4. The following are two popular approaches used by automobile dealers: (a) Cash

Question

4. The following are two popular approaches used by automobile dealers:

(a) Cash Rebate Versus Low Rate Dealer Financing You are given two mutually exclusive options from the dealer on a $20,000 car:

(i) $1,500 cash rebate or (ii) 36-month low rate loan at 3% APR. The prevailing APR on 36-month auto loan from a typical bank is 8%. Which option is a better deal?

(b) Buying Versus Leasing You are interested in a $25,000 car. A simplified leasing contract includes the following:

(i) up-front cost of $3,000,

(ii) $400 monthly lease payment over a 36-month period, and

(iii) purchase cost of $12,000 at the end of the lease.

What are the “implied” APR and EAR of the lease? Should you lease the car or buy and finance the car with a loan from the bank in (a)?

Explanation / Answer

(a) (1)

_________________________________________________________

                                                                            CASH REBATE              

DEALER PRICE OF CAR                                      $20,000                                         

lESS CASH REBATE                                                1,500                                       

PURCHASE PRICE                                                18,500                                             -     

LOAN COMPONENT                                              18,500                                                

MONTHLY PAYMENT                            A = P X (r(1+r)n/(1+r)n- 1                   

Rate of interest                                         8% p.a or 0.00667 p.m                        

No. of payments ie n                                             36 months                                   

Loan amount i.e P                                                 $18,500                                  

A= monthly payment =18,500 x (0.00667 (1+0.00667)36)/(1+0.00667)36-1;

                                  = 18,500 x 0.00847349115/0.27038847916 = $579.75

LOW RATE LOAN @ 3% p.a          

LOAN AMOUNT $20,000

RATE OF INTEREST = 3% p.a or 0.0025 p.m

No.of payments = 36      

A=P x (r(1+r)n / (1+r)n- 1 ; A = monthly payment; P = loan amount; r= rate of interest; n= no. of period                                                                                   

A = 20,000 x (0.0025(1+0.0025)36 /(1+0.0025)36- 1    

   = 20,000 x 0.0027351285/0.09405140063 = $581.62  

RESULT: UNDER REBATE, MONTHLY PAYMENT IS $579.75, WHERE AS UNDER LOW RATE LOAN IT IS $581.62; HENCEE, IT IS BETTER TO GO FOR REBATE AND BANK LOAN @ 8% P.A      

(b) Buying cost                = $ 25,000; Loan amount $25,000;

     Monthly payment (A) = P x (r(1+r)36/(1+r)36- 1

                                       = 25,000 x (0.00667(1+0.00667)36/(1+0,00667)36 - 1

                                       = 25,000 x (0.00847349115/0.27038847916)

                                      = $783.46

Total payment under loan option = 783.46 x 36 = $28,204.56

Total payment under lease option :

    Up-front cost $3,000 + Monthly payment @ 400 x 36 = 14,400 + purchase cost at the end $ 12,000 = $29,400   

Hence, it is better to buy the car by taking a loan of $25,000 rather than taking by lease as it cost more by $ 1195.44 (i.e $29,400 - 28,204.56)    

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