1. Consider the graph above. Suppose that the discount factor is 0.85. What is the optimal present value for the initial node A? (Assume that cash flows occur at the beginning of periods.)

Highlight the optimal path in the graph.

	A.	31.56
	B.	35.63
	C.	36.45
	D.	38.91
	E.	None of the above.

2. A company has $10M to invest. There are three possible alternatives of investment: The i^th alternative requires an investment of C_i and gives benefits with a present value of P_i. The following table provides values, in millions of dollar, of C_i and P_i for the alternatives.

Alternative,i	Investment Ci	Present Value of Benefits Pi
1	4	7
2	7	14
3	6	11

Suppose you make a decision based on the benefit-cost ratio analysis. Then you will invest in alternative (or alternatives):

	A.	2 only
	B.	3 only
	C.	1 only
	D.	1, 2 and 3
	E.	1 and 3 only
	F.	2 and 3 only

o 35 2 B 10F 32 6 2 C 8 27 3 10 5 13 30