Question

12-6. Rockyford Company must replace some machinery that has zero book value and a current market value of $3,000. One possibility is to invest in new machinery costing $52,000. This new machinery would produce estimated annual pretax cash operating savings of $20,800. Assume the new machine will have a useful life of 4 years and depreciation of $13,000 each year for book and tax purposes. It will have no salvage value at the end of 4 years. The investment in this new machinery would require an additional $4,200 investment of net working capital. (Assume that when the old machine was purchased, the incremental net working capital required at the time was $0.)

If Rockyford accepts this investment proposal, the disposal of the old machinery and the investment in the new one will occur on December 31 of this year. The cash flows from the investment are expected to occur over a four-year period.

Rockyford is subject to a 40% income tax rate for all ordinary income and capital gains and has a 8% weighted-average after-tax cost of capital. All operating and tax cash flows are assumed to occur at year-end. (For Parts 2 and 3, use the relevant table from Appendix C–Table 1 or Table 2.)

Required:

1. Determine the after-tax cash flow arising from disposing of the old machinery.

2. Determine the present value of the after-tax cash flows for the next 4-years attributable to the cash operating savings.

3. Determine the present value of the tax shield effect of depreciation for year 1.

Answer 1

1.

After-tax cash flow arising from disposing of the old machinery

= $3,000 * (1 - tax rate)

= $3,000 * (1 - 40%)

= $1,800

2.

After-tax cash flows for each of the next four years attributable to the cash operating savings

= $20,800 * (1 - 40%) = $12,480

present value of the after-tax cash flows for the next four years attributable to the cash operating savings

= $12,480 *  PVIFA (8%, 4)

= $12,480 * 3.312

= $41,333.76 or $41,334

3.

Tax shield effect of depreciation = Depreciation * Tax rate

= $13,000 * 40%

= $5,200

Present value of the tax shield effect of depreciation for year 1 = $5,200 * PVIF (8%,1)

= $5,200 * 0.925

= $4,810