what is gompertz function​

Answers

Answer 1

Answer:

The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. ... It is a special case of the generalised logistic function.


Related Questions

Gilberto manages a grocery store in a country experiencing a high rate of inflation. To keep up with inflation, he spends a lot of time every day updating the prices, printing new price tags, and sending out newspaper inserts advertising the new prices. His employees regularly deal with customer annoyance over the frequent price changes. This is an example of the of inflation.

Answers

Answer:

Menu Costs

Explanation:

From the question we are informed about Gilberto who manages a grocery store in a country experiencing a high rate of inflation. To keep up with inflation, he spends a lot of time every day updating the prices, printing new price tags, and sending out newspaper inserts advertising the new prices. His employees regularly deal with customer annoyance over the frequent price changes. This case is an example of the of Menu Costs inflation.

In domain of economics, menu cost can be regarded as the cost to a firm that results due to changing its prices. When there is high inflation, firms needs to often make a change to their prices ,so they can keep up with economy-wide changes. The name arised out of the cost of a printing new menus of a restaurants , but it is used by economists when they are generally referring to the costs of changing nominal prices

.

Bluebird Mfg. has received a special one-time order for 15,000 bird feeders at $2.30 per unit. Bluebird currently produces and sells 75,000 units at $6.30 each. This level represents 80% of its capacity. Production costs for these units are $3.55 per unit, which includes $1.90 variable cost and $1.65 fixed cost. If Bluebird accepts this additional business, the effect on net income will be:

Answers

Answer:

Increase

Explanation:

If Bluebird accepts this additional business, the effect on net income will be:

If the price per unit were doubled at the same time that the variable cost per unit was doubled, the break-even point would be:

Answers

Answer:

halved

Explanation:

Breakeven quantity are the number of  units produced and sold at which net income is zero

Breakeven quantity = fixed cost / price – variable cost per unit

Assume fixed cost is initially 1000 units, price is 10, variable cost is 5

breakeven quantity = 1000 / (10 - 5) = 200

assume price per unit were doubled at the same time that the variable cost per unit was doubled

1000 / ( 20 - 10) = 100

breakeven point is halved

A company purchased office supplies costing $5,000 and debited Supplies for the full amount. At the end of the accounting period, a physical count of office supplies revealed $900 still on hand. The appropriate adjusting journal entry to be made at the end of the period would be: debit Supplies Expense, $4,100; credit Supplies, $4,100. debit Supplies, $4,100; credit Supplies Expense, $4,100. debit Supplies Expense, $5,900; credit Supplies, $5,900. debit Supplies, $900; credit Supplies Expense, $900.

Answers

Answer:

Debit Supplies Expense, $4,100; Credit Supplies, $4,100

Explanation:

Based on the information given The appropriate adjusting journal entry to be made at the end of the period would be:Debit Supplies Expense, $4,100; Credit Supplies, $4,100

Debit Supplies Expense $4,100

Credit Supplies $4,100

($5,000-$900)

Service Pro Corp (SPC) is preparing adjustments for its September 30 year- end. For the following transactions and events, show the September 30 adjusting entries that SPC would make

a. Prepaid Insurance shows a balance of zero at September 30, but Insurance Expense shows a debit balance of $2,340, representing the cost of a three-year fire insurance policy purchased on September 1 of the current year.
b. On August 31 of this year, Cash was debited and Service Revenue was credited for $ 1,500. The $ 1,500 related to fees for a three- month period beginning September 1 of the current year.
c. The company’s income tax rate is 20%. After making the above adjustments, SPC’s net income before tax is $ 10,000. No income tax has been paid or recorded.

