Question

Ultra Co. is considering two mutually exclusive projects, both of which have an economic service life of one year with no salvage value. The initial cost and the net-year-end revenue for each project are given in the following table:

	Project 1		Project 2
Initial Cost	$1,200		$1,000
	Probability	Revenue	Probability	Revenue
Net Revenue given in PW	0.25	$1,800	0.3	$2,400
	0.35	$2,200	0.3	$1,600
	0.15	$3,500	0.2	$2,700
	0.25	$2,600	0.2	$2,800

Assuming both projects are statistically independent of each other,

1. Calculate the expected value for each project.
2. Calculate the variance for each project.
3. Which project should be chosen? Why?

Answer 1

a.

Expected Value for each project
Project 1			Project 2
Probability	Revenue	Expected Value	Probability	Revenue	Expected Value
0.25	$    1,800	$                                       450	0.3	$    2,400	$                                       720
0.35	$    2,200	$                                       770	0.3	$    1,600	$                                       480
0.15	$    3,500	$                                       525	0.2	$    2,700	$                                       540
0.25	$    2,600	$                                       650	0.2	$    2,800	$                                       560
		$                                   2,395			$                                   2,300

b. The variance between the two projects:

Project 1 has more expected value by $95 and more initial cost by $200

Net variance is $105

c. Project 2 should be chosen because it has a net benefit of $1,300 ($2300-$1000). while Project 1 has a net benefit of $1195 ($2395-1200)