A new $300,000 machine is expected to have a 5-year life and a terminal value of $0. It can produce 40,000 units a year at a variable cost of $4 per unit. The variable cost is $6.50 per unit with an old machine, which also has a capacity of 40,000 units a year and a book value of $100,000. It is being depreciated on a straight line basis at $20,000 per year. It too is expected to have a terminal value of $0. Its current disposal value is also $0 because it is highly specialized equipment.

The salesperson of the new machine prepared the following comparisons: –

new machine$ old machine$

Units 40,000 40,000

Variable costs 160,000 260,000

Straight line depreciation 60,000 20,000

Total cost 220,000 280,000

Unit cost 5.50 7.00

He said, The new machine is obviously a worthwhile acquisition. You will save $1.50 for every unit you produce.

Required:
(a) Do you agree with the salesperson’s analysis? If not, how would you change it? Be specific and ignore taxes. Would you suggest keeping the old machine or replacing it with the new one?
(b) Prepare an analysis of total and unit differential costs if the annual volume is 20,000 units.
(c) At what annual volume would both the old and new machines have the same total relevant costs?