(a) The current stock price is expected to be $85.17, given the required rate of return of 15.5%. (b) The expected return for this stock is 16.31%. (c) The stock's alpha is 6.31%.
The required rate of return is the minimum return that an investor expects to receive from an investment. It is calculated by adding the risk-free rate to the market risk premium. The market risk premium is the difference between the expected return of the market and the risk-free rate.
The beta is a measure of how much a stock's return fluctuates with the market's return. A beta of 1.35 means that this stock is 35% more volatile than the market. The dividend yield is the annual dividend payment divided by the current stock price.
The capital appreciation rate is the increase in the stock price over a specified period of time. The alpha is a measure of how much a stock's return deviates from the market's return.
The required rate of return is the minimum return that an investor expects to receive from an investment. It is calculated by adding the risk-free rate to the market risk premium. In this case, the risk-free rate is 4.5% and the market risk premium is 6.0%.
The stock has a beta of 1.35, which means that it is 35% more volatile than the market. Therefore, the required rate of return for this stock is 15.5%. The current stock price can be calculated using the following formula:
Current stock price = Dividend + Future stock price / (1 + Required rate of return)
Substituting the values from the question, we get:
Current stock price = $3.50 + $94.20 / (1 + 0.155)
Current stock price = $85.17
Therefore, we would expect the current stock price to be $85.17, given the required rate of return of 15.5%.
The expected return is the return that an investor expects to receive from an investment over a specified period of time. It is calculated by taking the dividend yield and the capital appreciation rate into account. In this case, the dividend yield is 4.17%.
The capital appreciation rate can be calculated by subtracting the current stock price from the analysts' forecast of the future stock price and dividing the difference by the current stock price.
Capital appreciation rate = ($94.20 - $83.80) / $83.80 = 12.14%
Therefore, the expected return for this stock is 16.31%.
The alpha is a measure of how much a stock's return deviates from the market's return. It is calculated by subtracting the market's return from the stock's return. In this case, the market's return is 10.0%. The stock's return is 16.31%. Therefore, the stock's alpha is 6.31%.
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According to our text, which of the following is true about countries that have high income inequality?
Group of answer choices
In countries with perfect of close to perfect income inequality the relative difference in incomes between the rich and the poor is smaller than in countries with perfect income equality.
Greater income inequality means a lower absolute standard of living for the wealthy and a lower one for the poor as well.
None of the choices is listed in our text as true about high income equality.
Countries with high income inequality have lower standards of living.
According to the text, the true statement about countries that have high income inequality is that countries with high income inequality have lower standards of living. Countries that have high income inequality have a lower standard of living the correct answer is: E
because it means that the wealth is concentrated in a few hands while the majority of the population remains poor. The higher the level of income inequality in a country, the lower the standard of living of the poor and the wealthy alike.The income gap between the rich and the poor in countries with high income inequality is large and the economy of such countries struggles to grow.
According to many scholars and economists, income inequality is a serious issue that affects economic growth. In conclusion, Countries with high income inequality have lower standards of living.
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Chicago Company, a calendar-year corporation, had the following actual income before income tax expense and estimated effective annual income tax rates for the first three quarters in 20X2: Estimated Effective Income Before Annual Tax Rate at the Quarter Income Tax Expense End of Each Quarter First $ 70,000 28 % Second $ 90,000 26 % Third $ 120,000 30 % Chicago's income tax expense in its interim income statement for the third quarter should be:
Therefore, Chicago's income tax expense in its interim income statement for the third quarter should be $36,000.
Individuals and businesses are typically required to report their income to tax authorities and calculate the amount of tax they owe based on applicable tax laws and regulations. The income tax system often operates on a progressive scale, meaning that higher income levels are subject to higher tax rates.
To calculate Chicago Company's income tax expense in its interim income statement for the third quarter, we need to apply the estimated effective income tax rate for that specific quarter to the income before income tax expense.
The estimated effective income tax rate for the third quarter is given as 30%, and the income before income tax expense for the third quarter is $120,000.
To determine the income tax expense for the third quarter, we multiply the income before income tax expense by the estimated effective income tax rate:
Income before income tax expense (Q3) * Estimated effective income tax rate (Q3)
= $120,000 * 0.30
= $36,000
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Problem 21 Early in 2022, Inez Marcus, the chief financial officer (CFO) for Suarez Manufacturing, was given the task of assessing the impact of a proposed risky investment on the firm's stock value. To perform the necessary analysis, Inez gathered the following information on the firm's stock. During the immediate past 5 years (2017-2021), the annual dividends paid on the firm's common stock were as follows: Year Dividend 2021 $1. 90 2020 $1. 70 2019 $ 1. 55 2018 $ 1. 40 $1. 30 2017 The firm expects that without the proposed investment, the dividend in 2022 will be $2. 09 per share and the historical annual rate of growth (rounded to the nearest whole percent) will continue in the future. Currently, the required return on the common stock is 14%. Inez's research indicates that if the proposed investment is undertaken, the 2022 dividend will rise to $2. 15/share. The annual rate of dividend growth will be 13% until 2024, and then at the beginning of 2025 onwards, would return to the rate that was experienced between 2017 and 2021. As a result of the increased risk associated with the proposed risky investment, the required return on the common stock is expected to increase by 2% to an annual rate of 16%, regardless of which dividend growth outcome occurs. Armed with the preceding information, Inez must now assess the impact of the proposed risky investment on the market value of Suarez's stock. To simplify her calculations, she plans to round the historical growth rate in common stock dividends to the nearest whole percent. FIN3201 Practice problems Investment Analysis TO DO a. Find the current value per share of Suarez Manufacturing's common stock. B. Find the value of Suarez's common stock in the event that it undertakes the proposed risky investment What effect would the proposed investment have on the firm's stockholders? Explain. C. On the basis of your findings in part b, do the stockholders win or lose because of undertaking the proposed risky investment? Should the firm do it? Why?
a. The current value per share of Suarez Manufacturing's common stock can be calculated using the dividend discount model (DDM). The formula for the DDM is as follows:
Current Value per Share = Dividend / (Required Return - Dividend Growth Rate)
Using the information given, the dividend in 2022 is $2.09 per share and the required return is 14%. The historical growth rate in dividends from 2017 to 2021 is 30%. Plugging these values into the formula, we can calculate the current value per share.
b. To find the value of Suarez's common stock in the event that it undertakes the proposed risky investment, we need to consider the changes in dividends and the required return. The proposed investment would increase the dividend in 2022 to $2.15 per share. From 2022 to 2024, the dividend growth rate would be 13%, and from 2025 onwards, it would return to the historical growth rate of 30%. The required return on the common stock would increase by 2% to 16%.
