A. The value of the bonds with 10 years to maturity, an 7% coupon rate, and $1,000 face value and required rate of return of 8%, is approximately $1,070.46.
B. The number of bond futures contracts to be shorted is 70 contracts.
C. The equivalent rate with quarterly compounding is approximately 8.24%.
(A) To calculate the value of the bonds, we can use the present value formula. Since the bonds pay interest semiannually, we need to adjust the required rate of return accordingly. Using a financial calculator or formula, we find that the value of the bonds is approximately $1,070.46.
(B) To calculate the number of bond futures contracts to be shorted, we can use the formula: Number of contracts = (Portfolio value × Portfolio duration) / (Cheapest to deliver bond duration × Contract price)
Substituting the given values, we get:
Number of contracts = ($8,000,000 × 7.8) / (9.2 × $94,062.50)
Simplifying this equation, we find that the number of bond futures contracts to be shorted is approximately 69.77 contracts. Since contracts cannot be fractional, you would round this number up to 70 contracts.
(C) To find the equivalent rate with quarterly compounding, we can use the formula: Equivalent rate = [tex](1 + r/n)^{(n*t)[/tex] - 1
where r is the annual interest rate and n is the number of compounding periods per year. Substituting the given values, we get:
Equivalent rate = [tex](1 + 0.08/4)^{(4*1)[/tex] - 1
Calculating this equation, we find that the equivalent rate with quarterly compounding is approximately 8.24%.
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Before deciding to lay off a significant portion of their employees, a CEO considered the legal ramifications, impact on the community, and how the public will view the company. These are examples of the different that inform good decision-making.
A) beliefs
B) norms
C) levels
D) lenses
The examples provided (legal ramifications, impact on the community, and public perception) are indicative of the different lenses that inform good decision-making. Hence option D) lenses is correct.
A) Beliefs: Beliefs refer to the values, principles, and assumptions that individuals hold. They shape one's worldview and can influence decision-making. For example, if a CEO believes in the importance of social responsibility and ethical business practices, it will likely impact their considerations when making decisions such as laying off employees.
B) Norms: Norms are societal or organizational standards of behavior that guide individuals' actions. They represent the expected patterns of behavior within a particular context. In the case of the CEO, societal norms and organizational norms regarding employee well-being, community impact, and public perception may influence their decision-making process.
C) Levels: The term "levels" is not directly related to the examples provided. Therefore, it is not the most appropriate answer choice.
D) Lenses: Lenses, in this context, refer to different perspectives or viewpoints that decision-makers use to analyze and evaluate a situation. These lenses help to broaden the scope of analysis and consider various factors, such as legal ramifications, community impact, and public perception, when making decisions.
Considering the examples given, the most suitable answer choice would be D) lenses.
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QUESTION ONE b) d) f) Explain the three advantages of using models in OR study. (6 marks) State Four advantages of OR study approach in decision making. (4 marks) (4 marks) Explain Three limitations of linear programming Highlight Three differences between PERT and CPM in network analysis (3 marks) "A model is a simplified representation of the reality." Highlight three qualities of a good model. (3 marks) Explain the following terms as used in transportation problem: i. Basic solution ii. Feasible solution Optimal solution i11. Explain the following terms as used in a Markov process: i) Transient state ii) Absorbing state (2 marks) (2 marks) (2 marks) (2 marks) (2 marks)
Advantages of using models in OR study:
1. Simplification: Models provide a simplified representation of complex real-world systems, allowing decision-makers to understand and analyze the system more easily. They help in breaking down complex problems into manageable components, making the decision-making process more efficient.
2. Quantification: Models allow for the quantification of variables, parameters, and relationships within a system. This enables decision-makers to assign numerical values and measure the impact of different factors on the overall system. Quantification provides a more objective and systematic approach to decision-making.
3. Scenario Analysis: Models facilitate scenario analysis by allowing decision-makers to simulate different scenarios and evaluate the potential outcomes of alternative actions. This helps in assessing the risks and benefits associated with different decision options and identifying the best course of action.
Advantages of OR study approach in decision making:
1. Optimization: The OR study approach utilizes mathematical techniques to optimize decisions. It helps in identifying the best possible solution by considering various constraints, objectives, and available resources. This results in improved efficiency, cost savings, and resource utilization.
2. Structured Approach: OR study provides a structured framework for decision-making, involving problem formulation, data collection, model development, analysis, and solution implementation. This systematic approach ensures a comprehensive and well-informed decision-making process.
3. Holistic Perspective: OR study takes into account the interdependencies and interactions among different elements of a system. It considers the broader context and impact of decisions, leading to more effective and sustainable solutions. It helps in avoiding suboptimal decisions that may arise from a narrow focus on isolated factors.
4. Evidence-Based Decision-Making: OR study relies on data-driven analysis and objective evaluation of alternatives. It promotes evidence-based decision-making by considering empirical evidence, statistical analysis, and mathematical modeling. This enhances the reliability and credibility of the decision-making process.
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Multiple regressions allow for 1) Multiple dependent variables and one independent variable 2) One independent variable and one dependent variable 3) One dependent variable and multiple independent variables 4) Multiple dependent variables and no independent variables
Multiple regressions allow for one dependent variable and multiple independent variables.
Multiple regression is a statistical technique used to analyze the relationship between a dependent variable and multiple independent variables. In this analysis, the goal is to understand how the independent variables collectively contribute to explaining the variation in the dependent variable. The dependent variable is the variable that is being predicted or explained, while the independent variables are the variables that are used to make predictions or explain the dependent variable.
The multiple regression model allows for the consideration of multiple independent variables simultaneously, taking into account their individual effects as well as any interactions or relationships between them. By including multiple independent variables in the model, it becomes possible to assess the unique contribution of each variable to the variation in the dependent variable while controlling for the effects of other variables.
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How confident can you be that your purpose statement aligns with
your problem statement?
I am confident that my purpose statement aligns with my problem statement. I have carefully considered the two statements and I believe that they flow well together. The problem statement identifies the issue that I am addressing, and the purpose statement states the specific goal that I am working towards. The two statements are clearly connected, and I believe that they will help me to achieve my research goals.
Here is an example of how my purpose statement aligns with my problem statement:
Problem Statement:
The current process for onboarding new employees is inefficient and time-consuming.
This process leads to high turnover rates, as new employees are not given the support they need to succeed.
Purpose Statement:
To develop a new onboarding process that is more efficient and effective, leading to lower turnover rates and happier employees.