Answers

Answer:

1 . Dr Prepaid Insurance $2,275

Cr Insurance Expense $2,275

2. Dr Service Revenue $1,000

Cr Deferred Revenue $1,000

3. Dr Income Tax Expense $2,000

Cr Income Tax Payable $2,000

Explanation:

Preparation of the journal entries

1 . Dr Prepaid Insurance $2,275

Cr Insurance Expense $2,275

($2,340 - $2,340 × 1 months ÷ 36 months

= $2,340 - $65

= $2,275)

2. Dr Service Revenue $1,000

Cr Deferred Revenue $1,000

($ 1,500 × 2 months ÷ 3 months

= $1,000)

3. Dr Income Tax Expense $2,000

Cr Income Tax Payable $2,000

(.20*$10,000)

If a company sells its smart phones for $400 and the phones have a COGS of $250, how many additional phones would the company have to sell if it decided to spend an extra $150,000 on advertising to promote the phones

Answers

Answer:

Units to be sold= 1,000

Explanation:

Giving the following information:

Selling price= $400

COGS= $250

Increase in costs= $150,000

To calculate the number of units to be sold to cover the incremental costs, we need to use the following formula:

Units to be sold= increase in costs/ contribution margin per unit

Units to be sold= 150,000 / (400 - 250)

Units to be sold= 1,000

On August 1, Lola Company’s assets are $30,000 and its liabilities are $10,000. On August 4, Lola issues a sustainability report. On August 5, ownership invests $3,000 cash and $7,000 of equipment in Lola. After the investment, what is the amount of equity for Lola?

Answers

Answer: $30,000

Explanation:

Before the investment, Equity was:

= Assets - Liabilities

= 30,000 - 10,000

= $20,000

The owner then invested $3,000 and $7,000 therefore making a total of $10,000.

Equity becomes

= 20,000 + 10,000

= $30,000

The equity is $30,000

Lola's company assets are $30,000

The liabilities are $10,000

Equity= $30,000-$10,000

= $20,000

On August 5, ownership invests $3,000 in cash and $7,000 in equipment

= $3,000+$7,000

= $10,000

The amount of equity for Lola is

= $20,000+$10,000

= $30,000

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You have $7,600 to deposit. Regency Bank offers 12 percent per year compounded monthly (1.0 percent per month), while King Bank offers 12 percent but will only compound annually.
How much will your investment be worth in 16 years at each bank? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Regency Bank
King Bank

Answers

Answer:

Regency Bank : $51,347.27

King Bank : $46,590.99

Explanation:

The formula for calculating future value:

FV = P (1 + r)^mn

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

m = number of compounding

Regency Bank : $7,600 x (1.01)^(16 x 12) = $51,347.27

King Bank : $7600 x 1.12^16 = $46,590.99

Seeing his son graduate from college is most likely a short-term goal for a
person of which of these ages?
A. 8 years old
B. 58 years old
C. 28 years old
D. 18 years old

Answers

The answer is c 28 years old

Two athletes of equal ability are competing for a prize of $10,000. Each is deciding whether to take a dangerous performance-enhancing drug. If one athlete takes the drug, and the other does not, the one who takes the drug wins the prize. If both or neither take the drug, they tie and split the prize. Taking the drug imposes health risks that are equivalent to a loss of X dollars

Required:
a. Draw a $2 payoff matrix describing the decisions the athletes face.
b. For what X is taking the drug the Nash equilibrium?
c. Does making the drug safer (that is, lowering X) make the athletes better or worse off? Explain.

Answers

Answer:

a) attached below.

b) for $x < $5000 will cause taking the drug to be part of the Nash equilibrium

c) will make the athletes feel better because the value their payoff will increase

Explanation:

a) 2 * 2  payoff matrix  describing the decision faced by the athletes

attached below

when both players take the drug the payoff for each player = $5000 - x

when neither player  takes the drug the payoff for each player = $5000

When only one player takes the drug his payoff = $10000 - x

b) If we consider the value of $x to be involved in the Nash equilibrium then

; $5000 - $x > 0  becomes the best response

hence for $x < $5000 will cause taking the drug to be part of the Nash equilibrium

c) Lowering the negative effect of the drug ( i.e. when the value of x is reduced )

will make the athletes feel better because the value their payoff will increase

Universal Containers wants to automatically assign a Task to account managers when a customer's agreement is about to expire. How should a System Administrator configure this functionality?

a. Create a Workflow on Account with a rule criteria of Agreement Eng Date < TODAY()
b. Create a Time-based Workflow on Account with a rule criteria of Agreement End Date > TODAY ()
c. Create a Workflow on Account with a rule criteria of Agreement Eng Date > TODAY()
d. Create a Time-based Workflow on Account with a rule criteria of Agreement End Date > TODAY ()

Answers

Answer:

