Question

In this​ problem, we consider replacing an existing electrical water heater with an array of solar panels. The net installed investment cost of the panels is ​$1,365 ​($2,100 less a 35​% tax credit from the​ government). Based on an energy​ audit, the existing water heater uses 180 kilowatt hours​ (kWh) of electricity per​ month, so at ​$0.13 per​ kWh, the cost of operating the water heater is ​$23.4 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 10 ​years?

Answer 1

A.

Net investment cost = $1365

Savings per month = 180*.13 + 23.4 = $46.8

So,

Simple payback period = 1365/46.8

Simple payback period = 29.17 or 29 months

B.

Time = 120 months (10 years)

Let, Monthly IRR = R

Then,

1365 = 46.8*(1-1/(1+R)^120)/R

If R = 3.5%

PV of savings = $1315.6

If R = 2.5%

PV of savings = $1775.3

As per the method of the interpolation,

R = 2.5% + ((1775.3-1365)/(1775.3-1315.6))*(3.5% - 2.5%)

R = 3.37% per month

Annual IRR = 12*3.37%

Annual IRR = 40.44%