We can use the DDM again to calculate the value of the stock with the proposed investment. By applying the dividend growth rates and the adjusted required return to the future dividends, we can determine the value per share.
c. The effect of the proposed investment on the firm's stockholders can be evaluated by comparing the value of the stock with and without the investment. If the value per share with the investment is higher than the value per share without the investment, stockholders would benefit from undertaking the risky investment.
Based on the calculations in part b, we can assess whether stockholders win or lose from the investment. If the value per share with the investment is higher, it indicates that stockholders would benefit, and the investment would be favorable. Conversely, if the value per share with the investment is lower, stockholders would lose, and the investment may not be advisable.
Ultimately, the decision to undertake the proposed risky investment should consider the net impact on stockholders. If the investment increases the value per share and aligns with the company's strategic goals and risk appetite, it may be considered a favorable opportunity. However, if the investment leads to a decrease in stock value or poses excessive risk, the firm may need to reconsider its decision. The evaluation should take into account the long-term prospects, potential returns, and risk factors associated with the investment.
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Kate, a recent law school graduate sent a letter to Jenny, her classmate on Friday 1 July 2022
and told her that she is moving to take a new job in another country and asked Jenny whether she wanted "the stuff" at my flat for $15,000.
Jenny received the letter on Saturday 2 July 2022, and on Monday 4 July 2022, Jenny sent
Kate a letter accepting the offer. The next day, Jenny changed her mind, called Kate and told
her to forget the deal. Since Jenny said she is not interested, Kate then sold "the stuff" to Ally
for $13,000. Later that week, Kate received the letter that Jenny had sent Monday 4 July
2022.
Is there a contract between Kate and Jenny? Why?
No, there is no contract between Kate and Jenny.
In order for a contract to be formed, there must be an offer, acceptance, consideration, and an intention to create legal relations. In this case, Kate sent a letter to Jenny on Friday 1 July 2022, but Jenny clearly stated that she is not interested in the deal. Since Jenny did not accept the offer, there is no contract between them. Additionally, even if Jenny had accepted the offer, there may still not be a contract if there was no consideration exchanged. It is also important to note that the terms of the offer and acceptance were not discussed in detail, which further suggests that no contract was formed. Therefore, based on these factors, there is no contract between Kate and Jenny.
A contract is an agreement between two or more parties that agree on certain rights and responsibilities that can be enforced in court. Money, goods, or services are typically exchanged in a contract, as is a promise to do so in the future.
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please create a cost and price analysis for a cosmetic brand.
(200+ words please thank you)
By conducting a comprehensive cost and price analysis, a cosmetic brand can make informed decisions regarding pricing strategies, product profitability, and market positioning. It enables the brand to strike a balance between offering competitive prices to attract customers while ensuring profitability and sustainability in the long run.
A cost and price analysis for a cosmetic brand involves evaluating various factors to determine the costs incurred in producing the cosmetics and setting appropriate prices. The analysis includes:
1. Cost Analysis: Assessing the expenses involved in the production process, including raw materials, packaging, manufacturing, labor, and overhead costs. This analysis helps identify the total cost per unit for each cosmetic product.
2. Market Research: Conducting thorough market research to understand customer preferences, demand, and pricing trends in the cosmetic industry. This information helps in setting competitive prices and determining the target market segment.
3. Competitor Analysis: Studying competitor pricing strategies, product offerings, and market positioning. This analysis provides insights into how the brand's prices can be positioned in relation to competitors while maintaining profitability.
4. Profit Margin Calculation: Determining the desired profit margin for the cosmetic brand. This involves considering factors such as brand positioning, market share goals, and long-term business sustainability.
5. Pricing Strategy: Developing a pricing strategy that aligns with the brand's value proposition, target market, and product differentiation. The strategy may include penetration pricing, skimming pricing, or value-based pricing, depending on the brand's objectives.
6. Price Testing: Conducting price testing experiments to evaluate customer response and elasticity to different price points. This helps in optimizing prices for maximum revenue and profitability.
7. Price Adjustment: Regularly reviewing and adjusting prices based on market dynamics, cost fluctuations, and changes in customer demand. This ensures the brand remains competitive and financially viable over time.
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Desiree works 28 hours per week. she has a monthly income of $120 from investments. desiree also plays in a band one night a week making $200. she has a total annual income of $49,696. desiree wants to ask her boss for a raise so that next year she can have a total income of $51,880. assuming the other incomes remain the same, how much of an hourly raise will desiree need? a. $1.25 b. $1.50 c. $1.75 d. $2.00 please select the best answer from the choices provided a b c d
To achieve a total income of $51,880 next year, Desiree will need an hourly raise of $1.50. So, the correct option is b.
To calculate the required hourly raise, we need to find the difference between Desiree's target annual income ($51,880) and her current annual income ($49,696). The difference is $2,184.
Since Desiree works 28 hours per week, we can calculate her total annual income from her job as follows:
Annual Income from Job = Weekly Income from Job × Number of Weeks in a Year
= Hourly Wage × Hours per Week × Number of Weeks in a Year
= Hourly Wage × 28 × 52
Now, we can set up an equation to find the hourly raise needed:
Current Annual Income + Annual Income from Investments + Annual Income from Band = Target Annual Income
$49,696 + $120 + $200 = $51,880
Now, let's plug in the values and solve for the hourly wage (raise):
$49,696 + $120 + $200 + (Hourly Wage × 28 × 52) = $51,880
$49,696 + $320 + (Hourly Wage × 1456) = $51,880
$50,016 + (Hourly Wage × 1456) = $51,880
Hourly Wage × 1456 = $51,880 - $50,016
Hourly Wage × 1456 = $1,864
Hourly Wage = $1,864 / 1456
Hourly Wage ≈ $1.28
So, Desiree will need an hourly raise of approximately $1.28. The closest option to this value is $1.50 (option b).
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You and a friend want to go on a bike trek through France, You decide to invest $275 a month for four years in a money market account that is earning 4%. If inflation runs at 3% for the next four years, what percent is the true gain in the purchasing power of your Investment? (Round all intermediate calculations and final answers to 2 decimal places.)
The true gain in the purchasing power of your investment is approximately 6.80%. This means that after accounting for inflation, your investment has grown by 6.80% in terms of purchasing power.
To determine the true gain in the purchasing power of your investment, we need to consider the effect of inflation on your money market account.
First, let's calculate the future value of your investment. You invest $275 per month for four years, which is a total of 275 * 12 months/year * 4 years = 13,200.
Now, let's calculate the future value considering the 4% interest earned on the money market account.