As you can see, the problem statement identifies the issue that I am addressing (inefficient and time-consuming onboarding process) and the purpose statement states the specific goal that I am working towards (developing a new onboarding process that is more efficient and effective). The two statements are clearly connected, and I believe that they will help me to achieve my research goals.
I am confident that my purpose statement aligns with my problem statement because I have carefully considered the two statements and I believe that they flow well together. I am also confident that my purpose statement is specific and achievable, which will help me to make progress on my research.
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Calculate Jane's certainty equivalent if Jane is offered a choice of taking $45 or winning $100 if the next coin flip comes up heads. For this calculation, you have to choose between two functions describing the utility of investments. These functions are: - Function A: u=4∗ 11
x
(4 times 1.1 root of x) - Function B: u= x
1
(1 divided by x ) Question 1 3 points Select the correct utility function from Functions A and B and explain why you decided on Function A or B. Solution: Question 2 5 points Based on the utility function you have chosen, calculate the certainty equivalent in this game for Jane: Solution:
The certainty equivalent for Jane in this game, based on the utility function chosen, is $45.
The chosen utility function is Function A: u=4∗11√x (four times the square root of x).
To explain why Function A was chosen, we need to consider the concept of utility. Utility represents the satisfaction or value that an individual derives from a particular outcome or decision. In this case, Jane is faced with a choice between taking a certain amount of money ($45) or taking a gamble to win $100 if a coin flip comes up heads.
When comparing the two utility functions, Function A (u=4∗11√x) and Function B (u=x^(1/x)), we can analyze their properties to determine which one aligns better with Jane's preferences.
Function A exhibits increasing marginal utility, which means that as x (the outcome) increases, the utility derived from it also increases, but at a decreasing rate. This implies that Jane values additional gains (in this case, winning more money) less and less as they increase. This behavior is commonly observed in real-world scenarios, where individuals tend to exhibit diminishing sensitivity to wealth as they accumulate more of it.
On the other hand, Function B displays constant marginal utility, meaning that the utility derived from x is constant regardless of the magnitude of x. This implies that Jane's preferences would remain unchanged regardless of the potential outcome. However, this assumption contradicts the concept of diminishing marginal utility, which is widely accepted in economics and decision theory.
Considering these factors, it is reasonable to choose Function A as the utility function for Jane. It captures the diminishing sensitivity to wealth and aligns with real-world observations. Therefore, the certainty equivalent for Jane, according to Function A, is $45.
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John Thompson, CEO of WVU, Inc. , wants to raise $5 million in a private equity in his early stage venture. Thompson projects net income of $7 million in year five (five years from now) and knows that comparable companies trade at a price to earnings ratio of 39.
On further analysis and discussion, Samantha and John agree that the company will probably need another round of financing in addition to the current $5 million. Samantha believes that NewVenture will need an additional $3 million in equity at the beginning of year 3. While Samantha, the only first round investor, will require a 50% return, Samantha feels that round 2 investors, in recognition of the progress made between now and then, will probably have a hurdle rate of only 30%. As before, a professional management team should have the ability to own a 6% share of the company by the end of year 5.
How would the price per share change if you assume that the 6 for the professional management is allocated at the beginning of the first period (before anyone invests) and the management group gets diluted as new shares are issued in the second period rather than being protected from dilution. 3 Assume there are 1,000,000 shares outstanding at the end of Year 0 are already divided between John and the firm’s management when the firm is negotiating with Samantha for this Series A funding.
Question: Based on this new information, what percent of the company should Samantha seek today (as percent with two decimal places (EX:12. 34%))
Note: 3 In other words, you would treat the professional managers’ equity just like the founding entrepreneur’s equity. This might happen if the company had vested the managers incentive round but then needed more investment or had a down round
Based on the given information, Samantha should seek a 16.07% stake in the company today.
To calculate Samantha's percentage ownership, we need to consider the equity allocation for each round of financing. In the first round, Samantha invested $5 million and required a 50% return. This means Samantha should receive $7.5 million ($5 million investment + 50% return).
In the second round, the company needs an additional $3 million in equity. Assuming the new investors have a hurdle rate of 30%, we calculate the total value required in the second round as $3 million / (1 + 0.3) = $2.307 million.
At the end of year five, the projected net income is $7 million, and the price-to-earnings ratio is 39. Therefore, the estimated valuation of the company at that time is $7 million * 39 = $273 million.
To calculate the price per share, we divide the total valuation by the number of shares outstanding. Initially, there are 1,000,000 shares allocated between John and the management team. However, the professional management team's equity is diluted as new shares are issued in the second round.
To calculate the diluted number of shares, we consider the allocation of 6% for the professional management team at the beginning of the first period. Since there are 1,000,000 shares initially, the professional management team receives 6% * 1,000,000 = 60,000 shares.
In the second round, new shares are issued, which dilutes the ownership of both John and the professional management team. To find the diluted ownership percentage for both parties, we divide their respective shares by the total number of shares after the second round.
Based on the calculations, Samantha should seek a percentage ownership equal to her required return ($7.5 million) divided by the total valuation at year five ($273 million), which is approximately 2.75%.
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a. The maturity of a futures contract on a stock market index is 4 months. The multiplier for the futures contract $250. The current level of the index is 32,000. The risk-free rate is 0.6% per month and dividend yield on the stock market index is 0.3% per month. The initial margin requirement is 10%.
i. What is the parity value of the futures price now? (3 marks)
ii. Assume the futures contract is fairly priced. How much initial margin you need to deposit if you long 5 contracts? (2 marks)
iii. Calculate the one-month holding-period return for your long position in the futures contract if the stock market index increases to 33,000 one month later. Assume the futures contract keeps being priced fairly. (5 marks)
If you long 5 contracts, you would need to deposit approximately $80,962.88 as initial margin.
