g production machine tool. The new machine would cost $3700, have a life of four years, have no salvage value, and save the firm $500 per year in direct labor cost and $200 per year indirect labor costs. The existing machine tool was purchased four years ago at a cost of $4000. It will last four more years and have no salvage value at the end of that time. It could be sold now for $1000 cash. Assume money is worth 8%, and that the difference in taxes, insurance, and so forth, for the two alternatives is negligible. Determine whether or not the new machine should be purchased

The new machine should NOT be purchased.

Explanation:

Annual total cost saving = Direct labor cost saving + Indirect labor costs saving = $500 + $200 = $700

Using the formula for calculating the present value of an ordinary annuity, the present value of the annual total cost saving can be calculated as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value the total annual cost saving = ?

P = Total annual cost saving = $700

r = interest rate = 8%, or 0.08

n = number of years = 4

Substitute the values into equation (1), we have:

PV = $700 * ((1 - (1 / (1 + 0.08))^4) / 0.08)

PV = $2,318.49

Net present value of new machine tool = – Cost of the new machine tool + PV = – $3700 + $2,318.49 = – $1,381.51

Salvage value existing machine tool now = $1,000

Since the Salvage value existing machine tool now is $1,000 while the Net present value of new machine tool is –$1,381.51, the new machine should NOT be purchased.