To resolve the special cases in a transportation problem, we can employ the following approaches:
i. Unbalanced transportation problem:
An unbalanced transportation problem occurs when the total supply does not equal the total demand. To address this, we can introduce a dummy source or dummy destination to balance the problem. A dummy source represents additional supply, while a dummy destination represents additional demand. These dummy variables have zero costs and are used to balance the problem.
ii. Degeneracy:
Degeneracy occurs when one or more of the basic variables in the initial basic feasible solution are zero. This can lead to difficulties in finding an optimal solution using conventional methods. To resolve degeneracy, we can use various techniques such as the stepping stone method or the modified distribution method. These techniques help us identify alternative routes in the transportation tableau and facilitate the search for an optimal solution.
iii. Maximization:
The standard transportation problem is typically formulated as a minimization problem, where the objective is to minimize the total transportation cost. However, if we need to maximize the objective, we can convert it into an equivalent minimization problem by taking the negative of the objective function coefficients. We then solve the modified minimization problem using standard transportation algorithms.
b) To obtain the initial basic feasible solution using the lowest cost entry method, we follow these steps:
Step 1: Identify the cell with the lowest cost in the transportation tableau. If there are multiple cells with the same lowest cost, choose any one.
Step 2: Allocate as much quantity as possible to the identified cell without violating the supply and demand constraints.
Step 3: Cross out the corresponding row or column if the supply or demand for that row or column is fulfilled.
Step 4: Repeat steps 1 to 3 until all supply and demand requirements are met.
In the given transportation problem:
Origin: 1 2 3 4
Destination:
1 2 3 4 5
2 8 7 6 5
3 6 3 4 2
Demand: 7 4 6 9
Supply: 4 1 2 5
Using the lowest cost entry method, we start by allocating quantity from the cell with the lowest cost, which is cell (3, 4) with a cost of 2. We allocate as much as possible, which is 2 units, and update the supply and demand values accordingly. The modified tableau is as follows:
Origin: 1 2 3 4
Destination:
1 2 3 4 5
2 8 7 6 5
3 6 3 4 -
Demand: 7 4 6 9
Supply: 4 1 2 3
Now, we continue the lowest cost entry method until all supply and demand requirements are fulfilled. We allocate the remaining quantities using the same approach. The final tableau would look as follows:
Origin: 1 2 3 4
Destination:
1 2 3 4 5
2 6 3 1 0
3 2 1 3 0
Demand: 7 4 6 9
Supply: 0 0 0 3
c) To find the optimal solution using the stepping stone method, we follow these steps:
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Today you are writing a put option on TSLA stock, which is currently valued at $200 per share. The put option has a strike price of $170, 2 months to expiration, and currently trades at a premium of $3.2 per share.
If at maturity the stock is trading at $154, what is your net profit on this position? Keep in mind that one option covers 100 shares.
After considering the premium paid for the option, the net profit on this put option position is $1,280.
To calculate the net profit on the put option position, we need to consider the premium paid for the option and the difference between the strike price and the stock price at maturity.
Stock price at maturity (S) = $154
Strike price (X) = $170
Premium paid per share (P) = $3.2
Number of shares per option = 100
First, let's determine the intrinsic value of the put option at maturity. The intrinsic value is the difference between the strike price and the stock price if it's lower than the strike price. Otherwise, it's zero.
Intrinsic Value = Max(0, X - S)
= Max(0, $170 - $154)
= Max(0, $16)
= $16
Since the stock price at maturity is below the strike price, the intrinsic value is $16.
To calculate the net profit, we need to subtract the premium paid per share from the intrinsic value and multiply it by the number of shares per option.
Net Profit = (Intrinsic Value - Premium) * Number of shares per option
= ($16 - $3.2) * 100
= $12.8 * 100
= $1,280
Therefore, the net profit on this put option position is $1,280.
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A mutual fund pays 3.6% APR compounded monthly. How much money should I deposit in the account today if I want the balance of the account to be $8,000 in 10 years
you should deposit approximately $5,262.92 in the mutual fund today if you want the balance of the account to be $8,000 in 10 years.
To find out how much money you should deposit in the mutual fund today, you can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the final balance of the account
P = the principal amount (the initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, you want the final balance (A) to be $8,000, the annual interest rate (r) is 3.6% (or 0.036 as a decimal), and the interest is compounded monthly, so n = 12. The number of years (t) is 10.
Let's plug in the values and solve for P:
$8,000 = P(1 + 0.036/12)^(12*10)
Simplifying the equation:
$8,000 = P(1.003)^120
Divide both sides by (1.003)^120:
P = $8,000 / (1.003)^120
Calculating this using a calculator or spreadsheet, you would find that P is approximately $5,262.92.
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A stock has had returns of 5 percent, 14 percent, −3 percent, and 4 percent over the last four years. What is the geometric average return over this period? 5.33\% 4.83% 7.67% 5.00% 5.00%
The geometric average return over the period is 4.83%.
The geometric average return is also referred to as the geometric mean. It is a statistical metric that calculates the average rate of return, which reduces the investment's variability over the entire period. When the period has just a few data points, the geometric mean is the most precise method of calculating the average return on an investment. The geometric mean is often used in finance because it produces a more comprehensive average return over time when compared to the arithmetic mean.
To calculate the geometric average return, use the following formula: ((1 + return1) x (1 + return2) x (1 + return3)…)^(1/n) – 1. Where “n” is the number of years (or periods) in the data set.The formula to calculate the geometric mean of the returns of a stock over a certain period is as follows:((1 + r1) (1 + r2) (1 + r3)…(1 + rn))1/n - 1, where n is the number of years.The geometric average return for the stock over the last four years can be calculated as follows:First, calculate the total return:5% + 14% - 3% + 4% = 20%
Then, find the geometric average:((1 + 0.05) × (1 + 0.14) × (1 − 0.03) × (1 + 0.04))^0.25 − 1=1.0483 - 1= 0.0483 = 4.83%
Therefore, the geometric average return over this period is 4.83%.
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HawkEye Sports Ltd. sponsors a defined benefit plan for its employees. They have 200 employees, 25 of whom are excludable. 30 of the non-excludable employees are HC, and the remaining 145 are NHC employees. 15 of the HC employees are covered under the defined benefit plan, and 115 of the NHC employees are covered under the defined benefit plan. The average benefit percentage for the HC is 18 percent, and the average benefit percentage for the NHC is 9.5 percent.
Question 9 Saved
Does this defined benefit plan pass the general safe harbor test?
Based on the given information, the defined benefit plan does not pass the general safe harbor test.
To determine whether the defined benefit plan passes the general safe harbor test, we need to compare the average benefit percentage for the highly compensated (HC) employees to the average benefit percentage for the non-highly compensated (NHC) employees.
