Question

Dorothy & George Company is planning to acquire a new machine at a total cost of $30,600. The machine's estimated life is 6 years and its estimated salvage value is $600. The company estimates that annual cash savings from using this machine will be $8,000. The company's after-tax cost of capital is 8% and its income tax rate is 40%. The company uses straight-line depreciation (non-MACRS- based). (Use Appendix C, Table 1 and Appendix C, Table 2.) (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round "Payback period" to 2 decimal places and all other answers to the nearest dollar amount.) Required: 1. What is this investment's net after-tax annual cash inflow? 2. Assume that the net after-tax annual cash inflow of this investment is $5,000; what is the payback period in years? 3. Assume that the net after-tax annual cash inflow of this investment is $5,000; what is the net present value (NPV) of this investment? 4. What are the minimum net after-tax annual cost savings that make the proposed investment acceptable (i.e., the dollar cost savings that would yield an NPV of $0)? Net after-tax annual cash inflow 1. 2. Payback period Years Net present value 3. 4 Minimum net after-tax annual cost savings

Answer 1

Annual cash flows = (Cash savings – Depreciation)(1-Tax Rate) + Depreciation

= (8000 – 5000)(1-40%)+5000

= $6800

2. Payback period = Initial Investment/Annual cash flow

= 30,600/5000

= 6 years

Since 600 salvage value will be recovered at the end of year 6

3.NPV = Present value of cash inflows – Present value of cash outflows

= 5000*PVAF(8%, 6 years) + 600*PVF(8%, 6 years) – 30,600

= 5000*4.623 + 600*0.630 – 30,600

= -$7,107

4.Minimum = (30,600-378)/4.623 = $6,537.31