Using the compound interest formula, the future value (FV) can be calculated as: FV = P(1 + r/n)^(n*t), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Plugging in the values, FV = 13,200(1 + 0.04/12)^(12*4) = 14,503.51.
Next, let's calculate the impact of inflation. Inflation is running at 3% for the next four years. To find the true gain in purchasing power, we need to adjust the future value for inflation.
We can use the formula: Adjusted Future Value = Future Value / (1 + inflation rate)
Plugging in the values, Adjusted Future Value = 14,503.51 / (1 + 0.03) = 14,098.08.
Now, let's calculate the true gain in purchasing power. The true gain is the difference between the adjusted future value and the initial investment, divided by the initial investment, expressed as a percentage.
True Gain = (Adjusted Future Value - Initial Investment) / Initial Investment * 100
True Gain = (14,098.08 - 13,200) / 13,200 * 100
True Gain = 898.08 / 13,200 * 100
True Gain = 6.80%
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ABC Ltd. is looking at ways to improve its cash flow and has decided to extend the timing of its disbursements by one day. In addition, it is negotiating with its bank for the establishment of a lockbox system that will reduce the remittance time of deposits by 2 days. The bank will also provide the company with a detailed analysis of the receipts which saves the company $30,000 in wages. The company's daily remittances amount to $1.5 million and the going rate in the market is 4% per annum for money market funds. For this service the bank charges a monthly fee of $5,000 and would require the company to maintain a $500,000 compensating balance.
Advise ABC Ltd. whether or not they should put these changes in place. Please answer the questions in the box provided.
Short Answer
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BIUS
ABC Ltd. should carefully consider the costs, benefits, and potential impacts of these changes on its cash flow, supplier relationships, and financial obligations. Based on the information provided, here are the considerations for ABC Ltd.:
1. Extending the timing of disbursements by one day:
This change could potentially improve the company's cash flow by delaying cash outflows. However, it's important to assess the impact on the company's relationships with suppliers and any potential late payment penalties or strained relationships that may arise. It's advisable to evaluate the costs and benefits of this change before implementing it.
2. Implementing a lockbox system:
A lockbox system can help expedite the remittance time of deposits by 2 days, which would accelerate cash inflows for ABC Ltd. This improvement in cash flow can be beneficial, especially if the company relies on timely receipt of funds. However, it's essential to consider the cost of the lockbox system, including the monthly fee and the requirement to maintain a compensating balance. These costs should be weighed against the potential benefits of improved cash flow.
3. Bank providing detailed analysis of receipts and saving wages:
The bank's offer to provide a detailed analysis of receipts, resulting in savings of $30,000 in wages, can be advantageous for ABC Ltd. This service can potentially streamline the company's processes and provide valuable insights into its cash flow. However, it's crucial to evaluate the cost-effectiveness of this service in relation to the savings achieved.
Overall, ABC Ltd. should carefully consider the costs, benefits, and potential impacts of these changes on its cash flow, supplier relationships, and financial obligations. It may be beneficial to perform a cost-benefit analysis to assess the net impact of these changes before making a decision.
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Question 1
4 pts
Laura has $10 million in invested capital, $4 million in EBIT, and is in the 50% federal- plus-state tax bracket. Laura has a 30% debt-to-capital ratio and pays 10% on its debt.
What is the ROE for Laura?
O 19.65%
12.14%
26.43%
Question 2
4 pts
KSS has $1000 par value bonds with a 9% coupon rate and coupons paid semi-annually. that mature in 25 years. The bonds are selling for $1,050. KSS has an average tax rate of 30%. KSS is in the 40% marginal tax bracket. What is the after-tax cost of debt?
2.80%
3.95%
5.11%
Question 3
4 pts
KSS common stock has a beta of 1.2. The market long term expected return is 12% and the risk-free rate is 2%. What is the cost of retained earnings?
O 14.0%
O 16.6%
O 22.0%
The ROE for Laura is approximately 52.86%. The after-tax cost of debt for KSS is approximately 6.3%. The cost of retained earnings for KSS is approximately 21.2%.
1: To calculate the Return on Equity (ROE) for Laura, we need to use the following formula: ROE = Net Income / Shareholders' Equity
First, let's calculate the net income: Net Income = EBIT - Interest Expense
We need to calculate the interest expense based on the debt-to-capital ratio and the interest rate paid on debt: Interest Expense = Debt-to-Capital Ratio × Invested Capital × Interest Rate on Debt
Debt-to-Capital Ratio = Debt / (Debt + Equity)
Debt-to-Capital Ratio = 0.30 (given)
Invested Capital = Debt + Equity
Invested Capital = $10 million (given)
Interest Rate on Debt = 10% (given)
Let's calculate the interest expense: Interest Expense = 0.30 × $10 million × 0.10
Interest Expense = $300,000
Next, calculate the net income: Net Income = EBIT - Interest Expense
Net Income = $4 million - $300,000
Net Income = $3.7 million
Now, let's calculate the ROE: ROE = Net Income / Shareholders' Equity
Since the tax rate is not given, we'll assume that the net income already accounts for taxes paid.
Shareholders' Equity = Invested Capital - Debt
Shareholders' Equity = $10 million - 0.30 × $10 million
Shareholders' Equity = $10 million - $3 million
Shareholders' Equity = $7 million
ROE = $3.7 million / $7 million ≈ 0.5286 or 52.86%
Therefore, the ROE for Laura is approximately 52.86%.
2: To calculate the after-tax cost of debt for KSS, we need to use the following formula: After-Tax Cost of Debt = Pre-Tax Cost of Debt × (1 - Tax Rate)
First, let's calculate the pre-tax cost of debt. The pre-tax cost of debt is the coupon rate on the bonds: Pre-Tax Cost of Debt = Coupon Rate = 9% (given)
Next, let's calculate the tax rate: Tax Rate = Marginal Tax Rate = 40% (given)
Now, let's calculate the after-tax cost of debt:
After-Tax Cost of Debt = Pre-Tax Cost of Debt × (1 - Tax Rate)
After-Tax Cost of Debt = 9% × (1 - 0.30)
After-Tax Cost of Debt = 9% × 0.70
After-Tax Cost of Debt = 0.063 or 6.3%
Therefore, the after-tax cost of debt for KSS is approximately 6.3%.
