exercise: Financing your vehicle: pay cash, take out a loan or to rent out? You intend to own or lease a vehicle for 42 months consider the following 3 vehicle financing options: a BMW i25 Ci 2-D Coupe 20 5. Option A: Buy the vehicle at the regular price of $32,508 and pay for it for 42 months, in equal monthly installments, at a nominal interest rate of 5.65%, compounded monthly. Option B: Purchase the vehicle by cash payment, at the reduced price of $31,020. Option C: Lease the vehicle for 42 months. 

element	debt financing	cash payment	rental agreement
price	32 508,00	31 020,00	32 508,00
advance payment	4 500,00	0	0
r(%)	5,65%
monthly payment	736,53		513,76
duration(months)	42		42
costs			994,00
amount due at the end of the contract			395,00
purchase option at the end of the contract			17 817,00
amount due on signature	4 500,00	31 020,00	1 507,76

The table in the excel file on sheet Prob 3 lists the items interest of each option. For each option, the fees associated with permits, property rights and registration, as well as taxes and insurance, are additional costs. Regarding the rental option, the tenant must provide $1507.76 to the signature. This amount payable upon signature includes the payment of the first month's rental of $513.76 and administrative fees of $994. The interest rate rental is based on 60,000 km during the term of the contract. Additional charges of $0.18 per kilometer will apply for each kilometer traveled beyond 60,000 km. No security deposit is required; however, alienation costs of $395 are payable at the end of the contract, the date on which the lessee has the option of buying the car for $17,817. the renter is also responsible for excessive wear and use. If the funds that are to be used to purchase the vehicle are currently earning interest annual of 4.5% compounded monthly, which financing option turns out to be the most advantageous?

Explanation: In the case of a rental contract, you pay the part of the vehicle you plan to use. At the end of the contract, all you have to do is return the vehicle to the dealership and pay a disposal fee agreed. With traditional financing, your monthly payment is calculated based on the vehicle's total value of $32,508, and you will be owner of the vehicle at the end of the financing. Since you are comparing the options over a period of 42 months, you must explicitly take into account the unused portion (resale value) of the vehicle at the end of the contract. In others terms, you must consider the resale value of the vehicle in order to determine the net cost of ownership. As resale value, you could use the $17817 mentioned by the dealer in the lease option. You then have to ask yourself if it is possible to get such a resale value after 42 months of use. Note that the nominal interest rate of 5.65% represents the interest rate that the concessionaire uses in calculating loan payments. Account given an interest rate of 5.65%, your monthly payments will be A = $32,508 - $4,500) (A/P, 5.65%/12.42) = $736.35. However, it should also be noted that the nominal rate of 4.5% represents your discount rate. In other words, if you don't buy the vehicle, your money continues to earn at that rate of 4.5%. Therefore, the 4.5% rate represents your opportunity cost associated with the purchase of the car. So what is the interest rate to use for your to analyse? Obviously, the 4.5% rate is the appropriate rate to use. Show your calculations in your working document.