A precision lathe costs 30000 and will cost 40000 a year to

A precision lathe costs $30,000 and will cost $40,000 a year to operate and maintain. If the discount rate is 10% and the lathe will last for 5 years, what is the equivalent annual cost of the tool? (Do not round intermediate calculations. Round your answer to 2 decimal places. Enter your answer as a positive value.)

Solution

Present value of annual payments=Annuity[1-(1+interest rate)^-time period]/rate

=$40000[1-(1.1)^-5]/0.1

=$40000*3.790786769

=$151631.4708

Total Present value of outflows

=$151631.4708+$30000

=$181631.4708

Hence equivalent annual cost =[rate*Total Present value of outflows]/[1-(1+rate)^-time period]

=[0.1*$181631.4708]/[1-(1.1)^-5]

=(18163.14708/0.379078676)

=$47913.92(Approx).