1. Suppose we have two blocks of masses m1 and m2. The block with mass m1 is moving towards block m2 at speed v. After the collision, we measure the total kinetic energy and find that the total kinetic energy after the collision is m2/(m1+m2) less than the kinetic energy before the collision. Find the final speeds of the two blocks. What type of collision is this?

2. Explain, in words, how we know that a freely spinning asteroid in space is rotating about an axis that passes through its center of mass?

3. You are handed a rod that is three times as dense on one end as it is on the other end. Find the moment of inertia when the axis of rotation is about the heavy end, and find the moment of inertia when the axis of rotation is about the light end.

Please answer all parts, Thank you!

Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $17,500 per month for 25 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $345,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $2,000,000 to his nephew Frodo. He can afford to save $2,350 per month for the next 10 years. If he can earn an EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30?

Suppose that you sell short 500 shares of XYZ, currently selling for $40 per share, and give your broker $15,000 to establish your margin account.

If you earn no interest on the funds in your margin account, and assume that XYC pays no dividends.

a.) So what will be your rate of return after one year if XYZ stock is selling at:

i.) $44.00

ii.) $40.00

iii.) $36.00

b.)

If the maintenance margin is 25%, how high can XYZ’s price rise before you get a margin call?

c.)

Try parts (a) and (b) again, but now assume that XYZ also has paid a year-end dividend of $1 per share. The prices in part (a) should be interpreted as ex-dividend, that is, prices after the dividend has been paid.

i.) $44.00

ii.) $40.00

iii.) $36.00

You are given a new puppy as a birthday present and are eager to play with her. However, you soon come to realize that your new puppy has other plans. She decides to ransack your room and go after anything she can grasp in her mouth. One of the items is a rigid ball that has 5 grams of liquid ethanol in it from an experiment you did in class. The hot breath of the puppy vaporizes 50% of the ethanol to create an air-ethanol mixture at 50°C. After a few minutes, she releases the ball and the air-ethanol mixture comes to a new equilibrium state at 30°C. Taking the total pressure inside of the ball to be 1 atm, estimate the percent of ethanol that condenses at the final state. [HINT: Think carefully about how much ethanol is in the vapor state before the actual process starts. This is your starting amount.]

Firm C currently has 250,000 shares outstanding with current market value of $47.40 per share and generates an annual EBIT of $1,250,000. Firm C also has $1 million of debt outstanding. The current cost of equity is 8 percent and the current cost of debt is 5 percent. The firm is considering issuing another $2 million of debt and using the proceeds of the debt issue to repurchase shares (a pure capital structure change). It is estimated that the cost of the new debt will be 5.5 percent and that the cost of equity will rise to 9 percent with the additional debt. The marginal tax rate is 21 percent.

1.) Before the capitalization, what is the firm's weighted average cost of capital? Answer in decimal form.

2.) What will the firm’s market value be after the announcement of the new debt issue?

3.) What will the estimated new share price be after the capital structure change announcement?

Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $23,000 per month for 30 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 15 years at an estimated cost of $606,000. Third, after he passes on at the end of the 30 years of withdrawals, he would like to leave an inheritance of $700,000 to his nephew Frodo. He can afford to save $1,900 per month for the next 15 years. If he can earn a 10 percent EAR before he retires and a 7 percent EAR after he retires, how much will he have to save each month in Years 16 through 30?

1. Inventory on the Income Statement: What conclusion can you derive out from the Income Statement (see table 2) in terms of: (10 pts. each)
   1. Profit after-tax income using FIFO method vs. LIFO and WAC
   2. Federal Income Tax (@ 40%) using LIFO method vs. FIFO and WAC