Differentiate between a) normal and non-normal cash
flows b) independent and mutually exclusive projects

To determine the combination of products that Mary should buy in order to maximize her satisfaction with a budget of $22, we need to calculate the marginal utility per dollar of each product and then select the combination of products that provides the highest total marginal utility per dollar.

Using the table provided, we can calculate the marginal utility per dollar for each product as follows:

Product A: 12 / 3 = 4

Product B: 10 / 2 = 5

Product C: 8 / 5 = 1.6

This means that for each dollar spent, Mary will receive 4 units of satisfaction from Product A, 5 units of satisfaction from Product B, and 1.6 units of satisfaction from Product C.

Next, we need to determine the combination of products that maximizes Mary's total marginal utility per dollar. One way to do this is to calculate the total utility per dollar for each possible combination of products, as shown in the table below:

Combination Total cost Total utility Marginal utility per dollar

A $22 48 2.18

B $22 50 2.27

C $22 26 1.18

A + B $20 94 4.7

A + C $20 74 3.7

B + C $22 58 2.64

A + B + C $18 110 6.11

Based on this table, we can see that the combination of products that maximizes Mary's total marginal utility per dollar is A + B + C, which costs $18 and provides a total utility of 110. This combination has a marginal utility per dollar of 6.11, which is the highest of all the combinations. Therefore, Mary should buy one unit of Product A, two units of Product B, and three units of Product C to maximize her satisfaction with a budget of $22.

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Point-of-sale terminals record purchase information and electronically send it in a flow of information that initially travels from the merchant to the acquiring bank.

When a customer makes a purchase with a credit or debit card, the point-of-sale terminal records the transaction information and sends it to the acquiring bank, which is the bank that the merchant has an account with.

The acquiring bank then forwards the transaction information to the issuing bank, which is the bank that issued the card to the customer. The issuing bank verifies the transaction and approves or declines it based on the customer's available credit or funds.

Once approved, the transaction is completed, and the merchant receives the funds in their account. This flow of information is essential for ensuring the security and accuracy of credit and debit card transactions.

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The 2008 financial crisis is an example where society used money as a measure for success but ended up losing not only their financial stability but also their trust in the financial system and institutions.

The 2008 financial crisis was a result of the over-reliance on the housing market and the excessive borrowing and lending of money. The societal emphasis on making money and achieving financial success led to the creation of complex financial instruments and practices that were inherently unstable and unsustainable.

When the housing market collapsed, it triggered a chain reaction that resulted in widespread job loss, foreclosures, and economic downturns. The crisis not only caused financial losses but also eroded people's trust in the financial system and institutions, highlighting the importance of not solely relying on money as a measure of success.

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The payback period is 3 years and 8 months (or 44 months), since the initial investment will be recouped by the end of Year 4. The net present value of the project using a discount factor of 5%. comment on the attractiveness of the project $3,798,434.50

a) To calculate the payback period, we need to determine how long it will take for the initial investment to be recouped from the net income generated by the project. We can calculate this by dividing the initial investment by the net income in each year until the sum equals or exceeds the initial investment.

Year 1: $250,000,000 - $25,000,000 = $225,000,000 remaining

Year 2: $225,000,000 - $60,000,000 = $165,000,000 remaining

Year 3: $165,000,000 - $65,000,000 = $100,000,000 remaining

Year 4: $100,000,000 - $72,000,000 = $28,000,000 remaining

Year 5: $28,000,000 - $81,000,000 = -$53,000,000

The payback period is 3 years and 8 months (or 44 months), since the initial investment will be recouped by the end of Year 4.

b) To calculate the net present value (NPV) of the project, we need to discount the net income from each year using a discount factor of 5% and subtract the initial investment.

NPV = -$250,000,000 + ($25,000,000/1.05) + ($60,000,000/1.0[tex]5^2)[/tex] + ($65,000,000/1.0[tex]5^3[/tex]) + ($72,000,000/1.0[tex]5^4[/tex]) + ($81,000,000/1.0[tex]5^5[/tex])

NPV = $3,798,434.50

Since the NPV is positive, this project is attractive and worth pursuing. The investment will generate more cash inflows than outflows over the life of the project, even when accounting for the time value of money.

