Question

                  Assume a firm has cash of $10 and a project that is either worth $130 or $80 (50% chance of each). The firm owes $110 to the bank. Similar to the example in class, the following shows the value of assets, debt, and equity where the amounts are calculated based on expected values.

Cash	$10	Debt	$100
Project	$105	Equity	$15
Total	$115	Total	$115

Assume the firm is considering a new project which requires an initial investment of $5. If the new project is accepted, the $5 will be paid for using the firm’s cash. The new project has a $10 cash flow in the good state (i.e., increasing the “project” cash flows in the good state from $130 to $140). In the bad state, the new project’s cash flow is -$10 (i.e., decreasing the “project” cash flows in the bad state from $80 to $70). What is the expected value of the firm’s equity if the firm decides to accept this new project?

Refer back to the facts in the previous problem. What is the expected value of the firm’s debt if the firm decides to accept this new project?

Answer 1

ANSWER:-

A	B	C	D	E	F	G	H	I	J
2
3		Value of Debt is the minimum of the value of project and the debt amount.
4		Debt Amount	$100
5		State	Probabilities	Value of project	Cash flow of new project	Total cash Flow	Value of Debt	Value of Equity
6		Good State	0.5	$130	$10	$140	$100	$40
7		Bad State	0.5	$80	($10)	$70	$70	$0
8
9		Expected Value of equity	=0.50*$40+0.50*$0
10			$20	=D6*I6+D7*I7
11
12		Hence Expected Value of equity is	$20
13

Formula sheet

A	B	C	D	E	F	G	H	I	J
2
3		Value of Debt is the minimum of the value of project and the debt amount.
4		Debt Amount	100
5		State	Probabilities	Value of project	Cash flow of new project	Total cash Flow	Value of Debt	Value of Equity
6		Good State	0.5	130	10	=E6+F6	=MIN($D$4,G6)	=G6-H6
7		Bad State	0.5	80	-10	=E7+F7	=MIN($D$4,G7)	=G7-H7
8
9		Expected Value of equity	=0.50*$40+0.50*$0
10			=D6*I6+D7*I7	=getformula(D10)
11
12		Hence Expected Value of equity is	=D10
13