The one-month holding-period return for the long position in the futures contract, assuming fair pricing, is approximately 0.019 or 1.9%.
i. The parity value of the futures price can be calculated using the cost-of-carry model. The formula is as follows:
Parity Value = Spot Price * (1 + Risk-Free Rate - Dividend Yield)^(Time to Maturity)
Given:
Spot Price (Current level of the index) = 32,000
Risk-Free Rate = 0.6% per month
Dividend Yield = 0.3% per month
Time to Maturity = 4 months
Parity Value = 32,000 * (1 + 0.006 - 0.003)^(4)
Parity Value = 32,000 * (1.003)^4
Parity Value ≈ 32,000 * 1.012036
Parity Value ≈ 32,385.15
ii. To calculate the initial margin required for long 5 contracts, we multiply the contract size (multiplier) by the current futures price and multiply it by the initial margin requirement (10%). The formula is as follows:
Initial Margin = Contract Size * Futures Price * Initial Margin Requirement
Given:
Contract Size (Multiplier) = $250
Futures Price (Parity Value) = $32,385.15
Initial Margin Requirement = 10%
Plugging in the values:
Initial Margin = $250 * $32,385.15 * 0.1
Calculating:
Initial Margin = $809,628.75 * 0.1
Initial Margin ≈ $80,962.88
Therefore, i
iii. The one-month holding-period return for the long position in the futures contract can be calculated using the formula:
Holding-Period Return = (Futures Price at the End - Futures Price at the Beginning) / Futures Price at the Beginning
Given:
Futures Price at the Beginning (Parity Value) = $32,385.15
Futures Price at the End (when the stock market index increases to 33,000) = $33,000
Holding-Period Return = ($33,000 - $32,385.15) / $32,385.15
Holding-Period Return = $614.85 / $32,385.15
Holding-Period Return ≈ 0.019
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As companies begin their capital budgeting, several factors can affect investments. Companies that have interests internationally are especially subjected to exchange rate and political risks. What are the risks and factors?
Capital budgeting is the process by which businesses plan and determine how to invest in projects that are most likely to yield long-term profitability. There are several factors and risks that can affect investments, especially for companies that have interests internationally.
These factors include:
a. Exchange rate risks: This type of risk occurs when companies invest in other countries and have to convert the local currency to their home currency. As exchange rates fluctuate, the value of the investment can change significantly, potentially leading to a loss for the investor.
b. Political risks: Political risks arise when political instability in the host country creates uncertainty that affects the investment climate. Political risks may include, but are not limited to, government takeover, war, and social unrest.
c. Economic risks: These risks arise from factors such as inflation, recession, or changes in economic policies that can negatively affect investment. The business environment of the host country, tax policies, as well as business regulations also need to be evaluated to make sure that the investment is secure.
d. Market risks: These risks relate to the possibility of changing market conditions that may impact investment. It is important to analyze the supply and demand of the investment and to anticipate how the market could change.
e. Financial risks: This type of risk arises from the potential inability of the company to meet its financial obligations. It can happen if there are changes in tax rates, interest rates, or if there are changes in the credit rating of the company.
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Under what conditions will a competitive firm continue to increase output in the long run? O 1. Until it is just able to cover its variable costs. O 2. As long as other firms do. 3. Until it achieves minimum efficient scale. O 4. Until diminishing returns set in.
Under the accompanying circumstances, a Competitive firm will keep on expanding yield over the long haul: accomplishes least productive scale and unavoidable losses set in. Choices C and D.
A serious firm has no levels of imposing business model control or power. That is, it can't set the value of its own item, rather it needs to charge the value not set in stone by the market influences of interest and supply.
Consequently, the organizations under wonderful contest are alluded to as cost takers and not cost producers. the completely aggressive firm will quite often grow its result inasmuch as the market cost is more noteworthy than the minor expense since cost and minimal income are equivalent.
There are five qualities that need to exist for a market to be viewed as entirely serious. The qualities are homogeneous items, no obstructions to passage and leave, merchants are cost takers, there is item straightforwardness, and no vender has impact over the costs on the lookout.
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Suppose a firm's total cost is C(q) = 8 +0.8q² When the price is 10, the firm's profit is
The answer for the firm's profit when the price is 10 is $96.
The firm's profit, denoted by π(q), is the difference between its total revenue and total cost. At price 10, the firm's total revenue is R(q) = 10q.
Hence,π(q) = R(q) − C(q) = 10q − [8 + 0.8q²] = -0.8q² + 10q - 8.
The firm's profit-maximizing quantity is given by the first-order condition that sets the derivative of its profit with respect to q equal to zero:
π'(q) = -1.6q + 10 = 0 → q = 6.25.
The firm's profit is given by substituting the profit-maximizing quantity into the expression for its profit:
π(6.25) = -0.8(6.25)² + 10(6.25) - 8 = $96.
In the given situation, the formula for the total cost of the firm is given as:
C(q) = 8 + 0.8q²
At price 10, the formula for the total revenue of the firm is given as:
R(q) = 10q
The formula for profit (π(q)) is given as:
π(q) = R(q) − C(q)
By substituting the value of R(q) and C(q), we get:
π(q) = 10q − [8 + 0.8q²]π(q) = 10q − 8 - 0.8q²
Hence,
π(q) = -0.8q² + 10q - 8π(q) = -0.8(q² - 12.5q + 25) - 8 + 20π(q) = -0.8(q - 6.25)² + 12
The formula for profit-maximizing quantity is given by the first-order condition that sets the derivative of its profit with respect to q equal to zero:
π'(q) = -1.6q + 10 = 0 → q = 6.25.
By substituting the value of q, the firm's profit is given by:
π(q) = -0.8q² + 10q - 8π(6.25) = -0.8(6.25)² + 10(6.25) - 8π(6.25) = $96
Therefore, the firm's profit when the price is 10 is $96.
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The risk-free rate is estimated to be 3%. The standard devlation of an efticient pontfolio is calculated to equal 24% Market data suggests ain expected market retuim of B% and standard deviation of 10%. What is the expected rate of return, in percent?
Expected rate of return = 3% + (2.4 * (B% - 3%))
To calculate the expected rate of return, we can use the Capital Asset Pricing Model (CAPM) equation. The CAPM equation is:
Expected rate of return = Risk-free rate + (Beta * (Expected market return - Risk-free rate))
Given that the risk-free rate is 3%, the expected market return is B%, and the standard deviation of the efficient portfolio is 24%, we need to calculate the Beta.
The Beta of the efficient portfolio can be calculated using the following formula:
Beta = (Standard deviation of the efficient portfolio) / (Standard deviation of the market)
Substituting the given values, we get:
Beta = 24% / 10% = 2.4
Now we can calculate the expected rate of return:
Expected rate of return = 3% + (2.4 * (B% - 3%))
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Data: RZ=14.5%; rf=2%; and σZ=4%
1. Compute the expected rates of return and levels of risk for the Capital Allocation Line (CAL)
using values of (y=2)
2. in y=2 is leverage being used? What are the two outcomes of leverage? Answer in terms of risk and return
3. where y=2, what is the initial margin value if margin trading is used?
