Decision Analysis Comparing Automobile Leases You are inter

Decision Analysis -- Comparing Automobile Leases

You are interested in leasing a Toyota Corolla. There are three local car dealers that are offering different financial terms for the three-year lease as shown in the following table:

Dealers

Fixed Monthly Cost

Allowable Annual Miles

Cost Per Mile Below Allowable Annual Miles

Cost per Mile Above Allowable Annual Miles

Alissa

$205.00

5,000 miles

$0.60 for the first 5,000 miles

$0.70 for each mile over 5,000

Becky

$225.00

15,000 miles

$0.55 for the first 15,000 miles

$0.70 for each mile over 15,000

Christine

$200.00

10,000 miles

$0.50 for the first 10,000 miles

$0.75 for each mile over 10,000

The leases differ based on the fixed monthly payment and the cost per annual miles. Please note that the cost per annual miles is a disjoint function with one cost for miles below the allowable annual miles and a different cost for miles above the allowable annual miles.

Since you do not know with certainty the number of annual miles that you will travel, you decide to construct a payoff table for your cost of the three-year leases for each of the three dealers for the five estimated number of annual miles given in the table below. Round the calculations for the payoffs to the nearest dollar.

Hint #1: To calculate the values in the payoff table, first calculate your annual cost and then multiply by the years in the lease. Be careful of the different units of time stated in the problem.

Hint #2: In a payoff table, revenues are positive and costs are negative.

Payoff Table

P(5,000) = 0.10

P(10,000) = 0.15

P(15,000) = 0.20

P(20,000) = 0.25

P(25,000) = 0.30

Dealer

5,000 mi/yr

10,000 mi/yr

15,000 mi/yr

20,000 mi/yr

25,000 mi/yr

Alissa

Becky

Christine

Dealers	Fixed Monthly Cost	Allowable Annual Miles	Cost Per Mile Below Allowable Annual Miles	Cost per Mile Above Allowable Annual Miles
Alissa	$205.00	5,000 miles	$0.60 for the first 5,000 miles	$0.70 for each mile over 5,000
Becky	$225.00	15,000 miles	$0.55 for the first 15,000 miles	$0.70 for each mile over 15,000
Christine	$200.00	10,000 miles	$0.50 for the first 10,000 miles	$0.75 for each mile over 10,000

Solution

Firstly we will take the case of Alissa

Fixed payment for 3 years = 205*12*3 = $7380

For the case 0f 5000mi/yr

     Total variable cost = 0.60*5000*3 = $9000

Total cost = $(7380+9000) = $16380

For the case of 10000mi/yr

Total cost = $7380 + 0.60*5000*3 + 0.70*(10000-5000)*3 = $26880

For the case of 15000mi/yr

Total cost = $7380 + 0.60*5000*3 + 0.70*(15000-5000)*3 = $37380

For the case of 20000mi/yr

Total cost = $7380 + 0.60*5000*3 + 0.70*(20000-5000)*3 = $47880

For the case of 25000mi/yr

Total cost = $7380 + 0.60*5000*3 + 0.70*(25000-5000)*3 = $58380

Similary we can calculate the cost for the other two cases.

The updated table

	P(5000) = 0.10	P(10,000) = 0.15	P(15,000) = 0.20	P(20,000) = 0.25	P(25,000) = 0.30
Dealer	5,000 mi/yr	10,000 mi/yr	15,000 mi/yr	20,000 mi/yr	25,000 mi/yr
Alissa	16,380	26,880	37,380	47,880	58,380
Becky	16,350	24,600	32,850	43,350	53,850
Christine	14,700	22,200	33,450	44,700	55,950