Universal Containers

Configuring the Functionality of Assigning Task to Account Managers

b. Create a Time-based Workflow on Account with a rule criteria of Agreement End Date > TODAY ()

d. Create a Time-based Workflow on Account with a rule criteria of Agreement End Date > TODAY ()

Explanation:

A Time-based Workflow depends on actions being executed at a specific time, which is clearly defined by the workflow.  It means that an alert is triggered when the time elapses. With the passage of the specified time, the workflow rule re-evaluates the options to check that the record can still meet the rule criteria going forward.  Time-based workflows are usually deployed in the creation of email alerts and in Salesforce.  It can automatically remind the account managers or team to take action by triggering an alert.

Dorsey Company manufactures three products from a common input in a joint processing operation. Joint processing costs up to the split-off point total $350,000 per quarter. The company allocates these costs to the joint products on the basis of their relative sales value at the split-off point. Unit selling prices and total output at the split-off point are as follows:

Product Selling Price Quarterly Output
A $16 per pound 15,000 pounds
B $8 per pound  20,000 pounds
C $25 per gallon 4,000 gallons

Each product can be processed further after the split-off point. Additional processing requires no special facilities. The additional processing costs (per quarter) and unit selling prices after further processing are given below:

Product Additional  Processing Costs Selling Price
A $63,000 $20 per pound
B $80,000 $13 per pound
C $36,000 $32 per gallon

Required:
Which product or products should be sold at the split-off point and which product or products should be processed further?

Answers

Answer:

The incremental selling price for product 1 is 60,000, product 2 is 100000 and product 3 is 28,000.

Sell at split off for product 1 is Yes and product 2 is No and product 3 is Yes.

Explanation:

Here,

How much would you have had to invest now in an account paying 8% / year to to have $20,000 in 21 years

Answers

Answer:

PV= $3,978.115

Explanation:

Giving the following information:

Interest rate (i)= 8% = 0.08

Future value (FV)= $20,000

Number of periods (n)= 21 years

To calculate the lump-sum to be invested today, we need to use the following formula:

PV= FV / (1 + i)^n

PV= 20,000 / (1.08^21)

PV= $3,978.115

It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her four hungry dogs and seven hungry cats at home. Dog food costs $1 per can and cat food costs $0.50 per can. Lisa wants to minimize her pet food cost. What is an appropriate objective function for this scenario?

Answers

Answer: Min Z = X1 + 0.50X2

Explanation:

Based on the information given in the question, the appropriate objective function for this scenario will be explained this:

Let X1 be the number of dog food cans which will be bought

Let X2 be the number of cat food cans which will be bought

Then, the objective function will be:

Min Z = 1X1 + 0.50X2

The appropriate objective function for this scenario is Min Z = X1 + 0.50X2

Objective function:

Since in her purse there is $40 also there is four hungry dogs and seven hungry cats at home. Dog food costs $1 per can and cat food costs $0.50 per can.

So based on this, here we assume that X1 be the no of dog And, X2 should be no of cat

So, the objective function is Min Z = X1 + 0.50X2

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Fraser Company will need a new warehouse in five years. The warehouse will cost $500,000 to build. Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using tables. Required: What lump-sum amount should the company invest now to have the $500,000 available at the end of the five-year period? Assume that the company can invest money at: (

Answers

Answer:

Results are below.

Explanation:

Giving the following information:

Future value (FV)= $500,000

Number of periods= 5 years

We were not provided with an interest rate, I will assume an interest rate of 7% compounded annually.

To calculate the initial investment, we need to use the following formula:

PV= FV / (1 + i)^n

PV= 500,000 / (1.07^5)

PV= $356,493.1

The beta coefficient A stock's contribution to the market risk of a well-diversified portfolio is called risk. According to the Capital Asset Pricing Model (CAPM), this risk can be measured by a metric called the beta coefficient, which calculates the degree to which a stock moves with the movements in the market. Based on your understanding of the beta coefficient, indicate whether each statement in the following table is true or false: Statement True False A stock that is more volatile than the market will have a beta of less than 1.0. Over time, a stock with a beta of 1.0 produces a return that goes up and down with a 1:1 relationship with the return on the market Beta measures the volatility in stock movements relative to the market. There are different ways of calculating the beta coefficient for a stock. Using the information given in the following table, calculate the beta coefficient of Stocki: Data 35.00% 32.00% Stock I's standard deviation Market's standard deviation Correlation between Stock i and the market Beta coefficient of Stock i: 0.65 To calculate the beta of another company, using regression analysis, you get the value of Ra as 0.27. Based on your calculation, which of the following interpretations is true? The percentage of variance in the company's stock explained by the market is lower than that of a typical stock. The percentage of variance in the company's stock explained by the market is higher than that of a typical stock.

Answers

Solution :

1. The relevant risk is considered as the "unknown unknowns" which may occur due to the risk in everyday life. In all risky investments, it is unavoidable. The contribution of the stock to the market risk in a well diversified portfolio is called as the relevant risk. Diversification is the main strategy for minimizing the relevant risk.

2.

Statement : A stock that is more volatile than the market will have a beta of less than 1.0.

---- False, as it will be more volatile with that of the market.

Statement : Over time, a stock with a beta of 1.0 produces a return that goes up and down with a 1:1 relationship with the return on the market

---- True as beta of the market is 1 and therefore, the stock beta is also 1.

Statement : Beta measures the volatility in stock movements relative to the market.

--- True. The beta measures all the volatility in the stock moments relative to the market.

3. We know that :

[tex]$\text{Beta= Correlation coefficient} \times \frac{\text{SD of stock}}{\text{SD of market}} $[/tex]

        [tex]$=0.65 \times \frac{35}{32}$[/tex]

        = 0.71

4.  The percentage of the variance in the stock of the company that is explained by the market is lower than that of the typical stock.

Sandy purchased a new dress through Zappos. When it arrived, she opened the package and saw that the dress had very small cap sleeves. Slightly annoyed that they dress did not look like the photo on the website, she tried the dress on only to realize that it was too short for her. She regretted buying this dress. Luckily for her, Zappos included an easy return label for free return shipping and a comment card where she could indicate why she was returning the purchase. Zappos made it easy for Sandy to address her cognitive dissonance by focusing on processes for which area of the consumer decision-making process?
a. evaluating alternatives process.
b. postpurchase process.
c. making the purchase process.

Answers

Answer:

Option b: Post purchase process

Explanation:

There are several reasons or outcomes of post-purchase processes/evaluation of a product by consumers. They includes:

1. Post-purchase dissonance

2. Regret

3. Satisfaction/dissatisfaction

Post-purchase dissonance

This is simply known as a well-known feeling of anxiety over if the correct purchase decision was made concerning a product or services. It is said to occur when there is more than one alternative that is attractive thereby making the decision process important.

Post-purchase regret

This is simply regarded as a feeling that a wrong purchase decision has been made concerning a particular product or services. It is said to occur when one cannot reverse the decision and have experienced a negative outcome from the decision made.

product satisfaction.

This is said to exist when the consumer makes a positive evaluation and feels happy with their decision made concerning a particular product purchased.

Which of the following is true about an opportunity cost? Multiple Choice they are recorded in the accounting records of the company. is a cost that has already been incurred and can not be changed by any decision. is the potential benefit given up when one alternative is selected over another. should never be considered in decision-making.

Answers

Answer:

potential benefit given up when one alternative

Explanation:

1. Implicit cost or opportunity cost : Implicit cost is the cost of the next best option forgone when one alternative is chosen over other alternatives. It is used in calculating economic profit

for example, if you start your business and earn 100,000 but you have to leave your job where you earn 10,000. opportunity cost is 10,000

Which of the following occurs when a party threatens to file a legitimate (in other words, a non-frivolous) civil lawsuit unless another party gives consent to the terms of a contract?

a. Duress
b. Undue influence
c. Durable fraud
d. Criminal influence
e. None of these choices are correct.

Answers

Answer: E. None of the above

Explanation:

Duress occurs when there's threat by a party to file a criminal lawsuit unless the terms of a contract is given consent.

Duress occurs when a party was being forced into an agreement due to the wrongful act of another party. An example of this is when a party threatens to file a frivolous civil lawsuit unless another party gives consent to the terms of the contract.

Based on the options given, the answer to this is none of the above.

what is mextura give one example​

Answers

Answer:

A mixture is a substance made by combining two or more different materials in such a way that no chemical reaction occurs. A mixture can usually be separated back into its original components. Some examples of mixtures are a tossed salad, salt water and a mixed bag of M&M's candy.

Answer:

Mextura is a hybrid font, which combines elements of sansserif and black letter types.

what does the "S" represent for the designation GMAW-S?
A. Spray Transfer
B. Pulsed Spray
C. Solid wire
D. Short Circuit Transfer
Help me bro​

Answers

Answer:

C. Solid wire

Explanation:

HOPE IT' HELP YOU

At the start of the year, your firm's capital stock equaled $10 million, and at the end of the year it equaled $15 million. The average depreciation rate on your capital stock is 20%. Net investment during the year equaled:________

a. $7 million
b. $4 million
c. $5 million
d. $3 million

Answers

Answer:

c. $5million

Explanation:

Net investment = Gross investment - Depreciation

Also, Net investment equals investment at the beginning of the year minus investment at the end of the year

Net investment = $15million - $10million

Net investment = $5million

Therefore, net investment during the year equals $5million

Suppose Cold Goose Metal Works Inc. is evaluating a proposed capital budgeting project (project Beta) that will require an initial investment of $3,000,000. The project is expected to generate the following net cash flows:

Year Cash Flow
Year 1 $350,000
Year 2 $450,000
Year 3 $450,000
Year 4 $450,000

Cold Goose Metal Works Inc.'s weighted average cost of capital is 8%, and project Beta has the same risk as the firm's average project. Based on the cash flows, what is project Beta's NPV?

Answers

Answer:

Cold Goose Metal Works Inc.

Based on the cash flows, project Beta's NPV is negative:

= ($1,602,200).

Explanation:

a) Data and Calculations:

Initial investment in project Beta = $3,000,000

Weighted average cost of capital = 8%

Net cash flows:

Year        Cash Flow    Discount Factor   Present Value

Year 1     $350,000           0.926                  $324,100  

Year 2    $450,000           0.857                    385,650

Year 3    $450,000           0.794                    357,300

Year 4    $450,000           0.735                    330,750

Total cash inflows =                                   $1,397,800

Investment cost =                                     $3,000,000

NPV =                                                        -$1,602,200

b) Cold Goose should not pursue the investment.  The cash outflows outweigh the cash inflows by more than 50%.  The net present value of the project is negative.

Comparing each item on a financial statement with a total amount from the same statement is referred to as

Answers

Answer: vertical analysis

Explanation:

Vertical analysis is when each item on a financial statement is compared with a total amount from the same statement.

Vertical analysis refers to a financial statement analysis method whereby each line item in a statement is listed as a percentage of the base figure. In such case, each amount in the income statement will then be restated as a percentage of sales.

Ida Sidha Karya Company is a family-owned company located on the island of Bali in Indonesia. The company produces a handcrafted Balinese musical instrument called a gamelan that is similar to a xylophone. The gamelans are sold for $875. Selected data for the company’s operations last year follow: Units in beginning inventory 0 Units produced 14,000 Units sold 12,000 Units in ending inventory 2,000 Variable costs per unit: Direct materials $ 200 Direct labor $ 420 Variable manufacturing overhead $ 64 Variable selling and administrative $ 23 Fixed costs: Fixed manufacturing overhead $ 860,000 Fixed selling and administrative $ 410,000 Required: 1. Assume that the company uses absorption costing. Compute the unit product cost for one gamelan

Answers

Answer:

Unitary product cost= $745.43

Explanation:

The absorption costing method includes all costs related to production, both fixed and variable. The unit product cost is calculated using direct material, direct labor, and total unitary manufacturing overhead.

Direct materials $200

Direct labor $420

Variable manufacturing overhead $ 64

Fixed manufacturing overhead $ 860,000

First, we need to calculate the unitary fixed overhead:

Unitary fixed overhead= 860,000 / 14,000= $61.43

Now, the unitary product cost:

Unitary product cost= 200 + 420 + 64 + 61.43

Unitary product cost= $745.43

ohn and Lisa form a partnership to operate a restaurant. Lisa signs a two-year lease on a space for the restaurant without consulting John. Under the legal concept of ________, John and the partnership are responsible for this lease, although it was only signed by Lisa.

