1. First, calculate annual net cash flow:
Determine increase in after-tax net income:
Labor savings: 10,000 hours @ $5.50 per hour $55,000
Other operating savings 4,000
Annual cash savings before tax 59,000
Less: annual depreciation expense 20,000
Increase in net income before tax 39,000
Less: Increase in annual income tax @ 40% 15,600
Increase in net income after tax $23,400
Then, add back depreciation expense (noncash):
Increase in net income after tax $23,400
Plus annual depreciation expense 20,000
Annual net cash flow $43,400
Payback period equals cost of new machine divided by annual net cash flow or
$200,000 / $43,400 = 4.6 years.
2. The rate of return on average investment equals the increase in net income after
tax divided by the amount of the average investment.
The average investment would be $200,000 / 2, or $100,000.
Rate of return on average investment = $23,400 / $100,000 = 23.4%
3(a) There is a cash savings of $59,000 each year for 10 years if income taxes are
ignored. The present value factor for a 10-year annuity at 10% is 6.1446.
Present value of cash savings ($59,000 x 6.1446) $362,531
Present value of investment 200,000
Net present value (positive) $162,531
Profitability Index = Net Present Value = $ 162,531 = .813
Cost of Investment $ 200,000
3(b) There is a cash savings of only $43,400 each year for 10 years if income taxes are
considered.
Present value of cash savings ($43,400 x 6.1446) $266,676
Present value of investment 200,000
Net present value (positive) $ 66,676
Profitability Index = Net Present Value = $ 66,676 = .333
Cost of Investment $ 200,000