Problem 1: Teenager Mike wants to borrow the car. He can ask either parent for permission to take the car. If he asks his mom, there is a 20% chance she will say ”yes,” a 30% chance she will say ”no,” and a 50% chance she will say, ”ask your father.” Similarly, that chances of hearing ”yes”/”no”/”ask your mother” from his dad are 0.1, 0.2, and 0.7 respectively. Imagine Mike’s efforts can be modeled as a Markov chain with state (1) talk to Mom, (2) talk to Dad, (3) get the car (”yes”), (4) strike out (”no”). Assume that once either parent has said ”yes” or ”no,” Mike’s begging is done.

1. Construct the one-step transition matrix for this Markov chain.

2. Identify the absorbing state(s) of the chain.

3. Determine the mean times to absorption.

4. Determine the probability that Mike will eventually get the car if (1) he asks Mon fist and (2) he asks Dad first. Whom should he ask first?

Examine the following book-value balance sheet for University Products Inc. The preferred stock currently sells for $30 per share and pays a dividend of $3 a share. The common stock sells for $20 per share and has a beta of 0.7. There are 2 million common shares outstanding. The market risk premium is 12%, the risk-free rate is 8%, and the firm’s tax rate is 40%. BOOK-VALUE BALANCE SHEET (Figures in $ millions) Assets Liabilities and Net Worth Cash and short-term securities $ 1.0 Bonds, coupon = 6%, paid annually (maturity = 10 years, current yield to maturity = 8%) $ 15.0 Accounts receivable 4.0 Preferred stock (par value $20 per share) 3.0 Inventories 8.0 Common stock (par value $0.10) 0.2 Plant and equipment 24.0 Additional paid-in stockholders’ equity 10.8 Retained earnings 8.0 Total $ 37.0 Total $ 37.0 a. What is the market debt-to-value ratio of the firm? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

3. Vacation Island has only one hotel on the entire island. The demand schedule to rent a room for a-night at the hotel is given bellow. Price per night Quantity demanded $150 0 $130 1 $110 2 $90 3 $70 4 $50 5 $30 6 a) Calculate the hotel’s total revenue and its marginal revenue. Fill in the table below. Price Quantity Total Revenue Marginal Revenue $150 0 - $130 1 $110 2 $90 3 $70 4 $50 5 $30 6 b) The marginal costs are listed in the table below. What price will the hotel charge to maximize its profit? Explain. Quantity Marginal Cost 0 - 1 $40 2 $43 3 $50 4 $61 5 $76 6 $95 c) How many rooms will be rented, when the hotel maximizes its profit? Explain.

R& V Hotel is consistently incurring losses for the past 2 years though the sales clerk receives customer orders, raises sales invoices at a higher price and processes payments for customers. Hotel customers have contracted prices, however online trade prices automatically loaded in to the system but the Brenda clerk used to amend manually. Mr. Zakariya an internal auditor found some deficiencies, who has taken some necessary actions to cross check those invoices and employees responsibilities and suggested the management immediately to prevent from loss of customers and good will of the hotel.
Based on the above scenario:
1. How the internal audit for R and V hotel can be helpful in resolving the issues they are confronting at the moment? Justify your answer practically
2. If you were Mr. Zakariya, prepare doable audit plan that Mr. Zakariya that you can use for the company and provide recommendations on how to overcome the deficiencies cited in the case?

This is the probability distribution between two random variables X and Y:

a) Are those variables independent?

b) What is the marginal probability of X?

c) Find E[XY]

1. Calculate the expected rate of return for Stock J. Round your answer to two decimal places.
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2. Calculate the standard deviation for the market. Round your answer to two decimal places.
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   Calculate the standard deviation for Stock J. Round your answer to two decimal places.
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Question 2

You are an auditor on the BLUE Limited (BLUE) audit engagement for the financial year ending 30 September 2019. BLUE is a large hotel company with more than 1000 hotels in Australia and Asia under a range of hotel brands. You are in the process of undertaking audit planning procedures for the BLUE audit. You have noted a number of significant risks outlined below.