According to the given information:
Total employees: 200
Excludable employees: 25
Non-excludable employees: 200 - 25 = 175
HC employees: 30
NHC employees: 175 - 30 = 145
HC employees covered under the defined benefit plan: 15
NHC employees covered under the defined benefit plan: 115
Average benefit percentage for HC: 18%
Average benefit percentage for NHC: 9.5%
To determine if the plan passes the general safe harbor test, the ratio of the average benefit percentage for HC employees to the average benefit percentage for NHC employees should not exceed the safe harbor threshold.
Calculating the ratio:
Ratio = (Average benefit percentage for HC) / (Average benefit percentage for NHC)
Ratio = 18% / 9.5%
Ratio ≈ 1.89
The safe harbor threshold for the general safe harbor test is typically 1.25. If the ratio exceeds 1.25, the plan would not pass the test.
In this case, since the ratio is approximately 1.89, which is higher than 1.25, the defined benefit plan does not pass the general safe harbor test.
Therefore, based on the given information, the defined benefit plan does not pass the general safe harbor test.
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(Topic: WACC) Here is some information about Stokenchurch Inc.:
Beta of common stock = 0.3
Treasury bill rate = 0.25%
Market risk premium = 4.37%
Yield to maturity on long-term debt = 1.23%
Preferred stock price = $35
Preferred dividend = $3 per share
Book value of equity = $142 million
Market value of equity = $309 million
Long-term debt outstanding = $275 million
Shares of preferred stock outstanding = 3.4 million
Corporate tax rate = 21%
What is the company's WACC?
(Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Answer:
The company's WACC is 1.07%.
Explanation:
I calculate the cost of each type of financing as follows:
Cost of equity:
Re = Rf + beta * (Rm - Rf)
where Rf is the risk-free rate, Rm is the market return, and beta is the beta of the company's common stock.
Re = 0.0025 + 0.3 * 0.0437 = 0.01561 or 1.561%
Cost of debt:
Rd = YTM = 0.0123 or 1.23%
Cost of preferred stock:
Rp = Dp / Pp
where Dp is the preferred dividend and Pp is the preferred stock price.
Rp = 3/35 = 0.08571 or 8.571%
Next, we calculate the weights of each type of financing in the company's capital structure:
Weight of equity = market value of equity / (market value of equity + book value of debt + market value of preferred stock)
= $309 million / ($309 million + $275 million + $119 million)
= 0.4386
Weight of debt = book value of debt / (market value of equity + book value of debt + market value of preferred stock)
= $275 million / ($309 million + $275 million + $119 million)
= 0.3883
Weight of preferred stock = market value of preferred stock / (market value of equity + book value of debt + market value of preferred stock)
= $119 million / ($309 million + $275 million + $119 million)
= 0.1731
Finally, we can calculate the WACC as the weighted average of the cost of each type of financing:
WACC = (weight of equity * cost of equity) + (weight of debt * cost of debt) + (weight of preferred stock * cost of preferred stock) * (1 - corporate tax rate)
= (0.4386 * 0.01561) + (0.3883 * 0.0123) + (0.1731 * 0.08571) * (1 - 0.21)
= 0.0107 or 1.07%
Therefore, the company's WACC is 1.07%.
Janis, owner of Joplin’s Mercedes Benz Dealership, has just purchased a new hydraulic lift for her dealership. The lift cost her $10,000. She estimates that the equipment will last for 3 years. She also estimates that her additional net cash revenues from the purchase and use of the machine will be: $3,000 at the end of year 1, $3,500 at the end of year 2, and $4,000 at the end of year 3. The interest rate that Janis could have earned if she invested the $10,000 for three years in a financial institution is 4.5% per year. Janis is now having second thoughts on whether this was a smart purchase and wants to know the resale value of the hydraulic lift at the end of three years that she will need in order to breakeven by the end of 3 years. Assuming Janis focuses on just breaking even, determine the resale value Janis would need in order to breakeven. Show all your work and present the cash flows on a timeline.
Janis would need a resale value of $312.57 in order to break even by the end of 3 years.
To determine the resale value Janis would need in order to break even by the end of 3 years, we need to calculate the present value of the cash flows and compare it to the cost of the hydraulic lift.
Step 1: Calculate the present value of the cash flows.
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3
PV = $3,000/(1+0.045)^1 + $3,500/(1+0.045)^2 + $4,000/(1+0.045)^3
PV = $2,869.57 + $3,242.63 + $3,575.23
PV = $9,687.43
Step 2: Compare the present value to the cost of the hydraulic lift.
Cost of hydraulic lift = $10,000
If the present value is equal to the cost of the hydraulic lift, then Janis will break even. Therefore, the resale value Janis would need in order to break even is:
Resale value = Cost of hydraulic lift - Present value
Resale value = $10,000 - $9,687.43
Resale value = $312.57
Therefore, Janis would need a resale value of $312.57 in order to break even by the end of 3 years.
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Janis would need to sell the hydraulic lift for a resale value of $9,394.23 in order to break even.
To determine the resale value Janis would need in order to break even, we need to calculate the present value of the net cash revenues and compare it to the initial cost of the hydraulic lift.
Step 1: Calculate the present value of the net cash revenues:
- Year 1: $3,000 / (1 + 0.045) = $2,873.56
- Year 2: $3,500 / (1 + 0.045)^2 = $3,161.55
- Year 3: $4,000 / (1 + 0.045)^3 = $3,359.12
Step 2: Calculate the total present value of the net cash revenues:
Total PV = $2,873.56 + $3,161.55 + $3,359.12 = $9,394.23
Step 3: Compare the total present value of the net cash revenues to the initial cost:
$9,394.23 - $10,000 = -$605.77
Since the total present value is negative, it means Janis would need to sell the hydraulic lift for at least $605.77 less than the initial cost of $10,000 in order to break even.
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A broker offers to sell shares of Bay Area Healthcare, which just paid a dividend of $2 per share. The dividend is expected to grow at a constant rate of 5 percent per year. The stock's required rate of return is 12 percent.
a. What is the expected dollar dividend over the next three years?
b. What is the current value of the stock and the expected stock price at the end of each of the next three years?
c. What is the expected dividend yield and capital gains yield for each of the next three years?
d. What is the expected total return for each of the next three years?
e. How does the expected total return compare with the required rate of return on the stock? Does this make sense? Explain your answer.
a. Expected dollar dividend over the next three years
= D₁ (1+ g) + D₂ (1+ g)² + D₃ (1+ g)³. Here D1 = $2, growth rate = 5%, D2 = D1 (1 + g) = $2.10, D3 = D2 (1+g) = $2.205.
Thus, the expected dollar dividend over the next three years = $2 (1+.05) + $2.10 (1+.05)² + $2.205 (1+.05)³ = $6.8267 (rounded to $6.83).
b. Using the dividend discount model: P0 = D₁ / (1+ r) + D₂ / (1+ r)² + D₃ / (1+ r)³ + P₃ / (1+ r)³, where P₃ is the expected price of the stock at the end of year 3. P0 = $2 / (1+.12) + $2.10 / (1+.12)² + $2.205 / (1+.12)³ + P₃ / (1+.12)³. Using the formula, we get P0 = $6.76 and P₃ = $74.09. Thus, the current value of the stock is $6.76 and the expected stock price at the end of year 1 is $8.72, at the end of year 2 is $11.28 and at the end of year 3 is $74.09.
c. Dividend yield = D₁/P₀ , Capital gains yield = (P₁ - P₀) / P₀.
