Question

A heat exchanger is to be used in a heating process. A standard type of heat exchanger with a negligible scrap value of $20,000 and will have a useful life of 6 years. Another type of heat exchanger with equivalent design capacity is priced at $34,000 but with a useful life of 10 years and a scrap value of $4000.Assume an effective compound interest rate of 6 percent per year and that the replacement cost of each exchanger is the same as that of the original exchanger. Determine which heat exchanger is cheaper by comparing the capitalized cost of each.

Answer 1

capitalized cost of equipment is used to determine the cost spread of equipment over the long period.

replacement cost of exchanger is same as original cost

For heat exchanger 1

Total cost Cv = $20,000

Replacement cost C_R = $20000

Years n = 6

effective compound interest rate i = 6 % = 0.06

Capitalized cost of heat exchanger 1

= ($20000) + ($20,000)/[(1+0.06)⁶ - 1]

= $67787.54

For heat exchanger 2

Total cost Cv = $34,000

Replacement cost C_R = $34000 - $4000 = $30000

Years n = 10

effective compound interest rate i = 6 % = 0.06

Capitalized cost of heat exchanger 2

= ($34000) + ($30,000)/[(1+0.06)¹⁰ - 1]

= $71934

Capitalized cost of heat exchanger 1 < capitalized cost of heat exchanger 2

Heat exchanger 1 is cheaper.