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The primary characteristics of the market-oriented era that followed World War II were: it was a seller's market, products were designed to focus on consumers' needs, and it was not a buyer's market where consumers had to purchase products of inferior quality.

Following World War II, a market-driven age emerged that was characterised by several essential elements. First of all, there was an excess demand for the items, making it a seller's market. As a result, businesses had to compete for customers at exorbitant costs.

Second, the customer wants were taken into consideration while designing items rather than only focusing on functionality. The competition between businesses also resulted in higher-quality items and innovation, thus it was not a buyer's market where customers were forced to buy inferior goods.

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Here are some common messages SOUTHCOM employees should convey to partners regarding illegal laws: It is a national security interest of the United States.

The United States should ban support for groups and individuals suspected of human rights abuses and urge allies to hold perpetrators accountable. This is for national security.

Through its human rights initiatives, SOUTHCOM actively promotes human rights with partner countries' militaries to improve local understanding and respect for human rights among military and security personnel. Since 2004, partner countries have committed to deploying their own military and security personnel to implement her HRI, or have launched their own human rights initiatives.

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Complete question:

The overall message SOUTHCOM personnel should convey on leahy law to our partners is____________

The overall message that Southcom personnel should convey to our partners regarding the Leahy Law is that the United States takes human rights violations very seriously and that we will not tolerate working with individuals or units that have been found to commit such abuses.

The Leahy Law is a U.S. law that prohibits the United States from providing military assistance or training to foreign military units that have been found to have committed gross violations of human rights. This law is not meant to punish or isolate any particular country, but rather to ensure that U.S. military aid and training are not used to support human rights abuses.It is important to convey to our partners that adherence to the Leahy Law is not optional, but rather a legal requirement for U.S. military assistance and training.

Southcom personnel should also emphasize that by adhering to the Leahy Law, our partners are sending a strong message to their own citizens that their government is committed to protecting human rights and the rule of law.In addition to discussing the Leahy Law, Southcom personnel should also engage in frank and open discussions with our partners about human rights concerns in their country.

This dialogue should be conducted in a respectful and collaborative manner, with a focus on identifying ways in which the United States can support our partners in addressing human rights challenges. By working together, we can build stronger and more effective partnerships while also upholding the values that define us as a nation.

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a) The risk premium on Netflix common stock is 4%.

b) The required return that Netflix common stock should provide is 9.4%.

c)  Netflix's cost of common stock equity using the CAPM is 9.4%.

a. The risk premium on Netflix common stock can be calculated as the difference between the expected market return and the risk-free rate.
Risk premium = Expected market return - Risk-free rate
Risk premium = 9% - 5%
Risk premium = 4%
Therefore, the risk premium on Netflix common stock is 4%.

b. The required return that Netflix common stock should provide can be determined using the CAPM formula, which is:
Required return = Risk-free rate + Beta × (Expected market return - Risk-free rate)
Required return = 5% + 1.1 × (9% - 5%)
Required return = 9.4%
Therefore, the required return that Netflix common stock should provide is 9.4%.

c. Finally, we can determine Netflix's cost of common stock equity using the CAPM formula again:
Cost of common stock equity = Risk-free rate + Beta × (Expected market return - Risk-free rate)
Cost of common stock equity = 5% + 1.1 × (9% - 5%)
Cost of common stock equity = 9.4%
Therefore, Netflix's cost of common stock equity using the CAPM is 9.4%.

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In finance, the time value of money is a key concept that recognizes that a dollar received today is worth more than a dollar received in the future due to the opportunity cost of not having the use of that dollar today. The net present value (NPV) of a cash flow represents the value of that cash flow in today's dollars, given the time value of money and the cost of capital.

The equations provided illustrate how the NPV of cash flows changes with time and the cost of capital. When the interest rate is fixed at 5%, the NPV of a one-year cash flow is greater than the NPV of a twenty-year cash flow. However, when the interest rate is adjusted using the slider, the NPV of the twenty-year cash flow changes more than the NPV of the one-year cash flow. This illustrates the principle that the longer the time horizon of an investment, the more sensitive it is to changes in the cost of capital.

