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I 9/2/2006
Chapter 20. Solution to Ch 20-06 Build a Model
As part of its overall plant modernization and cost reduction program, Western Fabrics' management has decided to install a new automated weaving loom. In the capital budgeting analysis of this equipment, the IRR of the project was found to be 20% versus the project's required return of 12%. The loom has an invoice price of $250,000, including delivery and installation charges. The funds needed could be borrowed from the bank through a 4-year amortized loan at a 10% interest rate, with payments to be made at the end of each year. In the event that the loom is purchased, the manufacturer will contract to maintain and service it for a fee of $20,000 per year paid at the end of each year. The loom falls in the MACRS 5-year class, and Western's marginal federalplus-state tax rate is 40%. Gardial Automation Inc., maker of the loom, has offered to lease the loom to Westen for $70,000 upon delivery and installation (at t=0) plus 4 additional annual lease payments of $70,000 to be made at the ends of Years 1 through 4. (Note that there are 5 lease payments in total.) The lease agreement includes maintenance and servicing. Actually, the loom has an expected life of eight years, at which time its expected salvage value is zero; however, after 4 years, its market value is expected to equal its book value of $42,500. Tanner-Woods plans to build and entirely new plant in 4 years, so it has no interest in either leasing or owning the proposed loom for more than that period. a. Should the loom be leased or purchased? First, we want to lay out all of the input data in the problem. INPUT DATA Invoice Price Length of loan Loan Interest rate Maintenance fee Tax Rate Lease fee Equipment expected life Expected salvage value Market value after 4 years Book value after 4 years $250,000 4 10% $20,000 40% $70,000 8 $0 $42,500 $42,500
First, we can determine the annual loan payment that must be made on the new equipment. We will do so using the function wizard for PMT. Annual loan payment = Year Beginning loan balance Interest payment Principal payment Ending loan balance $78,868 1 $250,000 $25,000 $53,868 $196,132 2 $196,132 $19,613 $59,254 $136,878 3 $136,878 $13,688 $65,180 $71,698 4 $71,698 $7,170 $71,698 $0
Now, we see that the decision being made is whether to purchase the equipment at a net cost of $250,000 (with annual payments of $78,868) or lease the equipment and make annual payments of $70,000. To make this decision, we must analyze the incremental cash flows.
Now, we see that the decision being made is whether to purchase the equipment at a net cost of $250,000 (with annual A B D E H payments of $78,868) or lease theC equipment and make annual payments ofF$70,000. To G make this decision, we mustI 55 analyze the incremental cash flows. 56
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Before proceeding with our NPV analysis we must determine the schedule of depreciation charges for this new equipment. MACRS 5-year Depreciation Schedule Year 1 2 Depr. Rate 20% 32% Depr. Exp. $50,000 $80,000
3 19% $47,500
4 12% $30,000
5 11% $27,500
6 6% $15,000
We can now construct our table of incremental cash flows from these two alternatives. Remember, that the appropriate discount rate in this scenario is the after tax cost of borrowing, or: 10%*(1-40%) = 6%. NPV LEASE ANALYSIS OF INCREMENTAL CASH FLOWS Year = Cost of ownership Purchase cost Loan proceeds After-tax interest payment Principal payment Maintenance cost Tax savings from maintenance cost Tax savings from depreciation Salvage value Net cash flow from ownership PV cost of ownership Cost of leasing Lease payment Tax savings from lease payment Net cash flow from leasing PV cost of leasing Cost Comparison PV ownership cost @ 6% PV of leasing @ 6% Net Advantage to Leasing 0 ($250,000) $250,000 ($15,000) ($53,868) ($20,000) $8,000 $20,000 $0 ($185,112) ($60,868) ($11,768) ($59,254) ($20,000) $8,000 $32,000 ($51,022) ($8,213) ($65,180) ($20,000) $8,000 $19,000 ($66,393) ($4,302) ($71,698) ($20,000) $8,000 $12,000 $42,500 ($33,500) 1 2 3 4
($70,000) $28,000 ($42,000) ($187,534)
($70,000) $28,000 ($42,000)
($70,000) $28,000 ($42,000)
($70,000) $28,000 ($42,000)
($70,000) $28,000 ($42,000)
($185,112) ($187,534) ($2,423)
Our NPV Analysis has told us that there is a negative advantage to leasing. We interpret that as an indication that the firm should forego the opportunity to lease and buy the new equipment.
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A B C D E F G H I b. The salvage value is clearly the most uncertain cash flow in the analysis. Assume that the appropriate salvage value pre-tax discount rate is 15 percent. What would be the effect of a salvage value risk adjustment on the decision? All cash flows would remain unchanged except that of the salvage value. Our new array of cash flows would resemble the following: Standard discount rate Salvage value rate Year = Net cash flow PV of net cash flows NPV of ownership New Cost Comparison PV ownership cost @ 6% PV of leasing @ 6% Net Advantage to Leasing 10% 15% 0 $0 $0 ($188,667) 1 ($60,868) ($57,422) 2 ($51,022) ($45,410) 3 ($66,393) ($55,744) 4 ($76,000) ($60,199) 4 $42,500 $30,108
($188,667) ($187,534) $1,133
Under this new assumption of using a greater discount factor for the salvage value, we find that the firm should lease, and not buy, the equipment. c. Assuming that the after-tax cost of debt should be used to discount all anticipated cash flows, at what lease payment would the firm be indifferent to either leasing or buying? We will use the Goal Seek function to determine the lease payment that makes the Net Advantage to Leasing zero. Crossover = 69,096