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 of all the required payments under the lease will be

10000 +200 ((1- (1+0.06/12)^-60)/.06/12) =$ 20345 {Using Pv of annuity formula taking Pmt--$200

i=0.06/12 &n=5*12=60}

2) Anticipated Future Value of the car will be

Amt.= Current price (1+i) ^n [i= -0.07 ; n=5

=35000( 1+ -0.07)^5 =$24349

3)Since the Future Value as calculated as per (2) above ie $24349 exceeds $21000

I am likely to buy the car.

4) Current Cost price=$35000

   PV of lease =$20345

Considering the cost of borrowing @ 6% (comp.mthly) I would lease the BMW

5) increasing the option purchase price (BUY option) & decreasing the lease price by the same amount

(both FutureValue) will encourage people to choose the LEASE option more. BUYING option may be

discouraged.

   6) The dealer wants to change the payment terms from end of the month to beginning of the month. With this change, the customers will lose one month interest on the instalment. Since the dealer wants to give effect of the interest in the monthly payments @ 6% p.a. for one month, the interest works out to $ 1 per month ($ 200 (1+.06/12). Hence the reduction in the monthly payment with the change is $ 1/-. The customer will have to pay a monthly instalment of $ 199 (200-1)

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