Question

Tamera graduated from college and found a job as an online marketing specialist in a social networking company. Within a year, she saved $2000 and was determined to buy a new car. However, she was unsure as to whether she should lease it or buy it by financing the amount from a bank. A car salesman at the showroom gave her the following table illustrating the comparison of the lease vs. finance options for the car she liked. "Additional purchase costs include freight \& PDI, Air Conditioner Tax, Tire Tax, and registration fees. Assume that money was worth 5.5% compounded annually. a. Which option would be economically better for Tamera? b. Which option would be economically better if the residual value was $15,500 (including HST) for the lease option? c. What size of equal, beginning-of-month lease payments (including HST) would make the lease option economically equivalent to the finance option? Assume the original residual value and the term is still 48 months.

Answer 1

To determine the economically better option for Tamera, we need to calculate the present value of both the lease and finance options. By comparing the present values, we can determine which option is economically better. Additionally, we can calculate the size of the lease payments that would make the lease option economically equivalent to the finance option by setting the present value of the lease payments equal to the present value of the finance option.

Step-by-step explanation:

When comparing the lease and finance options for buying a new car, there are several factors to consider. First, let's determine the economically better option for Tamera. To do this, we need to calculate the present value of both options using the given interest rate of 5.5% compounded annually. Next, we can compare the present values to see which option is lower.

a. To determine the present value of the lease option, we need to calculate the present value of the lease payments, which are equivalent in size and paid at the beginning of each month. We can use the formula for the present value of an annuity to calculate this. The present value of the lease payments is the annuity of $x paid over 48 months, with the interest rate of 5.5%. We can solve for x by setting the present value of the lease payments equal to the present value of the finance option, which is $2000. By solving this equation, we can find the size of the equal, beginning-of-month lease payments that would make the lease option economically equivalent to the finance option.

b. If the residual value for the lease option is $15,500, we need to adjust the present value of the lease payments to reflect this. The present value of the lease payments is the annuity of $x paid over 48 months, with the interest rate of 5.5%. We can solve for x by setting the present value of the lease payments plus the present value of the residual value equal to the present value of the finance option. By solving this equation, we can find the size of the equal, beginning-of-month lease payments that would make the lease option economically equivalent to the finance option.

c. To determine the size of the equal, beginning-of-month lease payments that would make the lease option economically equivalent to the finance option, we need to set the present value of the lease payments plus the present value of the residual value equal to the present value of the finance option. We can solve this equation to find the value of x, which represents the size of the lease payments.