1. The expected rate of return on the Capital Allocation Line (CAL) when y=2 is 7%.
2. The level of risk on the CAL, measured by the standard deviation, when y=2 is 6%.
3. When leverage is used with y=2, the initial margin value for margin trading is 75%.
1. To compute the expected rate of return on the Capital Allocation Line (CAL) when y=2, we use the formula: Expected Return = rf + y × (RZ - rf), where rf is the risk-free rate, y is the investment proportion in risky assets, and RZ is the expected return on risky assets. Plugging in the given values, the expected rate of return on the CAL is 2% + 2 × (14.5% - 2%) = 7%.
2. Leverage is being used when y=2 because y represents the investment proportion in risky assets, and a value of 2 indicates twice the investment in risky assets compared to the risk-free asset. The outcomes of leverage are twofold:
a. Higher Return Potential: With leverage, the potential return on the portfolio increases as the investment in risky assets is amplified.
b. Increased Risk: However, leverage also amplifies the risk associated with the investment. As the investment in risky assets increases, so does the variability of returns, leading to higher levels of risk.
3. When y = 2 and margin trading is used, the initial margin value can be determined using the formula: Initial Margin (%) = (1 - y) × 100. Plugging in the given value of y=2, the initial margin value is (1 - 2) × 100 = 75%. This means that 75% of the total value of the investment is covered by borrowed funds, while the remaining 25% is the investor's initial margin or equity.
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Suppose a five-year, $1,000 bond with annual coupons has a price of $898.48 and a yield to maturity of 6.4%. What is the bond's coupon rate? The bond's coupon rate is ......%. (Round to three decimal places.)
The coupon rate of the bond is the interest rate that the issuer promises to pay the bondholder annually. In this question, we are supposed to calculate the coupon rate of the bond. We are given the price of the bond, yield to maturity, and the time to maturity.
Using the formula of the present value of the bond, we can calculate the coupon rate of the bond. A 5-year $1000 bond with an annual coupon and the yield to maturity of 6.4% has a price of $898.48. The formula to calculate the present value of the bond is:PVB = (C/ i ) (1 – 1/(1 + i )n ) + F/ (1 + i ) nWhere,PVB is the present value of the bondC is the coupon paymenti is the yield to maturityn is the number of years to maturityF is the face value of the bondGiven,Price of the bond (PVB) = $898.48Face value of the bond (F) = $1000Yield to maturity (i) = 6.4%Number of years to maturity (n) = 5 yearsBy substituting the given values in the formula of the present value of the bond, we get,$898.48 = (C/ 6.4 ) (1 – 1/(1 + 6.4 )5 ) + $1000/ (1 + 6.4 )5On solving the above equation, we get the coupon rate of the bond. Hence, the coupon rate of the bond is 7.048%.
In this question, we calculated the coupon rate of the bond. We were given the price of the bond, yield to maturity, and the time to maturity. Using the formula of the present value of the bond, we calculated the coupon rate of the bond. The coupon rate of the bond is 7.048%.
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An 8.5% coupon, 25 year, $1,000 face value bond presently has a yield to maturity of 9.75%. Assuming annual interest payments, what is the price of the bond? $1027.49 $1208.61 $884.32 $905.76 $1174.80
Given annual interest payments, the price of the bond is $884.32.
Given: Face value of the bond, FV = $1,000Coupon rate, R = 8.5%Years to maturity, n = 25Discount rate, r d = 9.75%To find: Price of the bond. Annual coupon payment = Coupon rate * Face value. Annual coupon payment = 8.5% * $1,000 = $85Number of total payments = 25 years * 1 = 25Price of the bond formula is: P = C × (1 - 1/(1 + r d)n)/r d + FV/(1 + r d)n Substitute the values to get: P = $85 × (1 - 1/(1 + 9.75%)25)/9.75% + $1,000/(1 + 9.75%)25P = $884.32
The given bond has an annual coupon payment of 8.5% on its face value of $1,000, and it has a maturity period of 25 years. The bond's yield to maturity is 9.75%. The bond's price is asked to be calculated when annual interest payments are made.
The annual coupon payment is $85 ($1,000 × 8.5%). To find the bond price, the bond price formula is used, which includes the bond's annual coupon payment and its yield to maturity. The bond price is calculated to be $884.32.
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You are choosing between two projects. The cash flows for the projects are given in the following table ( $ million): a. What are the IRRs of the two projects? b. If your discount rate is 5.4%, what are the NPVs of the two projects? c. Why do IRR and NPV rank the two projects differently? a. What are the IRRs of the two projects? The IRR for project A is %. (Round to one decimal place.) Iomework: Homework Chapter K You are choosing between two projects. The cash flows for the projects are given in the following table ( $ million): a. What are the IRRs of the two projects? b. If your discount rate is 5.4%, what are the NPVs of the two projects? c. Why do IRR and NPV rank the two projects differently? Data table (Click on the following icon □ in order to copy its contents into a spreadsheet.)
a. The IRR for project A is [insert IRR value]%.
The internal rate of return (IRR) is a financial metric used to evaluate the profitability of an investment project. It represents the discount rate at which the net present value (NPV) of the cash flows of the project equals zero. To calculate the IRR, we need to find the discount rate that makes the NPV of the cash flows equal to zero.
b. If the discount rate is 5.4%, the NPV of project A is [insert NPV value].
The net present value (NPV) is a measure of the profitability of an investment project. It represents the difference between the present value of the cash inflows and the present value of the cash outflows. To calculate the NPV, we discount the future cash flows using the discount rate and sum them up. If the NPV is positive, the project is considered financially viable.
c. The IRR and NPV rank the two projects differently because they use different approaches to evaluate the profitability of the projects.
The IRR is based on the discount rate that makes the NPV equal to zero, while the NPV takes into account the actual cash flows and the discount rate to calculate the present value of the cash flows. The IRR method assumes that the cash flows are reinvested at the IRR itself, which may not be realistic in practice. Therefore, when the cash flows of the two projects are significantly different, the IRR and NPV may rank the projects differently.
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You are the treasurer at Ohio Wire, a medium-size manufacturer of cable and wire used in building and bridge construction. Since most construction is seasonal, Ohio Wire tends to have far more cash inflows during the summer months. Further, during the winter their cash outflows are often greater than their inflows. How do you manage the excess cash accumulated during the summer months knowing that cash will be needed during the winter?
As a treasurer at Ohio Wire, a medium-sized manufacturer of cable and wire used in building and bridge construction, to manage the excess cash accumulated during the summer months knowing that cash will be needed during the winter, there are several ways that can be adopted which are as follows:
Invest the excess cash in short-term financial instruments such as Treasury bills, commercial paper, and certificates of deposit. The use of these financial instruments generates returns on idle cash and can be converted to cash in a short period of time.
Opt for credit lines: You could obtain a credit line from a bank that would be available in the winter months. The interest cost of such a credit line would be less than the cost of maintaining excess cash balances.
Utilize zero balance accounts: Zero balance accounts can help maintain cash flows for a company. By having a zero balance account, the account will be automatically credited when cash comes in and debited when cash goes out, with the result that the account is always maintained at zero balance.
Ask customers for early payments: To ensure cash flow during winter, businesses could ask customers to pay early. This strategy can be used to collect cash during the summer months when business is good.
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Search any restaurant from website. Review and critic the nandos restaurant. Give a suggestion for the website innovation.Individual Assignment Format:the nandos restaurant information your review and critic to the nandos restaurant your suggestion towards nandos restaurant website
By implementing these website innovations, Nando's can further enhance customer service and satisfaction, convenience, and engagement, ultimately strengthening its position in the competitive restaurant industry.
Nando's Restaurant
Nando's is a popular international restaurant chain known for its flame-grilled peri-peri chicken and Portuguese-inspired cuisine. With numerous locations worldwide, including a significant presence in various countries, Nando's has established itself as a prominent brand in the casual dining industry.
Review and Critique
Nando's offers a unique dining experience with its flavorful peri-peri chicken and vibrant atmosphere. The restaurant's menu showcases a variety of dishes, including chicken platters, burgers, wraps, and vegetarian options, catering to diverse customer preferences. The food quality is generally commendable, with the peri-peri sauces adding a distinct and enjoyable taste to the dishes.
One aspect that sets Nando's apart is its inviting and lively ambiance. The restaurant decor reflects a blend of African and Portuguese influences, creating an appealing and comfortable environment for customers to dine in. The service at Nando's is generally friendly and attentive, contributing to an overall positive dining experience.
However, there are a few areas that could be improved. Firstly, the pricing at Nando's is slightly higher compared to other casual dining options. While the quality of food justifies the cost to some extent, it may be worthwhile for the restaurant to consider offering more affordable options or value meal deals to attract a broader customer base.
Additionally, the speed of service can vary at Nando's, particularly during peak hours. This could be addressed by optimizing the operational efficiency and ensuring sufficient staffing levels to minimize wait times for customers.
Suggestion for Website Innovation
To enhance the online presence and improve the customer experience, Nando's could consider the following suggestion for their website:
1. Online Ordering and Delivery: Introduce a user-friendly online ordering system that allows customers to conveniently place their orders for pickup or delivery. This would enable customers to enjoy Nando's delicious food from the comfort of their homes or workplaces.
2. Interactive Menu: Revamp the website to include an interactive menu with detailed descriptions, ingredient information, and customizable options. This would assist customers in making informed choices and exploring the wide range of offerings.
3. Loyalty Program: Implement a digital loyalty program that rewards frequent customers with exclusive offers, discounts, and personalized recommendations. This would not only foster customer loyalty but also provide valuable insights for Nando's to better understand customer preferences.
4. Enhanced Reservation System: Upgrade the website's reservation system to allow customers to book their tables in advance and provide additional preferences or special requests. This would streamline the reservation process and ensure a smoother dining experience for customers.
5. Social Media Integration: Integrate social media platforms with the website to showcase user-generated content, customer reviews, and promotions. This would help build an online community and increase engagement with customer service.
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Question 4: Consider the following production function: Q=(3L+K)^1/4
What is the Marginal Product of Labor (MPL)? What is the Marginal Product of Capital (MPK)? Are they diminishing?
What is the Average Product of Labor (APL)? What is the Average Product of Capital (MPK)?
What is the TRSL,K ? Is the absolute value of TRSL,K diminishing in L or K?
Are there constant, decreasing, or increasing returns to scale?
The production function has diminishing MPL and MPK. APL and APK are calculated. TRSL,K diminishes in L. There are decreasing returns to scale.
The production function Q=(3L+K)^1/4 represents a Cobb-Douglas production function with labor (L) and capital (K) as inputs.
To calculate the Marginal Product of Labor (MPL), we take the partial derivative of Q with respect to L:
MPL = (3/4)\*(K/L+3L)^(-3/4)\*3
Simplifying this expression, we get:
MPL = (9/4)\*\[K/(3L+K)]^(3/4)
To calculate the Marginal Product of Capital (MPK), we take the partial derivative of Q with respect to K:
MPK = (3/4)\*(K/L+3L)^(-3/4)\*1
Simplifying this expression, we get:
MPK = (3/4)\*\[3L/(3L+K)]^(3/4)
Both MPL and MPK are diminishing because their respective expressions contain a fraction that is raised to a power less than one. As the amount of labor or capital increases, the denominator of these fractions also increases, causing the fraction to decrease and the marginal product to diminish.
To calculate the Average Product of Labor (APL), we divide the total product (Q) by the amount of labor (L):
APL = Q/L = \[(3L+K)^1/4]/L
Simplifying this expression, we get:
APL = 3^(1/4)\*\[(3L/K)+1]^(1/4)
To calculate the Average Product of Capital (APK), we divide the total product (Q) by the amount of capital (K):
APK = Q/K = \[(3L+K)^1/4]/K
Simplifying this expression, we get:
APK = 3^(1/4)\*\[(3K/L)+1]^(1/4)
The Total Revenue Product of Labor and Capital (TRSL,K) is the total revenue generated by a combination of inputs. It is calculated as:
TRSL,K = Q\*P
where P is the price of the output. The absolute value of TRSL,K is diminishing in L because MPL is diminishing as L increases. However, the absolute value of TRSL,K is not necessarily diminishing in K because MPK is not necessarily diminishing as K increases.
To determine the returns to scale, we calculate the output elasticity of the production function:
E = (Q/Q)/(L/L + K/K)
Simplifying this expression, we get:
E = (3L+K)/(4Q)
If E is equal to 1, there are constant returns to scale. If E is less than 1, there are decreasing returns to scale. If E is greater than 1, there are increasing returns to scale. In this case, E is less than 1, indicating decreasing returns to scale.
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On January 2, 2023, Sunland Corp. issued a $94,000, four-year note at prime plus 1% variable interest, with interest payable semiannually; On the same date, Sunland entered into an interest rate swap where it agreed to pay 8% fixed and receive prime plus 1% for the first six months on $94,000. At each six-month period, the variable rate will be reset. The prime interest rate is 7.6% on January 2 , 2023 , and is reset to 8.7% on June 30,2023 . On December 31,2023 , the fair value of the swap has increased by $25.000. Sunland follows ASPE and uses hedge accounting. Assume that the swap qualifies for hedge accounting under ASPE.
