You are considering buying or leasing a new latest BMW model. The Dealer offers

Question

You are considering buying or leasing a new latest BMW model. The Dealer offers you the following terms on a lease: Down Payment 10,000 Maturity 5 Years Annual Rate 6% Monthly Payment $200 made at the end of each period 1) What is the present value of all required payments under the lease contract? 2) A check of the Auto Lease Guide (ALG) reveals an anticipated depreciation of 7% per annum, if the current price is $35,000 what is the anticipated future value of the car, in 5-years? Consider depreciation as negative interest rate compounded yearly. 3) Suppose the dealer gives you the option to purchase the vehicle at the maturity of the lease for $21,000. How likely will you be to buy the car then? Explain and show your calculations. 4) If you could borrow and lend at a monthly compounded rate of 6%, would you rather buy or lease the BMW? Show your supporting calculations. 5) The sales manager emphatically argues that the down payment is too high and turns clients away. He proposes to change the policy to lower upfront and monthly payments so that the future value of these changes is $3,333 while increasing the option purchase price by the same amount. What should the management be concerned about and why? 6) The BMW dealer from informs you that monthly payments are due at the beginning of the month rather than at the end of the month as he has previously told you. You protest the changes and the dealer agrees to make you whole by adjusting the monthly payment. What monthly payment would the dealer require so that the present value of monthly payments is unchanged?

Explanation / Answer

1) Present value = Down Payment + Monthly Annuity*(1-(1+r/12)^-12n)/(r/12)

Present value = 10000 + 200*(1-(1+6%/12)^-(12*5))/(6%/12)

Present value = $ 20,345.11

2)

Anticipated future value of the car, in 5-years = 35000*(1-7%)^5

Anticipated future value of the car, in 5-years = $ 24,349.09

3)

Amount likely will you be to buy the car then = (35000-20345.11)*(1+6%/12)^(12*5)

Amount likely will you be to buy the car then = $ 19,767.25

4)

Cost of Buying = 35000

Cost of Leasing = PV of Lease + PV of Anticipated future value of the car, in 5-years

Cost of Leasing = 20345.11 + 24349.09/(1+6%/12)^(12*5)

Cost of Leasing = $ 38,396.85

Decision : You Should buy the BMW

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