Objective:

I$$d like to buy a brand$-$new BMW $430$i convertible at the end of this year $(2023),$ keep the car for $5$ years, and sell it after that $($at the end of $2029).$ I have two different alternatives to finance this BMW$.$ You are tasked to determine which alternative is the best $($cheapest$)$ way. Below, I describe each of the alternatives along with all the information you need. To clarify timing, I want to sign the papers today $($December of $2023)$ so that I have the car starting in January $2024.$

Alternative $1$:

I can finance this BMW with the BMW dealership of Eugene. BMW of Eugene provides qualified customers, with excellent credit history, financing for up to $60$ months on any new $2024$ BMW $430$i Convertible model with $5\mathrm{.}29\%$ APR$1.$ The $2024$ BMW $430$i Convertible that I have picked has MSRP of $$58,100\mathrm{.}00,$ excluding tax, shipment, title, and license. I plan to put a down payment of $$1,000$ at the

beginning and finance the rest of the MSRP with the given APR for $60$ months. The dealership also offers a $$1,500$ credit against the MSRP if I use this alternative $($it means that $$1,500$ off the price$).$ After $5$ years, I plan to sell the car. To get an idea of how much I can sell the car for in five years, I looked up the current selling price of a $2019$ model of a similar BMW on Carmax. The $2019$ model is currently priced at $$28,990.$Therefore, assume that I can sell my BMW at the end of $2029$ for $$28,990.$

a$)$ Report the cash flow chart of this alternative.

b$)$ Calculate the net present value of ownership with this alternative, if the discount rate to calculate the net present value of the cash flow is $3\mathrm{.}5\%$ APR with monthly compounding. Note that the APR in the main part of the prompt above should be used to calculate the financing payments $($the monthly payments$)$ and the discount rate should be used to calculate the present values of the cash flows.

Alternative $2$:

I can lease the BMW for $36$ months and give it back at the end of the lease term. Then, lease a new model for the next $24$ months and give it back at the end of $2029.$ This way, I will have a BMW for the next $5$ years, like alternative $1.$ Lease is available on new $2024$ BMW $430$i Convertible models to qualified customers with excellent credit history. For the model I picked with MSRP of $$58,100\mathrm{.}00,$ I must put a down payment of $$3,000$ plus a destination and handling fee of $$925$ at the beginning $($today$).$ The monthly lease payments are $$724$ per month for $36$ months. After $36$ months $($in December $2027),$ I will turn in the $2024$ model and lease new BMW $430$i Convertible for $24$ months $($until the end of $2029).$ The

lease agreement is very similar to the first one. I must put a down payment of $$3,000$ plus a destination and handling fee of $$925$ at the beginning. However, since it is my second lease, I receive a $$1,500$ credit against my down payment which reduces it to only $$1,500.$ The monthly lease payments are $$620$ per month for $24$ months. At the end of $2029,$ I turn in the car and walk away.

a$)$ Report the cash flow chart of this alternative.

b$)$ Calculate the net present value of ownership with this alternative, if the discount rate to calculate the net present value of the cash flow is $3\mathrm{.}5\%$ APR with monthly compounding.

Bottom line:

Based on your answers in part b of each alternative, which alternative is the less expensive way to own a BMW $430$i Convertible for five years? Lease or finance?

THANK YOU!