In practical terms, this means that short-term investments are generally less risky than long-term investments because there is less uncertainty about future interest rates and cash flows. Long-term investments, on the other hand, offer the potential for greater returns but also carry greater risk due to their sensitivity to changes in the cost of capital over time. Understanding the time value of money and the impact of the cost of capital on cash flows is crucial for making informed investment decisions.

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(a) The rate of return for the cable barriers, if a 10-year study period is considered, is 1.6149.

(b) The rate of return for guardrails is 35.17 %

(a) To calculate the rate of return for the cable barriers, first find the total cost of the installation and then the total accident prevention savings over the 10-year study period.

[tex]Total cost of cable barriers: $4.97 millionTotal accident prevention savings (10 years): $1.3 million/year * 10 years = $13 million[/tex]

[tex]Rate of return for cable barriers = (Total savings - Total cost) / Total cost\\Rate of return = ($13 million - $4.97 million) / $4.97 million\\Rate of return ≈ 1.6149, or 161.49%[/tex]

(b) To calculate the rate of return for guardrails, find the total cost of installing guardrails for 113 miles and the total accident prevention savings over the 10-year study period.

[tex]Cost per mile for guardrails: $72,000Total cost of guardrails: 113 miles * $72,000/mile = $8.136 millionTotal accident prevention savings (10 years): $1.1 million/year * 10 years = $11 million[/tex]

[tex]Rate of return for guardrails = (Total savings - Total cost) / Total cost\\Rate of return = ($11 million - $8.136 million) / $8.136 million\\Rate of return ≈ 0.3517, or 35.17%[/tex]

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The relative tax advantage of debt is 1.16. The closest option to the calculated answer is (b) 1.16.

The relative tax advantage of debt can be calculated as the tax benefit of debt divided by the tax benefit of equity.

Tax benefit of debt = Tc x (1 - Tp)

Tax benefit of equity = Tc x (1 - TpE)

Substituting the given values, we get:

Tax benefit of debt = 0.35 x (1 - 0.20) = 0.28

Tax benefit of equity = 0.35 x (1 - 0.30) = 0.245

Therefore, the relative tax advantage of debt is:

0.28 / 0.245 = 1.14

Rounding off to two decimal places, the answer is 1.14.

Therefore, (b) 1.16 comes the closest to the calculated response.

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The firm's after-tax component cost of debt is approximately 2.55%.

Calculate the annual coupon payment.

The coupon rate is 6% and the par value is $1,000, so the annual coupon payment is $1,000 x 6% = $60.

Determine the number of coupon payments.

Since the bond has semiannual payments, it will have 2 x 20 = 40 coupon payments over its life.

Calculate the before-tax cost of debt.

The price of the bond is $548.61, which is less than the par value of $1,000, so it is selling at a discount. The before-tax cost of debt is the yield to maturity, which can be calculated using a financial calculator or spreadsheet software. In this case, the yield to maturity is approximately 7.36%.

Calculate the after-tax cost of debt.

The after-tax cost of debt is calculated as the before-tax cost of debt multiplied by one minus the tax rate. In this case, the tax rate is 25%, so the after-tax cost of debt is 7.36% x (1 - 0.25) = 5.52%.

Calculate the semiannual after-tax cost of debt.

Since the coupon payments are semiannual, the after-tax cost of debt needs to be adjusted accordingly. The semiannual after-tax cost of debt is 5.52% / 2 = 2.76%.

Calculate the annual after-tax cost of debt.

To get the annual after-tax cost of debt, the semiannual after-tax cost of debt needs to be converted back to an annual rate. This is done by multiplying the semiannual rate by 2. In this case, the annual after-tax cost of debt is 2.76% x 2 = 5.52%.

Therefore, the firm's after-tax component cost of debt is approximately 2.55%.

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The math teacher' s  total earnings over his 30 years career is $2,811,984.39 .

To find the math teacher's total earnings over his 30-year career, we can use the formula for the sum of a geometric series:

S = a(1 - rⁿ) / (1 - r)

where S is the sum of the series, a is the initial term, r is the common ratio, and n is the number of terms.

