Please detail it !!

Example 2.8 (Machine replacement) Aspecialized machine essential for a com- pany's operations costs $10,000 and has operating costs of $2,000 the first year. The operating cost increases by $1,000 each year thereafter. We assume that these oper- ating costs occur at the end of each year. The interest rate is 10%. How long should the machine be kept until it is replaced by a new identical machine? Assume that due to its specialized nature the machine has no salvage value. This is an example where the cash flow stream is not fixed in advance because of the unknown replacement time. We must also account for the cash flows of the replacement machines. This can be done by writing an equation having PV on both sides. For example, suppose that the machine is replaced every year. Then the cash flow (in thousands) is (-10,-2) followed by (0, -10,-2) and then (0,0, -10, -2). and so forth. However, we can write the total PV of the costs compactly as PV=10+2/ 1.1 + PV/ 1.1 because after the first machine is replaced, the stream from that point looks identical to the original one, except that this continuing stream starts 1 year later and hence must be discounted by the effect of 1 year's interest. The solution to this equation is PV = 130 or, in our original units, $130,000