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. Which option do you prefer?

Year 1	Year 2	Year 3	Year 4	Year 5	NPV
Buy	-25000	0	0	0	5000	($19,484.29)
Lease	-5000	-5000	-5000	-5000	-5000	($18,023.88)

Leasing has a less negative NPV, so it is more attractive.  If the
discount rate were lower, then buying would eventually be more
attractive.

Sincerely,

Wonko

"Go with the cash flow: Calculate NPV and IRR in Excel " Microsoft
(2005) http://office.microsoft.com/en-us/assistance/HA011136321033.aspx

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Request for Answer Clarification by shemrob-ga on 13 Jul 2005 08:47 PDT

This answer is incorrect please clarify your answer

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Clarification of Answer by wonko-ga on 13 Jul 2005 10:22 PDT

I initially formulated the problem the other way, and then decided I
had misread the question and changed it.  My apologies.

Sincerely,

Wonko

answer was not even close to be correct

While I agree that leasing is more attractive. I disagree with the
figures derived from the calculations.

I propose approaching the question as such:

       Year 0   Year 1   Year 2   Year 3   Year 4   Year 5   Present Value
Buy    (25,000)   -        -         -        -      5,000  (25,000) +
5000/(1.12)^5
Lease  (5,000)  (5,000)  (5,000)  (5,000)  (5,000)     -     5000 x (1
+ 1/(1.12) + 1/(1.12^2) + 1/(1.12^3) + 1/(1.12^4))

I say this because when you buy the car, you pay upfront (therefore
Year 0). But when you sell the car, you wait until the end of Year 5
before you sell it. Therefore you immediately lose $25000 in present
value whilst the $5000 you receive has to be discounted by 12% for 5
years.

When you lease, I assume you pay $5000 at the start of every year for
the car. So to use the car for Year 1, you would pay $5000 NOW, and to
use the car for Year 2, you would pay exactly one year later, etc.
This explains why you only discount the last payment at 12% for 4
years.

After you punch the numbers through the calculator, you get PV(buy) =
(22162.9) whilst PV(lease) = (20186.7)

Therefore, the rational individual must conclude that leasing is
preferable under these conditions. And yes, if the discount rate
falls, buying does become more attractive as an option. You can
substitute numbers into the workings shown above to show this (try
using a discount rate of 5%, you'll see), but a more impressive way
would be to use algebra (that's irrefutable proof).

You might want to consider asking for a refund from this guy. *laughs*
And please feel free to send feedback about me to Google Answers. I've
always wanted to be a Google Answers "expert".

Hi there, sorry, but I'm a stickler for detail. I notice I forgot to
put brackets around the 5000 figure when calculating the present value
of leasing. It's a payment so it should have brackets to indicate the
negative nature of cash flow. Apologies.

It should read (5000) x (1 + 1/(1.12) + 1/(1.12^2) + 1/(1.12^3) +
1/(1.12^4)) instead. Ok?

Best of luck in your studies.
Cheerio!

To mammonite, your answer is correct because it is the same answer my
professor has. Thank you. PLEASE SEE MY NEXT QUESTION AND SEE IF YOU
CAN ANSWER IT FOR ME. THANKS