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? <$579.72; $581.62>

IGNORE PART A. ONLY WORK ON (b)

(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)? <8.45%; 8.79%>

PLEASE indicate how to arrive at the 8.45% and 8.79%. Thank you.

Explanation / Answer

Present value of leasing cash flow: (i) Present value of upfront cost Let Interest rate is 12% = Upfront cost*Discount factor Monthly interest rate is 1% = 3000*1 = 3000 (ii) Present value of monthly lease payment for 36 months = Monthly Lease payment*cumulative discount factor = 400*30.108 Cumulative discount factor = 12043.2 = {1-(1+i)^-n}/i = {1-(1+.01)^-36}/.01 (iii) Present value of purchase cost at the end of lease period = 30.108 = Purchase cost*discount factor = 12000*.699 = 8388 Totalof (i) and (ii) and (iii) = 23431.2 Purchase cost 25000 Difference -1568.8 Present value of leasing cash flow: (i) Present value of upfront cost Let Interest rate is 6% = Upfront cost*Discount factor Monthly interest rate is .5% = 3000*1 = 3000 (ii) Present value of monthly lease payment for 36 months = Monthly Lease payment*cumulative discount factor = 400*32.871 Cumulative discount factor = 12043.2 = {1-(1+i)^-n}/i = {1-(1+.005)^-36}/.005 (iii) Present value of purchase cost at the end of lease period = 32.871 = Purchase cost*discount factor = 12000*.836 = 10032 Totalof (i) and (ii) and (iii) = 25075.2 IRR = .5+.5*75.2/75.2+1568.8 Purchase cost 25000 = 0.5229 Monthly = 6.2748 Annually Difference 75.2

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