This is a question with the answer, the confusion is regarding the "what will the factory be worth after five years". why would the factory's value be the present value of the remaining $170,000 cash flows?

lets assume its "what will the factory be worth at the end of six year?"

why should we consider the remaining 4 years cash flow, and not the 6 years that passed?

why should the t be equal to 4 and not 6?

please explain in details.

A factory costs $800,000. You believe that it will produce a cash flow of $170,000 a year for 10 years. If the opportunity cost of capital is 14 percent, what is the NPV of the factory? What will the factory be worth at the end of five years? The present value of the 10-year stream of cash inflows is: PV=$170,000[0.1410.14(1.14)101]=$886,739.66 Thus: NPV=$800,000+$886,739.66=+$86,739.66 At the end of five years, the factory's value will be the present value of the five remaining $170,000 cash flows: PV=$170,000[0.1410.14(1.14)51]=$583,623.76