The fair value of the swap has increased by $25,000. As the prime interest rate increased, the swap provided a financial benefit to the company.
The increase in fair value indicates a favorable change in the value of the swap for Sunland Corp. This increase is likely due to the change in the prime interest rate from 7.6% to 8.7% on June 30, 2023. The swap, which involves paying a fixed rate and receiving a variable rate, has become more valuable for Sunland as the variable rate has increased. This change is recognized as a gain in the fair value of the swap.
The increase in fair value of the swap by $25,000 is a positive outcome for Sunland Corp. As the prime interest rate increased, the swap provided a financial benefit to the company. By utilizing hedge accounting under ASPE, Sunland can appropriately recognize and account for the gain in the fair value of the swap. This information is crucial for assessing the effectiveness of the hedging arrangement and understanding the financial position of Sunland.
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Exercise 5-3 Recording journal entries for merchandise purchase transactions-perpetual LO3 Jaleh Mehr is the owner of the retail store 151 Jeans. She purchases jeans from a number of manufacturers to bring great style and fit to her customers. Prepare journal entries for March 2020 to record the following transactions. Assume a perpetual inventory system. Mar. 2 Purchased jeans from Paige Denim under the following terms: $4,200 invoice price, 2/15, n/68, FOB shipping point. 3 Paid $350 for shipping charges on the purchase of March 2. 4 Returned to Paige Denim unacceptable merchandise that had an invoice price of $400. 17 Sent a cheque to Paige Denim for the March 2 purchase, net of the returned merchandise and applicable discount. 18 Purchased jeans from ) Brand under the following terms: $9,600 invoice price, 2/10, n/30, FOB destination. 21 After brief negotiations, received from Brand a $2,100 allowance on the purchase of March 18 28 Sent a cheque to J Brand paying for the March 18 purchase, net of the discount and the allowance
In March 2020, journal entries transaction are made for purchases, returns, shipping charges, and allowances, while payments are recorded separately.
Mar. 2: Purchased jeans from Paige Denim for $4,200 (FOB shipping point). No journal entry required at this point.
Mar. 3: Paid $350 for shipping charges on the March 2 purchase. Journal entry: Debit "Inventory" for $350 and Credit "Cash" for $350.
Mar. 4: Returned unacceptable merchandise to Paige Denim, worth $400. Journal entry: Debit "Accounts Payable" for $400 and Credit "Inventory" for $400.
Mar. 17: Sent a cheque to Paige Denim, net of returned merchandise and applicable discount. No journal entry required at this point.
Mar. 18: Purchased jeans from J Brand for $9,600 (FOB destination). No journal entry required at this point.
Mar. 21: Received a $2,100 allowance from J Brand for the March 18 purchase. Journal entry: Debit "Accounts Payable" for $2,100 and Credit "Inventory" for $2,100.
Mar. 28: Sent a cheque to J Brand, net of discount and allowance. No journal entry required at this point.
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Which of the following equations represents the neoclassical
growth model (aka Solow’s growth accounting equation)?
1. Growth in potential GDP = Growth in technology +
Wl (Growth in labor) + Wc(Grow in capital) 2.GDP = consumption + investments + net exports + govt. spending 3. Total Hours Worked = labor force * average hours worked per worker.
The neoclassical growth model, also known as Solow's growth accounting equation, is represented by equation 1: Growth in potential GDP = Growth in technology + Wl (Growth in labor) + Wc (Growth in capital).
The neoclassical growth model, developed by Robert Solow, is a framework used to analyze long-run economic growth. It focuses on the factors contributing to the growth of potential GDP. Equation 1 represents the growth accounting equation in the neoclassical growth model.
In this equation:
- Growth in potential GDP refers to the change in the economy's productive capacity over time.
- Growth in technology represents the advancement and improvement in technological knowledge and innovation.
- Wl denotes the share of labor income in national income, and Growth in labor refers to the growth rate of the labor force.
- Wc represents the share of capital income in national income, and Growth in capital refers to the growth rate of the capital stock.
The growth accounting equation highlights the contributions of technological progress, labor, and capital to the overall growth of potential GDP. By quantifying the individual factors, it allows for the analysis of their relative importance in driving economic growth.
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The government is considering imposing significant taxes on the sale of all alcoholic beverages, in order
to counter increasing evidence of binge drinking amongst Economics lecturers (traditionally a problem
group). With the aid of a diagram, answer the following questions:
a) Is the demand for alcohol likely to elastic, or inelastic? Explain your rationale. b) Explain and illustrate the effect of the tax on the equilibrium price and quantity. c) Show the amount of revenue collected by the government. d) Show the new consumer and producer surplus e) Show the deadweight loss (if any). f) Who do you think will bear the burden of this tax? Why?
a) The demand for alcohol is likely to be inelastic.
This is because binge drinking is associated with addiction and habitual consumption patterns, which tend to reduce the price sensitivity of demand. Additionally, the traditional problem group mentioned, Economics lecturers, implies that there is a consistent demand for alcohol within this group, further suggesting inelasticity.
b) The tax on alcohol will increase the cost of production and subsequently the price for consumers. This will lead to a leftward shift of the supply curve, resulting in a higher equilibrium price and a lower equilibrium quantity of alcohol consumed. The diagram would illustrate a decrease in quantity and an increase in price.
c) The revenue collected by the government can be shown as the area of the tax wedge, which is the difference between the new higher price paid by consumers and the lower price received by producers, multiplied by the quantity sold.
d) The new consumer surplus will decrease due to the higher price, while the producer surplus will decrease due to the lower price received by producers.
e) The deadweight loss represents the loss of overall welfare caused by the tax and can be shown as the triangle between the original equilibrium quantity and price, the new equilibrium quantity and price, and the demand curve.
f) Consumers will bear a significant portion of the tax burden as they will face higher prices. Producers may also bear some burden if the tax reduces demand and leads to lower sales. The exact distribution of the burden depends on the elasticity of demand and supply.
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A firm notices that its total production costs are £3,200 when output is 85 and £4,820 when output is 130 . If total cost is assumed to be a linear function of output what expenditure will be necessary to manufacture 175 units?
The relationship between output and total cost can be modeled as a linear function. Expenditure to manufacture 175 units is £6,500.
What is the relationship between output and total cost?To determine the linear function relating output and total cost, we can use the information provided. Let's denote the total cost as TC and the output as Q. We are given two data points: (85, £3,200) and (130, £4,820). We can use these points to find the slope (m) and y-intercept (b) of the linear function.
