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# Leasing problems 22.2-22.7.doc

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Economics
Course
ECN 104
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Fall

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FIN401 – Solutions to Questions 2-7 in Chapter 22 (Editions 5 and 6) Note: Assume that all cash flows other than initial cost occur at the end of a period, unless otherwise state. Solutions to Questions 2-7 (Edition 6 ) Information: Initial Cost (IC) = \$2.5M, Before Tax Lease Payment (BTLP) = \$800K, Number of years = N=4, Before tax discount rate = .075, Tax rate = .37, After tax Lease Payment (ATLPA) = (800*(1-.37)) = \$504K, After tax discount rate (ATDR) = (.075*(1-.37)) = .04725, CCA rate = . 30 2. Should you lease or buy? You need to calculate the NAL and make a decision based on that information. NAL = + IC – PV(ATLP) – PV(CCATB) The PV(ATLP) is based on N=4, PMT=\$504,000, and r=.04725, …PV(ATLP) = 1,798,635 PV(CCATB) = [(Cdt)(r+d)][(1+.5r)/(1+r)] = [(\$2.5M*.3*.37)/(.04725+.3)][(1+.5(.04725))/ (1.04725)] = \$781,108 NAL = \$2.5M -\$1,798,635 - \$781,108 = -\$79,743 The NAL is negative. The firm should buy. 3. What are the cash flows from the lessor’s point of view, given a 37% tax rate? The cash flows are exactly the same, but reversed. NAL = - IC + PV(ATLP) + PV(CCATB) = \$79,743 4. What would the lease payment have to be for both the lessor and lessee to be indifferent to the lease? This question is asking us to calculate the Break-even lease payment. In order to answer this question, set the NAL = 0 (the point at which the lessee breaks even) and solve for the before-tax lease payment that sets the NAL equal to zero. NAL = + IC – PV(ATLP) – PV(CCATB) 0 = \$2.5M – PV(ATLP) - \$781,108 PV(ATLP) = \$2.5M - \$781,108 = \$1,718,892 We need to derive the annual after-tax lease payments from the PV(ATLP). So, given a PV(ATLP)=\$1,718,892, r=.04725, and N= 4, the PMT will be \$481,655 We have not yet quite solved the problem, because we were asked for the lease payment that we will make to the lessor (which is the before-tax lease payment, not the ATLP). If ATLP = BTLP(1-t), then BTLP = ATLP / (1-t) = \$481,655 / (1-.37) = \$764,532 5. What is the NAL if the lessee does not pay taxes? NAL = + IC – PV(ATLP) – PV(CCATB) PV(CCATB) = \$0, because you can only get a tax benefit if you pay taxes. NAL = \$2.5M – PV(ATLP) - \$0 The PV(ATLP) is based on N=4, PMT= BTLP*(1-t) = \$800K*(1-0) = \$800K, and r= BTDR(1-t) = . 075(1-0) = .075 …PV(ATLP) = 2,679,461 NAL = \$2.5M – \$2,679,461 - \$0 = -\$179,461 6. If the lessee does not pay any taxes and if the lessor has a 37% tax rate, what is the range of annual lease payments that will have a positive NAL for both parties? This question requires to piece together information from questions 2, 4 and 5. In question 4, we determined that the lessor would be indifferent if it received \$764,532 per year, but no less. In question 2 and 5, we determined that the lessee was even worse off if there were no taxes (NAL = -\$179,461 vs. - \$79,743). The lessee also had a breakeven lease payment (the maximum that it would pay) of \$764,532 based on a tax rate of .37. If the lessee is worse off paying no taxes, it must mean that its maximum breakeven lease payment paying no taxes would be less than \$764,532. If the lessor would never accept less than \$764,532, and the lessee would never even pay as much as \$764,532, it must mean that there is NO range of lease payments that will work. 7. What is the NAL if the CCA rate is 50%, not 30%? This question requires you to rework question 2 with a different CCA rate. I haven’t worked it out, but I know that a higher CCA rate will make for a higher PVCCA
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