You have been assigned to purchase a new molding machine. One vendor offered a machine that will cost $200,000$, with an estimated installation of $10,000$. The machine has an expected life of $10$ years, with an annual operating cost of $10,000$. At the end of the machine life, there is an expected salvage value of $5,000$. Your estimation shows an expected $45,000$ of revenues directly related to the new machine during the first year, which is expected to increase by $2,000$/year till the end of the machine's life. The company uses a $10\%$ interest rate to evaluate equipment purchasing alternatives. Should you buy this machine?
I am approaching this problem using $PV=A(1+i)^{-n}$, although I am having trouble implementing the numbers given to me. I was recommended to use it from a friend but I believe that it is not correct since he hasn't taken economics in quiet a few years.
Yes, you need to see if the PV of the machine is positive. I'm a little rusty but here's how I apply the amounts: \begin{align*} PV=-200000-\sum_{i=0}^{10}10000\cdot 1.1^{-i}+5000\cdot 1.1^{-10}+\sum_{i=1}^{10}(45000+2000 \cdot (i-1))\cdot 1.1^{-i} \end{align*} The main concern I have is when I should apply the amounts. Specifically, each of the amounts I applied at the end of the year and I'm not sure if this is correct.