Using the formula, we get
Dividend yield for year 1 = $2/$6.76 = 0.2959 (rounded to 29.59%),
Dividend yield for year 2 = $2.10/$8.72 = 0.2408 (rounded to 24.08%),
Dividend yield for year 3 = $2.205/$11.28 = 0.1955 (rounded to 19.55%).
Capital gains yield for year 1 = ($8.72-$6.76)/$6.76 = 0.2896 (rounded to 28.96%),
Capital gains yield for year 2 = ($11.28-$8.72)/$8.72 = 0.2936 (rounded to 29.36%),
Capital gains yield for year 3 = ($74.09-$11.28)/$11.28 = 5.5611 (rounded to 556.11%).
d. Expected total return = Dividend yield + Capital gains yield.
Using the formula,
we get
Expected total return for year 1 = 29.59% + 28.96% = 58.55%,
Expected total return for year 2 = 24.08% + 29.36% = 53.44%,
Expected total return for year 3 = 19.55% + 556.11% = 575.66%.
e. The expected total return for year 3 is much higher than the required rate of return. The expected total return for year 3 is 575.66%, and the required rate of return on the stock is 12%. It does not make sense to have a total return of 575.66% because it is too high and unrealistic.
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1. What does Wall Street have to do with home mortgages? Should Wall Street have its hand in home mortgages?
2. What is shorting, collateralized debt obligation (CDO), and credit default swaps (CDS)? Knowing that the market works on supply and demand, should it be allowed to short on CDO's & CDS's?
3. What did you think about the punishment for people involved in this collapse?
4. What are your thoughts on the credit rating agencies? As a business did they have an obligation to the public?
5. Who is to blame for the financial crisis, the public's greed or Wall Street's greed?
1.Wall Street has a connection to home mortgages because it plays a significant role in the financial industry, including the mortgage market.
2.Horting refers to the practice of betting against an asset's value. Collateralized debt obligations (CDOs) are securities created by pooling various types of debt, including mortgages.
3. The punishment for people involved in the collapse of the financial crisis varied.
4.Credit rating agencies are businesses that assess the creditworthiness of debt issuers and their securities.
5.The financial crisis was the result of a combination of factors, including both the public's and Wall Street's greed.
1. Wall Street firms buy mortgages from lenders, package them into securities called collateralized debt obligations (CDOs), and sell them to investors. This helps lenders manage their risks and provides funds for more mortgages. However, Wall Street's involvement in home mortgages also contributed to the 2008 financial crisis.
As for whether Wall Street should have its hand in home mortgages, opinions may vary.
Some argue that the involvement of Wall Street can lead to innovation and access to capital for homebuyers.
Others believe that Wall Street's profit-driven approach can create incentives for risky behavior and contribute to economic instability.
2. Shorting refers to the practice of betting against an asset's value.
Collateralized debt obligations (CDOs) are securities created by pooling various types of debt, including mortgages.
Credit default swaps (CDS) are financial contracts that provide insurance against the default of a debt instrument, including CDOs.
Allowing shorting on CDOs and CDSs is a controversial topic.
Proponents argue that shorting can help provide liquidity and reveal market inefficiencies.
However, critics argue that shorting can exacerbate market downturns and lead to price manipulation.
Ultimately, whether shorting on CDOs and CDSs should be allowed is a complex policy question that requires consideration of potential risks and benefits.
3. Some individuals faced legal consequences, such as fines or imprisonment,
for their involvement in fraudulent activities or illegal practices.
Financial institutions also faced repercussions, including bailouts, fines, and regulatory changes aimed at preventing similar crises in the future.
4These agencies assign ratings that help investors make informed decisions.
During the financial crisis, credit rating agencies were criticized for providing overly optimistic ratings to certain mortgage-backed securities, which contributed to the crisis.
As businesses, credit rating agencies have a duty to the public to provide accurate and unbiased ratings.
The financial crisis highlighted shortcomings in their practices, such as potential conflicts of interest and a lack of transparency.
Since then, regulatory reforms have been implemented to enhance the accountability and reliability of credit rating agencies.
5. The financial crisis was the result of a combination of factors, including both the public's and Wall Street's greed.
On one hand, the public's desire for homeownership and access to credit led to increased demand for mortgages.
On the other hand, Wall Street's pursuit of profits led to the creation and sale of complex financial products tied to mortgages, which were often risky and poorly understood.
Blaming one party solely would oversimplify the complexity of the crisis.
It was a systemic failure involving various stakeholders, including lenders, borrowers, regulators, and financial institutions.
Addressing the root causes of the crisis requires a comprehensive approach that addresses both individual responsibility and structural issues in the financial system.
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Elaborate on the four methods to optimize cash flow between subsidiaries as well between subsidiaries and parent companies.
Optimizing cash flow between subsidiaries as well as between subsidiaries and parent companies are crucial to the financial success of companies.
Here are the four methods that can be used to optimize cash flow:
Centralization of cash management: Centralization of cash management is a process whereby the cash resources of the subsidiaries are consolidated and managed centrally by the parent company. This can be done by creating a cash pool that is made up of the cash balances of all the subsidiaries.
Cash concentration systems: Cash concentration systems can be used to optimize cash flow. This system involves consolidating the cash from various subsidiaries into a single account held by the parent company. This method helps to reduce the number of bank accounts that a company has to maintain.
Payment and cash collection systems: Payment and cash collection systems can be optimized by using electronic payment systems. Electronic payment systems can help to speed up the payment and collection process. This, in turn, can improve the cash flow of the subsidiaries and the parent company.
Cash flow forecasting: Cash flow forecasting is an essential tool for optimizing cash flow. Cash flow forecasting can help to identify potential cash flow issues and help to develop strategies to mitigate these issues. By forecasting cash flow, the parent company can make informed decisions about how to allocate resources and make investments.
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Consider an economy where the production function is Yt = AtK^atL^1-at, with a = 0.75. If capital is growing at a rate of 3% per year, labour growing at a rate of 2% per year and the rate of output growth is 4% per year, then the annual growth rate of total factor productivity is;
a) 0.75%
b) 1.5%
c) 0.5%
d) 1%
e) 1.25%
We are given that K is growing at a rate of 3% and L is growing at a rate of 2%. In that case, Now, to solve for Y, we must use the production function: We now have all of the values we require to solve for the rate of TFP growth: Therefore, the TFP growth rate is approximately 1.25%. The correct option is (e) 1.25%.
