Question

Your company uses the same large electric drive motor at several locations in its electric power generating plants. A new motor, which is much more efficient, is available. The market price of the new model is $70,000. Assume the following:

- Analysis period is 9 years.

- General inflation rate is 3%.

- The increase rate on annual savings in operating expenses is 5 % per year. Assume any savings in year one would escalate at this rate therafter.

- MARR = 10% per year (does not include inflation component.i.e. it is inflation-free interest rate) -

Base time period is year zero.

What would the annual savings in year one need to be per motor to break even?

Answer 1

The annual savings in operating expenses for the analysis period of 9 years is equivalent to a growing annuity with 5% growth rate and 9 years as period. Since the cost of new motor is $70,000 the break even cash flow (stream of annual savings) is the growing annuity of which present value (PV) is equal to $70,000.

Since the inflation-free MARR is 10% and inflation rate is 3%, PV shall be ascertained with discount rate at 10% + 3% = 13%.

Savings in operating expense for the first year, in order to break even is the first cash flow of the growing annuity ascertained at  $11,580.14 as follows: