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gulaghasi [49]
3 years ago
10

The Acme Widget Company has found that if widgets are priced at s 389, then 1000 will be sold. They have also found that for eve

ry increase of $ 10, there will be 600 fewer widgets sold. The marginal cost of widgets is $ 97.25. The fixed costs for the Acme Widget Company are $ 8000. lf x represents the price of a widget find the following in terms of x The number of widgets that will be sold: The revenue generated by the sale of widgets: The cost of producing just enough widgets to meet demand: The proft from selling widgets: Find the price that will maximize profits from the sale of widgets:
Business
1 answer:
kvv77 [185]3 years ago
4 0

Answer:

See the explanation below.

Explanation:

a. The number of widgets that will be sold

Let y represent the number of widgets that will be sold, and and we already have x as price of widget, we therefore have:

y - 1,000 = (-600/10) * (x - 389)

y - 1,000 = -60 * (x - 389)

y = 1,000 - [60 * (x - 389) ]

y = 1,000 - 60x + 23,340

y = 24,340 - 60x

b. The revenue generated by the sale of widgets

Let R represent Revenue, therefore we have:

R = xy

R = x(24,340 - 60x)

R = 24,340x - 60x²

c. The cost of producing just enough widgets to meet demand

Let C represent total cost, we therefore have:

C = 8,000 + 97.25y  

C = 8,000 + 97.25(24,340 - 60x)

C = 8,000 + 2,367,065  - 5,835x

C =  2,375,065  - 5,835x

d. The proft from selling widgets

Let P represent profit, we therefore have:

P = R - C

P = 24,340x - 60x²  - (2,375,065  - 5,835x)

P = 24,340x - 60x²  - 2,375,065  + 5,835x

P = - 60x²  + 30,175x - 2,375,065

e. Find the price that will maximize profits from the sale of widgets

Profit is optimum when dP/dx = 0

Therefore, we have

0 = - 120x + 30,175

120x = 30,175

x = 30,175/120 = $251.46

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The Evanstonian is an upscale independent hotel that caters to both business and leisure travelers. On average, one-third of the
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Explanation:

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Scubapro Corporation currently has 500,000 shares of common stock outstanding and plans to issue 200,000 more shares in a season
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Scubapro Corporation

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E) 8,000 shares.

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Read 2 more answers
The relationship between financial leverage and profitability Pelican Paper, Inc., and Timberland Forest, Inc., are rivals in th
OLEGan [10]

Answer:

Pelican Paper, Inc., and Timberland Forest, Inc.

Financial leverage and profitability Ratio Analysis

A. Computation of debt and coverage ratios:

1. debt ratio  = Total debt to Total assets x 100

Pelican = $1,000,000/$10,000,000 x 100

= 10%

Timberland =v$5,000,000/$10,000,000 x 100

= 50%

2. times interest earned ratio = EBIT/Interests

Pelican = $6,250,000/$100,000

= 62.5 times

Timberland = $6,250,000/$500,000

= 12.5 times

A discussion of their financial risk and ability to cover the costs:

Pelican Paper's financial leverage is 10% compared to Timberland's 50%, showing that debt creditors finance and lay claim to half of the company's assets.  This is very high and not attractive to potential investors and creditors.  Timberland has already hampered its ability to borrow more as it is highly leveraged.  Whereas Pelican Paper can meet its debt obligations and pay its interest expenses 62.5 times from current earnings, these pale in comparison with Timberland's 12.5 times, further jeopardizing its opportunities for more debt financing.

B. Calculation of the profitability ratios:

1. Operating profit margin  = EBIT/Sales x 100

Pelican Paper = $6,250,000/$25,000,000 x 100 = 25%

Timberland = $6,250,000/$25,000,000 x 100 = 25%

2. Net profit margin  = (EBIT less Interest)/Sales x 100

Pelican Paper = ($6,250,000 - $100,000)/$25,000,000 x 100

= $6,150,000/$25,000,000 x 100 = 24.6%

Timberland = ($6,250,000 - $500,000)/$25,000,000 x 100

= $5,750,000/$25,000,000 x 100 = 23%

3. Return on total assets  = EBIT/Total Assets x 100

Pelican Paper = $6,250,000/$10,000,000 x 100

= 62.5%

Timberland = $6,250,000/$10,000,000 x 100

= 62.5%

4. Return on common equity = Earnings available to Common Stockholders/Equity x 100

Pelican = $3,690,000/$9,000,000 x 100

= 41%

Timberland = $3,450,000/$5,000,000 x 100

= 69%

A discussion of their profitability relative to one another:

The two companies make the same level of operating profit margin at 25%, but Pelican's net profit margin of 24.6% is better than Timberland's 23%.  They show that Pelican's management has better ability to control expenses than Timberland's.

The returns on assets are similar for both companies, but Timberland performed better than Pelican Paper in terms of the return on equity.  This shows that Timberland with ROE of 69% is making larger returns for its common stockholders than Pelican because it is leveraging debts, whose interests are tax-deductible, and also using less equity in generating the returns.

C. The larger debt of Timberland has made it more profitable than Pelican Paper because the debt interests are deductible from EBIT before tax expense is computed and it reduces the tax burden for the company, thus making it to pay less tax and saving more profits for distribution to its stockholders.

However, this higher return to the investors in Timberland also comes with higher risks, as the investors are exposed to debt risks, higher pressure to satisfy debt creditors, heightened interference and oversight from creditors since they own half of the assets of the company, and an increased threat of business takeover in case of debt default.

Explanation:

a) Data:

Items                        Pelican Paper, INC    Timberland Forest, INC

Total assets              $10,000,000               $10,000,000

Total equity                  9,000,000                   5,000,000

Total Debt                     1,000,000                   5,000,000

Annual Interest                100,000                      500,000

Total Sales                 25,000,000                25,000,000

EBIT                              6,250,000                  6,250,000

Earnings available for  common

stockholders               3,690,000                   3,450,000

b) Ratio computation and analysis help companies to compare their performances and positions with competitors.  They can spot risks facing a company and even point out ways to address such business risks.

8 0
3 years ago
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