A new semi-automatic machine costs $ 80,000 and is expected to generate revenues of $ 40,000 per year for 6 years. It will cost $ 25,000 per year to operate the machine. At the end of 6 years, the machine will have a salvage value of $ 10,000. Evaluate the investment in this machine using all four methods (payback period, present worth, uniform annual cost (UAC), and rate of return). Neglect the salvage value f

The complete part of the question is found below:

Neglect the salvage value for payback period rate of return

Applicable rate of return is 15%

Answers:

Payback is 5.33 years

Present worth is - $18,909.48

UAC is - $ 4,996.58

Rate of return is 18.75%

Explanation:

In case of an even cash flow like this when the net cash flow yearly is $15,000 ($40,000-$25000), the payback period is initial investment/net annual cash flow

Payback=$80,000/$15,000 = 5.33 years

Present is computed thus

Year cash flow discount factor pv=cash flow*discount factor

0 - $80,00 1 / (1+0.15) ^0 (80,000.00)

1 $15000 1 / (1+0.15) ^1 13,043.48

2 $15000 1 / (1+0.15) ^2 11,342.16

3 $15,000 1 / (1+0.15) ^3 9,862.74

4 $15,000 1 / (1+0.15) ^4 8,576.30

5 $15,000 1 / (1+0.15) ^5 7,457.65

6 $25,000 1 / (1+0.15) ^6 10,808.19

present worth (18,909.48)

The uniform annual cost=NPV*r / (1 - (1+r) ^-n

NPV is - $18,909.48*0.15 / (1 - (1+0.15) ^-6)

=-$ (2,836.42) / 0.567672404

=-$ (4,996.58)

The rate of return can be computed thus:

rate of return=annual cash flow/initial investment*100

annual cash flow is $15000

initial investment is $80,000

rate of return=15,000/80000*100

=18.75%