Answers

Answer:

General Partnership

Explanation:

The legal concept of General Partnership obliges two or more signing partners -Lisa and John in this case- to share all assets, all liabilities, and to be responsible for all matters related to the business, regardless of who signs a contract, or contracts new debt, or acquires a new asset, and so on.

So under this legal concept, even if John did not sign the lease, he is still legally responsible for it.

Sparky Corporation uses the weighted-average method of process costing. The following information is available for February in its Molding Department:

Units: Beginning Inventory: 25,000 units, 100% complete as to materials and 55% complete as to conversion.
Units started and completed: 110,000.
Units completed and transferred out: 135,000.
Ending Inventory: 30,000 units, 100% complete as to materials and 30% complete as to conversion.

Costs:
Costs in beginning Work in Process - Direct Materials: $43,000.
Costs in beginning Work in Process - Conversion: $48,850.
Costs incurred in February - Direct Materials: $287,000.
Costs incurred in February - Conversion: $599,150.

Required:
Calculate the equivalent units of conversion.

a. 110,000
b. 140,000
c. 144,000
d. 130,250
e. 165,000

Answers

Solution :

UNITS TO ACCOUNT FOR :

[tex]\text{Beginning Work}[/tex] in Process units            $ [tex]25,000[/tex]

[tex]\text{Add: Units Started}[/tex] in Process                  $ [tex]14,000[/tex]

Total Units to account for                         $ [tex]165,000[/tex]

UNITS TO BE ACCOUNTED FOR:

[tex]\text{Units completed}[/tex] and transferred out       $ [tex]135,000[/tex]

[tex]\text{Ending Work}[/tex] in Process                             $ [tex]30,000[/tex]

[tex]\text{Total Units}[/tex] to be accounted for                 $ [tex]165,000[/tex]

[tex]\text{Equivalent units}[/tex]

                                       Material cost                        Conversion

                               % of completion  Units        % of completion      Units

   

[tex]\text{Units started}[/tex]                  [tex]100\%[/tex]        $[tex]135,000[/tex]              [tex]100\%[/tex]        $[tex]135,000[/tex]        

and completed.

[tex]\text{Ending Work}[/tex] in Process [tex]100\%[/tex]         [tex]30,000[/tex]               [tex]30\%[/tex]          [tex]9000[/tex]

[tex]\text{Total equivalent units}[/tex]                     [tex]165,000[/tex]                               [tex]144,00[/tex]

Therefore, the equivalent units of conversion is [tex]144,000 \text{ units}.[/tex]              

Recognizing religious holidays, differing modes of dress, and dietary restrictions as well as allowing flexible scheduling are all ways to improve employee retention that may appeal to diverse employees. These types of efforts are referred to as

Answers

Answer: Systems accommodations

Explanation:

Systems accomodations refers to the recognizing religious holidays, dietary restrictions, differing dressing modes, and allowing flexible scheduling which is vital in the improvement of employee retention which may appeal to diverse employees.

This is required in order to create an environment in the workplace where everyone is welcomed and a harmonious workplace which is important in the achievement of organizational goals.

one markeitng action that can be taken to sell a single product or service to muylpele market segments is to

Answers

Answer: C. develop separate promotional campaigns.

Explanation:

Different market segments will have different norms and values that companies will have to take advantage of in order to sell their goods or services.

They will therefore need to develop separate promotional campaigns that are aimed at taking advantage of these norms and values in order to appeal to the people in the different segments.

What is the weighted average cost of capital if a business has a cost of equity of 11%, a yield on debt of 6%, a tax rate of 30%, 100 million market value of debt, and 250 million market value of equity

Answers

Answer:

9.028 %

Explanation:

weighted average cost of capital = cost of equity x weight of equity + cost of debt x weight of debt

where,

cost of equity = 11 %

cost of debt (consider after tax) = 6% x (1 - 0.30) = 4.20 %

weight of equity = 250 million ÷ 350 million = 0.71

weight of debt = 100 million ÷ 350 million = 0.29

therefore,

weighted average cost of capital = 11 % x 0.71 + 4.20 % x 0.29

                                                       = 9.028 %

Other Questions
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