Question

Ten firms are considering taking on risky projects. For each, if the project is not successful, it will fail, and the firm will earn $0. Probabilities of success, and payoffs if the projects are successful, are described in the below table:

Firm	Probability of Success (Otherwise, Failure)	Payoff if Successful
A	80%	$5,300
B	70%	$4,800
C	90%	$7,200
D	82%	$5,600
E	100%	$6,500
F	72%	$5,000
G	80%	$5,500
H	94%	$6,850
I	75%	$5,750
J	90%	$6,100

Use Excel to calculate the expected value for each firm’s project (5 points total). Then assume that each firm’s manager will experience utility as described by the following utility function as a result of undertaking the project:

U=4?V

Use Excel to calculate expected utility for each firm’s manager

Answer 1

Firm	Probability of Success	Payoff if Successful	Expected Payoff
A	80%	5,300	5,300*0.8= 4,240
B	70%	4,800	4800*0.7=3360
C	90%	7,200	7200*0.9=6480
D	82%	5,600	5600*0.82=4592
E	100%	6,500	6500
F	72%	5,000	5,000*0.72=3600
G	80%	5,500	0.8*5500=4400
H	94%	6,850	0.94*6850=6439
I	75%	5,750	5750*0.75=4312.5
J	90%	6,100	6100*0.9=5490

Utility

A=4*(4240)^1/2 = 260.46

B = 4*(3360)^1/2 = 231.86

C = 4*(6480)^1/2 = 321.99

D=4*(4592)^1/2 = 271.05

E = 4*(6500)^1/2 = 322.49

F = 4*(3600)^1/2 = 240

G = 4*(4400)^1/2 = 265.32

H = 4*(6439)^1/2 = 320.97

I = 4*(4312.5)^1/2 = 262.67

J = 4*(5490)^1/2 = 296.37