You are interested in a new Ford Taurus. After visiting your Ford dealer, doing your research on the best leases available, you have three options. (i) Purchase the car for cash and receive a $1,900 cash rebate from Dealer A. The price of the car is $19,000. (ii) Lease the car from Dealer B. Under this option, you pay the dealer $550 now and $225 a month for each of the next 36 months (the first $225 payment occurs 1 month from today). After 36 months you may buy the car for $10,900. (iii) Purchase the car from Dealer C who will lend you the entire purchase price of the car for a zero interest 36-month loan with monthly payments. The car price is $19,000. Suppose the market interest rate is 4%. What is the net cost today of the cheapest option?

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To find the net cost today of each option, we need to calculate the present value of the cash flows associated with each option. We will use the market interest rate of 4% to discount the future cash flows to their present values.

Option (i) - Purchase with cash and receive a $1,900 cash rebate from Dealer A:
The net cost today is the purchase price minus the cash rebate:
Net cost today = $19,000 - $1,900 = $17,100

Option (ii) - Lease the car from Dealer B and buy after 36 months:
We need to calculate the present value of all the lease payments and the future purchase price.
a) Lease payments: The lease payment of $225 occurs for each of the next 36 months, starting from one month from today. We can use the present value of an ordinary annuity formula to calculate the present value of these lease payments. Using the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r,

where PV is the present value, PMT is the monthly payment, r is the interest rate per period, and n is the number of periods, we can plug in the values:
PV of lease payments = $225 * (1 - (1 + 0.04/12)^(-36)) / (0.04/12) ≈ $7,342.94

b) Future purchase price: The price to buy the car after 36 months is $10,900.

The net cost today is the sum of the present value of lease payments and the future purchase price:
Net cost today = PV of lease payments + Future purchase price
Net cost today = $7,342.94 + $10,900 = $18,242.94

Option (iii) - Purchase from Dealer C with a zero-interest loan:
Since it is a zero-interest loan, the principal amount of the loan is equal to the purchase price of the car.
We need to calculate the present value of the monthly loan payments.
Using the formula for the present value of an ordinary annuity, we can calculate the present value of the loan payments:
PV of loan payments = $19,000 * (1 - (1 + 0.04/12)^(-36)) / (0.04/12) ≈ $19,000 * 0.0400418818 ≈ $760.77

The net cost today is the present value of the loan payments:
Net cost today = PV of loan payments = $760.77

Comparing the net cost today of each option:

Option (i): $17,100
Option (ii): $18,242.94
Option (iii): $760.77

Therefore, the cheapest option in terms of net cost today is Option (iii) - purchase from Dealer C with a zero-interest loan, with a net cost today of $760.77.