What is the present worth of energy-saving equipment costing $450,000 with annual savings of $65,000 over 10 years?

To determine the present worth of the energy-saving equipment, the concept of present value (PV) must be applied. The formula for present value of an annuity is:

[ PV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) ]

Where:

• ( C ) is the annual savings,
• ( r ) is the discount rate (which is not provided in this problem),
• ( n ) is the number of years.

Substituting the known values, we have:

[ PV = 65,000 \times \left( \frac{1 - (1 + r)^{-10}}{r} \right) ]

The present worth is calculated based on the $65,000 annual savings over 10 years. If a reasonable discount rate (commonly assumed in financial analysis, often around 5% to 8%) is used, you can calculate the present value of those savings.

For a discount rate of 5%:

[ PV = 65,000 \times \left( \frac{1 - (1 + 0.05)^{-10}}{0.05} \right) ]