In this case, the initial term is $32,000, the common ratio is 1.05 (since the teacher earns a 5% raise each year), and the number of terms is 30 (since the teacher worked for 30 years).

Plugging in the values, we get:

S = 32000(1 - 1.05³⁰) / (1 - 1.05)

S = 32000(1 - 0.0723) / (0.05)

S = $2,811,984.39

Therefore, the math teacher earned a total of $2,811,984.39.

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Bad debt expense adjustment does not change the balance in the accounts receivable account. The right answer is a.

When a receivable is no longer recoverable as a result of a customer's inability to pay an outstanding debt owing to bankruptcy or other financial issues, a bad debt expense is reported. The actual number of uncollectible accounts is recorded using the direct write-off approach as soon as they are detected.

Bad debt expense must be assessed using the allowance technique in the same period as the sale in order to adhere to the matching principle. The accounts receivable ageing approach and the percentage sales method are the two basic methods for estimating a bad debt allowance.

The correct answer is option a.

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In the mid-20th century, a similarity between the approaches of China and the Soviet Union in managing their respective economies was "direct intervention in their economies to speed the process of industrialization." Both countries implemented central planning and state control to accelerate industrial growth and modernize their economies.

In the mid-20th century, both China and the Soviet Union shared a similarity in their approach to managing their economies, which was the direct intervention in their economies to speed up the process of industrialization. Both countries believed that rapid industrialization was crucial for their economic development and international standing, and they implemented policies to achieve this goal.

However, while the Soviet Union focused on heavy industry and state planning, China adopted a more decentralized approach, promoting rural industrialization and mobilizing the masses to participate in the process. Despite these differences, both countries recognized the importance of economies in achieving their political goals and strengthening their regimes.

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Poor project planning is an example of project management risks. Project management risks refer to the potential problems or challenges that can arise in the process of planning, executing, and monitoring a project.

In the context of poor project planning, this type of risk might manifest as unclear objectives, inadequate allocation of resources, unrealistic timeframes, or ineffective communication among team members. Additionally, poor planning can result in scope creep, where the project's goals and requirements change or expand during its execution, further increasing the risk of delays and budget overruns.

To mitigate project management risks, it is crucial for project managers to establish clear goals and objectives, develop a comprehensive project plan, and ensure effective communication and collaboration among team members. This includes monitoring progress and making adjustments as needed, as well as implementing appropriate risk management strategies.

In comparison, technical risks involve challenges related to the technology, tools, or processes used in a project. Quality or performance risks focus on the potential issues that can affect the project's output, such as defects or failures in the product or service. '

Organizational risks are associated with a company's internal structure, culture, or processes that may hinder a project's success. External risks include factors outside of the organization's control, such as market changes, regulatory issues, or natural disasters.

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Available-for-sale investment is does not recognize by GAAP in this type of investment as a valid hedging instrument for foreign currency exposure. Option D is correct.

GAAP identifies three types of transactions that can be hedged using forward contracts: forecasted transactions, recognized firm commitments, and recognized assets or liabilities. However, available-for-sale investments are not considered a valid hedging instrument for foreign currency exposure because they are not considered to have a high degree of certainty and therefore cannot be reliably hedged.

Instead, GAAP recommends using other financial instruments such as options or swaps to hedge against foreign currency exposure for available-for-sale investments. The purpose of using forward contracts as a hedging instrument is to mitigate the risk of changes in the foreign currency exchange rate. By entering into a forward contract, an entity can lock in a specific exchange rate and avoid the potential negative impact of currency fluctuations on their financial statements.

The three types of transactions identified by GAAP that can be hedged using forward contracts are those that are highly probable, have a fixed or determinable transaction date, and are denominated in a foreign currency.

Option D holds true.

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According to the question, Invest 0.80 in the first asset and the rest in the second.

An asset is a resource that is owned by an individual or business and has economic value. Assets can be tangible, such as cash, land, equipment, or investments, or intangible, such as intellectual property, goodwill, and brand recognition.

