From the reference frame of the Earth, a 0.0500-kilogram ball moving in the +x
direction at 4.0 m/s overtakes and collides with a 0.1000-kg ball moving in the +x direction
at 2.0 m/s. Assume that the collision is perfectly elastic, with all motion after the collision
also along the x axis, and that the balls are moving on a horizontal, friction-less surface.
Only Galilean relativity is needed for this problem.

(1) Calculate the speed and directions of each ball after the collision. Hint: use energy
and momentum conservation.

(2) Use Galilean transformations to determine the velocities of each ball as measured in
the reference frame of the 0.0500-kg ball, both before and after the collision.

(3) Using your velocities from part (b), explicitly determine whether total energy and
momentum are conserved in the 0.0500-kg ball's reference frame.

Isabel, a calendar-year taxpayer, uses the cash method of accounting for her sole proprietorship. In late December she received a $75,000 bill from her accountant for consulting services related to her small business. Isabel can pay the $75,000 bill anytime before January 30 of next year without penalty. Assume her marginal tax rate is 37 percent this year and next year, and that she can earn an after-tax rate of return of 10 percent on her investments.

a. What is the after-tax cost if Isabel pays the $75,000 bill in December?

  

b. What is the after-tax cost if Isabel pays the $75,000 bill in January? Use Exhibit 3.1. (Round your answer to the nearest whole dollar amount.)

c. Based on requirements a and b, should Isabel pay the $75,000 bill in December or January?

• December

• January

On October 31, GRANGER Corporation’s liabilities totalled $201,000. Its shareholders’ equity consisted of 88,900 common shares issued, $889,000 and retained earnings, $260,000. GRANGER is considering the following three courses of action: (1) paying a $0.50 cash dividend, (2) declaring a 11% stock dividend, or (3) effecting a 3-for-1 stock split. The current market price for its common shares is $15 per share.

Complete the following tabular summary of the effects of the alternative actions on GRANGER’s shareholders’ equity and number of common shares.

(1)             (2)             (3)
Before Action           After Cash Dividend             After Stock Dividend            After Stock Split
Total assets            $1,350,000              $                       $                       $        
Total liabilities               $201,000                $                       $                       $        
Common shares           889,000                                                                  
Retained earnings               260,000                                                                  
Total shareholders' equity              1,149,000                                                                        
Total liabilities and shareholders’ equity              $1,350,000              $                       $                       $        
Number of common shares         88,900  

PLEASE BE DETAILED AND SHOW THE CALCULATIONS OF THE ANSWERS

A company is determined to purchase a special tool at a cost of $ 9,000. This team will generate savings amounting to $ 3,000 the first year, with an increase of $ 500 per year until the end of the fifth year. The company uses the MACRS depreciation method. Consider a 21% tax rate.

1. Complete the following table to determine the after-tax cash flow

b)      Consider that the tool was sold for $ 2,500 at the end of the fifth year. Recalculate flow cash after-tax taking into account the sale of the asset. (Only fifth year)

c)        If the equipment sold for $ 30,000 in the third year, determine the loss or recapture of corresponding depreciation.

You are a financial advisor and get the following question from one of your cllients M'' spoue and I each 62 and hope to retire in three year . After requirement we will received $7500 per month after taxes from our employees pension plans and $1500 per month after from the social security .Unfortunately , our monthly expenses are $15000.Our social obligation preclude further economies . We have $1000,000 invested in a high grade ,tax-free municipal -bond fund form. The return on the fund is 3.5% per year .We plan to make annual withdrawer from the mutual fund to cover the different between our pension nd social security income and our living expense .How year before we run out of money what do we tell our client?

The Kudos Company (TKC) is in the spaceship industry. Annual EBIT is projected to remain level at $50 million and is received at the end of each year. There are 4 million shares outstanding at a market price of $35 each; there is no debt. TKC is considering approval of a shareholder value plan under which $60 million would be borrowed in perpetuity and then immediately paid out to shareholders as a dividend. This debt bears an interest rate of 8%. TKC has no depreciable assets. The corporate tax rate is 30%; and there are no personal taxes. Markets are frictionless and semi‐strong efficient. (a) Calculate the market price per TKC share just after the : (i) approval of the plan before the public announcement. (ii) public announcement of the plan. (iii) implementation of the plan after the dividend is paid out. (b) Calculate rWACC for TKC after the implementation of the shareholder value plan.

The average length of time customers spent on waiting at ABC Store’s check-out counter before a new P.O.S. system was installed was 4.3 minutes. A sample of 40 customers randomly selected at the check-out counter after the new P.O.S. system was installed showed that the average waiting time was 3.5 minutes with a sample standard deviation of 2.8 minutes. We wish to determine if the average waiting time after the P.O.S. system was installed is less than 4.3 minutes.

1.   State the null and alternative hypotheses to be tested. (2 Points)

2.   Compute the test statistic. (2 Points)

3.   Determine the critical value for this test at the 0.05 level of significance. (2 Points)

4.   What do you conclude at the 0.05 level of significance? (2 Points)

5.   Construct a 95% confidence interval for the average waiting time after the new P.O.S. system was installed.

Data for Cash Flow Estimation for an Expansion Project
• Cost of new equipment: $200,000
• Life of the project: 5 years
• Depreciation for equipment: Straight-line to zero over five years
• Investment (increase) in net working capital: $30,000
• Annual sales: $220,000
• Annual cash operating expenses: $90,000
• Income tax rate: 40%
• At the end of year five, the company will sell off the equipment for $50,000.
• At the end of year five, the firm will recover the net working capital investment of $30,000.

What is the total initial investment outlay in Year 0?

What is the depreciation amount in Year 1?

What is the operating income BEFORE taxes in Year 1?

What is the operating income AFTER taxes in Year 1?

What is the after-tax operating cash flow in Year 1?

What is the total terminal year after-tax non-operating cash flow?

In a test of the effectiveness of garlic for lowering​ cholesterol, 43 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol​ (in mg/dL) have a mean of 2.7 and a standard deviation of 16.3. Complete parts​ (a) and​ (b) below.

A. What is the best point estimate of the population mean net change in LDL cholesterol after the garlic​ treatment?

B. Construct a 90​% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol? What is the confidence interval estimate of the population mean muμ​?

C. What does the confidence interval suggest about the effectiveness of the​ treatment? Do they contain 0? Did it affect the cholesterol levels?

An existing 36-inch diameter concrete gravity sewer installed on a slope of 0.25% currently conveys a peak flow rate of 12 cfs. A builder proposes to connect a new residential development to this existing sewer. Projected peak flow from this new development is 4 cfs.

a) Depth of flow in sewer before new development is connected

b) Depth of flow in sewer after new development is connected

c) Flow velocity in sewer after new development is connected

d) Flow type (critical, subcritical or supercritical) after new development is connected

e) Diameter of a sewer to convey combined peak flow of 16 cfs if maximum allowable D/d is 0.85 (i.e. assume you are designing new sewer on the same 0.25% slope)

Please show all work. Thank you so much in advance!