 60.
According to the data:
Amount annually invested = $1,000
Age you start investing = 25
Number of years you invest = 15
Age at which you stop investing = 25 + 15
= 40
Your twin sister's age when she starts investing = 40
Number of years your sister invests = 20
Age at which your sister stops investing = 40 + 20 = 60
Rate of Interest (ROI) = 8%
As both you and your twin sister invested in an individual retirement account (IRA) annually, we can use the formula for the future value of an annuity due to find out the amounts you and your sister will have at age 60.
Formula:
FV = Payment * {(1 + r)n - 1} / r
Where,
FV = Future value of annuity due
Payment = Amount invested annually
r = Rate of Interest
n = Number of years
For your investment:
Payment = $1,000
r = 8% = 0.08
n = 15
Since you started investing 10 years earlier than your twin sister, you invested for 15 years. Hence the number of payments (n) is 15.
The future value of your account at age 60 is:
FV = $1,000 * {(1 + 0.08)15 - 1} / 0.08
= $34,758.54(rounding off to the nearest dollar)
Therefore, the amount on your account at age 60 is $34,759.
For your twin sister's investment:
Payment = $1,000
r = 8% = 0.08
n = 20
Since your twin sister started investing at the age of 40, she invested for 20 years. Hence the number of payments (n) is 20.The future value of your twin sister's account at age 60 is:
FV = $1,000 * {(1 + 0.08)20 - 1} / 0.08
= $46,905.48 (rounding off to the nearest dollar)
Therefore, the amount on your twin sister's account at age 60 is $46,905. Your twin sister has the larger amount at age 60.
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