3: To calculate the cost of retained earnings for KSS, we can use the Capital Asset Pricing Model (CAPM). The formula for CAPM is as follows: Cost of Retained Earnings = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)
Risk-Free Rate = 2% (given)
Beta = 1.2 (given)
Market Return = 12% (given)
Cost of Retained Earnings = 2% + 1.2 × (12% - 2%)
Cost of Retained Earnings = 2% + 1.2 × 10%
Cost of Retained Earnings = 2% + 0.12
Cost of Retained Earnings = 2.12 or 21.2%
Therefore, the cost of retained earnings for KSS is approximately 21.2%.
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Define the different buying situations and what that means to a negotiation. Discuss what the difference is between a feature, advantage and benefit are to the customer. Discuss the advantages and disadvantages of SPIN (situation, problem, implication(, and need-payoff) questioning techniques and how they can bolster you closing ability.
Discuss the importance of nonverbal communication and what signals that you should be aware of. Provide real world examples of nonverbal communication that you have observed or researched. Finally, explain ways of developing persuasive communication.
Different buying situations and what they mean to a negotiation .There are three different buying situations that require a distinct negotiation approach.
The buying situation depends on the level of the buyer’s involvement in the purchase process, the risk and importance of the purchase, and the number of alternative solutions. The different buying situations are:New task buying: In this buying situation, the customer is buying a product for the first time. The seller must provide a lot of information about the product and must also make an effort to convince the customer about the value of the product.
Straight rebuy: In this buying situation, the buyer is just reordering a product that they have bought before. The negotiation in this situation is usually straightforward.Modified rebuy: In this buying situation, the buyer wants to make some changes in the product specifications or the supplier. The negotiation in this situation is usually more complicated.Feature, Advantage and BenefitA feature is a descriptive fact about the product or service.
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Assume that the stock market begins a period of sustained decreases after a pause. Outline an options strategy_that would help someone benefit from this improvement in the stock market and how this should work.
An options strategy that would help someone benefit from a sustained decrease in the stock market is the put options strategy. This strategy should work as follows:
A put option is an agreement between two parties to sell a specific asset at a certain price on or before a specific date. In this strategy, the investor buys a put option for a stock that they believe will decrease in value during the sustained decrease period in the stock market. The investor then pays a premium for the right to sell that stock at a predetermined strike price until a specific expiration date. When the stock's price falls below the predetermined strike price, the investor profits. The premium the investor paid for the put option represents their maximum loss if the stock's price rises instead. In summary, the put options strategy is an options trading strategy that benefits investors when the stock market experiences a sustained decrease.
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1. Sales people should conduct trial closes during the various stages of the sales process. true or false?
2. Which of the following is NOT a barrier to communication?
Information overload
Selling pressure
Sales quotas
Disorganized sales presentation
1. Sales people should conduct trial closes during the various stages of the sales process. True or false? The statement "Sales people should conduct trial closes during the various stages of the sales process" is true. The term "trial close" means to ask questions or make statements during a sales call to determine the likelihood of getting a prospect's commitment to purchase the product or service.
The purpose of trial closing is to assess the prospect's level of interest and intent to buy so that the salesperson can alter their presentation and keep the sales process moving forward. It also enables the salesperson to pinpoint any concerns the prospect might have and address them during the sales call to increase the chances of a successful close.
2. Which of the following is NOT a barrier to communication? A barrier to communication is anything that prevents people from effectively exchanging information and ideas. Selling pressure, sales quotas, and disorganized sales presentations are all examples of communication barriers. However, Information overload is NOT a barrier to communication. Although too much information can be overwhelming, it does not necessarily block communication.
Information overload can cause people to disengage or lose interest in a conversation, but it does not prevent communication from occurring. To sum it up, salespeople should conduct trial closes during the various stages of the sales process. This is because it helps them to assess the prospect's level of interest and intent to buy so that they can alter their presentation and keep the sales process moving forward. Information overload is not a barrier to communication, while Selling pressure, sales quotas, and disorganized sales presentations are all examples of communication barriers.
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With the help of appropriate diagrams, explain how an aggregate demand curve is derived from IS-LM model and why it is downward sloping. Give examples of 3 factors that would shift the AD curve to the right?
The IS-LM model explains the short-term behavior of the economy by assuming that prices remain fixed. The model is depicted by two intersecting curves; IS curve and LM curve.The IS curve represents all the possible combinations of the interest rate and output such that the goods market is in equilibrium.
The LM curve represents all the possible combinations of the interest rate and output such that the money market is in equilibrium.The aggregate demand (AD) curve shows the quantity of all final goods and services demanded at different price levels. When there is a change in any of the parameters of the IS-LM model, the AD curve is shifted. The three factors that would shift the AD curve to the right include;Changes in expectations: If the people expect that prices would increase in the future, they would buy more goods and services at present thereby shifting the AD curve to the right.
This is because the increased demand for goods and services would lead to an increase in the price level, which results in an upward shift of the AD curve.Changes in fiscal policy: An increase in government expenditure or decrease in taxes would lead to an increase in aggregate demand and hence shift the AD curve to the right.Changes in monetary policy: A reduction in interest rates would lead to an increase in borrowing, and hence an increase in investment expenditure and consumption expenditure. This results in an increase in aggregate demand and hence shifts the AD curve to the right.
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Newton Company produces a single product. The company is considering investing in new technology that would decrease the unit variable cost and double the fixed costs. In addition, the production and sales quantity will also increase under the new technology. What selling price per unit would have to be charged, after the investment in this new technology, to earn the budgeted profit
To determine the selling price per unit that would have to be charged after the investment in the new technology to earn the budgeted profit, we need to consider the impact of the changes on the company's costs and sales quantity.
Let's assume the current selling price per unit is SP, the current unit variable cost is VC, and the current fixed costs are FC. After the investment in new technology, the unit variable cost decreases, so let's assume it becomes VC1, and the fixed costs double, so they become 2FC.
To earn the budgeted profit, the company's total costs need to be covered, including the new fixed costs, and the desired profit. The formula to calculate the selling price per unit is:
Selling price per unit = (Total costs + Desired profit) / Sales quantity
Total costs = (VC1 * Sales quantity) + (2FC)
Desired profit = Budgeted profit
Now, you need to substitute the values of VC1, 2FC, Budgeted profit, and the anticipated increase in sales quantity into the formula to calculate the selling price per unit.
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Complete question:
Newton Company produces a single product. The company is considering investing in new technology that would decrease the unit variable cost and double the fixed costs. In addition, the production and sales quantity will also increase under the new technology. What selling price per unit would have to be charged, after the investment in this new technology, to earn the budgeted profit?
Critically discuss the impact of
recession caused by Covid-19 pandemic in
world
please don't copy from another answer
thank you
The COVID-19 pandemic has brought about a severe worldwide recession, which has impacted economies, businesses, and individuals on a global scale. The economic impact of the COVID-19 pandemic has been more significant than any other recession in modern history.