Total Factor Productivity (TFP) is a measure of the productivity of a production method that takes into account all of the inputs used in the production process. Total Factor Productivity (TFP) growth is caused by the advancement of technology, greater knowledge, and skill, or improved management practices. The Solow Model indicates that TFP growth is critical for long-term economic development.
Given: The production function is Yt = AtK^atL^1-at, with a = 0.75.
Capital is growing at a rate of 3% per yearLabour growing at a rate of 2% per yearThe rate of output growth is 4% per yearWe can use the Solow-Swan growth model to solve for the TFP growth rate. The Solow-Swan growth model, in its simplest form, is: It is important to note that this formula is derived from the production function Y = F (K, L), where K is capital, L is labor, and Y is output. Solow proposed that technology and knowledge advancements drive long-term economic growth. So, Solow assumed that the technological progress is exponential at the rate of n.
This means that in our formula above, Therefore, to determine the rate of TFP growth, we must first calculate the growth rates of K, L, and Y. Here's how to do it:
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A Ceramic Compay, KERAMIKU, produces two types of ceramic, Rough Ceramic and Smooth Ceramic. The Production Manager has been successful in formưlating a model to maximize profit to produce both types of ceramic. The model is given as follows: K=25A 1−0.8A 12+30A2 −1.2A 2 Producing Rough Ceramic and Smooth Ceramic requires 1 and 2 labor hours respectively and the total labor hour available per day is 40 hours 1. Using Lagrange Multipliers Method, determine the number of Rough Ceramic and Smooth Ceramic to produce in order to maximize the profit! What is the total profit? 2. Use solver to find the solution 3. What is the meaning of Lagrange Multiplier value that is obtained in point (a)?
1. The number of Rough Ceramic and Smooth Ceramic to be produced in order to maximize the profits is 0.5 units of Rough Ceramic and 19.5 units of Smooth Ceramic to maximize profit. The total profit is $12.5.
2. To use the solver to find the solution, you can input the profit function and the constraint into a solver tool (such as Microsoft Excel Solver or any optimization software) to obtain the optimal values for A and B.
3. The Lagrange multiplier value obtained in point (a) (λ = 0.625) represents the marginal rate of substitution between the constraint (labor hours) and the objective function (profit).
To maximize the profit and determine the number of Rough Ceramic and Smooth Ceramic to produce, we can use the Lagrange Multipliers Method.
1. To find the number of each type of ceramic, we set up the following equations:
- Maximizing the profit: Maximize K = 25A(1 - 0.8A^2) + 30A^2 - 1.2A^2
- Subject to the constraint: 1A + 2B = 40 (where A represents Rough Ceramic and B represents Smooth Ceramic)
We introduce a Lagrange multiplier (λ) to solve this problem: L = K - λ(1A + 2B - 40)
Taking partial derivatives and setting them to zero, we get:
∂L/∂A = 0: 25 - 80A + 60A^2 - λ = 0
∂L/∂B = 0: -2λ = 0 (since there is no B term in K)
Solving these equations, we find A = 0.5 and λ = 0.625.
Therefore, we should produce 0.5 units of Rough Ceramic and 19.5 units of Smooth Ceramic to maximize profit.
To calculate the total profit, substitute the values back into the profit function:
K = 25(0.5)(1 - 0.8(0.5)^2) + 30(0.5)^2 - 1.2(0.5)^2 = $12.5
So, the total profit is $12.5.
2. Alternatively, we can use Solver, an optimization tool in software like Microsoft Excel, to find the solution numerically. By setting up the objective function and the constraints, we can let the Solver algorithm determine the optimal values of A and B that maximize the profit.
3. The Lagrange multiplier value obtained in point (a) (λ = 0.625) represents the rate at which the profit changes with respect to a unit increase in the constraint (labor hours available per day). It indicates the marginal value of an additional unit of labor hours in terms of profit.
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during its first five years of operations, white consulting reports net income and pays dividends as follows. required: calculate the balance of retained earnings at the end of each year. note that retained earnings will always equal $0 at the beginning of year 1. chegg
The balance at the end of Year 4 becomes the beginning balance for Year 5
To calculate the balance of retained earnings at the end of each year, we need to consider the net income and dividends paid during each year.
Year 1: Since the retained earnings begin at $0, the balance at the end of Year 1 will be the net income minus the dividends paid.
Year 2: The balance at the end of Year 1 becomes the beginning balance for Year 2. To calculate the balance at the end of Year 2, add the net income to the beginning balance and subtract the dividends paid.
Year 3: Similarly, the balance at the end of Year 2 becomes the beginning balance for Year 3. Add the net income to the beginning balance and subtract the dividends paid to find the balance at the end of Year 3.
Year 4: Repeat the same process. The balance at the end of Year 3 becomes the beginning balance for Year 4. Add the net income and subtract the dividends paid to find the balance at the end of Year 4.
Year 5: Finally, the balance at the end of Year 4 becomes the beginning balance for Year 5. Add the net income and subtract the dividends paid to find the balance at the end of Year 5.
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What is the most basic economic problem?
a. the theory of demand and supply
b. greed
c. economic growth
d. productivity
e. scarcity
f. profit
The most basic economic problem is scarcity. Scarcity refers to the condition in which resources are limited and unable to satisfy all human wants and needs. The correct option is e.
Scarcity is the fundamental challenge faced by individuals, societies, and economies. It stems from the fact that resources such as land, labor, capital, and time are finite, while human wants and needs are virtually unlimited.
This creates a situation where choices must be made about how to allocate these scarce resources to fulfill various competing needs and desires.
Due to scarcity, individuals and societies must make trade-offs and prioritize their needs and wants. It drives the necessity for economic decision-making, resource allocation, and the study of how individuals and societies manage limited resources to meet their unlimited wants and needs.
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Direction: Answer the following question by using the required calculation and facts.(10 Marks)
1. Partner Ali & Partner Marhoon entered into Mudarabah contract of 3 years. Partner Ali invested BD10000/- as part of capital investment. Profit and loss ratio will be 70:30. Answer the following: Appraise valid explanation on the below questions.
A. Who is the Mudarib ? Rab ul Mal?why?(4 marks)
B. Is this transaction Sharia Compliant? State the rulings? (3 marks)
C. Can partner A terminate the contract on his own? Why? ( 3 marks)
D. Profit of BD 20000/-accumulated during the year after deducting admin expenses of BD2000/- how much will be PLS between them.
The profit and loss ratio of 70:30 indicates that the Mudarib (Partner Marhoon) will receive 70% of the profits, and the Rab ul Mal (Partner Ali) will receive 30% of the profits.
Based on the information provided, this transaction appears to be Sharia compliant as it follows the principles of Mudarabah, which is a type of Islamic financial contract. Mudarabah involves a partnership where one party provides the capital (Rab ul Mal) and the other party provides the expertise and labor (Mudarib). The profit and loss sharing ratio is agreed upon in advance, and the profits are distributed accordingly. As long as the transaction adheres to the principles of Mudarabah, such as transparency, fairness, and avoidance of prohibited activities, it would be considered Sharia compliant.
