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Q: Present Value Lease Problem—Calculating Annual Payments ( Answered ,   2 Comments )
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 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 payment.```
 Subject: Re: Present Value Lease Problem—Calculating Annual Payments Answered By: omnivorous-ga on 11 Apr 2005 15:09 PDT Rated:
 ```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: http://www.mooneyevents.com/pvlease1.xls 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: http://www.mooneyevents.com/pvlease2.xls 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 amount: http://www.mooneyevents.com/pvlease3.xls Best regards, Omnivorous-GA```
 sting44-ga rated this answer: and gave an additional tip of: \$2.00 `Excellent answer.`

 ```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```
 ```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.```