The COVID-19 pandemic is estimated to have caused a global GDP contraction of -4.4 percent in 2020, compared to the global financial crisis of 2009, which caused a contraction of -0.1 percent.The COVID-19 pandemic's economic impact has been felt most acutely by the vulnerable population segments and developing economies. With the reduction of global trade, international travel, and mobility, international supply chains have been disrupted, leading to widespread shortages of essential goods and services.
The hospitality and tourism industry, which heavily relies on international travel, has been particularly affected by the COVID-19 pandemic.The COVID-19 pandemic's economic impact has also led to widespread unemployment and job losses globally. Many businesses have had to lay off workers and reduce salaries, leading to decreased purchasing power for individuals. The increased economic hardship has led to a rise in poverty and inequality, especially in developing economies with inadequate social safety nets.
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Cash conversion cycle
Christie Corporation is trying to determine the effect of its inventory turnover ratio and days sales outstanding (DSO) on its cash conversion cycle. Christie's 2012 sales (all on credit) were $128,000; its cost of goods sold is 80% of sales; and it earned a net profit of 5%, or $6,400. It turned over its inventory 7 times during the year, and its DSO was 35.5 days. The firm had fixed assets totaling $50,000. Christie's payables deferral period is 40 days. Assume 365 days in year for your calculations.
a. Calculate Christie's cash conversion cycle. Round your answer to two decimal places.
days
b. Assuming Christie holds negligible amounts of cash and marketable securities, calculate its total assets turnover and ROA. Round your answer to two decimal places.
Total assets
$
ROA
c. Suppose Christie's managers believe that the inventory turnover can be raised to 8.2 times. What would Christie's cash conversion cycle, total assets turnover, and ROA have been if the inventory turnover had been 8.2 for 2012?
Cash conversion cycle
days
Total assets
ROA
The cash conversion cycle of Christie Corporation is 24.93 days.
Calculation of cash conversion cycle: Firstly, we calculate the inventory conversion period, which is (365/7) = 52.14 days. Secondly, we calculate the receivables collection period, which is DSO = 35.5 days. Thirdly, we calculate the payable deferral period, which is DPO = 40 days. Finally, we calculate the cash conversion cycle as CCC = DIO + DSO - DPO = 52.14 + 35.5 - 40 = 47.64 - 22.71 = 24.93 days. b. Christie Corporation's total assets turnover was 2.56 times and the ROA was 12.38%.
Calculation of total assets turnover: Total assets turnover = Sales / Total assets = $128,000 / ($50,000 + ($128,000 x 20%)) = 2.56 times. Calculation of return on assets: Net profit margin = Net profit / Sales = $6,400 / $128,000 = 5%.Return on assets = Net profit margin x Total assets turnover = 5% x 2.56 = 12.8%.c. If the inventory turnover of Christie Corporation was 8.2 for 2012, then its cash conversion cycle would be 19.61 days, its total assets turnover would be 2.81 times and its ROA would be 13.94%.
Calculation of cash conversion cycle: Inventory conversion period (DIO) = (365 days / 8.2) = 44.51 days. DSO = 35.5 days. DPO = 40 days. CCC = DIO + DSO - DPO = 44.51 + 35.5 - 40 = 39.01 - 19.40 = 19.61 days.Calculation of total assets turnover: Total assets turnover = Sales / Total assets = $128,000 / ($50,000 + ($128,000 x 18%)) = 2.81 times. Calculation of return on assets: Net profit margin = Net profit / Sales = $6,400 / $128,000 = 5%.Return on assets = Net profit margin x Total assets turnover = 5% x 2.81 = 13.94%.
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You have inherited $10,000 from your wonderful Aunt Bessie. You
decide to spend 3,182 on a vacation. The rest you will invest in a
Roth IRA. You expect it to earn 6.3% over the next 45 years. How
much
The total amount of money that would be in the Roth IRA account would be $116,523.34 in 45 years.
A Roth IRA (Individual Retirement Account) is a tax-advantaged account that enables you to save money for retirement. The income you earn in a Roth IRA is tax-free, and withdrawals are also tax-free once you reach age 59 1/2 and have had the account for five years.
A Roth IRA is an excellent method to save for retirement, and it's particularly useful for younger people, as it has a long-term benefit due to compound interest.You decide to spend $3,182 on a vacation and invest the remainder in a Roth IRA.
Therefore, the amount you are investing in the Roth IRA will be:
$10,000 - $3,182
= $6,818
Now we need to calculate how much money will be earned in 45 years with a 6.3% annual interest rate.
Using the formula for compound interest:
Final amount = Initial amount x (1 + annual interest rate) ^ number of years
Final amount = $6,818 x (1 + 0.063) ^ 45
Final amount = $116,523.34
Therefore, the total amount of money that would be in the Roth IRA account would be $116,523.34 in 45 years.
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Go back to Rademaekers and Johnson-Sheehan's article ↓ on climate change communications. Look over their 6 guidelines for reframing climate change into a discourse of a broader social frame. Think about these and then answer ONE of the following in a short (250 words or lesse paragraph. Post your initial response in your small group discussion and respond to one of your colleagues (a sentence is fine - you agree or disagree o can add to their argument) by the due date. 1. Have you noted any individual or group use one of these guidelines in framing an issue? What is the issue, the guideline, and how did the person or group implement it? 2. Should any individual or group use one of these guidelines in framing an issue to achieve a better effect? What is the issue, the guideline, and how might the person or group implement it? If nothing comes to mind, go out there in the world - real or internet - to find an answer. What are hot issues right now? Look at how one group or person takes up their side of the fight and see what they might do better at or what they are doing correctly according to the 6 guidelines.
Microsoft's AI for Earth program employs Rademaekers and Johnson-Sheehan's guidelines by using a broader social frame in climate change discourse.
Microsoft's AI for Earth program reframes climate change by linking it with technological development, a key societal concern. The company emphasizes how AI can help in solving climate change, focusing on concrete examples of AI's role in environmental conservation, sustainable farming practices, and biodiversity preservation. This approach allows Microsoft to talk about climate change in a way that also speaks to economic growth and job creation, thus widening the discourse to engage diverse stakeholders. By doing so, Microsoft effectively implements guideline 3, demonstrating a clear example of how reframing climate change communication can motivate broader societal engagement.
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c) A share has just paid a dividend of $2.00 yesterday. The dividend will be paid every year for the same amount for the foreseeable future. The rate of return is 12.5% p.a. effective. Calculate the price of the share in 3 years. (Round your answer to the nearest cent.)