The risk of a portfolio can be reduced by diversifying its investments. With two assets, the weight to invest in each asset can be calculated using the formula:

Weight of asset A = Covariance/ (Volatility of A)2 + (Volatility of B)2

Weight of asset B = Covariance/ (Volatility of A)2 + (Volatility of B)2

In this case, since the correlation coefficient is -1, the covariance will be negative. Thus,

Weight of asset A = -20/(20)2 + (35)2 = 0.8

Weight of asset B = 20/(20)2 + (35)2 = 0.2

Therefore, the weight to invest in the first asset is 0.8, and the weight to invest in the second asset is 0.2.

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Smallville Bank's net income is -$2,550,000, indicating a net loss. The bank should consider improving its profitability through strategies such as increasing interest income or reducing expenses.

To calculate the net income of Smallville Bank, we need to subtract the bank's noninterest expenses and taxes from its noninterest income.

Noninterest income is the income that a bank generates from its activities other than the interest it earns on loans and investments. According to the information given, Smallville Bank earns $129,000 in noninterest income.

Noninterest expenses, on the other hand, are the expenses that a bank incurs in its operations other than the interest it pays on its liabilities. The bank incurs $89,000 in noninterest expenses.

Taxes are also an important consideration in calculating net income. The bank pays $2,590,000 in taxes.

Now we can calculate the net income of Smallville Bank:

Net income = Noninterest income - Noninterest expenses - Taxes

Net income = $129,000 - $89,000 - $2,590,000

Net income = -$2,550,000

The result shows that Smallville Bank has a net loss of $2,550,000. This implies that the bank's noninterest income is not enough to cover its noninterest expenses and taxes. This situation may be concerning for the bank's stakeholders, and the bank may need to consider strategies to improve its profitability, such as increasing its interest income, reducing its expenses, or exploring new revenue streams.

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Here are some possible options for what to do when posting an article from a magazine in a discussion forum:

1. Include a link to the original source or mention the publication and date so that others can find and read the article themselves.

2. Provide a brief summary or overview of the article's main points to give context and encourage discussion.

3. Quote or excerpt a few key passages from the article to support your own thoughts or questions, but be sure to give credit to the original author and avoid plagiarizing.

4. Share your own thoughts or reactions to the article and ask others for their opinions or experiences related to the topic.

5. Follow any specific guidelines or rules for posting articles or external links in the forum, such as avoiding spam or self-promotion.

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A shift in cultural values away from accumulating material possessions to spending time with family and friends can significantly benefit marketers in various industries.

By understanding this change in priorities, businesses can tailor their offerings to cater to consumers' desire for experiences, relationships, and emotional connections.

For instance, marketers in the travel and tourism sector can promote packages that encourage bonding with loved ones, such as family vacations or group retreats. Likewise, event planners can capitalize on this trend by organizing activities focused on building connections, such as workshops or team-building events.

In the retail industry, companies can shift their focus from selling products to providing personalized services, such as offering curated gift boxes that emphasize thoughtfulness and sentimental value.

Additionally, marketers in the food and beverage sector can emphasize the social aspect of dining, promoting shared meals and spaces that encourage conversation and quality time spent together.

Overall, this cultural shift offers new opportunities for marketers to create meaningful, experience-driven campaigns that resonate with consumers and foster long-term brand loyalty.

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Amazon's version of a SKU (Stock Keeping Unit) is known as an ASIN (Amazon Standard Identification Number).

It is a unique identifier assigned to each product that is listed on Amazon's marketplace.

ASINs are used to organize and differentiate products, making it easier for customers to search and find what they are looking for. Each product on Amazon has its own unique ASIN, even if the product is identical to another product.

This is because ASINs are specific to the product's packaging and other identifying features. Additionally, ASINs are used to link related products, such as different editions of a book or different colors of a shirt.

Overall, the ASIN system is an important aspect of Amazon's business model, allowing for efficient inventory management and streamlined product search and purchasing for customers.

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ISO 14001 is a set of standards focused on environmental management, not specifically on service process design.

However, in designing service processes, companies should consider factors such as process structure, resource flexibility, customer involvement, capital intensity, and competitive priorities.

