Consider two firms with identical assets company a is all

Question

1. Consider two firms with identical assets. Company A is all equity financed and company B is financed with a mix of debt and equity. There are also two equally likely states of the world which will occur at time 1. Company B has debt with a face value of $45,000 that is due at time 1.

Demonstrate that under the assumptions of the Modigliani-Miller theorem, VA = VB.

Market Value of Assets (T=1)	Company A	Company B
Good State	$120,000	$120,000
Bad State	$30,000	$30,000

1. Assume the same information from the previous question. Now, suppose Company A's equity instrument trades for $78,750, whilst company's B's equity instrument trades for $37,500 and its debt instrument trades for $37,500. In the absence of market frictions, does this represent an arbitrage opportunity? If it does, how would you take advantage of this opportunity?
2. As my good friend Aimee can tell you, short selling in the real world is not straightforward. Assume the same information from the previous question. If you answered the question correctly, you should have engaged in a short transaction on one of the firm's equity instruments. Now, suppose that your broker has an initial margin requirement of 50%, and a maintenance margin of 30%. At what price would you receive a margin call?
3. Assume a Modigliani-Miller world, with a tax advantage to debt, in which Company C is unlevered and would like to include debt in its capital structure. The firm is presently valued at $35,000 with 5,000 shares outstanding. The plan is to issue $10,000 of new perpetual debt (that will be used to repurchase old stock) with an interest rate of 8%. The corporate tax rate is 25%. Calculate the value of Company C if they make this change.
4. Assume a Modigliani-Miller world in which Company D is currently financed entirely with equity, but would like to include debt in its capital structure. Also, assume that there are three states of the world that may occur at time 1 (good, fair and bad). The current and proposed capital structures are listed below, and the simplified income statements for each state of the world are listed in the table after:

Variable	Current	Proposed
Assets	$20,000	$20,000
Debt	$0	$8,000
Equity	$20,000	$12,000
Debt/Equity Ratio	0.00%	66.67%
Yield	N/A	8.00%
Shares Outstanding	400	240
Share Price	$50	$50

Current	Good	Fair	Bad
EBIT	$1,000	$2,000	$3,000
Interest	$0	$0	$0
EBT	$1,000	$2,000	$3,000

Fill out the table below that calculates operating ROA. Also, calculate "operating ROE" and EPS on an EBT basis for Company D under the new capital structure i.e. these two ratios use EBT as opposed to Net Income in the numerator.

Proposed	Good	Fair	Bad
EBIT	$1,000	$2,000	$3,000
Interest
EBT
Operating ROA
Operating ROE
EPS

1. Assume the same information about Company D from the previous question. Also, assume that you have perfect information about which states of the world CAN* occur, but not which one will actually occur, and that all three states are equally likely. Calculate the standard deviation of the operating ROE under both capital structures. Explain your results. *Because we are accounting for all possibilities, please use the population version of the standard deviation equation (Scroll down to the population variance chapter on Wiki).
2. Assume the same information from the previous problem about Company D. Why is Company D's operating ROA the same irrespective of its capital structure?
3. As my good friend Aimee can tell you, there are a variety of financial products one can use to mitigate the consequences of negative outcomes. This process is called hedging (Read the document on the last page of the test). Assume the same information from the previous problem. Show how one could hedge the exposure to the levered version of Company D, so as to replicate the payoffs of its unlevered state. For example, you might be an investor who does not like the decision to change the capital structure. Assume you have $2,000 to work with. Slide 25 of this PowerPoint presentation may be helpful.
4. The pecking order theory is an apparent violation of Modigliani-Miller. Explain, in one page, what the pecking order theory is and how it more closely approximates real-life than the MM world.
5. Consider firm E. Firm E has a state (S) dependent value V(S). Firm E also has a state dependent loss function L(S) that occurs in the event of catastrophe (the building burns down, the federal government bans its products due to safety concerns, the firm hires my other good friend Amy, as opposed to my good friend, Aimee etc...) Now, also suppose that the firm can be restored to full capacity after the catastrophe with a state dependent investment I(S). Show how under debt and equity financing, there exist states of the world in which the firm will not be restored, even though restoration is a positive NPV proposition. For full credit, plot a graph that shows the relationship between dollars in state S (vertical axis) against the states of the world (increasing values on the horizontal axis indicate better states).

Attachment:- 1612818_1_FINE-6140.pdf