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Q: Present Value Lease Problem—Calculating Annual Payments ( Answered 5 out of 5 stars,   2 Comments )
Subject: Present Value Lease Problem—Calculating Annual Payments
Category: Business and Money > Finance
Asked by: sting44-ga
List Price: $5.00
Posted: 11 Apr 2005 01:13 PDT
Expires: 11 May 2005 01:13 PDT
Question ID: 507739
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.)

Hints for students:

There are 3 major steps that need to be accomplished in order to
calculate the annual lease payment.

Step A: You need to calculate the amount to be amortized. This would
be the cost of the machine less the PV of the after tax salvage value
of the machine and less the PV of the depreciation tax shield

Step B: You need to calculate the annual after-tax required lease
income. (Remember, in this step, you need to calculate it as an
annuity due?a beginning of the year payment.) Take your answer from
Step A as a present value, and using the number of years and the
required rate of return, calculate the payment.

Step C: Calculate the lease payment. You need to adjust for the
appropriate tax rate. Therefore, take your answer in Step B and divide
it by (1 - the tax rate). This will give you the required lease
Subject: Re: Present Value Lease Problem—Calculating Annual Payments
Answered By: omnivorous-ga on 11 Apr 2005 15:09 PDT
Rated:5 out of 5 stars
Sting44 ?

The following 3 spreadsheets do this problem step-by-step, as it?s set
up in the question.  NH786 in the comment is close ? but is off
slightly, perhaps because of the timing of lease payments.  They?re
made at the START of each year.

STEP A: Amount to be amortized.  In the attached Excel spreadsheet
(which is viewable in your browser, even if you don?t have the
Microsoft program), it is:

So, the NPV of the lease/purchase is -$126,474.

STEP B, C: Let?s set up the spreadsheet with the tax payments, as
noted in C to see how close we get with $40,000 per year:

As you can see in the spreadsheet above, NPV is still negative ?
indicating that the lease isn?t high enough.  You can save this
spreadsheet and replace line 5 with $60,000, you?ll find that it?s too
high.  But at $53,860, you?ll get an NPV of zero ? your precise lease

Best regards,

sting44-ga rated this answer:5 out of 5 stars and gave an additional tip of: $2.00
Excellent answer.

Subject: Re: Present Value Lease Problem—Calculating Annual Payments
From: nh786-ga on 11 Apr 2005 14:01 PDT
a)Present value of tax sheild(40000*40%=16000) per year  for 5 years =
54,929.3 (can be easily found using excels NPV function)
b)Present value of salvage value 5 years hence = 35000*.6 = 21000/1.14^5 = 10906.75
c) cash outflow today = -200,000

Net amorization amoount = a+b+c above = -134,163.96

Using excel's PMT function get the yearly amount 
=Pmt(14%,5,-134163.96,0,1) = 34,280.49

Now this is the return  after tax
Before tax lease payment will be = 34,280.49/0.60 = 57,134.14
Subject: Re: Present Value Lease Problem—Calculating Annual Payments
From: dclmwop-ga on 01 May 2005 00:10 PDT
Hmmm.  Interesting.  I haven't had time to go through Omnivorous's
spreadsheets in detail yet, but I am already confused about the timing
of the depreciation.  Although lease payments are made in the
beginning of each year, wouldn't the effects of depreciation still
start in Year 1, instead of Year 0?  nh786's present value of the
depreciation tax shield seems correct to me.

Also, sting44's question states, for Step A, that the amount equals
"cost of the machine less the PV of the after tax salvage value of the
machine and less the PV of the depreciation tax shield."  Is that
correct, or should the PV of the after-tax salvage value be ADDED to,
rather than subtracted from, the cost?  Both Omnivorous's answer and
nh786's comment seems to suggest the value should be added -- which,
btw, makes sense to me.

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