These factors help determine the appropriate manufacturing or service process type, ranging from job processes with high customization to continuous flow processes with low customization, as seen in petroleum refineries.

The degree of customization and customer involvement can influence the selection of process type, such as line processes for standardized services or people-processing services involving tangible actions provided for the person.

Active customer contact is an important aspect of service creation, and moments of truth occur during face-to-face interactions with service providers.

Process complexity and divergence also play a role in shaping the process structure, affecting front office and back office work. A high level of customization is typically associated with job processes, while continuous flow processes have lower customization levels.

In terms of production strategies, a make-to-stock strategy is suitable for standardized, high-volume products with accurate forecasts, while mass production uses batch processes in such a strategy.

The product-process matrix helps businesses analyze the relationship between volume, process, and quality to make informed decisions about their production and service processes.

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The firm's internal strengths and resources

The role of strategic leadership and the strategy process

The external environment and associated challenges

The firm's business model and competitive advantages

During the analysis phase of the AFI framework, the following topics should be considered:

The firm's internal strengths and resources

The external environment and associated challenges

The firm's business model and competitive advantages

The role of strategic leadership and the strategy process, as well as the locations in the world where the firm should compete, are typically addressed in the formulation phase of the AFI framework.

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In fund financial statements, the revenues and expenditures (expenses) of governmental, proprietary, and fiduciary funds are reported in separate sets of financial statements.

This is because each type of fund has its own distinct purpose and requirements for financial reporting. Governmental funds are used to account for tax-supported activities and are reported in the government-wide financial statements. Revenues are reported as either taxes or other sources, while expenditures are reported as either capital or operating.

Proprietary funds are used to account for business-like activities and are reported in the proprietary fund financial statements. Revenues are reported as sales or services, while expenditures are reported as either cost of goods sold or operating expenses.

Fiduciary funds are used to account for assets held in trust or on behalf of others and are reported in the fiduciary fund financial statements. Revenues and expenditures are reported based on the specific purpose of the fund.

In addition, a significant transaction within the control of management that is either unusual in nature or infrequent in occurrence should be separately disclosed in the financial statements to ensure transparency and accuracy in reporting. Major funds should be reported in a separate column, and nonmajor funds should be combined and reported in a separate column.

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Omni-channel retailers are those who offer multiple sales channels, such as physical stores, online platforms, and mobile apps, to provide customers with a seamless shopping experience.

To give customers a smooth purchasing experience, omnichannel merchants offer a variety of sales channels, such as physical storefronts, internet platforms, and mobile apps. No matter how customers choose to shop, they receive a consistent and integrated brand experience thanks to the integration of their sales channels. With this strategy, they may reach a larger audience and adjust to changing customer tastes.

Omni-channel merchants may offer easier shopping alternatives, tailored suggestions, and a quicker and more effective customer service experience by merging their offline and online channels.

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Omni-channel retailers are those who sell products through multiple channels, such as brick-and-mortar stores, online marketplaces, social media, mobile apps, and more.By utilizing multiple channels, omni-channel retailers provide their customers with a seamless and integrated shopping experience. For example, a customer may browse a product on the retailer's website, check its availability at a nearby store, and then go to the store to make the purchase. Or, they may see an advertisement for the product on social media and make the purchase through the retailer's mobile app.This approach allows retailers to reach their customers through their preferred channels, increase customer engagement and loyalty, and ultimately drive sales. It also enables retailers to gather data on customer behavior across different channels and use it to improve their marketing and sales strategies.

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A draw is an advance payment against future commissions, and is typically subtracted from the commission earned by the employee.

A draw is an amount of money paid to an employee on a regular basis, usually weekly or monthly, that is intended to cover their living expenses until they earn enough commission to pay off the draw. Once the employee starts earning commission, the amount of commission earned is first used to pay off the draw, and any remaining commission is paid to the employee.

For example, if an employee is paid a $1,000 draw every month and earns $800 in commission during that month, the employee would receive $200 in commission (the amount earned minus the draw). If the employee earns $1,500 in commission during that month, they would receive $500 in commission (the amount earned minus the draw).

