Question 8. There are two types of works: some have a high productivity, aH, and some have low productivity, aL. Workers can get a job after leaving high school or they can 2 go to college at a cost of cH for high productivity workers and cL for low productivity workers. Assume that aH > aL > 0 and cL > cH > 0. Education has no impact on productivity. Describe a separating equilibrium in which employers pay workers a wage equal to the expected productivity conditional on the level of education. What conditions must be satisfied by the parameters aH, aL, cH and cL in order for such as separating equilibrium to exist?

A homemade capacitor is assembled by placing two 10 in pie pans 8 cm apart and connecting them to the opposite terminals of a 9 V battery.

(a) Estimate the capacitance.
  pF
(b) Estimate the charge on each plate.
pC
(c) Estimate the electric field halfway between the plates.
V/m
(d) Estimate the work done by the battery to charge the plates.
J
(e) Which of the above values change if a dielectric is inserted? (Select all that apply.)

electric fieldchargework done by the batterycapacitance

Two electric bulbs of 100 ohms are used for 8 hours daily. What is the cost of them for 1 day if the rate is 75 paise per unit?

A double pane window consists of two pieces of glass each of 8 mm thick that enclose an air space of 8 mm thick. The window separates room air at 18°C from outside ambient air at -8°C. The convection coefficient associated with the inner (room-side) surface is 12W/m2 .K. The thermal conductivity of the glass is kg=1.35 W/m. K and that of the air is ka=0.027 W/m. K Q1- If the outside air convection coefficient is ho = 76 W/m2 .K what is the heat loss through a window that is 0.8 m long by 0.5 m wide? Neglecting radiation and assume the air enclosed between the panes to be stagnant. Q2- We consider now that the heat transfer in the air gap is transferred by conduction and radiation and that the radiation coefficient hrad = 3 W/m2 K . Show the thermal circuit representing the steady state situation and define the new heat transfer loss through the window

Problem 1 (3 + 3 + 3 = 9) Suppose you draw two cards from a deck of 52 cards without replacement. 1) What’s the probability that both of the cards are hearts? 2) What’s the probability that exactly one of the cards are hearts? 3) What’s the probability that none of the cards are hearts?

Problem 2 (4) A factory produces 100 unit of a certain product and 5 of them are defective. If 3 units are picked at random then what is the probability that none of them are defective?

Problem 3 (3+4=7) There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3 has 45 red and 55 blue marbles. Now a bag is chosen at random and a marble is also picked at random. 1) What is the probability that the marble is blue? 2) What happens when the first bag is chosen with probability 0.5 and other bags with equal probability each?

Probem 4 (3+3+4=10) Before each class, I either drink a cup of coffee, a cup of tea, or a cup of water. The probability of coffee is 0.7, the probability of tea is 0.2, and the probability of water is 0.1. If I drink coffee, the probability that the lecture ends early is 0.3. If I drink tea, the probability that the lecture ends early is 0.2. If I drink water, the lecture never ends early. 1) What’s the probability that I drink tea and finish the lecture early? 2) What’s the probability that I finish the lecture early? 3) Given the lecture finishes early, what’s the probability I drank coffee?

Problem 5 (4+4+4=12) We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Find the probability that doubles were rolled. 2) Given that the roll resulted in a sum of 4 or less, find the conditional probability that doubles were rolled. 3) Given that the two dice land on different numbers, find the conditional probability that at least one die is a 1. Problem 6 (8) For any events A, B, and C, prove the following equality: P(B|A) P(C|A) = P(B|A ∩ C) P(C|A ∩ B)

Compute the cost of the​ following:

a. A bond that has ​$1000 par value​ (face value) and a contract or coupon interest rate of 11 percent. A new issue would have a floatation cost of 6 percent of the ​$1125 market value. The bonds mature in 9 years. The​ firm's average tax rate is 30 percent and its marginal tax rate is 32 percent.

b. A new common stock issue that paid a ​$1.50 dividend last year. The par value of the stock is​ $15, and earnings per share have grown at a rate of 7 percent per year. This growth rate is expected to continue into the foreseeable future. The company maintains a constant​ dividend-earnings ratio of 30 percent. The price of this stock is now ​$31​, but 8 percent flotation costs are anticipated.

c. Internal common equity when the current market price of the common stock is ​$48. The expected dividend this coming year should be ​$3.00​, increasing thereafter at an annual growth rate of 11 percent. The​ corporation's tax rate is 32 percent.

d. A preferred stock paying a dividend of 9 percent on a ​$100 par value. If a new issue is​ offered, flotation costs will be 12 percent of the current price of ​$175. e. A bond selling to yield 12 percent after flotation​ costs, but before adjusting for the marginal corporate tax rate of 32 percent. In other​ words, 12 percent is the rate that equates the net proceeds from the bond with the present value of the future cash flows​ (principal and​ interest).

a. What is the​ firm's after-tax cost of debt on the​ bond? % ​(Round to two decimal​ places.)

b. What is the cost of external common​ equity? ​% ​(Round to two decimal​ places.)

c. What is the cost of internal common​ equity? ​% ​(Round to two decimal​ places.)

d. What is the cost of capital for the preferred​ stock? ​% ​(Round to two decimal​ places.)

e. What is the​ after-tax cost of debt on the​ bond? % ​(Round to two decimal​ places.)

