A company needs a certain type of machine for the next 5 years. They presently own such a machine, which is now worth $6,000 but will lose $2,000 in value in each of the next 3 years, after which it will be worthless and unusable. The (beginning-of-the-year) value of its yearly operating cost is $9,000, with this amount expected to increase by $2,000 in each subsequent year that it is used. A new machine can be purchased at the beginning of any year for a fixed cost of $22,000. The lifetime of a new machine is 6 years, and its value decreases by $3,000 in each of its first 2 years of use and then by $4,000 in each following year. The operating cost of a new machine is $6,000 in its first year, with an increase of $1,000 in each subsequent year. When should the company purchase a new machine?

(a) If the interest rate is 20%

(b) This time assume that the yearly interest rate is 10% and that the cost of a new machine increases by $1,000 each year.