Question

A company can buy a machine that is expected to have a three-year life and a $23,000 salvage value. The machine will cost $1,772,000 and is expected to produce a $193,000 after-tax net income to be received at the end of each year. If a table of present values of $1 at 12% shows values of 0.8929 for one year, 0.7972 for two years, and 0.7118 for three years, what is the net present value of the cash flows from the investment, discounted at 12%?

Multiple Choice

• $108,245

• $568,728

• $618,627

• $692,890

• $1,880,245
  
  

  A company is considering the purchase of a new machine for $59,000. Management predicts that the machine can produce sales of $17,100 each year for the next 10 years. Expenses are expected to include direct materials, direct labor, and factory overhead totaling $6,900 per year including depreciation of $5,100 per year. Income tax expense is $4,080 per year based on a tax rate of 40%. What is the payback period for the new machine?

  Multiple Choice

• 3.45 years.

• 6.48 years.

• 5.26 years.

• 11.57 years.

• 33.91 years.

Answer 1

Answer 1)

Calculation of Net Present Value

Net Present Value = Present value of cash inflows – Present value of cash outflows

                                   = $ 1,880,245 - $ 1,772,000

                                   = $ 108,245

Therefore the net present value of investment is $ 108,245.

Working Note:

Calculation of Present value of cash inflows

Present value of cash inflows = (Annual cash flow in Year 1 X Present value factor at 12% for year 1) + (Annual cash flow in Year 2 X Present value factor at 12% for year 2) + (Annual cash flow in Year 3 X Present value factor at 12% for year 3) + (salvage in Year 3 X Present value factor at 12% for year 3)

                             = (776,000 X 0.8929) + ($ 776,000 X 0.7972) + ($ 776,000 X 0.7118) + ($ 23,000 X 0.7118)

                              = $ 692,890.40 + $ 618,627.20 + $ 552,356.80 + $ 16,371.40

                               = $ 1,880,245

Calculation of annual depreciation expense:

Annual depreciation expense = (Original cost – salvage value)/ number of years of useful life of the machine

                                                              = ($ 1,772,000 - $ 23,000)/ 3 years

                                                              = $ 583,000

Calculation of annual cash inflows:

Annual cash inflows = Annual net income after tax + annual depreciation expense

                                      = $ 193,000 + $ 583,000

                                       = $ 776,000

Answer 2)

Calculation of Payback period

Payback period = Initial investment in machine/ Annual cash inflows from machine

                               = $ 59,000/ $ 11,220

                               = 5.26 years

Therefore payback period of machine is 5.26 years

Working Note:

Calculation of annual cash inflows from machine:

Annual cash inflows = Annual net income after tax + annual depreciation expense

                                      = $ 6,120 + $ 5,100

                                       = $ 11,220

Calculation of Annual net income after tax

Annual net income after tax = Annual sales – Annual expenses – Income tax expense

                                                     = $ 17,100 - $ 6,900 - $ 4,080

                                                      = $ 6,120