BLUE’s revenue is made up of management fees earned from hotels managed by BLUE under long-term contracts with hotel owners, and from the rental of rooms and food and beverage sales from hotels owned and leased by the company directly. In hotels owned and leased directly by BLUE, the company’s practice is to confirm hotel bookings by taking credit card details and collecting payment for accommodation and incidentals at the end of a customer’s stay. You have noted an increasing incidence of corporate clients prepaying for their employees’ accommodation. These have been recorded as revenue when payment has been received.

It has also come to your attention that there have been a growing number of disputes with hotel owners in relation to the amount of management fees being charged. Management fees included a base fee, a percentage of hotel revenue, and an incentive fee based on the hotel’s profitability. Individual contracts negotiated with hotel owners include provisions for percentage increases of the base fee either annually or biannually to take effect at specific dates. Based on your initial review of the correspondence, it appears that BLUE has been applying percentage increases to the base fee charged to hotel owners prior to their effective date as contained in the contracts with individual hotel owners.

BLUE runs a hotel loyalty program which enables members of the program to earn points for every dollar spent on accommodation, food and beverages at BLUE branded hotels. These points may be redeemed at a later date for free accommodation or other benefits. BLUE records a loyalty program future redemption liability on the basis of the number of points expected to be redeemed prior to their expiry multiplied by redemption cost per point. An announcement was made on 30 May 2017 that points earned under the loyalty program would now expire in two years rather than five years from the time they are earned. BLUE’s management subsequently reduced the amount provided in the loyalty program future redemption liability by $80 million based on their estimate of the revised amount required to meet the liability given the impact of the change.

BLUE has embarked on a large-scale software development project in the current year to internally develop improved guest reservation and hotel management systems. An amount of $37 million for the year has been capitalised as software development during the year. Your initial review has revealed that this amount includes repairs and maintenance of a range of BLUE’s hardware incurred during a year.

Required

(a) Considering the information provided, determine the four key account balances and related assertions at risk. Briefly justify your answer. (4 X 5 Marks = 20 Marks)

b) Recommend one audit procedure in relation to each of the assertions identified above (4 X 2.5 Marks = 10 Marks)

Confidence Interval Worksheet with Sample Data MTH 160: Statistics

Read the following scenario and complete each of the problems below:

A flashlight company claims that the new bulb in its heavy-duty flashlight will average 246 hours of light. A statistics student decides that he/she wants to test this claim at a 5% level of significance to determine if there is evidence to support the claim. The student randomly selects and tests 15 flashlight bulbs and records how long the bulb lasts until it burns out. Assume the life of a bulb is normally distributed. T

he data is in the table below

Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Hrs: 246 224 231 242 237 240 243 236 239 255 256 239 247 231 253

A. The standard deviation of the population is 7.4 hours. Construct a 95% confidence interval for this study.

B. Same scenario, but the population’s standard deviation is not known. Construct a 95% confidence interval for this study.

C. Write a statement comparing and contrasting the two confidence intervals and results.

Read the following scenario and complete each of the problems below:

A new car manufacturing company has emerged and has claimed that its new hybrid car, the Pusho, gets a better gas mileage than the highest ranked Toyota Prius. Consumer Reports Magazine decides to test this claim at a 5% level of significance. Consumer Reports randomly selects 10 of each type of car, calculates the miles per gallon for each car in the study, and records the data in the table below. Assume miles per gallon of the cars is normally distributed.

Pusho 54.1 52.4 55.7 49.7 50.6 48.9 51.8 54.5 56.9 49.8

Prius 53.2 54.3 49.8 50.1 50.5 56.1 47.8 53.4 56.8 48.7

A. Construct a 90% confidence interval for the difference in the gas mileage of Pusho and Prius.

B. Construct a 95% confidence interval for the difference in the gas mileage of Pusho and Prius.

C. Write a statement comparing and contrasting the two confidence intervals and the significance of having 0 in both of those intervals.