Although the Chen Company's milling machine is old, it is still in relatively good working order and would last for another 10 years. It is inefficient compared to modern standards, though, and so the company is considering replacing it. The new milling machine, at a cost of $104,000 delivered and installed, would also last for 10 years and would produce after-tax cash flows (labor savings and depreciation tax savings) of $18,300 per year. It would have zero salvage value at the end of its life. The project cost of capital is 10%, and its marginal tax rate is 25%. Should Chen buy the new machine?

Yes they Should.

Explanation:

Should Chen buy the new machine is dependent on the Net Present Value of buying it. That is, over it's useful life, will it bring in cash flows that will cover discounted the outflows.

The cash flow of $18,300 is AFTER TAX so no need to worry about the given Marginal rate there.

Because the cash flows are even, we can use the Present Value of an Annuity formula which is,

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

Where,

P is payment / cash flow

r is rate(WACC in this case)

n is the number of periods

Meaning the NPV formula will be,

= -Initial outflows + present value of inflows

= -104,000 + (P( 1 -( (1+r)^ -n )/ r))

= -104,000 + ( 18,300 ( 1 - ( 1 + 0.1) ^ 10)/0.01))

= - 104,000 + 112,445.58

= $8,445.58

$8,445.58 is the NPV they would gain from getting the New Machine.

Chen SHOULD buy the machine.