Buy versus Lease. You can buy a car for $25,000 and sell it in 5 years
for $5,000. Or you can lease the car for 5 years for $5,000 a year.
The discount rate is 12 percent per year.
a. Which option do you prefer?
b. What is the maximum amount you should be willing to pay to lease
rather than buy the car

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Request for Question Clarification by joey-ga on 16 Jan 2005 13:17 PST

Is this a homework question?

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Clarification of Question by stinkatfigures-ga on 17 Jan 2005 06:31 PST

Yes, this is a homework question.

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Request for Question Clarification by omnivorous-ga on 18 Jan 2005 03:50 PST

Stinkatfigures --

It makes a big difference if it's a profitable corporation doing the
lease vs. buy decision because they can depreciate the vehicle.  It's
not in your assumptions for this problem but that's a real-world
issue.

Best regards,

Omnivorous-GA

a. You should take option of lease. The NPV of buying a car is -$4138
b. Maximum willing to pay for lease is $6,148.19 where NPV is zero.

A)
  0------1------2------3------4------5
25000                              5000

PVB = 25000-5000/(1.12)^5 = 22162.87

  0------1------2------3------4------5
5000   5000   5000   5000    5000

PVL = 5000(1-1/(1.12)^5)/(1-1/(1.12))= 20186.75


Diff in present values = 22162.87-20186.75=1976.12

Leasing in better

B)

22162.87 = pmt (1-1/(1.12)^5)/(1-1/(1.12))

pmt = 5490.28



I think the solution proposed to you by a11634 is if you were paying
the 5000 at the "end" of the year

thanks very much for the help!