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?

Answer 1

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