Objective:

I$\text{'}$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 $430i$

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.$

${?}^1$ APR or annual percentage rate in any loan is the interest rate you should use to calculate the

monthly payments of the loan. For example, if you finance for $60$ months a $$50k$ BMW with $4\%$ APR, the

monthly payment can be calculated using the $"m"$ version of the formula to get $C$ where $PV$ is $50k,m$ is

$12,t$ is $5,$ and $r$ is $0\mathrm{.}04.$

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?