​​​​​​The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Age distribution and location are not independent.
H₁: Age distribution and location are not independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are independent.    H₀: Age distribution and location are not independent.
H₁: Age distribution and location are independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

uniformchi-square    normalStudent's tbinomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent.At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.    

1. Net Present Value (NPV) and Internal Rate of Return (IRR) (question)

The City and County of Denver is completing a $45 million renovation of City Park Golf Course. To complete the renovation, the course has been closed to the public for 2.5 years (planned re-opening is Spring 2020). The project updated the course, built a new clubhouse that can accommodate golf and community events, resulted in a “net gain of 500 trees”, and reduced flood risk “for thousands of homes”.[1] All of these updates are expected to provide either increased revenue or reduced costs. Assume the $45 million cost was paid upfront by Denver and the following are the estimated cash receipts and disbursements associated with the project.[1] If the cost of capital is 6%, does the project make sense based on NPV and IRR over a 30-year useful life? Does your finding change if the cost of capital is actually 4%?

[

Suppose you work for an insurance company. You know that there are equal numbers of individuals who will get in an accident with probability 0.2 and 0.3 and that the loss from getting in an accident is $4,000. Suppose you wish to screen individuals by offering full- coverage insurance as well as 30 percent coinsurance (i.e., the insurance pays 30 percent of the loss amount, or $1,200, in the event of an accident). You wish to include a 5 percent premium over the actuarially fair values for these policies to help cover overhead and pro- vide a profit margin for your company.

Will this pair of policies screen individuals into risk classes if we assume that all insuredindividuals have utility function U(X) ? 2000 · (X/4000)0.5 where X is income? Hint: Calculate utility (or expected utility) for each of the three options (no insurance, full- coverage insurance, and coinsurance) for both types of individuals and compare ex- pected utility levels to see what each will choose.

Background on Expected Utility: In this conceptualization of utility, we can compare uncertain outcomes with certain outcomes. For example, if an individual does not have insurance and does not get into an accident, he or she has a utility level of 2,000 (because X ? $4,000) or zero if he or she gets into an accident (because then X ? $0). The expected utility (EU) is based on the likelihood of each event occurring. A per- son facing a 10 percent chance of having an accident would have an expected utility of 1,800 using this utility function because EU ? 0.9 · 2,000 ? 0.1 · 0. This person would be indifferent between facing this “lottery” and having $3,240 with certainty (because U(3240) ? 1,800). This certainty equivalent value was obtained by solving for X in the equation 1800 ? 2000 · (X/4000)0.5. The lottery would be preferred to amounts less than $3,240 offered with certainty.

Mr. John Backster, a retired executive, desires to invest a portion of his assets in rental property. He has narrowed his choices to two apartment complexes, Windy Acres and Hillcrest Apartments. The anticipated annual cash inflows from each are as follows:

Mr. Backster is likely to hold the apartment complex of his choice for about 20 years and will use this period for decision-making purposes. Either apartment can be purchased for $180,000. Mr. Backster uses a risk-adjusted discount rate approach when evaluating investments. His scale is related to the coefficient of variation (for other types of investments, he also considers other measures).

a. Compute the risk-adjusted net present value for Windy Acres and Hillcrest Apartments. (Round "PV Factor" to 3 decimal places. Enter the answers in thousands of dollars. Do not round intermediate calculations. Round the final answers to nearest whole dollar.)

b-1. Which investment should Mr. Backster accept if the two investments are mutually exclusive?

• Hillcrest

• Windy Acres

• Both

• None

b-2. Which investment should Mr. Backster accept If the investments are not mutually exclusive and no capital rationing is involved?

