Leases R Us, Inc. (LRU) has been contracted by Robotics of Beverly
Hills (RBH) to provide lease financing for a machine that would assist
in automating a large part of their current assembly line. Annual
lease payments will start at the beginning of each year. The purchase
price of this machine is $200,000, and it will be leased by RBH for a
period of 5 years. LRU will utilize straight line depreciation of
$40,000 per year with a zero book salvage value. However, salvage
value is estimated to actually be $35,000 at the end of 5 years. LRU
is required to earn a 14% after tax rate of return on the lease. LRU
uses a marginal tax rate of 40%. Calculate the annual lease payments.
(Remember, these payments are to be considered at the beginning of
each year ? annuity due.)

 
Please show me how to calculate this?

Muntzster --

You can calculate the lease payments in 3 steps ?

Step A: Calculate the Net Present Value (NPV) of the amount to be amortized.

Step B: Calculate the annual after-tax required lease income. By
taking your answer from Step A as an NPV then  use the number of years
and the required rate of return to get the required payment.

Step C: Calculate the lease payment by taking the answer from Step B
and adjusting for taxes.   You?ll divide it by (1 - the tax rate).

In Step A it?s very important to note that the salvage value of the
machine ($35,000) will get discounted for net present value (NPV) ?
but not for tax effects.

Why no taxes?  Because the leasing company is already showing a
-$40,000 income ? and the salvage simply reduces the loss.  In other
words, a company that?s losing money doesn?t have to worry about
paying taxes on any gains that are less than its losses.

The calculations in the three steps are all in this Excel spreadsheet,
which your browser should be able to read, even if you don?t have
Excel itself.  By netting up the year 5 salvage and depreciation, we
avoid the potential error mentioned in the previous paragraph.  If you
do have Excel, you can download and change the spreadsheet:

NPV Cash Flow
http://www.mooneyevents.com/npvlease1.xls

If you have any questions about these calculations, please let us know
via a Clarification Request.

Best regards,

Omnivorous-GA

---

Request for Answer Clarification by muntzster-ga on 02 Sep 2005 19:00 PDT

The market value is 2 million.

---

Clarification of Answer by omnivorous-ga on 02 Sep 2005 19:28 PDT

Tracy --

Thanks for the kind words and the extra sum.

I should point out that there's an alternate way to look at (and
answer) this question.  Depreciation could also be set up on the net
value of the project -- or $165,000 over the 5 years.

That's not the assumption in this question, of course.  And in real
life, projecting salvage value is no easier than projecting the
weather in 5 years, so it's rarely done this way.

Best regards,

Omnivorous-GA

Awesome job.  Thanks for helping me out.  Tracy