Question

You are considering two projects with the following cash flows:

	Project Y	Project X
Year 1	$9,500	$6,000
Year 2	$9,000	$6,900
Year 3	$6,900	$9,000
Year 4	$6,000	$9,500

Which one of the following statements is true concerning the two projects given a positive discount rate?

	A.	Project Y has both a higher present value and a higher future value than project X.
	B.	Both projects have the same future value at the end of year 4.
	C.	Project X has a higher present value at time zero than project Y
	D.	Both projects have the same present value at time zero.

Answer 1

The statement that is true is "A" - Project Y has both a higher present value and a higher future value than project X.

Calculations:

Here i have assumed a positive discount rate of 10% for both the projects and computed both the project's present value and future value:

Year	Y's cash flow	X's cash flow	1+r	PVIF = 1/(1+r)^n	PV of Y	PV of X
1	9500	6000	1.10	0.9091	8,636.36	5,454.55
2	9000	6900		0.8264	7,438.02	5,702.48
3	6900	9000		0.7513	5,184.07	6,761.83
4	6000	9500		0.6830	4,098.08	6,488.63
				NPV	25,356.53	24,407.49

FV of Y = 9500*1.1^3 + 9000*1.1^2 + 6900*1.1 + 6000

= 37,124.50

FV of X = 6000*1.1^3 + 6900*1.1^2 + 9000*1.1 + 9500

= 35,735