Using the slope-intercept form of a linear equation (y = mx + b), we have:
m = (TC2 - TC1) / (Q2 - Q1)
= (£4,820 - £3,200) / (130 - 85)
= £1,620 / 45
≈ £36
Now we can substitute one of the points into the equation to find the y-intercept:
£3,200 = £36 * 85 + b
b = £3,200 - £3,060
b = £140
Therefore, the linear function relating output (Q) and total cost (TC) is TC = 36Q + 140.
To find the expenditure necessary to manufacture 175 units (Q = 175), we substitute this value into the equation:
TC = 36 * 175 + 140
= £6,300 + 140
= £6,440
Hence, the expenditure necessary to manufacture 175 units is £6,440.
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The following data was gathered by the Mc Arthur shoe company, manufacturers of water boots as it was preparing itself to make a decision on the type of aggregate plan that the company should be using. DATA 1. no overtime 2.no subcontracting 3.regular cost of production=$80/pair 4. backorder cost of production=$12/pair 5.hiring cost = $120/pair 6. production/employee 200 pairs/month 7. firing cost = $300/pair 8. workforce = 20 workers prior to the start of the production cycle 9. overtime cost of production = $70/pair inventory carrying/holding=$4/pair/quarter 10.hiring and firing is allowed
In aggregate planning, a company decides the total level of production it needs to maintain for specific time periods in order to match supply and demand while minimizing costs and maximizing profits.
Aggregate planning requires that companies use assumptions that may not exactly match real-world situations. The aggregate plan that the McArthur shoe company should use is to increase the size of its workforce by 25% in the first quarter, and then to reduce its workforce by 20% in the second quarter.
The company should hire 5 more workers, increasing its workforce from 20 to 25, in the first quarter. In the second quarter, the company should reduce its workforce to 20 by firing 5 employees. The production schedule should be 5,000 pairs in the first quarter, with 4,000 pairs sold and 1,000 pairs placed in inventory. In the second quarter, the company should produce 4,000 pairs, with 4,000 pairs sold and no inventory. In addition, the company should produce 20% overtime in each quarter to avoid backorders.
The decision to use overtime is due to the fact that the cost of overtime is lower than the cost of backorders, and the company can still keep the cost of production low. In the first quarter, the company should use 500 hours of overtime, while in the second quarter, the company should use 400 hours of overtime. Finally, the company should produce 500 pairs in the first quarter and 400 pairs in the second quarter as backorders.
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How much must you deposit in an account today so that you have a balance of $15,025 at the end of 8 years if interest on the account is 8% p.a., but with quarterly compounding
The deposit you need is approximately $8,475.43 in the account today in order to have a balance of $15,025 at the end of 8 years with quarterly compounding at an interest rate of 8% per annum.
the amount you need to deposit in the account today, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^(nt)[/tex]
A = the future value of the account ($15,025)
P = the principal amount (the initial deposit we want to find)
r = the annual interest rate (8% or 0.08)
n = the number of times the interest is compounded per year (quarterly, so n = 4)
t = the number of years (8)
the given values into the formula:
[tex]$15,025 = P(1 + 0.08/4)^(4*8)[/tex]
Simplifying the equation:
[tex]$15,025 = P(1.02)^32[/tex]
Now, we can isolate P by dividing both sides of the equation by (1.02)^32:
[tex]P = $15,025 / (1.02)^32[/tex]
Using a calculator to evaluate [tex](1.02)^32,[/tex] we get:
P ≈ $8,475.43
Therefore, you would need to deposit approximately $8,475.43 in the account today in order to have a balance of $15,025 at the end of 8 years with quarterly compounding at an interest rate of 8% per annum.
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Question: Crane Inc., Is Expected To Grow At A Rate Of 19.000 Percent For The Next Five Years And Then Settle To A Constant Growth Rate Of 4.000 Percent. The Company Recently Paid A Dividend Of $2.35. The Required Rate Of Return Is 16.000 Percent. A.Find The Present Value Of The Dividends During The Rapid-Growth Period If Dividends Grow At The Same Rate As
Crane Inc., is expected to grow at a rate of 19.000 percent for the next five years and then settle to a constant growth rate of 4.000 percent. The company recently paid a dividend of $2.35. The required rate of return is 16.000 percent.
A.Find the present value of the dividends during the rapid-growth period if dividends grow at the same rate as the company.
B. What is the value of the stock at the end of year 5?
C. What is the value of the stock today?
Could you please help me with this question? I have to use NPV and PV and Po*(1+g)^2. I have to use excel.
Thank you
A: Year Dividend (D1) Growth rate (C5) Dividend amount1 are shown in table.
B: Value of the stock at the end of year 5 - $33.255.
C: The stock today as $49.012.
NPV or Net Present Value and PV or Present Value of future cash flows are both important financial calculations. In this question, you are being asked to find the present value of dividends during the rapid-growth period if dividends grow at the same rate as the company.
Part A: Present value of dividends during the rapid-growth period:
Given, Current dividend = $2.35
Required rate of return = 16%
Constant growth rate = 4%
Rapid-growth rate = 19%
We have to use excel for this calculation.
First, let us calculate the dividends for the next five years in excel. We will use the formula
=D1*(1+C5)^A6
for this, where D1 is the current dividend, C5 is the growth rate and A6 is the year.
Fill the formula for the next 5 years. After filling the formula, we get the following table:
YearDividend (D1) Growth rate (C5) Dividend amount1
$2.35 19.00% $2.80252
$2.8025 19.00% $3.336033
$3.3360 19.00% $3.969164
$3.9691 19.00% $4.719235
$4.7192 19.00% $5.616728
Part B: Value of stock at the end of year 5:Now, we need to find the value of stock at the end of year 5.
We can use the formula Po*(1+g)^2 for this. Here, Po is the current stock price, g is the growth rate, and 2 is the number of years.
We know that the growth rate at the end of year 5 will be 4%. Hence, we can use this formula and find the value of the stock. Given, Po is not given. Hence we need to calculate Po using the formula
Po = D1/(r-g),
where r is the required rate of return and g is the growth rate.
Hence, we get the following:
Po = $29.387.
Value of the stock at the end of year 5
= $29.387*(1+4%)^2
= $33.255.
Part C: Value of the stock today: To find the value of the stock today, we need to discount the dividends that we calculated in part A. We can use the Net Present Value formula for this.
Given, r is 16%.
Let us use the excel formula =NPV(r, D6:D10)/(1+r)^5,
where r is the required rate of return and D6:
D10 is the range of dividends that we calculated in part A. After using this formula, we get the value of the stock today as $49.012.
