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.)

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Clarification of Question by yolira-ga on 26 Oct 2004 12:50 PDT

I'm hoping that someone might be able to help me with this problem.  

Thanks in advance...

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Request for Question Clarification by omnivorous-ga on 26 Oct 2004 14:11 PDT

Yolira --

This is not too tough, except for tax factors:
1.  often first-year depreciation is limited to 1/2 year, especially
in accelerated depreciation cases.  Is that the case here -- or should
we take a full-year's depreciation during the year?  And do we assume
that it comes at year-end -- or that taxes get paid during the year,
so we can offset income with tax savings?

2.  when we recoup the salvage value at the end, is it subject to
normal taxation at 40%?  Or could we claim it as a long-term holding,
reducing taxes to half their normal rate (which is how U.S. tax code
would handle it)?

Sorry to make this harder than it is but timing assumptions can be
everything in PV problems.

Best regards,

Omnivorous-GA

Yolira --

There are two common ways to figure this problem out: one using NPV of
cash flows and the other using Internal Rates of Return, trying to get
the 5 lease payments to yield an IRR of 14%.

I'm going to use the former because IRR gets hidden by lots of things
when you use a spreadsheet.

The first thing that you should do is set up an Income Statement to
account for cash flows.  You'll start with Year 0 -- using that to
represent what happens TODAY.  Year 1 will be cash flows at the end of
that year -- and so on through Year 5.  I've timed depreciation to
MATCH income because while you and I pay taxes at the end of the year,
a corporation is paying them quarterly.

You'll see the income statement here for all 5 years -- but note that
there's no lease payment:
PV Lease: Income Statement
http://www.mooneyevents.com/pvlease1.xls


In the above spreadsheet, which should appear in your browser AND be
downloadable to your own system, you'll see that there are NO lease
payments.
However, when we enter lease payments -- so it's not surprising that
there's a BIG negative NPV to all of the cash flows.

What's our objective now?  Add in equal annual lease payments on line
5 to get an NPV of zero!  We've already figured in our minimum hurdle
of 14%.  Now we want an NPV of each year's cash flows to get back to
zero -- which is the precise definition of IRR:
"Intermediate Financial Management," (Ramana Sonti)				
http://business.kent.edu/courses/spring02/Fin/36054/lecture_notes/chapter6.htm

"An easy way of thinking about IRR is to define it as the rate that
forces the NPV of the project to zero," notes Prof. Sonti.

---

Let's see what happens if we make the lease payments simply match the
depreciation, so that there's no income each of the first 4 years:
http://www.mooneyevents.com/pvlease2.xls

Not surprisingly, the NPV is still strongly negative (but it gives us
a chance to check the integrity of our calculations).

----

So let's try to generate some profit here by making the lease payments
$80,000 per year:
http://www.mooneyevents.com/pvlease3.xls

We're still running a negative NPV because of the enormous first-year
outlay and the high discount rate of 14%!

----

It's not until you get monthly lease payments over the $120,500 level
that the NPV goes above zero:
http://www.mooneyevents.com/pvlease4.xls


Why is it this way?
1.  the high up-front capital outlay
2.  the conservative straight-line depreciation (today's tax law is
much more liberal, allowing a double-declining balance AND an
investment tax credit)
3.  and the high 14% return rate (with a prime rate around 5%, leasing
companies today would seek something like a 9% return).

As always, if there are any questions about what's been done here,
please contact the researcher with a clarification request before
rating this answer.

Best regards,

Omnivorous-GA

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Clarification of Answer by omnivorous-ga on 27 Oct 2004 03:20 PDT

Yolira --

The previous versions of the spreadsheet didn't account for CASH IN properly.

The correct lease payment should be $53,860.

See these three corrected spreadsheets, with lease payments of $0,
$40,000 and $53,860 respectively.  As you'll see, the last spreadsheet
gets us to an NPV close to zero with the discount rate of 14%:
http://www.mooneyevents.com/pvlease1.xls

http://www.mooneyevents.com/pvlease2.xls

http://www.mooneyevents.com/pvlease3.xls

My apologies for the mistake on the calculation: I woke up this
morning and realized that the lease payments were WAY too high and
re-checked the calculations to find the mistake.

Best regards,

Omnivorous-GA

Omnivorous-ga...what can I say, I've seen some of the help you've
provided in the past and you are an incredible resource.  I appreciate
the help.  I especially like the Excel work.  I'm a big fan of Excel
and the tables make comprehension much easier.  Outstanding work!  I
suspect I'll be using yout talents again in the future...

Cheers

Your Step A calculations are not correct. Year 0 NPV is  ($200,000
because is occurs immediately. You need to move depreciation expense
to years 1-5, instead of starting in year 0.

You calculated tax expense for depreciation, not the effect of the tax
shield. Same concept with the salvage value.

You have the cash flow correct for salvage value in Year 5. Salvage
value is cash inflow and taxes are an outflow. The net cash flow is
the difference between them.