Question

For the following problem you should provide your answers and show work (if you want) in the spaces below each part of the question.

DrillCorp. is considering the purchase of a new drill press to replace the one currently being used. The old press is expected to last another 5 years and have no salvage value. The old press has a current book value of $5,000 and can be sold today for $4,500.
The new drill press costs $19,500 and has an expected useful life of 5 years. Salvage value in year 5 is expected to be $2,000. The new machine is expected to save the company $6,000 per year before taxes.
DrillCorp. uses straight-line depreciation and pay taxes at the rate of 40 percent. The appropriate discount rate is 12 percent. Assume that the sale price minus the book value of sold equipment is treated as a taxable gain (or loss, if negative). Also, assume that the tax consequences of any sales are recognized at the time of the sale (i.e., year 0 in this case.)
a. If the old machine is replaced, what is the incremental effect on the firm's after-tax cash flow in year 0?
b. What are the additional (years 1-5) incremental cash flow effects of the replacement?
c. What is the net present value of making the replacement? Should the company replace the old press?

Answer 1

The incremental effect on the firm's after-tax cash flow in year 0 of replacing the old drill press with a new one is -$15,200. The additional incremental cash flow effects of the replacement in years 1-5 are as follows: $2,200 in each year. The net present value (NPV) of making the replacement is $675.99, indicating that the company should replace the old press with the new one.

Step-by-step explanation:

The incremental effect of replacing the old drill press with a new one can be calculated by comparing the cash inflow and outflow in year 0. In this case, the cash outflow is the cost of the new drill press ($19,500), and the cash inflow is the sale value of the old drill press ($4,500). However, the sale value is treated as a taxable gain, so it needs to be adjusted for taxes. The taxable gain is the difference between the sale value ($4,500) and the book value ($5,000), which is -$500. With a tax rate of 40%, the tax on the gain is -$200. Therefore, the incremental effect on the firm's after-tax cash flow in year 0 is: -$19,500 + $4,500 - $200 = -$15,200.

The additional incremental cash flow effects of the replacement in years 1-5 can be calculated by subtracting the annual savings from the tax shield on depreciation. For each year, the annual savings are $6,000 and the tax shield on depreciation is calculated as the depreciation expense ($19,500 - $2,000) multiplied by the tax rate (40%). The incremental cash flow effects in years 1-5 are as follows: Year 1: $6,000 - ($19,500 - $2,000) * 0.40 = $2,200; Year 2: $6,000 - ($19,500 - $2,000) * 0.40 = $2,200; Year 3: $6,000 - ($19,500 - $2,000) * 0.40 = $2,200; Year 4: $6,000 - ($19,500 - $2,000) * 0.40 = $2,200; Year 5: $6,000 - ($19,500 - $2,000) * 0.40 = $2,200.

The net present value (NPV) of making the replacement takes into account the time value of money. It is calculated by discounting all the incremental cash flows to the present value and summing them up. The appropriate discount rate is 12%. The present value of the incremental cash flows in years 1-5 are: PV1 = $2,200 / (1 + 0.12)^1 = $1,964.29; PV2 = $2,200 / (1 + 0.12)^2 = $1,749.14; PV3 = $2,200 / (1 + 0.12)^3 = $1,559.20; PV4 = $2,200 / (1 + 0.12)^4 = $1,383.04; PV5 = $2,200 / (1 + 0.12)^5 = $1,219.32. The NPV is the sum of these present values minus the initial cash outflow: NPV = -$15,200 + $1,964.29 + $1,749.14 + $1,559.20 + $1,383.04 + $1,219.32 = $675.99. Since the NPV is positive, the company should replace the old press with the new one.