7.7.3. Consider a vibrating quarter-circular membrane, 0 < r < a,0 < θ < π/2, with u =0 on the entire boundary. [Hint: You may assume without derivation that λ>0 and that product solutions
u(r,θ,t)=φ(r,θ)h(t)=f(r)g(θ)h(t)
satisfy
∇2φ+λφ =0 dh dt =−λkh d2g dθ2 =−μg
r
d drrdf dr+(λr2 −μ)f =0 .]

*(a) Determine an expression for the frequencies of vibration.

(b) Solve the initial value problem if u(r,θ,0) = g(r,θ), ∂u ∂t (r,θ,0) = 0.

(c) Solve the wave equation inside a quarter-circle, subject to the conditions
∂u ∂r
(a,θ,t)=0,u (r,0,t)=0 ur, π 2,t=0,u (r,θ,0) = 0 ∂u ∂t (r,θ,0) = β(r,θ)

Duffy Dog Retailers expects to make inventory purchases in the next quarter as follows:

Prior experience has shown that 70 percent of a month’s purchases are paid in the month of purchase and 30 percent are paid in the month following purchase. March purchases were $51,900.

Estimate cash disbursements related to purchases for April, May, and June.

Question 2.

The Central Division of Miller's Quarter Horse Company has sales of $4,500,000. It also has invested assets of $2,500,000 and operating expenses of $3,800,000. The company has established a minimum rate of return of 7%.

Required:

1. Determine the following for the Central Division:

• Profit Margin
• ROI using DuPont formula
• Residual Income

2. Miller has offered a new investment opportunity to the Central Division, which has a Return of Investment of 20% calculated as an operating income of $160,000 divided by the invested asset of $800,000.

Explain by undertaking required calculation, whether the manager of the Central division would undertake the additional investment opportunity if:

• He was paid a bonus based upon his division’s overall ROI.
• He was paid a bonus based upon his division’s overall RI

Solution:

Central Division

Before accepting the new investment:

ROI:

RI:

After accepting the new investment

ROI:

RI:

Raelynn is preparing its master budget for the quarter ended September 30. Budgeted sales and cash payments for merchandise for the next three months follow.

Sales are 20% cash and 80% on credit. All credit sales are collected in the month following the sale. The June 30 balance sheet includes balances of $15,000 in cash; $45,000 in accounts receivable; $4,500 in accounts payable; and a $5,000 balance in loans payable. A minimum cash balance of $15,000 is required. Loans are obtained at the end of any month when a cash shortage occurs. Interest is 1% per month based on the beginning-of-the-month loan balance and is paid at each month-end. If any excess balance of cash exists, loans are repaid at the end of the month. Operating expenses are paid in the month incurred and consist of sales commissions (10% of sales), office salaries ($4,000 per month), and rent ($6,500 per month).

Use the information provided above to prepare a cash budget, and any necessary supplemental schedules. Then use the information above, your budget and your supplemental schedules to answer the following questions.

1. How much cash is expected to be collected in July?

2. How much cash is expected to be collected in August?

3. How much cash is expected to be paid out in July?

4. How much cash is expected to be paid out in September?

5. How much interest is expected to be paid out in August?

6. What is the ending cash balance at the end of July?

7. What is the ending cash balance at the end of September?

8. How much of the loan can be paid back at the end of August?

Anchor Ltd paid $15,000 last quarter for a feasibility study regarding the demand for motorboat replacement parts which would require the purchase of a new metal-shaping machine. Today, they wish to conduct an analysis of the proposed project.
The machine costs $250,000 and will operate for five years and tax rules allow the machine to be depreciated to zero over a five-year life. The machine is expected to produce sales of $135,000 annually for the five years. Anchor has already agreed to sell the machine in five years’ time to an unrelated firm for $80,000.
The project will result in a $35,000 increase in accounts receivable and require an increase in inventory levels by $20,000 to $95,000. Anchor has negotiated with its bank to borrow $180,000 to help pay for the project. Loan repayments are $48,000 each year for five years.
If Anchor buys the machine they will be able to use some equipment that they currently own. This is part of the driving force in the decision making as it enables the company to save money in not buying additional new equipment. This equipment was bought for $120,000 six years ago and could be sold today for $63,000. This equipment has been written off for tax purposes and would be worthless in five years’ time.
If the company tax rate is 30% and the appropriate discount rate is 19.5%, should Anchor buy the new machine?

1.)How much is this annuity worth today? It will payout $630 each quarter for 30 years. Your desired annual interest return is 4.8 %. (Don't forget to adjust the interest rate for quarterly, in addition to the time period.) $40,473.27 $39,954.22 $46,003.28 $46,486.44 $39,637.64

2.)Your savings contract will pay you $260 each month for the next 4 years . With a 7 percent nominal annual interest rate, what is this contract worth today? Adjust the interest rate and number of periods for monthly (see practice)

Grand Touring Ltd paid $25,000 last quarter for a feasibility study regarding the demand for car customisation which would require the purchase of a new metal-shaping machine. Today, they wish to conduct an analysis of the proposed project. The machine costs $350,000 and will operate for five years and tax rules allow the machine to be depreciated to zero over a four-year life. The machine is expected to produce sales of $135,000 annually for the five years. GT Ltd has already agreed to sell the machine in five years’ time to an unrelated firm for $100,000. The project will result in a $35,000 increase in accounts receivable and require an increase in inventory levels by $25,000 to $95,000. Anchor has negotiated with its bank to borrow $250,000 to help pay for the project. Loan repayments are $57,700 each year for five years. If GT Ltd buys the machine they will be able to use some equipment that they currently own. This is part of the driving force in the decision making as it enables the company to save money in not buying additional new equipment. This equipment was bought for $160,000 six years ago and could be sold today for $63,000. This equipment has been written off for tax purposes and would be worthless in five years’ time.

(a) What are the relevant cash flows for each year of the new machine’s life? Assume the company tax rate is 30%.

(b) Assuming the nominal cost of capital for the project is 12% p.a, and inflation is currently 3% p.a, What is the NPV of the project?

(c) Should GT Ltd go ahead with the project? Why, why not? (1 mark)

Dorothy's budgeted production figures (in units) for burlap sweatshirts for next quarter are shown below:

                                    July                August             September

Expected Production    3,600               4,100                  5,000

            Dorothy uses 1.2 yards of burlap per sweatshirt and pays $0.75 per yard of burlap. Dorothy likes to have half of the next month's burlap needs in ending inventory. What is the expected cost of burlap to be purchased for sweatshirts in August?

A.        $5,460

B.         $4,550                         D.        $3,285

C.         $4,095                         E.         none of the above

Refer to Revenue Data Excel File. The 4 QTR Centered Moving Average for the 2nd quarter of 2017 is: Select one: a. 222.125 b. 333.875 c. 269.250 d. 243.625

Using the financial statements for HealthSouth Corp for the quarter ending 6/30/2002, or use the current financial statements for either Microsoft or Facebook. Choose your primary ratio and post your analysis.

2 Calculate several ratios—I would suggest at least one from each of the categories (profitability, liquidity, solvency, and activity/efficiency) from chapter 4 (chapter 11 in Marshall) in the text plus at least one ratio that you have found somewhere else or even made up. You should examine these ratios over a 4 year period (No need to look at every quarter). For example you might look at quarter 2 every year for 4 years—including the quarter that I have chosen. Once you are used to looking up financial statements--if you do this strategically you should be able to examine 4 years of data by looking at only two separate years of financial statements.   Please do not discuss all of these ratios. Your goal in calculating a number of ratios is to increase your chances of finding a ratio that is interesting and important.