In a Mudarabah contract, the Rab ul Mal (Partner Ali) generally has the right to terminate the contract if there is a valid reason, such as a breach of the agreed-upon terms or misconduct by the Mudarib (Partner Marhoon). However, it is important to note that the specific terms and conditions of the contract need to be reviewed to determine the exact rights and provisions related to contract termination. Without further information, it is not possible to definitively state whether Partner Ali can terminate the contract on their own.
The profit sharing between Partner Ali and Partner Marhoon would be based on the agreed profit and loss sharing ratio of 70:30. From the total accumulated profit of BD 20,000, after deducting the admin expenses of BD 2,000, the remaining profit available for distribution would be BD 18,000. Applying the profit sharing ratio, Partner Marhoon would receive 70% of the profit (70% of BD 18,000 = BD 12,600), and Partner Ali would receive 30% of the profit (30% of BD 18,000 = BD 5,400).
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and $3,000 in GM stoek with an expected rate of return of 159 , the 13.08. 12.41. 14.51. 13.5% 9.65.
The expected return on your portfolio is 13% if you put $2,000 into GM stock and $3,000 into a stock with an expected rate of return of 10%. Option E is correct.
Amount invested 1 = $2,000
Amount invested 2 = $3,000
Expected return 1 = 10%
Expected return 2 = 15%
Weight of stock 1 = Amount invested 1 / (Amount invested 1 + Amount invested 2)
Weight of 1 = $2000 / ($2000 + $3000)
Weight of 1 = $2000 / $5000
Weight of 1 = $0.40
Weight of 2 =(1- Weight of 1)
Weight of stock 2 =(1- 0.40)
Weight of stock 2 =0.60
Portfolio expected return is 13%
Portfolio return alludes to the addition or misfortune acknowledged by a speculation portfolio containing a few sorts of ventures. Based on the stated goals of the investment strategy and the risk tolerance of the investors targeted by the portfolio, portfolios aim to deliver returns.
Over a given time period, interest, capital gains, dividends, and distributions are included in total return. All in all, the complete profit from a venture or a portfolio incorporates both pay and appreciation. Complete return financial backers ordinarily center around the development in their portfolio over the long haul.
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Complete question as follows:
If you invest $ 2000 in a stock with expected rate of return 10% and $3,000 in GM stock with an expected rate of return of 15% , then expected return on your portfolio is
A. 13.08. %
B. 12.41. %
C. 14.51.%
D. 13.5%
E. 13%
1. Royal Lawncare Company produces and sells two packaged products—Weedban and Greengrow. Revenue and cost information relating to the products follow:
Product
Weedban Greengrow
Selling price per unit $ 11.00 $ 36.00
Variable expenses per unit $ 2.80 $ 11.00
Traceable fixed expenses per year $ 135,000 $ 38,000
Last year the company produced and sold 44,000 units of Weedban and 18,500 units of Greengrow. Its annual common fixed expenses are $113,000.
2.. Variable costs per unit: Manufacturing: Direct materials Direct labor Variable manufacturing overhead Variable selling and administrative Fixed costs per year: Fixed manufacturing overhead Fixed selling and administrative expenses Required: 1. Assume the company uses variable costing: a. Compute the unit product cost for Year 1 and Year 2. During its first year of operations, Walsh produced 50,000 units and sold 40,000 units. During its second year of operations, it produced 40,000 units and sold 50,000 units. The selling price of the company's product is $54 per unit. Complete this question by entering your answers in the tabs below. Req 1A b. Prepare an income statement for Year 1 and Year 2. 2. Assume the company uses absorption costing: a. Compute the unit product cost for Year 1 and Year 2. b. Prepare an income statement for Year 1 and Year 2. 3. Reconcile the difference between variable costing and absorption costing net operating income in Year 1. Req 18 Unit product cost Reg 2A Year 1 $ 23 $ 10 Req 28 Year 2 $5 $4 Req 3 $ 320,000 $ 100,000 Assume the company uses variable costing. Compute the unit product cost for year 1 and year 2. He Req 1A Req 18 Req 2A Net operating income (loss) Req 28 Req 3 Assume the company uses variable costing. Prepare an income statement for Year 1 and Year 2. Walsh Company Income Statement Year 1 Year 2
The contribution layout earnings announcement segmented by using product strains for Royal Lawncare Company's well-known shows that whilst the Weedban product line incurred an internet lack of $24,000, the Greengrow product line generated an internet profit of $42,000. The overall net earnings for the employer is $18,000.
Royal Lawncare Company Contribution Format Income Statement (Segmented by using Product Lines)
Product Line Weedban Greengrow Total
Units Sold 15,000 28,000
Selling Price according to Unit $6.00 $7.50
Sales Revenue $ninety,000 $210,000 $300,000
Variable Expenses according to Unit $2.40 $5.25
Variable Cost of Goods Sold $36,000 $147,000 $183,000
Contribution Margin $54,000 $63,000 $117,000
Traceable Fixed Expenses $45,000 $21,000
Common Fixed Expenses $33,000
Total Fixed Expenses $78,000 $21,000
Net Income ($24,000) $42,000 $18,000
Note: The contribution format earnings declaration separates prices into a variable and fixed additives. It gives a clear view of the profitability of every product line by deducting variable expenses from income revenue to achieve the contribution margin. Then, constant fees, both traceable and common, are subtracted to decide the net earnings for each product line.
In this case, Weedban incurred an internet loss of $24,000, at the same time as Greengrow generated a net profit of $42,000. The total net earnings for the employer is $18,000.
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The correct question is:
"Royal Lawncare Company produces and sells two packaged products: Weedban and Greengrow.
Revenue and cost information relating to the products follow:
Product
Weedban Greengrow
Selling price per unit $6.00 $7.50
Variable expenses per unit $2.40 $5.25
Traceable fixed expenses per year $45,000 $ 21.000
Common fixed expenses in the company total $33,000 annually.
Last year the company produced and sold 15,000 units of Weedban and 28,000 units of Greengrow.
Required:
Prepare a contribution format income statement segmented by product lines."
1. what is the market size and revenues of the top 5 companies in the global hotel industry?
2. barriers to enter the global hotel industry?
The market size and revenues of the top 5 companies in the global hotel industry vary depending on the specific companies and the time period in question. Barriers to enter the global hotel industry include high initial investment costs, competition from established hotel chains, government regulations and policies.
1. What is the market size and revenues of the top 5 companies in the global hotel industry?
The market size and revenues of the top 5 companies in the global hotel industry vary depending on the specific companies and the time period in question. It is difficult to provide exact figures without specific data. However, some of the largest companies in the industry include Marriott International, Hilton Worldwide Holdings, InterContinental Hotels Group, AccorHotels, and Wyndham Hotels & Resorts.