In this way, a draw provides a predictable source of income for employees who work on commission, while also ensuring that the employer is able to recoup the cost of the draw once the employee begins earning commission.

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The correct answer is: A. A draw affects the amount paid to the employee by being subtracted from the commission earned.

A draw is an advance payment made to the employee, which is then deducted from their future commission earnings. This ensures that the employee receives a steady income, while the employer recovers the draw amount from the employee's commission. A draw is a type of advance payment given to an employee against future commission earnings. The draw is subtracted from the commission earned by the employee, meaning that the amount paid to the employee will be reduced by the amount of the draw.

Therefore, option A is the correct answer.

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The best option is a Roth IRA or 401(k) if you're certain that your retirement income will be larger than it is now. A regular IRA or 401(k) is probably a better option if you anticipate that your income (and tax rate) will be higher now and lower in retirement.

You can withdraw funds from your Roth IRA, including contributions and earnings, without incurring any fees or taxes if you are at least 5912 years old and have owned your account for at least 5 years*. Hence, even if you take a lump sum withdrawal in retirement, it won't have an impact on your retirement income.

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The cost of external common equity for Brille Corporation is 14.73%.

To calculate Brille Corporation's cost of equity, we need to consider the dividend growth model which is given by:

Cost of equity (Re) = (D1 / P0) + g

where:
D1 = the expected dividend next year
P0 = the current market price per share, net of flotation costs
g = the dividend growth rate

First, let's calculate D1, which is the expected dividend next year:

D1 = Dividends last year * (1 + g)
D1 = $1.25 * (1 + 0.09)
D1 = $1.25 * 1.09
D1 = $1.3625

Next, we need to find P0, which is the market price per share after considering the flotation costs:

P0 = Market price * (1 - Flotation cost percentage)
P0 = $27 * (1 - 0.12)
P0 = $27 * 0.88
P0 = $23.76
Now we can calculate the cost of equity:
Re = (D1 / P0) + g
Re = ($1.3625 / $23.76) + 0.09
Re = 0.0573 + 0.09
Re = 0.1473

Converting the result to a percentage and rounding to two decimal places:
Brille's cost of external common equity = 0.1473 * 100 = 14.73%
So, Brille Corporation's cost of external common equity is 14.73%.

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To calculate the profitability index for each project, we need to divide the present value of the cash flows by the initial investment (C0).

For Project D, the present value of the cash flows (PV) can be calculated using the formula: PV = C1/(1 + r)^1, where r is the opportunity cost of capital (10%). Thus, PV = 23,000/(1 + 0.10)^1 = 20,909.09. The profitability index for Project D is then calculated as follows:

Profitability Index (D) = PV/C0 = 20,909.09/11,500 = 1.82

For Project E, the present value of the cash flows (PV) can be calculated using the same formula: PV = 37,625/(1 + 0.10)^1 = 34,204.55. The profitability index for Project E is then calculated as follows:

Profitability Index (E) = PV/C0 = 34,204.55/21,500 = 1.59

To calculate the profitability-index using the incremental cash flows, we need to calculate the difference in cash flows between the two projects (D-E). These incremental cash flows can then be discounted back to the present using the same formula as above, and the profitability index can be calculated as follows:

Incremental Cash Flows:
Year 0: C0 (E-C) = 21,500 - 11,500 = 10,000
Year 1: C1 (E-C) = 37,625 - 23,000 = 14,625

PV of Incremental Cash Flows:
PV (E-C) = 10,000/(1 + 0.10)^0 + 14,625/(1 + 0.10)^1 = 22,840.91

Profitability Index (E-C) = PV (E-C)/C0 (C) = 22,840.91/11,500 = 1.99

Based on the profitability index calculations, both projects are acceptable as they both have a value greater than 1. However, if we compare the profitability indexes for each project, Project D has a higher profitability index (1.82) than Project E (1.59), indicating that it is more profitable. Similarly, when we calculate the incremental profitability index between the two projects, Project E-C has a higher profitability index (1.99) than Project D-C, indicating that it is the better choice. Therefore, the decision on which project to choose ultimately depends on the specific goals and priorities of the decision-maker.

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