a) To find the after-tax cash flow from leasing relative to the after-tax cash flow from purchasing in years 1-9, we consider two components: The after-tax cash flow from lease payments and the after-tax cash flow from depreciation tax shield.
First, we need to calculate the after-tax lease payments:
- Lease payments = $1,000
- Tax benefit from lease payments = $1,000 × 30% = $300
- After-tax lease payments = $1,000 - $300 = $700
Second, we calculate the after-tax cash flow from the depreciation tax shield:
- Annual depreciation = Total cost of the asset ÷ useful life = $7,650 ÷ 9 = $850
- Tax savings from depreciation expense = $850 × 30% = $255
Now, we can compare the leasing and purchasing cash flows:
- After-tax cash flow from leasing = -$700 (negative because it's an outflow)
- After-tax cash flow from purchasing = +$255 (positive because it's a tax saving)
The difference between the two is:
- After-tax cash flow from leasing relative to purchasing = -$700 - $255 = -$955 in years 1-9.
b) In year 0, the after-tax cash flow from leasing would be -$1,000 (the first lease payment) whereas the after-tax cash flow from buying the asset would be -$7,650. The difference between the two is:
- After-tax cash flow from leasing relative to purchasing = -$1,000 - (-$7,650) = +$6,650 in year 0.
c) To calculate the NPV of the lease relative to the purchase, we need to discount the cash flows and calculate the present value:
- Years 1-9 cash flows discount factor: (1 - (1 + 8%)^(-9)) / 8% = 5.985
- NPV of after-tax leasing cash flows relative to purchasing year 1-9: -$955 * 5.985 = -$5,715.03
- NPV of after-tax leasing cash flows relative to purchasing year 0: $6,650
Total NPV of the lease relative to the purchase:
- NPV of the lease = $6,650 - $5,715.03 = $934.97
d) If the asset had a residual value of $500, the after-tax cash flow in year 9 would be:
- After-tax cash flow from selling the asset = $500 × (1 - 30%) = $350.
So, the after-tax cash flow in year 9 would be $350 if the asset had a residual value of $500 (ignoring any possible risk differences).
Your firm is considering leasing a new computer. The lease lasts for 9 years. The lease calls for 10 payments of $1,000 per year with the first payment occurring immediately. The computer would cost $7,650 to buy and would be straight-line depreciated to a zero salvage over 9 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 8%. The corporate tax rate is 30%.
a) What is the after-tax cash flow from leasing relative to the after-tax cash flow from purchasing in years 1-9?
b) What is the after-tax cash flow from leasing relative to the after-tax cash flow from purchasing in year 0?
c) What is the NPV of the lease relative to the purchase?
d) What would the after-tax cash flow in year 9 be if the asset had a residual value of $500 (ignoring any possible risk differences)?
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