Question

Mark can purchase a new car for $35,000. Alternatively, in addition to a down payment of $2,600, Mark can make lease payments of $475 at the beginning of each month for three years to lease the car. The car has a residual value of $17,500. Assume that the cost of borrowing is 4.03% compounded monthly.

a. Which option is economically better for Mark?
(1).Buy Now
(2).Lease

Answer 1

The economically better option for Mark is to buy the car now (Option 1).

Step-by-step explanation:

To determine the economically better option, we compare the total costs associated with buying and leasing the car. For the buying option, Mark pays the full price of $35,000 upfront. For the leasing option, Mark makes a down payment of $2,600 and pays $475 per month for 36 months. Additionally, at the end of the lease term, there is a residual value of $17,500.

To calculate the total cost for each option, we need to consider the present value of future cash flows for the leasing option. The present value accounts for the time value of money, given the cost of borrowing of 4.03% compounded monthly.

By comparing the total present value of costs for both options, it is evident that buying the car now is economically better for Mark. The calculations involve discounting future cash flows to their present value, considering the borrowing cost and the residual value of the leased car.

In summary, the buy now option is economically preferable for Mark, as it involves a one-time payment of the full price without the added costs associated with leasing and interest payments.

Answer 2

A comparison between leasing and buying a car for Mark involves calculating the total leasing cost with the down payment and monthly payments versus the outright purchase price. Leasing's total cost does not consider the borrowing cost, while the buying option may incur interest if financed. The incorrect interest calculation on the lease indicates that a further investigation into borrowing costs for both options may be necessary to make an accurate decision.

Step-by-step explanation:

To determine whether leasing or buying a new car is more economically favorable for Mark, we need to compare the total costs associated with both options. For the lease, we consider the initial down-payment plus the sum of all monthly payments, and compare it with the cost of purchasing the car outright.

Mark has the option to buy the car for $35,000 or to lease it with a $2,600 down payment and $475 monthly payments for three years. For the lease option, there are 36 payments (3 years * 12 months per year), and the total cost of leasing then becomes:

Initial down payment: $2,600
Monthly payments: $475 * 36 = $17,100

Adding these together gives a total lease cost of $2,600 + $17,100 = $19,700. However, this does not take into account the residual value and the cost of borrowing. Since the residual value is $17,500, Mark does not actually pay for this portion through the lease, only for the depreciation (difference between the initial value and residual value).

For buying, Mark pays the $35,000 outright. If Mark has to borrow this amount, there will also be interest incurred at a rate of 4.03% compounded monthly. This would lead to a different computation where the total cost of borrowing would need to be compared with the lease option.