Equivalent annual costs

Hi Cath. I hope you are well. I have been busy studying this past week and looking to sit my exam w/c 22nd.. or a little later if I am not ready. I am just going to focus on questions for the next 2 weeks or so... Just a question from the BPP questions bank on Equivalent annual costs- Chapter on further aspects of decision making. An investor is indifferent between replacing a machine every 2 years and replacing it every 4 years. The present value of the first 2 years replacement cycle is 17,360 and the PV of the first 4 years replacement cycle is 31,700. What discount rate is the investor using? A) 5% B)10% C)15% D)20% Answer: The solution says with such a question is is trail and error and we should us the different multiple choice questions as a basis. It then goes on to say that for an investor to be indifferent the annual equivalent cost must be the same. This is the point I do not get. ... the answer then goes on to calculate the annual equivalent cost y2= 17,360/1.736 ( using 10% discount rate) 10,000 y4= 31,700/3.170= 10,000 (again using the same discount rate) I am trying to take a step back and ensure I understand the theory.. so an equivalent annual cost is a method used to calculate an optimal replacement cycle. It helps us with asset replacement decisions. If an investor is indifferent..so he does not care.. then the annual equivalent rate.. should be the same..I think I may have answered my own question- but please Cath can you check my logic.. thought process?