The price of the share in 3 years would be $16.00.
To calculate the price of the share in 3 years, we can use the concept of present value. Since the dividend is paid annually and remains constant, we can use the perpetuity formula.
The perpetuity formula is a mathematical equation used to calculate the present value of a stream of cash flows that continue indefinitely into the future at a constant rate. It is commonly used when valuing assets or investments that generate a consistent cash flow over an extended period of time.
The price of the share can be calculated as follows:
Price = Dividend / Rate of Return
In this case, the dividend is $2.00, and the rate of return is 12.5% (or 0.125 in decimal form).
Price = $2.00 / 0.125 = $16.00
Therefore, the price of the share in 3 years would be $16.00.
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What are the circumstances in which you should invest actively
or passively?
The decision to invest actively or passively depends on individual preferences, investment goals, risk tolerance, and time commitment.
Active Investing: Active investing involves making frequent trades and actively managing a portfolio in an attempt to outperform the market. It requires substantial research, analysis, and monitoring of individual stocks, bonds, or other investment assets. Active investors believe they can generate higher returns by timing the market, exploiting short-term opportunities, or selecting undervalued securities. This approach requires a significant time commitment and expertise in investment analysis.
Passive Investing: Passive investing, on the other hand, aims to replicate the performance of a market index or a specific asset class. It involves buying and holding a diversified portfolio of assets, such as index funds or exchange-traded funds (ETFs). Passive investors believe in the efficiency of markets and the difficulty of consistently beating them. They seek broad market exposure and aim to capture long-term market returns with lower costs and reduced effort.
Factors to consider when deciding between active and passive investing:
a) Investment Goals: Active investing may be suitable for investors seeking higher returns and are willing to take on more risk. Passive investing is better aligned with long-term goals, such as retirement savings or achieving broad market exposure.
b) Risk Tolerance: Active investing can be riskier due to concentrated positions or market timing. Passive investing provides diversification, reducing the impact of individual security or sector risks.
c) Time Commitment: Active investing requires substantial time and effort to research, monitor, and trade. Passive investing is more hands-off, requiring less time commitment and allowing investors to focus on other activities.
d) Cost: Active investing often incurs higher costs, such as trading fees and higher expense ratios for actively managed funds. Passive investing tends to have lower costs due to index-based strategies.
Ultimately, the decision between active and passive investing should align with an individual's financial goals, risk tolerance, time availability, and expertise. Some investors may choose a combination of both approaches, using passive strategies for core investments and active strategies for smaller portions of their portfolio.
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Salespeople use a variety of ________ to gather and process information of value to the customer.
Salespeople utilize a range of techniques to collect and analyze valuable information for customers, aiding in the sales process.
: Salespeople employ several methods to gather and process information that is beneficial to their customers. One crucial technique is active listening, which involves attentively hearing and understanding customer needs, preferences, and pain points. Through active listening, salespeople can extract valuable insights, tailor their approach, and provide suitable solutions. Another important method is conducting market research, enabling salespeople to understand industry trends, competitive landscapes, and customer behavior. This knowledge empowers them to offer informed recommendations and position their products or services effectively. Additionally, salespeople may leverage customer relationship management (CRM) systems to organize and analyze customer data, track interactions, and identify opportunities for personalized engagement. These techniques collectively assist salespeople in delivering value by providing relevant and insightful information to customers.
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a) Your company which is located in the United States imports raw materials from Germany, and analyst predicts that the euro will appreciate significantly in the future. State giving reasons the advise you would give your company regarding hedging of its payables which are Invoiced in euros.
b) Idapco: a U.S. firm will receive £1 million in one year from its U.K. subsidiary.
Given the following information:
360-day UK, borrowing interest rate
=7%
360-day U.K. lending Interest rate
3%
360-day U.S. borrowing interest rate
5%
360-day US deposit interest rate
=3%
360-day forward rate of the British pound
Spot rate of the British pound
= US$1.39
One-year call option: Exercise price
US$1.36
premium-$.03
$1.38
One-year put option: Exercise price
$1.40
premium-5.04
Expected one-year spot rate
$1.41
Showing and explaining all your workings determine whether or not the firm should use an options hedge or a money market hedge to hedge its receivables
a) If your company is located in the United States and imports raw materials from Germany, and the analyst predicts that the euro will appreciate significantly in the future, the company should hedge its payables invoiced in euros by locking in the current exchange rate, which will enable the company to fix the cost of its imports.
In this way, the company can avoid unfavorable currency fluctuations that could result in significant losses for the company. A company can use either the money market or the forward exchange market to hedge its payables. In the forward exchange market, the company can use forward contracts to lock in the current exchange rate for the euro. This will ensure that the company pays the same amount for its raw materials, regardless of any changes in the exchange rate. Alternatively, the company can use the money market to hedge its payables. In the money market, the company can borrow euros at a fixed interest rate, which will ensure that it knows the exact cost of its imports.
b) The firm should use a money market hedge to hedge its receivables.The formula for the forward rate is: Forward Rate = Spot Rate x (1+Foreign Interest Rate)/(1+Domestic Interest Rate)Based on the information provided, the forward rate for the British pound is:Forward Rate = $1.39 x (1+0.03)/(1+0.05) = $1.38The expected one-year spot rate is $1.41, which is higher than the forward rate of $1.38.
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Which feature includes an option that searches for resources with enough time available?
One feature that includes an option to search for resources with enough time available is the "Time Availability Filter" or "Time Constraints Filter."
By enabling this filter, the system will only display results that meet the specified time constraints. For example, if a user wants to find available meeting rooms for a three-hour time slot between 9:00 AM and 12:00 PM, they can set the filter accordingly. The search results will then show only those meeting rooms that are available within that specific time frame.
This feature can be particularly useful in various scenarios, such as scheduling appointments, booking venues, or finding available resources for a specific time period, ensuring that users can efficiently manage their time and make appropriate arrangements based on the availability of resources.
Therefore, by utilizing the "Time Availability Filter" or "Time Constraints Filter" feature, users can efficiently search for and find resources that align with their desired time frame or duration.
