Jodi wants to lease a new car and start a part time business to give people car
ID: 364811 • Letter: J
Question
Jodi wants to lease a new car and start a part time business to give people car rides. She has contacted three automobile dealers for pricing information. Each dealer offered Jodi a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The three dealers provided the details about the monthly lease cost, the mileage allowance, and the cost for additional miles.
Jodi is not sure how many miles she will drive over the next three years for this business but she believes it is reasonable to assume that she will drive 10,000 miles per year, 15,000 miles per year, or 20,000 miles per year. With this assumption, Jodi estimated her total profit for the three lease options. The three lease options and the associated profits for each option are given below:
Dealer 10000 Miles 15000 Miles 20000 Miles
A $10000 $10000 $ 8000
B $ 7500 $11000 $10500
C $ 8500 $ 9000 $ 8800
Determine the optimal decision to lease the car from a dealer and the profit associated with it by using the following decision criteria.
a. Maximax
b. Maximin
c. Equal likelihood
d. Minimax regret criterion.
Explanation / Answer
a) Maximax criteria
Dealer
Three lease options
Maximum of rows
10000 miles
140000 miles
18000 miles
A
$7000
$10500
$13500
$13500
Maximax
B
$8500
$11500
$11000
$11500
C
$10000
$9500
$9800
$10000
The maximax profit is $13500 when selected dealer A for 18000 miles
b) Maximin criteria
Dealer
Three lease options
Minimum of rows
10000 miles
140000 miles
18000 miles
A
$7000
$10500
$13500
$7000
B
$8500
$11500
$11000
$8500
C
$10000
$9500
$9800
$9500
Maximin
The maximin profit is $9500 when selected dealer C for 14000 miles
c) Equal likelihood
Dealer
Three lease options
Maximum of rows
A
Minimum of rows
B
P = XA + (1-X)B
10000 miles
140000 miles
18000 miles
A
$7000
$10500
$13500
$13500
$7000
$12200
B
$8500
$11500
$11000
$11500
$8500
$10900
C
$10000
$9500
$9800
$10000
$9500
$9900
Where X is a co-efficient of optimism and is assumed to be 0.8
The equal likelihood profit is $12200 when selected dealer A
d) Minimax regret criteria
Dealer
Three lease options
Maximum of rows
10000 miles
140000 miles
18000 miles
A
$3000
$1000
0
$3000
B
$1500
0
$2500
$2500
Minimax
C
0
$2000
$3700
$3700
note: select maximum value from the column and subtract.
The minimax profit is $2500
a. Compute the expected value for each decision and select the best one.
Expect value (A) = 0.5*$7000 + 0.3*$10500 + 0.2*$13500 = $9350
Expect value (B) = 0.5*$8500 + 0.3*$11500 + 0.2*$11000 = $9990
Expect value (C) = 0.5*$10000 + 0.3*$9500 + 0.2*$9800 = $9810
Therefore, in accordance to expected value dealer B can be selected.
b. Compute the expected regret value for each decision and select the best one.
Regret table:
Dealer
Three lease options
10000 miles
140000 miles
18000 miles
A
$3000
$1000
0
B
$1500
0
$2500
C
0
$2000
$3700
Expect regret value (A) = 0.5*$3000 + 0.3*$1000 + 0.2*$0 = $1800
Expect regret value (B) = 0.5*$1500 + 0.3*$0 + 0.2*$2500 = $1250
Expect regret value (C) = 0.5*$0 + 0.3*$2000 + 0.2*$3700 = $1340
Since the expected regret value for B is very less which is the best alternative
c. Calculate and interpret the expected value of perfect information(EVPI)
EVPI = Epected payoff under certainity(EPC) – Max of expected value
EPC = 0.5*$10000 + 0.3*$11500 + 0.2*$13500 = $11150
Max. of expected value = $9900
EVPI = $11150 - $9900 = $1250
EVPI is equal to Expected regret value of B. Hence B is the best alternative.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.