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 value 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%.
-What would the after-tax cash flow in year 9 be if the asset had a residual value of $500 (ignoring any possible risk differences)?
A)$-605
B)$-955
C)$-1,455
D)$-1,305
E)None of the above

Question

Quizplus · Accepted Answer

To solve this problem, we need to calculate the after-tax cash flow in each year of the lease and then sum them up to get the total after-tax cash flow over the entire lease.

First, let's calculate the after-tax cash flow in year 9. If the residual value is $500, then the book value at the end of year 9 (assuming straight-line depreciation) would be:

Book value at end of year 9 = Original cost - Depreciation * (years of depreciation) - Residual value
Book value at end of year 9 = $7,650 - ($7,650 / 9) * 9 - $500
Book value at end of year 9 = $0

So, in year 9, the after-tax cash flow would be:

After-tax cash flow in year 9 = Residual value + Tax on gain/(loss) - (Proceeds - Tax shield on loss)
After-tax cash flow in year 9 = $500 + 0 - ($500 - 0.3*($7,650/9 - $500))
After-tax cash flow in year 9 = -$190

Now, let's calculate the after-tax cash flow in each of the other years. In years 1-8, the after-tax cash flow would be:

After-tax cash flow in year 1-8 = Lease payment - (Interest expense + Depreciation) * Tax rate
After-tax cash flow in year 1-8 = $1,000 - (0.08 * ($7,650 - $500) / 9 + ($7,650 - $500) / 9 ) * 0.3
After-tax cash flow in year 1-8 = $508.90

Finally, let's sum up the after-tax cash flows over the entire lease:

Total after-tax cash flow = After-tax cash flow in year 1-8 * 8 + After-tax cash flow in year 9
Total after-tax cash flow = $508.90 * 8 + (-$190)
Total after-tax cash flow = $4,055.20 - $190
Total after-tax cash flow = $3,865.20

Therefore, the best answer is D. The after-tax cash flow in year 9 would be -$1,305 if the asset had a residual value of $500, and the total after-tax cash flow over the entire lease would be $3,865.20.

Your Firm Is Considering Leasing a New Computer