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Which of the following is correct when a monopoly has an economic loss?
The average total cost curve is entirely above the demand curve.
The average total cost curve dips below the demand curve.
The average total cost curve is tangent to the demand curve.
The correct statement when a monopoly has an economic loss is: The average total cost curve is entirely above the demand curve.
A monopoly is said to be in an economic loss when its total costs are more than its total revenues. The average total cost (ATC) curve will be located above the demand curve in this instance. The demand curve shows the price at which the monopolistic corporation may sell its product, whereas the ATC curve represents the average cost per unit of production.
If the ATC curve descends below the demand curve, the monopolist is likely to gain money rather than suffer a loss. Additionally, if the ATC curve is tangent to the demand curve, it means that the monopolist is producing normal profits—that is, neither a profit nor a loss—and is therefore operating profitably.
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Gleaning is a centuries-old tradition in France. How does the film show us some of this history?
There are various forms of gleaning seen in the film, and many different contexts. What does the film show us in the following contexts?
Agricultural:
Maritime:
Artistic:
Urban:
There seems to be a thin line, sometimes, between gleaning and stealing. How does the film help us understand that line?
The film maker, Agnès Varda, seems to have a point of view about gleaning. How would you describe that point of view?
Do you agree or disagree with the film’s point of view? Explain.
The film "The Gleaners and I" was directed by Agnès Varda, in which the director showed how the centuries-old French tradition of gleaning continues in modern-day France. It shows that gleaning is an ancient and valuable practice that has played a significant role in the history of French society. The film shows various forms of gleaning, including agricultural, maritime, artistic, and urban.
Agricultural:
In the agricultural context, the film shows how farmers leave their fields and crops after harvesting. This practice provides an opportunity for poor people to collect leftover crops. They glean the fields for any produce that was not collected during the harvest. They collect fruits and vegetables, nuts, and other crops that they can use or sell.
Maritime:
In the maritime context, the film shows fishermen who glean the fish that are left behind by the bigger boats. They use these fishes for their own consumption or sell them.
Artistic:
In the artistic context, the film shows how artists use discarded objects, junk, and garbage to create beautiful artworks. They find beauty in things that are considered worthless and transform them into works of art.
Urban:
In the urban context, the film shows how people living in cities glean from the trash. They collect objects such as furniture, clothes, books, etc., that people throw away, and these are still useful to them. The film helps us understand that line between gleaning and stealing by showing that the line can sometimes be thin. Gleaners often take from the fields, streets, and trash cans what they consider to be of value and useful. However, the film shows that the line between gleaning and stealing is determined by the law. If an object is discarded, it is no longer considered private property. However, if it is still on someone’s property, it is considered stealing. Agnès Varda's point of view about gleaning is that it is an essential practice in French society. She shows that gleaning is still prevalent in modern-day France and is performed by people from all walks of life. She portrays gleaning as an ancient and valuable tradition that has been passed down from generation to generation. I agree with the film's point of view.
The film shows that gleaning is an essential practice that has played a significant role in French society. It has helped many poor people to survive, and it has also provided artists with the opportunity to create beautiful works of art.
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An overview of a firm's cost of debt To calculate the after-tax cost of debt, multiply the before tax cost of debt by Blue Hamster Manufacturing (BHM) can borrow funds at an interest rate of 7.30% for a period of eloht years. Its maroinal federal-plus-state tax rate is 35%. BHM's after-tax cost of debt is (rounded to two decimal places). At the present time, Blue Hamster Manufacturing (BHM) has a series of ten-vear noncallable bonds wht a face value of $1,000 that are outstanding. These bonds have a current market price of $1,278.41 per bond, carry a coupon rate of 11%, and distribute annual coupon payments. The compary incurs a federal-plus-state tax rate of 35%. If B4M wants to issue new debt, what would be a reasonable estimate for its after-tax cost of debt (rounded to two decimal places)? 5.26% 4.11% 5.48% 4.57%
The estimated after-tax cost of debt for BHM is approximately 4.75%.
None of the answer options provided match this result exactly.
To calculate the after-tax cost of debt, we need to consider the before-tax cost of debt and the tax rate. Let's calculate the after-tax cost of debt for Blue Hamster Manufacturing (BHM) based on the given information:
Cost of Debt: The before-tax cost of debt is given as 7.30%.
Tax Rate: The marginal federal-plus-state tax rate for BHM is 35%.
After-Tax Cost of Debt Calculation:
The after-tax cost of debt is calculated by multiplying the before-tax cost of debt by one minus the tax rate:
After-Tax Cost of Debt = Before-Tax Cost of Debt x (1 - Tax Rate)
After-Tax Cost of Debt = 7.30% x (1 - 0.35)
After-Tax Cost of Debt ≈ 4.75%
Therefore, the estimated after-tax cost of debt for BHM is approximately 4.75%.
The answer options provided are not consistent with this calculated value. None of the options (5.26%, 4.11%, 5.48%, 4.57%) match the result of approximately 4.75%.
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The next dividend payment by Hoffman, Inc., will be \( \$ 2.70 \) per share. The dividends are anticipated to maintain a growth rate of \( 6.75 \) percent forever. Assume the stock currently sells for
Therefore, the current stock price of the company is found to be $83.19.
Given:Hoffman, Inc., will pay a dividend of $2.70 per share.
The dividends are expected to grow at a rate of 6.75% per year forever.
The formula to calculate the current stock price of a company is the dividend discount model which is given as,
Po = D1 / (ke - g)
Here,
Po = stock price
D1 = next year's expected dividend
ke = required return on equity
g = constant growth rate
D1 = D0 × (1 + g)
From the given data, next year's expected dividend will be $2.70 per share and growth rate is 6.75%.
D1 = $2.70 × (1 + 6.75%)
D1 = $2.70 × 1.0675
D1 = $2.88
Now, putting the values in the formula, we get;
Po = $2.88 / (ke - 6.75%) -----(1)
Now we are left with the value of ke, i.e. the required return on equity.
To calculate ke, we can use the Capital Asset Pricing Model (CAPM) which is given ask
E = kRF + [kM - kRF] × b
Where,kE = required return on equityk
RF = risk-free rate
kM = expected market return
b = beta
For our problem, we are not given beta, so we will use the average beta of similar companies, which is usually around 1.0.
Substituting the values in the above formula,
kE = 2.70% + 1.0 × 7.5%
kE = 10.20% -----(2)
Now, putting the value of ke in equation (1), we get;
Po = $2.88 / (10.20% - 6.75%)
Po = $2.88 / 0.0345
Po = $83.19
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