2. What are the barriers to enter the global hotel industry?
There are several barriers to enter the global hotel industry. These can include high initial investment costs, competition from established hotel chains, government regulations and policies, difficulty in acquiring suitable properties in prime locations, and the need for significant marketing and advertising efforts to establish a brand presence. Additionally, maintaining high service standards and ensuring customer satisfaction can also pose challenges for new entrants.
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You Are Also Trying To Demonstrate The Value Of Compound Interest To A Client Who Is Just Starting To Save For Retirement. Build A Yearly Model Based On The Client Saving $5,000 Per Year And Earning 8% Per Year In Their Investment Portfolio. Investment Returns Are Earned On The Closing Balance From The Prior Year. What Is The Client’s Retirement Savings
The client's retirement savings, based on saving $5,000 per year and earning 8% per year with compound interest, will be approximately $384,255.33.
To calculate the client's retirement savings, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the client saves $5,000 per year, so the principal (P) is $5,000. The interest rate (r) is 8%, which can be written as 0.08. Assuming interest is compounded annually (n = 1), and let's consider a retirement period of 30 years (t = 30).
Using the formula,
A = 5000(1 + 0.08/1)^(1*30), we can calculate the final amount:
A = 5000(1.08)^30
A ≈ $384,255.33
By saving $5,000 per year and earning an 8% annual return with compound interest, the client can accumulate approximately $384,255.33 for their retirement savings over a 30-year period.
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"
Suppose an economy's real GDP is $100,000 in year 1 and $110,000 in year 2. What is the growth rate of its GDP? Assume that population was 200 in year 1 and 205 in year 2. What is the growth rate in GDP per capita"
The growth rate in GDP per capita is approximately 7.32%.
To calculate the growth rate of GDP, we use the formula: Growth rate = ((GDP Year 2 - GDP Year 1) / GDP Year 1) * 100.
Using the given values:
GDP Year 1 = $100,000
GDP Year 2 = $110,000
Growth rate = ((110,000 - 100,000) / 100,000) * 100 = 10%
To calculate the growth rate in GDP per capita, we use the formula: Growth rate = ((GDP per capita Year 2 - GDP per capita Year 1) / GDP per capita Year 1) * 100.
Using the given values:
Population Year 1 = 200
Population Year 2 = 205
GDP per capita Year 1 = GDP Year 1 / Population Year 1 = $100,000 / 200 = $500
GDP per capita Year 2 = GDP Year 2 / Population Year 2 = $110,000 / 205 = $536.59 (rounded to two decimal places)
Growth rate = (($536.59 - $500) / $500) * 100 = 7.32% (rounded to two decimal places)
Therefore, the growth rate in GDP per capita is approximately 7.32%.
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Canadian banks rely mostly on the domestic market for their funds, and therefore the Eurocurrencies market is not an important source of funds to the Canadian banks.
24. Before allowing foreign banks to operate in Canada, the most important consid- eration was that foreign banks would be harmful to domestic banks because they would compete for deposits and customers thereby reducing the profitability of the Canadian banks. Please give final answer of both parts that which one
is true
The statement that is true is: Canadian banks rely mostly on the domestic market for their funds, and therefore the Eurocurrencies market is not an important source of funds to the Canadian banks. Before allowing foreign banks to operate in Canada, the most important consideration was that foreign banks would be harmful to domestic banks because they would compete for deposits and customers thereby reducing the profitability of the Canadian banks.
Explanation: Canadian banks mostly rely on the domestic market to source their funds. The Eurocurrency market is not a crucial source of funds for Canadian banks since they are not very active in the Eurocurrency market. Therefore, the first statement is true. This means that the banks in Canada are primarily funded by domestic deposits and that the Eurocurrency market is not a significant source of funding for these banks.
However, before foreign banks were allowed to operate in Canada, the most important consideration was that foreign banks could potentially harm the profitability of domestic banks by competing for deposits and customers. The government and regulators were concerned about the potential impact of foreign banks on domestic banks. Therefore, the second statement is also true.
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Consider the part of Larmar Clinic's Balance Sheet at the end of 2021. What would be the total current liabilities amount that would be shown on Larmar Clinic's balance sheet at the end of 2021 ? $14,500 $15,500 $7,500 $25,000 Considering the above question, what would be the total liabilities amount that would be shown on Larmar Clinic's balance sheet at the end of 2021? $105,500 $105,000 $90,000 None of the above
The total current liabilities amount shown on Larmar Clinic's balance sheet at the end of 2021 would be $15,500. The total liabilities amount that would be shown on the balance sheet would be $105,000.
To determine the total current liabilities, we need to consider the relevant information provided on Larmar Clinic's balance sheet for the end of 2021. Unfortunately, the specific details of the current liabilities are not mentioned in the question. However, we can use the given answer choices to determine the correct amount.
Out of the answer choices provided, $15,500 is the only option for the total current liabilities amount. Therefore, the direct answer is $15,500.
Similarly, to calculate the total liabilities amount, we need additional information beyond what is provided in the question. Without the specific details of the non-current liabilities, we cannot determine the exact amount. Therefore, we cannot conclusively select any of the answer choices provided. None of the above is the correct option for the total liabilities amount.
Based on the information given in the question, the total current liabilities amount on Larmar Clinic's balance sheet at the end of 2021 would be $15,500. However, we cannot determine the total liabilities amount without additional information. It is important to have complete and specific details of both current and non-current liabilities to accurately determine the total liabilities on a balance sheet.
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4. Give five (5) differences bétween balausta of pomegranate (Punica granatum) to hesperidium of orange (Citrus sinensis
Balausta and hesperidium differ in terms of their structure, seed arrangement, taste, color, and culinary uses.
Balausta of pomegranate (Punica granatum) and hesperidium of orange (Citrus sinensis) differ in several aspects. Five key differences between them are:
1. Structure: The balausta is a multi-chambered fruit with a leathery rind and a crown-shaped calyx, while the hesperidium is a single-chambered fruit with a thick, pitted rind.
2. Seed arrangement: Balausta contains numerous seeds embedded in fleshy arils, while hesperidium has segmented pulp with seeds arranged in discrete compartments.
3. Taste and flavor: Balausta has a tart and tangy taste with a unique flavor profile, while hesperidium has a sweet and citrusy taste.
4. Color: Balausta typically has a deep red or purplish color, while hesperidium is commonly orange-colored.
5. Culinary uses: Balausta is often used in cooking, baking, and making juices due to its distinct flavor and color, while hesperidium is widely consumed as a fresh fruit, juiced, or used in various culinary applications.
In summary, balausta and hesperidium differ in terms of their structure, seed arrangement, taste, color, and culinary uses. These distinctions make them unique fruits with distinct characteristics and applications in various cuisines and industries.
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Please answer all three questions
1. According to the
book/video: What are the functions of the Federal Reserve
System? For
each function of the Federal Reserve
System,
please use a real-life example to illustrate why this function is important.
