Jessica Walsh is interested in leasing a well-equipped 6-cylinder Toyota Camry XSE and has contacted four dealers - Brooklyn Toyota, Hopkins Toyota, Baldwin Toyota, and Zangwill Toyota for pricing information. Each dealer has offered Jessica a closed end 32 year (42-month) lease with different down payments, different lease turn in fee, excess mileage fee and monthly lease charges. The information is provided in the table below. Mileage Lease Turn in Down Payment Monthly Lease Payment Allowance over Fee due at end Excess Mileage Cost per mile 42 months of the lease Brooklyn Toyota $2,500 $275 42,000 $400 $0.22 Hopkns Toyota $3,000 $309 48,000 SO $0.25 Baldwin Toyota $2,400 $310 54,000 $700 $0.25 Zangwill Toyota $2,600 $295 60,000 $200 $0.20 Notes: 1) Down payment is due at the beginning of the lease. 2) Monthly lease payments are due at the beginning of every month. 3) Lease Turn In fee is due at the end of the lease term. 4) Excess mileage charge is payable at the end of lease term for miles more than the allowed maximum, and no credit is given if the miles is less than allowed maximum. Jessica wants to choose the lease option that will minimize the total cost. Total Cost = sum of all costs. For example, If Jessica leases from Baldwin Toyota, and drives 54,000 miles over the lease term, total cost will be = $2,400 for down payment + {310(42) or $13,020} for lease payments + $700 turn in fee + {0.25(54,000-54000) or $0} for excess mileage fee = $16,120. Note that the cost computations are not adjusted for time value of money. Jessica's difficulty in making the correct decision lies in the uncertainty related how many miles she may drive over 3.5 years. She captures the situation as three distinct states of nature - drive 36,000 miles, drive 45,000 miles or drive 54,000 miles. She thinks that there is a 70% chance she will drive 36,000 miles, a 20% chance that she will drive 45,000 miles and a 10% chance that she will drive 54,000 miles. That information is shown below. Total Miles Driven in 3 years 36,000 45,000 54,000 Probability 70% 20% 10% a. Identify what is the decision and what is the chance event. Construct a payoff table for Jessica's problem. The payoff table will be all costs. b. Construct the decision tree. Make sure key elements are shown including Expected Values. What should Jessica do? c. If the probabilities change from 70/20/10 to 40/40/20, what would be the optimal decision? d. If the probabilities change from 70/20/10 to 10/60/30, what would be the optimal decision? For parts c and d, you don't have to show the decision tree - just give the correct decision and the Expected Value associated with the decision by filling in the table below. Best decision Dealer EV Cost in $ Case 1(7/2/1) Case 2(4/4/2) Case 3(1/6/3) Jessica Walsh is interested in leasing a well-equipped 6-cylinder Toyota Camry XSE and has contacted four dealers - Brooklyn Toyota, Hopkins Toyota, Baldwin Toyota, and Zangwill Toyota for pricing information. Each dealer has offered Jessica a closed end 32 year (42-month) lease with different down payments, different lease turn in fee, excess mileage fee and monthly lease charges. The information is provided in the table below. Mileage Lease Turn in Down Payment Monthly Lease Payment Allowance over Fee due at end Excess Mileage Cost per mile 42 months of the lease Brooklyn Toyota $2,500 $275 42,000 $400 $0.22 Hopkns Toyota $3,000 $309 48,000 SO $0.25 Baldwin Toyota $2,400 $310 54,000 $700 $0.25 Zangwill Toyota $2,600 $295 60,000 $200 $0.20 Notes: 1) Down payment is due at the beginning of the lease. 2) Monthly lease payments are due at the beginning of every month. 3) Lease Turn In fee is due at the end of the lease term. 4) Excess mileage charge is payable at the end of lease term for miles more than the allowed maximum, and no credit is given if the miles is less than allowed maximum. Jessica wants to choose the lease option that will minimize the total cost. Total Cost = sum of all costs. For example, If Jessica leases from Baldwin Toyota, and drives 54,000 miles over the lease term, total cost will be = $2,400 for down payment + {310(42) or $13,020} for lease payments + $700 turn in fee + {0.25(54,000-54000) or $0} for excess mileage fee = $16,120. Note that the cost computations are not adjusted for time value of money. Jessica's difficulty in making the correct decision lies in the uncertainty related how many miles she may drive over 3.5 years. She captures the situation as three distinct states of nature - drive 36,000 miles, drive 45,000 miles or drive 54,000 miles. She thinks that there is a 70% chance she will drive 36,000 miles, a 20% chance that she will drive 45,000 miles and a 10% chance that she will drive 54,000 miles. That information is shown below. Total Miles Driven in 3 years 36,000 45,000 54,000 Probability 70% 20% 10% a. Identify what is the decision and what is the chance event. Construct a payoff table for Jessica's problem. The payoff table will be all costs. b. Construct the decision tree. Make sure key elements are shown including Expected Values. What should Jessica do? c. If the probabilities change from 70/20/10 to 40/40/20, what would be the optimal decision? d. If the probabilities change from 70/20/10 to 10/60/30, what would be the optimal decision? For parts c and d, you don't have to show the decision tree - just give the correct decision and the Expected Value associated with the decision by filling in the table below. Best decision Dealer EV Cost in $ Case 1(7/2/1) Case 2(4/4/2) Case 3(1/6/3)
