Question

please show work that is easy to UNDERSTAND

3. A machine is purchased for S70,000. Life is 10 years with a S 10,000 salvage. MARR is 10%, and the tax rate is 50%. Cash operating costs are $4500 per year. Five year MACRS (20, 32, 19.2. 11.52, 11.52,5.76) depreciation will be used. Calculate the annual equivalent revenue requirements for this machine.

Answer 1

Solution:

Given

Initial investment = $70,000

Straight line depreciation in each year = (Investment – Salvage) ÷ Life

                                                            = ($70,000 - $10,000) ÷ 5

                                                            = $12,000

After tax cash flows for first five years = -$4,500 - (-$4,500 - $12,000) × (1-0.50)

                                                              = -$4,500 + $8,250

                                                              = $3,750

After tax cash flows for subsequent five years = -$4,500 – (-$4,500 × 0.50)

                                                                        = -$2,250

Net present value (NPV) is the difference between the present values of after tax cash flows and the initial investments.

NPV = {($3,750 × 3.7908) + (-$2,250 × 2.3538) + ($10,000 × 0.3855)} - $70,000

        = {$14,215.5 -$5,296.05 + $3,855} - $70,000

        = -$57,225.55

Equivalent annual cost = MARR (NPV) [(1 + MARR)^year / {(1 + MARR)^year -1}]

                                     = 0.1(-$57,225.55) [(1.1)^10 / (1.1)^10 -1]

                                     = -9,313.29

The annual equivalent revenue requirement would be $9,313.29