Unformatted text preview: discount rate may be appropriate, we’ll use the aftertax cost of debt to discount the residual value as is common in practice. Setting the NAL equal to zero: NAL = 0 = $7,000,000 – X(1.0594)(PVIFA5.94%,5) – 476,000(PVIFA5.94%,5) – 700,000/1.05945 X = $999,374.14 So, the maximum pretax lease payment is: Pretax lease payment = $999,374.14/(1 – .34) = $1,514,203.24 11. The security deposit is a cash outflow at the beginning of the lease and a cash inflow at the end of the lease when it is returned. The NAL with these assumptions is: NAL = $7,000,000 – 500,000 – 1,089,000 – $1,089,000(PVIFA5.94%,4) – $476,000(PVIFA5.94%,5) + $500,000/1.05945 NAL = –$1,364.10 With the security deposit, the firm should buy the equipment since the NAL is less than zero. We could also solve this problem another way. From Problem 9, we know that the NAL without the security deposit is $123,947.57, so, if we find the present value of the security deposit, we can simply add this to $123,947.57. The present value of the security deposit is: PV of security deposit = –$500,000 + $500,000/1.05945 = –$125,311.67 So, the NAL with the security deposit is: NAL = $123,947.57 – 125,311.67 = –$1,364.10 12. The lessee is paying taxes, so will forego the depreciation tax shield if it leases the equipment. The depreciation tax shield for the lessee is: Depreciation tax shield = ($2,600,000 / 6)(.25) Depreciation tax shield = $108,333.33 427 The aftertax cost of debt for the lessee is: Aftertax debt cost = .09(1 – .25) = .0675 Using all of this information, we can calculate the maximum pretax lease payment for the lessee as: NAL = 0 = $2,600,000 – PMT(1 – .25)(PVIFA6.75%,6) + $108,333.33(PVIFA6.75%,6) PMT = $577,243.94 For the lessor, the depreciation tax shield is: Depreciation tax shield = ($2,600,000 / 6)(.40) Depreciation tax shield = $173,333.33 The aftertax cost of debt for the lessor is: Aftertax debt cost = .09(1 – .40) = .0540 Using all of this information, we can calculate the minimum pretax lease payment for the lessor as: NAL = 0 = $2,600,000 – PMT(1 – .40)(PVIFA5.40%,6) + $173,333.33(PVIFA5.40%,6) PMT = $575,805.54 13. a. Since both companies have the same tax rate, there is only one lease payment that will result in a zero NAL for each company. We will calculate cash flows from the depreciation tax shield first. The depreciation tax shield is: Depreciation tax shield = ($475,000/3)(.34) = $53,833.33 The aftertax cost of debt is: Aftertax debt cost = .10(1 – .34) = .0660 Using all of this information, we can calculate the lease payment as: NAL = 0 = $475,000 – PMT(1 – .34)(PVIFA6.60%,3) + $53,833.33(PVIFA6.60%,3) PMT = $190,674.18 428 b. To generalize the result from part a: Let T1 denote the lessor’s tax rate. Let T2 denote the lessee’s tax rate. Let P denote the purchase price of the asset. Let D equal the annual depreciation expense. Let N denote the length of the lease in years. Let R equal the pretax cost of debt. The value to the lessor is: ValueLessor = − P + ∑
t =1 N L(1 − T1 ) + D(T1 ) [1 + R(1 − T1 )]t And the value to the lessee is: ValueLessee = P − ∑
t =1 N L(1 − T2 ) + D(T2 ) [1 + R(1 − T2 )]t Since all the values in both equations above are the same except T1 and T2 , we can see that the values of the lease to its two parties will be opposite in sign only if T1 = T2. c. Since the lessor’s tax bracket is unchanged, the zero NAL lease payment is the same as we found in part a. The lessee will not realize the depreciation tax shield, and the aftertax cost of debt will be the same as the pretax cost of debt. So, the lessee’s maximum lease payment will be: NAL = 0 = –$475,000 + PMT(PVIFA10%,3) PMT = $191,004.53 Both parties have positive NAL for lease payments between $190,674.18 and $191,004.53. 14. The decision to buy or lease is made by looking at the incremental cash flows. The loan offered by the bank merely helps you to establish the appropriate discount rate. Since the deal they are offering is the same as the market-wide rate, you can ignore the offer and simply use 9 percent as the pretax discount rate. In any capital budgeting project, you do not consider the financing which was to be applied to a specific project. The only exception would be if a specific and special financing deal were tied to a specific project (like a lower-than-market interest rate loan if you buy a particular car). 429 a. The incremental cash flows from leasing the machine are the lease payments, the tax savings on the lease, the lost depreciation tax shield, and the saved purchase price of the machine. The lease payments are due at the beginning of each year, so the incremental cash flows are: Year 0 Lease: Lease payment Tax savings on lease Lost dep. tax shield Equipment cost –$1,500,000 525,000 5,100,000 $4,125,000 The aftertax discount rate is: Aftertax discount rate = .09(1 – .35) Aftertax discount rate = .0585 or 5.85% So, the NAL of leasing is: NAL = $4,125,000 – $1,421,500(PVIFA5.85%,3) – $446,250 / 1.05854 NAL = –$40,065.81 Since the NAL is negative, the company should buy the equipment. – –$1,421,250 $1...
View Full Document