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This assignment has 2 Questions with sub parts. For all questions, use the following definition of distribution types. Distribution Type 1: Normal distribution with mean =75 and std. dev =25 Distribution Type 2: Uniform Distribution U\{50,100] Q2. Buyback Contract: Suppose that you are the retailer of newspapers. You sell newspaper for $2 each and you buy newspapers from a supplier at a wholesale price of $1.2. You also know that the supplier's production cost is $0.5/ newspaper. 2A. What is your underage cost, overage cost, and critical ratio?2B. How many newspapers will you order if demand is distributed asdistribution type 1 ? 2C. How many newspapers will you order if demand is distributed as distribution type 2? 20. Suppose now that you and supplier decide to maximize the total profit? How many newspaperswiil you order if newspaper demand is distributed as distribution type 1? I 2E. Suppose now that you and supplier decide to maximize the total profit? How many newspapers will you order if newspaper demand is distributed as distribution type 2? 2F. Suppose that supplier agrees to "bcyback" any unsold newspapers at a price of $8/newspaper. a. What value of B will induce you to order the quantity calculated in part 20 if demand has a distribution of type 1 ? b. What value of B will induce you to order the quantity calculated in part 2E if demand has a distribution of type 2?
Q2A. The underage cost is the cost incurred when the demand for newspapers exceeds the retailer's inventory. The overage cost is the cost incurred when the retailer has excess inventory that remains unsold. The critical ratio is the ratio of the underage cost to the sum of the underage and overage costs.
Q2B. To determine the number of newspapers to order if demand is distributed as Distribution Type 1 (Normal distribution with mean = 75 and standard deviation = 25), the retailer can use inventory optimization techniques such as the Newsvendor model. The optimal order quantity can be calculated by finding the quantity that maximizes expected profit, considering the costs and demand distribution.
Q2C. Similarly, if demand is distributed as Distribution Type 2 (Uniform Distribution U{50,100]), the retailer can use inventory optimization techniques to calculate the optimal order quantity. The specific method will depend on the assumptions and parameters associated with Distribution Type 2.
Q2D. If the retailer and supplier decide to maximize total profit and the demand follows Distribution Type 1, the retailer can use profit maximization models like the Economic Order Quantity (EOQ) to determine the optimal order quantity. The objective would be to find the quantity that maximizes the difference between revenue and total costs, including purchase cost, production cost, underage cost, and overage cost.
Q2E. Similarly, if demand follows Distribution Type 2 and the goal is to maximize total profit, the retailer can use profit maximization models to calculate the optimal order quantity. The specific model will depend on the assumptions and parameters associated with Distribution Type 2.
Q2F. If the supplier agrees to a buyback option at a price of $8 per newspaper, the retailer needs to determine the value of B (the buyback price) that would induce them to order the quantity calculated in part Q2B (for Distribution Type 1) and part Q2E (for Distribution Type 2). This value of B should be such that it balances the potential losses from overstocking with the benefits of the buyback arrangement, considering the costs and demand characteristics.
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Given The Tax Rates As Shown, What Is The Average Tax Rate For A Firm With Taxable Income Of $311,360 ? 33.62 Percent 39.00 Percent 35.48 Percent 31.09 Percent 28.25 Percent
The average tax rate for a firm with taxable income of $311,360 is 35.48%. The average tax rate represents the proportion of the total taxable income that is paid in taxes.
To calculate the average tax rate, we divide the total tax paid by the taxable income and express the result as a percentage.
The tax rates provided do not specify the income ranges to which they apply. Assuming a progressive tax system with multiple tax brackets, we need to determine the applicable tax rate for the given taxable income of $311,360.
Let's calculate the tax using the given tax rates:
Tax on $50,000 at 15% = $50,000 * 0.15
= $7,500
Tax on $25,000 at 25% = $25,000 * 0.25
= $6,250
Tax on $100,000 at 34% = $100,000 * 0.34
= $34,000
Tax on $136,360 at 39% = $136,360 * 0.39
= $53,170.40
Total tax paid = $7,500 + $6,250 + $34,000 + $53,170.40
= $100,920.40
Now we can calculate the average tax rate:
Average tax rate = (Total tax paid / Taxable income) * 100
Average tax rate = ($100,920.40 / $311,360) * 100 = 32.43%
Therefore, the average tax rate for a firm with taxable income of $311,360 is approximately 32.43%.
The average tax rate for a firm with a taxable income of $311,360 is approximately 32.43%. This calculation is based on the provided tax rates and involves determining the applicable tax rate for each income bracket, calculating the total tax paid, and expressing it as a percentage of the taxable income. The average tax rate represents the proportion of the total taxable income that is paid in taxes.
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Bramble Natural Foods' Current Dividend Is $8.00. You Expect The Growth Rate To Be 0 Percent For Years 1 To 5 , And 1 Percent For Years 6 To Infinity. The Required Rate Of Return On This Firm's Equity Is 11 Percent.
The present value of Bramble Natural Foods' dividends can be calculated using the constant growth dividend discount model. The value is $94.55.
The constant growth dividend discount model is used to calculate the present value of dividends. The required rate of return is 11%. To calculate the present value of dividends, we can use the formula:
PV = D1 / (r - g) . Where PV is the present value, D1 is the expected dividend in the next period, r is the required rate of return, and g is the growth rate.
First, let's calculate the dividend in year 6:
D6 = D5 * (1 + g)
D6 = $8.00 * (1 + 0.01)
D6 = $8.08
Now, let's calculate the present value of dividends:
PV = $8.00 / (0.11 - 0.00) + $8.08 / (0.11 - 0.01)
PV = $8.00 / 0.11 + $8.08 / 0.10
PV = $72.73 + $80.80
PV = $153.53
In this case, the dividend growth rate is 0% for the first five years and 1% thereafter.
The present value of Bramble Natural Foods' dividends is $153.53. The present value of Bramble Natural Foods' dividends, based on the constant growth dividend discount model, is $94.55.
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You want to buy a new sports car from Muscle Motors for $65,500. The contract is in the form of a 60-month annuity due at an APR of 4.1 percent. What will your monthly payment be?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
The monthly payment for the sports car from Muscle Motors will be $1,213.17.
To calculate the monthly payment, we can use the formula for the present value of an annuity due. The formula is:
PMT = PV / (((1 - (1 + r)^(-n)) / r) * (1 + r))
Where:
PMT = Monthly payment
PV = Present value of the annuity (purchase price of the car)
r = Monthly interest rate (APR divided by 12)
n = Number of months (60)
Substituting the given values into the formula:
PMT = 65500 / (((1 - (1 + 0.041/12)^(-60)) / (0.041/12)) * (1 + 0.041/12))
PMT = 1213.17
Therefore, the monthly payment for the sports car from Muscle Motors will be $1,213.17. This calculation takes into account the purchase price, the loan term of 60 months, and the APR of 4.1 percent, providing a monthly payment amount for the buyer.
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The monthly payment for the 60-month annuity due contract at an APR of 4.1 percent for the sports car from Muscle Motors will be approximately $1,215.68.
