In this problem we consider replacing an existing electrical

In this problem, we consider replacing an existing electrical water heater with an array a solar panels. The net installed investment cost o the panels is $1520 $1900 less a 20% tax credit the government). Based on an energy audit, the existing water heater uses 190 kilowatt hours (kWh) of electricity per month, so at $0.13 per kWh, the cost of operating the water heater is $24.7 per month. Assuming the solar panels can save the entire cost of heating water with electricity, answer the following questions. a. What is the simple payback period for the solar panels? b. What is the IRR of this investment if the solar panels have a life of 11 years? a. The simple payback period is 62 months. (Round to the nearest whole number.,) b. The IRR of the investment is 1% per month. (Round to two decimal places.)

Solution

IRR is the interest rate which makes Present worth of Benefit equals to Present worth of Cost

PW of Benefit=(190*0.13*12)/(1+irr)+(190*0.13*12)/(1+irr)^2+(190*0.13*12)/(1+irr)^3+(190*0.13*12)/(1+irr)^4+...+(190*0.13*12)/(1+irr)^11

Installation Cost=$1520

1520=(190*0.13*12)/(1+irr)+(190*0.13*12)/(1+irr)^2+(190*0.13*12)/(1+irr)^3+(190*0.13*12)/(1+irr)^4+...+(190*0.13*12)/(1+irr)^11

After sloving with trial and error we get irr=15.5%