Question

Consider a new car costing $25,000. The dealer offers you $2,500 cash back (net price $22,500) if you buy the car paying in full (Option A) or 0% financing for 5 years with 10% down up front (Option B).

a) What will your monthly payments be
under the dealer’s 0% financing option. Don’t forget the 10% down,
and assume that the car will be paid off after five years (your
60^{th} equal payment).

b) At what interest rate are the two options (A and B) equivalent?

c) Your answer to part ‘b’ determines your course of action (whether you take the cash back or take the 0% financing). Explain by considering the following four scenarios: 1) you have sufficient funds sitting in a bank account earning 2%; 2) you must borrow all needed funds at a rate of 6%; 3) you have sufficient funds sitting in a bank account earning 6%; 4) you must borrow all needed funds at a rate of 2%. For each scenario, state whether it is more economical to take the cash back (Option A), or the 0% financing (Option B)

Answer #1

(a) | Loan amount = | 25000 x (1-10%) | ||||

22500 | ||||||

Interest rate = | 0 | |||||

N = | 5 x 12 = | |||||

60 | ||||||

Monthly payments = | Loan amount/PVAF(r,n) | |||||

22500/60 | ||||||

375.00 | ||||||

(b) | Let the rate be r= | |||||

22500 = | 2500 + 375xPVAF(r,60) | |||||

20000 = | 375 PVAF(r,60) | |||||

PVAF(r,60) = | 53.33333 | |||||

r | PVAF(r,60) | |||||

1.00% | 44.9550 | |||||

r | 53.3333 | -6.6667 | ||||

0.00% | 60.0000 | -15.0450 | ||||

0.443116 | ||||||

Using linear interpolation - | ||||||

r-0/1-0 | (53.3333-60)/(44.9550-60) | |||||

r-0/1-0 | 0.44 | |||||

r-0 = | 0.44 | |||||

r = | 0.44 | |||||

Approx | ||||||

(C ) | If interest rate is more then the indifference rate then option B should be selected. | |||||

1 | 2% | Option B | ||||

2 | 6% | Option B | ||||

3 | 6% | Option B | ||||

4 | 2% | Option B | ||||

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