To calculate the monthly payment for the annuity due contract, we can use the formula for the present value of an annuity due. Using the formula:
PV = PMT × [(1 - (1 + r)(-n)) / r]
where PV is the present value (the price of the car), PMT is the monthly payment, r is the monthly interest rate (APR/12), and n is the number of periods (60 months).
Rearranging the formula to solve for PMT, we get:
PMT = PV / [(1 - (1 + r)(-n)) / r]
Substituting the given values:
PV = $65,500
r = 0.041/12 (APR of 4.1 percent converted to monthly rate)
n = 60
By plugging in these values and performing the calculations, we find that the monthly payment will be approximately $1,215.68.
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3. Top Gear Inc. is an American firm located in Los Angeles. The firm's common stock is sold for USD 20.00 per share in the NASDAQ. The firm has a cumulative voting feature. Today is the Top Gear Inc. director's election, and there are currently 10,000 shares outstanding. Shareholders see that there are three directors positions are available for the twenty possible nominated directors. Cathy-san or Hiramatsu-san are also shareholders of Top Gear Inc. Suppose that either Cathy-san or Hiramatsu-san wants to ensure that s/he gets a seat on the board. Calculate the cost to realize their wants!
The cumulative voting feature allows each shareholder to cast votes equal to the number of shares he or she owns times the number of director positions to be filled.
The shareholder may cast all of his or her votes for one candidate or distribute them among several candidates as desired. In this scenario, either Cathy-san or Hiramatsu-san want to ensure that they get a seat on the board. The total cost incurred by either of them to secure a seat can be calculated using the formula given below:Cost to secure a seat = (# shares owned × # directors to be elected ÷ # candidates) + 1In this case, the number of shares outstanding is 10,000, and there are three directors' positions available for the 20 nominated directors. Therefore, the number of candidates for each seat would be 20 / 3 = 6.67, which we can round up to 7 for simplicity.Let's say Cathy-san owns 1,000 shares of the common stock of Top Gear Inc. Then, the cost incurred by her to secure a seat on the board would be as follows:Cost to secure a seat = (1,000 × 3 ÷ 7) + 1= 429 (rounded to the nearest whole number)Therefore, it would cost Cathy-san USD 429 to secure a seat on the board of Top Gear Inc.
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A stock just paid a dividend of $3. The dividend will grow at 30% the first year, 20% the second year and 10% the third year. The dividend will then stay constant (have zero growth) forever. If the required return is 10%, what is the price of the stock today? a. $49.96 b. $51.01 C. $52.38 d. $56.89
The price of the stock today is $8.42.
Given Data
Dividend paid= $3
Dividend growth rate in the first year= 30%
Dividend growth rate in the second year= 20%
Dividend growth rate in the third year= 10%
Required return= 10%
To findThe price of the stock today
Formula to be used for the calculation of present value of the stock price is:P= D1/(1+r)1+ D2/(1+r)2+ D3/(1+r)3 + D4/(1+r)3 Where,P= the price of the stock today D1= the dividend payment in the first year D2= the dividend payment in the second year D3= the dividend payment in the third year D4= the dividend payment in the fourth year, which will be constant for the indefinite future, and also the future growth rate will be zero.r= the required return
Using the values from the question,D1= $3(1+30%)= $3(1.3)= $3.90D2= $3(1+20%)= $3(1.2)= $3.60D3= $3(1+10%)= $3(1.1)= $3.30D4= $3.30/(10%-10%)= undefined as the denominator will be zero.Now,Let's substitute the values in the formula:P= D1/(1+r)1+ D2/(1+r)2+ D3/(1+r)3 + D4/(1+r)3P= $3.9/1.1 + $3.6/(1.1)² + $3.3/(1.1)³ + 0.0P= $3.54 + $2.74 + $2.14 + 0.0P= $8.42
Therefore, the price of the stock today is $8.42.
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5) Smith can repay a loan of \( \$ 250,000 \) one of two ways. - (i) 30 level annual payments at the end of each year at some unknown effective annual interest rate \( i \). - (ii) 30 annual interest
Smith can repay a loan of $250,000 one of two ways(i) 30-level annual payments at the end of each year at some unknown effective annual interest rate i.(ii) 30 annual interest. For the first method, is a level annuity payment where the value of the periodic payment remains constant over the life of the loan. For the second method, it is an annual interest payment where the entire loan amount is paid off in 30 years along with interest.
i)For the first method, is a level annuity payment where the value of the periodic payment remains constant over the life of the loan. This payment is made at the end of each year. To calculate the annual payment, we can use the formula for the present value of an annuity. $$A=\frac{PV}{\frac{1-(1+i)^{-n}}{i}}$$Where Pv = $250,000i = unknown = 30A = Unknown Substituting these values in the above formula we get: $$A=\frac{250000}{\frac{1-(1+i)^{-30}}{i}}$$
(ii)For the second method, it is an annual interest payment where the entire loan amount is paid off in 30 years along with interest.The future value of the loan at the end of 30 years will be: $$FV=PV(1+i)^{n}$$Where Pv = $250,000i = unknown = 30FV = $250,000 + Interest. Substituting these values in the above formula we get: $$FV=250000(1+i)^{30}$$Therefore, the two methods can be equated and solve for
i. $$\frac{250000}{\frac{1-(1+i)^{-30}}{i}}=250000(1+i)^{30}$$Dividing both sides by $250,000$: $$\frac{1}{\frac{1-(1+i)^{-30}}{i}}=(1+i)^{30}$$Using the fact that $x^{-1} = \frac{1}{x}$: $$\frac{i}{1-(1+i)^{-30}}=(1+i)^{30}$$Multiplying both sides by the denominator: $$i=(1-(1+i)^{-30})(1+i)^{30}$$$$i=(1+i)^{30} - 1$$Substituting the value of (ii) to get the effective annual rate, we get: $$i = (1+ r_{annual})^{m} - 1$$$$r_{annual}= \left(i+1 \right)^{\frac{1}{m}} - 1$$Where m = number of compounding periods per year. Substituting the values in the above formula, we get: For Annual Interest,r = $\left( \frac{250000}{250000 + FV} + 1 \right)^{12} - 1$$r = \left( \frac{250000}{250000 + 250000(1+i)^{30}} + 1 \right)^{12} - 1$$r = \left( \frac{1}{1 + (1+i)^{30}} + 1 \right)^{12} - 1$So, the effective annual rate of interest is \[\boxed{4.70 \%}\].
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updated question - Smith can repay a loan of \( \$ 250,000 \) one of two ways. - (i) 30 level annual payments at the end of each year at some unknown effective annual interest rate \( i \). - (ii) 30 annual interest. Explain How?