A gas in a piston–cylinder assembly undergoes a compression process for which the relation between pressure and volume is given by pVⁿ = constant. The initial volume is 0.2 m³, the final volume is 0.04 m³, and the final pressure is 2 bar.

For n = 1.3, determine the initial pressure, in bar, and the work for the process, in kJ.

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a SD of 20%. The hedge fund risk premium is estimated at 10% with a SD of 35%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

a-1. Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation?  

a-2. What is the expected return on the portfolio?

a-3 Calculate Greta’s capital allocation using an annual correlation of 0.3?

STPL is considering acquiring Pie Smiles, a small chain bakery that specialise in making gourmet pies. A sales manager from Pie Smiles has provided the following actual sales:

The sales manager from Pie Smiles has suggested that sales would be $8,200 in year 1.  

Required:

1. Using exponential smoothing with a weight of α =0.3, develop forecasts for years 2 through to 6 .
2. Using smoothing constants of 0.6 and 0.9, develop forecasts for the sales of pies.
3. What effect did the smoothing constant have on the forecast for the sale of pies?
4. Use a 3-year moving average forecasting model to forecast the sales of pies.
5. Using the trend projection model, develop a forecasting model for the sales of pies.
6. Which is the preferred method to predict the sales of pies: exponential smoothing with a smoothing constant of 0.3, a 3-year moving average or a trend line? In your response justify why you made that choice.

Tharaldson Corporation makes a product with the following standard costs:

The company reported the following results concerning this product in June.

The company applies variable overhead on the basis of direct labor-hours. The direct materials purchases variance is computed when the materials are purchased.

The variable overhead efficiency variance for June is:

Garrison 16e Rechecks 2017-10-31

Multiple Choice

$1,696 F

$1,600 U

$1,696 U

$1,600 F

Suppose x has a distribution with μ = 20 and σ = 5. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μ x = 20 and σ x = 1.25. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 20 and σ x = 5. Yes, the x distribution is normal with mean μ x = 20 and σ x = 0.3. (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? Yes, the x distribution is normal with mean μ x = 20 and σ x = 0.3. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 20 and σ x = 5. Yes, the x distribution is normal with mean μ x = 20 and σ x = 1.25. Find P(16 ≤ x ≤ 21). (Round your answer to four decimal places.)

There are two traffic lights on a commuter's route to and from work. Let X₁ be the number of lights at which the commuter must stop on his way to work, and X₂ be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X₁, X₂ is a random sample of size n = 2).

μ = 1, σ² = 0.6

Calculate σ_To².

σ_To² =

How does it relate to σ², the population variance?

σ_To² =  · σ²

(d)

Let X₃ and X₄ be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T_o = the sum of all four X_i's, what now are the values of E(T_o) and V(T_o)?

E(T_o)=V(T_o)=

(e)

Referring back to (d), what are the values of

P(T_o = 8) and P(T_o ≥ 7)

[Hint: Don't even think of listing all possible outcomes!]

P(T_o = 8)

=

P(T_o ≥ 7)

=

Recall the researcher who investigated the relationship between hours of sleep and reaction times in the Week 4 Application. As a follow up to that study, the researcher wants to conduct a correlation to investigate further if there is a relationship between hours of sleep and reaction time. For this experiment, participants are allowed to sleep as much as they would like (that is, they are not assigned to sleep any specific number of hours). When 20 participants come to their appointment time, they report to the researcher how many hours of sleep they had the previous night. The researcher then tests their reaction times.

data:

(a) Define 'tests of control' and explain the importance of tests of control in the audit of a
company.

(b) You are an audit senior in Asenso Boateng & Co a firm providing audit and assurance
services. One of your clients is an exclusive hotel called 'Rock City Hotel' situated in the
centre of Airport City Accra. As part of your audit procedures you are assessing the controls
surrounding payroll. You have read last year's audit file and have obtained the following
information:
The hotel employs both full and part time staff. Due to the nature of the business most of
the work is done in shifts. All staff are paid on a monthly basis.
New members of staff are given an electronic photo identification card on the day they join
by the personnel department. This card is used to 'clock in' and 'clock out' at the start and
end of the shift to record the hours worked.
At the end of each week the information recorded on the system is sent automatically to
the payroll department and also to the head of each of the three main operating divisions:
Rooms, Food & Beverage and Corporate Events. Each division head must reply back to the
payroll department by email to authorise the hours worked by their staff.
The payroll clerk collates all the authorised information and then inputs the hours worked
into a standardised computerised payroll package. This system is password protected using
an alphanumerical password that is only known to the payroll clerk and the finance
manager.
Once the hours have been entered, the calculation of the gross pay and taxation are
calculated automatically along with any other statutory deductions. At the end of the
calculations a payroll report is produced and printed. The finance manager reviews the
report and compares the data to last month to identify and follow up any unusual variances.
When he is satisfied with the information, he authorises the payroll run by signing the
payroll report and the payroll clerk submits the data.
Payslips are sent to the home address of each employee and payment is made by bank
transfer.
Required:

With reference to the scenario:
(i) Identify and explain FOUR STRENGTHS within the hotel's internal control system in
respect of payroll.

(ii) For each of the identified strengths, state a test of control the auditor could perform to
assess if the controls are operating effectively.

Please I need help on this question

a) A manager of a firm in the area of Dukagjini region is considering to knocking down the old barn to provide much needed parking space for tractors and equipment. This project would require an immediate expense of £110,000 to remove the asbestos and to knock down the barn. Building the car park would then cost £17,000. The space created would have spare capacity, which will be rented out at £45,000 (pre-tax) per year for parking and other uses. This project also lasts five years and has no residual value at the end. The farmer is able to depreciate the total cost of removing the asbestos, knocking down the building and building the car park. This is done over the five years of the project using the straight-line method. The corporate tax rate is 28%. The nominal discount rate is 3% and all cash flows are nominal values. . At the moment the farmer is paying £3,000 per year (post-tax) to park these on a neighbour’s land.

Calculate the net present value of this project.

b) An alternative is to expand its production capacities. The only possible location is an old barn owned by the farm but not utilised because of asbestos contamination. For legal reasons the building cannot be sold or leased. At a cost of £2,000, the farmer hired an environmental expert, who produced a report with detailed plans for the removal of the asbestos in compliance with environmental regulations. To refurbish the barn—including removing the chemical substances it is expected to cost £350,000. The cheesemaking equipment costs £150,000. Starting at the end of year one, cheese production is expected to yield £170,000 yearly for five years in pre-tax revenue minus cash expenses. The firm depreciates the refurbishment cost and the cost of the cheese-making equipment over the five years of the project using the straight-line method. There is no residual value at the end of the project. The corporate tax rate is 28%. The nominal discount rate is 7% and all values are nominal values.

Calculate the net present value of this project.

c) The farmer asks for your advice on how to choose between the two projects using the information in Parts (a) and (b. What would be your advice to the farmer? Explain.

d) Why might it be appropriate to use different discount rates for different projects, such as those in Parts (a) and (b)? Briefly explain.

Tharaldson Corporation makes a product with the following standard costs:

The company reported the following results concerning this product in June.

The company applies variable overhead on the basis of direct labor-hours. The direct materials purchases variance is computed when the materials are purchased.

The variable overhead rate variance for June is: