***Please show formula and working, thanks!***

(1) Given the data below, calculate the net present value of an infinite chain of replacement using the equivalent annual value method. Assume the cost of capital is 11% p.a.

Initial Outlay Year 1 Year 2 Year 3

-$10,000 $10,000 $20,000 $30,000

(2)What is the present value of a series of payments of $4000 every three years in perpetuity with the first payment made immediately, if the annual rate is 10% per annum?

(3)Given the following information and options, calculate how many years this project should be run before it is retired. Assume the cost of capital is 10% p.a. Maximum life is five years.

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Net Cash Flows ($) (10,000) 2,200 3,000 3,500 2,500 2,000

Retirement Values ($) 6,000 5,000 4,000 3,000 1,000

(4) Calculate the AE given a project with an outlay of -2000 and cash flows of 1500 per year for 4 years. The discount rate is 0.11. The rate is given as a decimal (eg .12 is 12%). Answer to the nearest dollar.