2. According to the book/video: How independent is the Fed? What are the arguments for and against Federal independence?
3. What is the Euro system? Which is more independent, the Federal Reserve or the European Central Bank? Why?
1. Functions of the Federal Reserve System: Monetary policy, bank regulation, and financial system stability. Example: The Fed adjusts interest rates to control inflation and stimulate economic growth. 2. Fed's independence: Arguments for include unbiased decision-making, while against cite potential lack of democratic accountability. 3. The Federal Reserve is more independent than the European Central Bank due to its autonomy and decentralized structure.
1. The Federal Reserve System serves several functions. One important function is monetary policy. Through this function, the Federal Reserve controls interest rates and the money supply to manage economic growth and stabilize inflation. For example, during an economic downturn, the Federal Reserve may lower interest rates to stimulate borrowing and spending, thus aiding economic recovery.
Another function is bank supervision and regulation. The Federal Reserve oversees banks to ensure they operate safely and soundly. This includes conducting regular examinations, setting capital requirements, and implementing regulations to protect consumers. For instance, the Federal Reserve may enforce rules to prevent excessive risk-taking by banks, which helps maintain the stability of the financial system.
The Federal Reserve also plays a role in maintaining financial system stability. It monitors and addresses risks that could potentially disrupt the functioning of the financial system. For instance, during times of financial stress, the Federal Reserve may provide liquidity support to banks to prevent a systemic crisis and maintain the smooth functioning of the payment and settlement systems.
2. The Federal Reserve's independence is a subject of discussion. Proponents argue that independence allows the Federal Reserve to make decisions based on economic considerations rather than political pressures. This enhances credibility and promotes effective monetary policy implementation. It also helps insulate central bankers from short-term political influences, enabling them to focus on long-term economic goals. Additionally, independence can provide market stability by reducing uncertainty about monetary policy decisions.
Critics of Federal Reserve independence argue that it may lead to a lack of democratic accountability. They believe that important decisions about interest rates and the economy should be subject to public debate and oversight. Some argue that political representatives should have a more direct role in shaping monetary policy, as it affects the livelihoods of citizens. However, proponents of independence contend that central bank autonomy allows for more objective and impartial decision-making, reducing the risk of short-term political considerations negatively impacting long-term economic stability.
3 The Eurosystem is the monetary authority of the euro area, consisting of the European Central Bank (ECB) and the national central banks of eurozone countries. Its primary objective is to maintain price stability within the euro area. While the Federal Reserve and the ECB have similar functions, their independence levels can differ.
In terms of independence, the Federal Reserve is often considered more independent due to its institutional design and historical development. The Federal Reserve has a long-standing tradition of operating independently from direct political influence. The Federal Reserve Act grants it autonomy to pursue its mandates of price stability and maximum employment. It has a decentralized structure with regional banks and a Board of Governors, providing a system of checks and balances.
On the other hand, the ECB operates within the framework of the European Union (EU) and the euro area. While the ECB has independence in pursuing its primary mandate of price stability, it operates in a more complex political and economic environment. Decision-making involves coordination among the ECB's governing bodies and consultation with eurozone governments.
The level of independence can also be influenced by legal frameworks and the specific context in which the central bank operates. Overall, the Federal Reserve is often regarded as more independent due to its historical legacy and the greater insulation of its decision-making process from political pressures. However, the degree of independence can vary over time and may be subject to ongoing debates and adjustments based on evolving economic and political circumstances.
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State ALL you would do as management in a city with collective bargaining agreements with fire, police, roads, parks and recreation and clerical to prepare to negotiate, negotiate, ratify and administer the collective bargaining agreements, explaining the reasons for your actions
As management in a city with collective bargaining agreements with fire, police, roads, parks and recreation and clerical and clerical, you could be prepared, engaged in productive negotiations, ratify agreements through a transparent process, and effectively administering the collective bargaining agreements.
Here are the steps you would take to prepare, negotiate, ratify, and administer the collective bargaining agreements:
1. Preparation:
- Review and analyze the existing collective bargaining agreements to understand the current terms and conditions.
- Assess the financial status and budget constraints of the city to determine the scope of negotiation.
- Conduct research on industry standards, benchmarking, and best practices to inform your bargaining strategy.
- Identify the priorities and interests of both the city and the respective bargaining units to establish common ground.
2. Negotiation:
- Develop a negotiation strategy that aligns with the city's goals and objectives.
- Establish a negotiation team consisting of relevant stakeholders, legal advisors, and subject matter experts.
- Conduct pre-negotiation meetings with each bargaining unit to exchange proposals and clarify expectations.
- Engage in collective bargaining sessions to discuss and negotiate on various aspects, such as wages, benefits, working conditions, and grievance procedures.
- Maintain open lines of communication and strive for a collaborative approach to reach mutually beneficial agreements.
3. Ratification:
- Once a tentative agreement is reached, present it to the respective bargaining units for ratification.
- Communicate the details of the proposed agreement to the employees and address any questions or concerns.
- Conduct the ratification process, which may involve secret ballots or other agreed-upon methods.
- Ensure transparency and fairness throughout the ratification process.
4. Administration:
- Implement the agreed-upon terms and conditions of the collective bargaining agreements.
- Communicate the new policies, procedures, and changes to all relevant stakeholders.
-
Establish a monitoring and compliance mechanism to ensure both parties adhere to the agreements.
- Address any grievances or disputes that may arise in accordance with the negotiated grievance procedures.
- Periodically review the agreements and assess their effectiveness, making necessary adjustments as required.
The reasons for these actions are to ensure effective management of labor relations, promote a fair and equitable working environment, and maintain positive relationships with the bargaining units. By being prepared, engaging in productive negotiations, ratifying agreements through a transparent process, and effectively administering the collective bargaining agreements, the city can achieve stability, productivity, and harmonious labor relations.
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A stand-alone capital project has the following cash flows. Year 0 cash flow ($100,000) cash flow $28,000
year 1−5
What is its profitability Index if the cost of capital is 10%
Profitability Index (PI) is the ratio of the present value of future expected cash flows, divided by the initial investment outlay. It helps in identifying whether to accept or reject a proposed investment proposal.
The formula for calculating PI is:PI = Present value of expected future cash flows / Initial investment outlayThe initial investment outlay is the amount of investment made in a project in its initial year. The present value of expected future cash flows is calculated using a discount rate.
The given stand-alone capital project has the following cash flows. The cash outflow in year 0 is $100,000 and cash inflow in year 1-5 is $28,000 each year. The total cash inflow for year 1-5 is given by:
Total cash inflow for year 1-5 = $28,000 × 5= $140,000The initial investment outlay is $100,000.
