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? I already know the answer to part a is 58 months. However please show work and provide the correct answer for part b. (not on excel)

Answer 1

initial cost = 1365

Saving per month = 23.4

Total month = 10*12 = 120

Let IRR be i% per month, then PW = 0 at i , therefore

-1365 + 23.4*(P/A, i%,120) = 0

(P/A, i%,120) = 1365/23.4 = 58.33333

Using trail and error

At i = 0.75%, (P/A, i%,120) = 78.94169

At i = 1%, (P/A, i%,120) = 69.700522

At i = 1.25%, (P/A, i%,120) = 61.982847

At i = 1.5%, (P/A, i%,120) = 55.498454

Using interpolation

i = 1.25% + [(61.982847-58.33333)/(61.982847-55.498454)]*(1.50-1.25)

i = 1.25% + 0.14070

i = 1.39070% per month = 1.39% per month (Approx)

IRR per year = 1.39070*12 = 16.688% = 16.69% per year (Approx)

Using RATE function in excel

Initial cost	1365
Total no. Of months	120
Monthly savings	23.4
IRR
1.3854% per month