PROBLEM NO$.1$

A machine used on a production line must be replaced at least every four years. The costs incurred in

running the machine according to its age are:

Future replacement will be identical machines with the same costs. Revenue is unaffected by the age of

the machine.

Assume there is no inflation and ignore tax.

The cost of capital is $15\%.$

Determine the optimum replacement cycle.

Present value factors at $15\%$ for years $1,2,3$ and $4$ are $0\mathrm{.}8696,0\mathrm{.}7561,0\mathrm{.}6575$ and $0\mathrm{.}5718$ respectively.

Present value of annuity at $15\%$ for years $1,2,3$ and $4$ are $0\mathrm{.}8696,1,6257,2\mathrm{.}2832$ and $2\mathrm{.}8550$ respectively.