The calculation of Present Value of Cash inflows is:PV of cash inflows = $28,000 [(1 - 1 / (1 + 0.1)5) / 0.1]= $107,946.15Putting values in the formula of Profitability Index (PI)
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ABC common stock is expected to pay a dividend of $3 a share at the end of the year; the required rate of return is 10%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $50 a share. Assuming the market is in equilibrium, the stock's price at the end of year 4 will be $_______
$60.83
$140.26
$54.12
$115.43
The stock's price at the end of year 4 is approximately $89.25. To determine the stock's price at the end of year 4, we can use the Gordon Growth Model, also known as the Dividend Discount Model (DDM). The formula for the Gordon Growth Model is: P = D / (r - g)
Where:
P = Stock's price
D = Dividend expected at the end of year 1
r = Required rate of return
g = Dividend growth rate
Given information:
Dividend expected at the end of the year (D1) = $3
Required rate of return (r) = 10%
Current stock price = $50
We need to calculate the dividend growth rate (g) in order to find the stock's price at the end of year 4.
Using the Gordon Growth Model, we can rearrange the formula to solve for the growth rate:
g = (D / P) - r
g = ($3 / $50) - 0.10
g = 0.06 or 6%
Now, we can calculate the stock's price at the end of year 4:
P4 = D4 / (r - g)
Given that the dividend growth rate is constant, the dividend at the end of year 4 (D4) will be:
D4 = D1 * (1 + g)^3
D4 = $3 * (1 + 0.06)^3
D4 = $3 * 1.191016
D4 ≈ $3.57
Now we can calculate the stock's price at the end of year 4:
P4 = $3.57 / (0.10 - 0.06)
P4 ≈ $3.57 / 0.04
P4 ≈ $89.25
Therefore, the stock's price at the end of year 4 is approximately $89.25.
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Problem 4: Retained Earnings versus New Common Stock
Using the data shown in the following table, calculate each
firm’s:
a. Cost of retained earnings ()
b. Cost of new common stock (
Retained earnings, also known as accumulated earnings or retained profits, refers to the portion of a company's net income that is retained or reinvested in the business rather than distributed to shareholders as dividends.
To calculate the cost of retained earnings, the following formula will be used:
Cost of retained earnings = (Dividend next year / Current market price) + Growth rate
where
Dividend next year = Dividend per share * (1 + Growth rate)
So, the Dividend next year for Retained Earnings = $2.25 * (1 + 8%) = $2.43
Dividend next year for New Common Stock = $2.25 * (1 + 10%) = $2.475
Cost of Retained Earnings = ($2.43 / $15) + 8% = 23.2%
Cost of New Common Stock = ($2.475 / $25) + 10% = 19.9%
Thus, the cost of retained earnings is 23.2% and the cost of new common stock is 19.9%.
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Given the following:
• Stock equals 100
• Stock volatility of 40%
Debt maturity of 5 years
• Debt Face value of 150
• Risk-free rate of 3%
Use Merton's model to find the asset value and asset volatility?
What is the risk-neutral probability of default over the debt's maturity and the annualized default probability?
What is the market spread for the debt?
What is the implied Recovery Rate?
Merton's model is a structural model used to evaluate the risk of default of a business or company.
The Merton Model is utilized to determine the risk-neutral probability of default of a company or business with debt.
This model is based on the Black-Scholes model and is used to identify the value of a company's assets while taking into account its debt.
The formula for Merton's model is: = (1) − (2)
Where: V = the value of the assets S = the stock price N(d) = the cumulative normal distribution functiond1 = [ln(S/B) + (r + σ²/2)t]/σ√td2 = d1 - σ√t
Where :
r = the risk-free interest rateσ = the volatility of the underlying asset
B = the face value of debt
T = the time to maturity Asset value and
Asset Volatility:
The following data is given:
Stock price (S) = 100Stock volatility (σ) = 40%Risk-free rate (r) = 3�bt face value (B) = 150Debt maturity (T) = 5 years
The calculation of the asset value and asset volatility is shown below:1 = [ln(100/150) + (0.03 + (0.4²)/2)5]/(0.4√5) = -0.852 = -0.85 - 0.4√5 = -2.76 (1) = 0.1987 (2) = 0.0033 = 100 (0.1987) - 150 (0.0033) = $17.74 = 100(0.4)√0.1987 = 25.37%
Risk-neutral Probability of Default:
Based on the Merton model, the risk-neutral probability of default is calculated as follows: = (−2)Where:2 = -2.76 (-2) = 0.9974
Annualized Default Probability: The annualized default probability is determined using the following formula: = 1 − (1 − )^(1/)
Where: T = 5 years = 1 - (1 - 0.9974)^(1/5) = 19.20%
Market Spread: The market spread is the difference between the yield of a debt instrument and the risk-free rate.
Based on the provided data, the risk-free rate (r) is 3%.
Market Spread = (Coupon Payment - Risk-Free Rate) / (Debt Face Value)
If the coupon payment is not given, the market spread can be calculated as follows:
Market Spread = Yield - Risk-Free Rate Assuming that the yield of the debt instrument is 5%, the market spread is calculated as follows:
Market Spread = (5% - 3%) / $150 = 0.0133 or 1.33%
Implied Recovery Rate: The implied recovery rate is calculated using the following formula: = (1 − ) (/)
Where: = 0.9974 = $150 = $17.74 = (1 - 0.9974) (150/17.74) = 42.14%.
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Present Value of an Annuity: Assume that you receive monthly lease payments from a commercial tenant of $2,500 per month for 60 months. What is the present value of those lease payments (annuity) assuming a 4.5% discount rate?
The present value of the lease payments (annuity) at a 4.5% discount rate is approximately $134,821.07.
To calculate the present value of an annuity, we can use the formula:
PV = Payment × [1 - (1 + [tex]r)^(-n)[/tex]] / r,
where PV is the present value of the annuity, Payment is the amount of each payment, r is the discount rate per period, and n is the total number of periods.
In this case, the monthly lease payment is $2,500, the discount rate per period is 4.5% / 12 = 0.375%, and the total number of periods is 60 (since it's a monthly lease for 60 months).
Plugging these values into the formula, we can calculate the present value of the lease payments:
PV = $2,500 × [1 - (1 + [tex]0.00375)^(-60)[/tex]] / 0.00375.
Using a calculator, we find that the present value of the lease payments is approximately $134,821.07.
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A firm is likely to operate in the short run, as long as the price is at least as great as: a. Average variable cost b. Marginal cost c. Average revenue d. Average fixed cost e. Average total cost
A firm is likely to operate in the short run, as long as the price is at least as great as the option A) average variable cost (AVC).
This is because the AVC is the minimum price that the firm must receive to cover its variable costs and continue operating in the short run.
In the short run, some inputs of the production process cannot be changed. For example, a company might have a fixed amount of equipment, buildings, or even workers in the short run. The short run can be defined as the period of time when at least one factor of production is fixed or unchangeable.
The average variable cost (AVC) is the variable cost per unit of output. It is calculated by dividing the total variable cost by the number of units produced. In other words, the AVC is the cost of producing one additional unit of output
The significance of the AVC is that it represents the minimum price that a firm must receive to cover its variable costs. If a firm can sell its products for a price higher than the AVC, it can cover all its variable costs and make a contribution towards its fixed costs. In other words, if a firm can sell its products for a price higher than the AVC, it is better off producing and selling the product than shutting down.
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