NPV formula:

-F0=outlay

Ft=positive cash flow

r=discount rate

4 A firm has to choose between two machines whose operating costs fall at the beginning of each year: Year Machine 1 Machine 2 1 1,000 1,600 2 200 100 3 400 200 4 300 5 400 6 500 After 3 years, Machine 1 will have no scrap value and will be replaced by an identical machine with the same costs. In each case, the first year cost includes purchase, installation and running costs. In subsequent years, maintenance and running costs are included. Over a 6 year period at a 10% p.a. discounting rate, show that Machine 1 is a better buy and, using a graph, show how the discounting rate affects the decision about which machine to choose. F1 NPV = -F. + (1+r)1 + F2 F3 + + (1+r)2 (1+r)3 Ft + (1+r)t