• Windy Acres

• Hillcrest Apartments

• Both

• None

Aiolos plc. is a small firm that produces and sells industrial machinery. The
following figures of the company are from the most recent financial period:
- Sales €20,000,000
- Earnings before interest and taxes €2,000,000
- Debt €10,000,000
- Interest expenses before tax €1,000,000
- Capital Expenditures €1,000,000
- Depreciation expenses are 50% of capital expenditures
- Book value of equity € 10,000,000
Also, you have collected financial information concerning the industrial
machinery sector of listed companies (all figures are on an average basis):
- Beta coefficient of listed companies of the sector 1.30
- Financial leverage in terms of debt to market value of equity 20%
- Firms in the sector trade three times (3x) their book value of equity.
- Effective tax rate 20% tax rate.
The management of Aiolos plc. expects that the company will experience a twostage
growth pattern. Specifically, during the first period which will last for the
next 5 years, net income, capital expenditures and depreciation will have a 25%
growth rate per annum, whereas during the second period (i.e. steady state),
net income will have a 7% growth rate to infinity and capital expenditures and
depreciation will offset each other.
Working capital requirements are estimated to remain stable during both growth
periods, while the proportion of net capital expenditure changes with debt will
remain to 0.3 for the next five years. The yield-to-maturity of the 10 year
government bond is 3%, while the market risk premium is 5%.

Required:
A. Estimate the cost of equity for this Aiolos plc. (5 points)
B. Estimate the value of the owner's stake in Aiolos plc., using the free cash
flow to equity approach. (15 points)
C. Identify and briefly describe any qualitative aspects of growth. (5 points)

Aiolos plc. is a small firm that produces and sells industrial machinery. The
following figures of the company are from the most recent financial period:
 Sales €20,000,000
 Earnings before interest and taxes €2,000,000
 Debt €10,000,000
 Interest expenses before tax €1,000,000
 Capital Expenditures €1,000,000
 Depreciation expenses are 50% of capital expenditures
 Book value of equity € 10,000,000
Also, you have collected financial information concerning the industrial
machinery sector of listed companies (all figures are on an average basis):
 Beta coefficient of listed companies of the sector 1.30
 Financial leverage in terms of debt to market value of equity 20%
 Firms in the sector trade three times (3x) their book value of equity.
 Effective tax rate 20% tax rate.
The management of Aiolos plc. expects that the company will experience a twostage
growth pattern. Specifically, during the first period which will last for the
next 5 years, net income, capital expenditures and depreciation will have a 25%
growth rate per annum, whereas during the second period (i.e. steady state),
net income will have a 7% growth rate to infinity and capital expenditures and
depreciation will offset each other.
Working capital requirements are estimated to remain stable during both growth
periods, while the proportion of net capital expenditure changes with debt will
remain to 0.3 for the next five years. The yield-to-maturity of the 10 year
government bond is 3%, while the market risk premium is 5%.

Required:

aEstimate the cost of equity for this Aiolos plc
b. Estimate the value of the owner's stake in Aiolos plc., using the free cash
flow to equity approach.
c. Identify and briefly describe any qualitative aspects of growth.

i need the estimation value of AIOLOS using the FCFE method and the c) question as well

1. The Alpha Company had sales of $2,000,000, net operating income of $320,000 and average operating assets of $575,000. What was the return on investment? Round your percentage answer to the nearest whole percent.

Answer:____________

2. ABC Industries is evaluating the amount of time between when a customer places an order and when the order is shipped. For last year, the following data was reported:

Inspection time           0.3 days

Wait time                    7.0 days

Process time             2.6 days

Move time                  0.8 days

Queue time                 3.4 days

What is the delivery cycle time in days? Enter the value with 1 decimal place.

Answer:__________

3. Which of the following activities adds value to the product?
   1. Queue time
   2. Process time
   3. Move time
   4. Inspection time

4. When a company has a manufacturing cycle efficiency ratio of 50%, that means that:
   1. Wait time is equal to 50% of the throughput time
   2. Inspection time is equal to 50% of the throughput time
   3. Process time is equal to 50% of the throughput time
   4. Queue time is equal to 50% of the throughput time

5. The net operating income that an investment center earns above the minimum required return on its average operating assets is:
   1. Net income
   2. Return on investment
   3. Residual income
   4. Gross margin

6. ABC Company had sales of $400,000, net operating income was $112,000, and average operating assets were $520,000. What is the company’s return on investment rounded to 2 decimals?
   1. 28.00%
   2. 21.54%
   3. 76.92%
   4. 21.92%

7. A company is deciding if they should add a new product line that would increase sales by $1,200,000, variable expenses are 45% of sales, and fixed costs are $500,000. The new product line would require an investment that would increase average operating assets by $200,000. What is the company’s return on investment for this new product line?
   1. 32%
   2. 30%
   3. 80%
   4. 75%