Use below terms to fill in blanks in the sentences that follow. Each term is used only once.

contingency table

control variable

correlated

cross-products

dependent variable

direction of association

expected values

gamma correlation coefficient

higher order gammas

independent variable


negative

Nominal


ordinal


positive


spurious association

statistical elaboration

statistically significant

strength of association

1. When conducting a two-way chi-square test to decide whether one variable probably influences a second variable, we compare the actual (observed) frequencies to the (1) ________________________, which are based on the pattern of responses for the overall group. When the actual (observed) values differ enough from these values, the difference between the two are determined to be (2) ______________________________. 

2. When we observe data for two variables arrayed in a 2 by 2 (3)_________________________________, we may suspect that the variables are (4) _________________________________ or related to each other if two cells on one diagonal contain a disproportionately large frequency of cases. Multiplying A*D and B*C produces two (5)________________________________, the larger of which reveals which diagonal is dominant. Multiplying A*D and B*C is the first part of the formula for computing the (6)_______________________________. 

3. When the frequencies in the A cell multiplied by the frequencies in the D cell are greater than the frequencies in B times the frequencies in C, the A-D diagonal is dominant and the direction of association is (7)_______________________. When the frequencies in the B cell multiplied by the frequencies in the C cell are greater than the frequencies in A times the frequencies in D, the B-C diagonal is dominant and the direction of association is (8)_______________________. 

4. The sign for a zero order gamma reveals the (9)_________________________________ and the absolute value tells us the (10)___________________________________. 

5. When we are studying hypothesized association between educational level and income level and we assume educational level (no college, graduated college) influences income level (low income, high income) educational level is the (11)__________________________ and income level is the 
(12)___________________________. Income level is an example of a 
variable measured at the (13)_________________ level of data. If we introduce the variable gender as a control, gender is measured at the (14)____________________ level of data.

6. The process of using a (15)___________________________ to test an apparent relationship between two variables measured at the nominal/ordinal level is referred to as (16)__________________________. 

7. When a control variable is introduced, two (17)_____________________________ are computed, one for each of the two sub-sets. For an apparent association to be reclassified as (18)______________________________, measured association in each sub-set must drop below an absolute value of 0.2. 


ACC20007 Assignment

Case

Part A

MelSwin is an accounting consultancy firm that provides its services to small, medium and large sized clients. The client size is determined by the number of employees as follows:

MelSwin uses a traditional overhead cost driver of “data analysis hours” to estimate the cost of providing its services. Although MelSwin does not operate in a competitive environment, the Finance Manager, Grainne, advocates to use advance costing methods like the activity-based costing. Otto, the CEO, argues that the current method provides an acceptable cost estimation and given the high cost of implementing ABC, it will not beneficial. However, he agreed to hire a university graduate to examine the costs and benefits of implementing ABC. To do so, Mary, a recent Swinburne graduate, has been hired to establish an activity-based costing system. The activities and associated costs are estimated as follows:

Mary has collected the following information about the average activity usage of three groups of clients:

Mary has also collected the following information about a client, Hawthorn Cabinet, with 60 employees.

Mary has been asked to prepare a report about the implementation of ABC and answer some relevant questions.

Part B

Mary has also become responsible to prepare cash budgets for the next six months. 15 % of the clients are small sized, 41% medium sized and the rest are large sized.

The patterns of billing receipts for each group of clients are presented as follows:

Estimated billings for the last six months of this year are listed below.

Estimated cash outflows for the last three months of this year are listed below.

MelSwin expects to have a cash balance of $50,000 on 1 October and has a policy of maintaining a minimum cash balance of $40,000 at the end of each month.

Mary has been asked to prepare a cash budget report for the next six months including answering some relevant questions.

Question 2

Calculate the average costs for each group of clients using the traditional method used in MelSwin?

Question 3

Calculate the average costs for each group of clients using the activity-based costing?

Question 4

Assume that the direct cost of visiting Hawthorn Cabinet is $2100. Estimate the cost of providing services for this client using both the activity-based costing and the traditional method used by MelSwin?

Question 5

Do you recommend using the activity-based costing at MelSwin? Briefly explain your reason.

Question 66

Prepare a cash budget for the last quarter of the year that includes monthly budgeted cash receipts and payments.

Question 7

MelSwin considers an investment to improve its productivity in the future including upgrading software and hardware equipment. Determine the amount of short-term borrowing, if any, necessary on 1 November for that potential investment which requires $350,000 cash on 1 November.

Question 8

The CEO is interested to know the impact of Covid-19 outbreak in their monthly budget considering a likely reduction of 50% in estimated billings from July. In addition, assume that 20% reduction in cash outflows is possible and cash balance will be $5,000 on 1 October and no minimum cash balance is required at the end of each month. . Prepare a cash budget for the last quarter of the year that includes budgeted monthly cash receipts and payments.

Question 9

What percentage reduction in cash outflows will be required in previous question to ensure no monthly cash shortfall will happen in the last quarter of the year.

Assuming that the population is normally​ distributed, construct a 99​% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

Sample​ A: 1   4   4   4   5   5   5   8

Sample B: 1   2   3   4   5   6   7   8

Construct a 99​% confidence interval for the population mean for sample A.

less than or equalsmuless than or equals Type integers or decimals rounded to two decimal places as​ needed.)

Construct a 99​% confidence interval for the population mean for sample B.

less than or equalsmuless than or equals ​(Type integers or decimals rounded to two decimal places as​ needed.)

Explain why these two samples produce different confidence intervals even though they have the same mean and range.

A. The samples produce different confidence intervals because their critical values are different.

B. The samples produce different confidence intervals because their sample sizes are different.

C. The samples produce different confidence intervals because their standard deviations are different.

D. The samples produce different confidence intervals because their medians are different.