A machine would cost $100,000, and would generate revenues of $21,000 per year. However, O&M costs would be $7,000 per year. The machine would last 10 years and your MARR is 7% annual rate compounded annually. (a) What is the net present value of this potential investment? (b) Should you invest in this machine? Give one sentence answer for why or why not.

(a) What is the net present value of this potential investment?

Net present value of Investment is $(3,903)

(b) Should you invest in this machine?

We should not invest in this investment because Net present value of this investment is negative by discounting Minimum acceptable rate of return.

Explanation:

Present Values:

Revenue                    $144,146

O&M Cost                  ($48,049)

Initial Investment      $(100,000)

Net Present value     $(3,903)

Working :

Present Value Calculation = P x ( (1- ( 1 + r )^-10) / r

Revenue = $21,000 x ( (1- ( 1 + 0.075 )^-10) / 0.075 = 144,146

O&M Costs = $7,000 x ( (1- ( 1 + 0.075 )^-10) / 0.075 = 48,049

A) NPV = -1669.6

B) Since this value is negative, the machine should not be invested in because the cash outflow is greater than the inflow.

Explanation:

The question is to determine whether we should invest in the machine or not using the net present value formula for calculation as follows:

Step 1: We determine the Net present Value of the annual receipts

=The Revenue expected yearly - the Costs incurred yearly

= $21,000 - $7,000

= $14,000

Based on this estimated amount, we then determine the present values of the cash flow as follows

To do this, we use the Present Value Interest Factors for a One-Dollar Annuity  Table

We use 7% annual rate  and 10 year period. We plug this into the table and get 7.0236

Also, using this formula we arrive at the same figure PVIFA = [1 - 1/(1 + k)n] / k

Based on the figure:

The present Value of the cash flow for 10 years

= $14,000 x (the Present Value of Annuity determined above)

= $14,000 x 7.0236

= $98,330.4

Finally, the Net present Value

= The Present Value of Cash inflows - The initial cost of the machine

= $98,330.4 - $100,000

= -1669.6

Since this value is negative, the machine should not be invested in because the cash outflow is greater than the inflow.