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 ​$1,300($2100 less a 35% tax credit from the​ government). Based on an energy​ audit, the existing water heater uses 220 kilowatt hours​ (kWh) of electricity per​ month, so at $0.15 per kHh, the cost of operating the water heater is ​$33 per month. Assuming the solar panels can save the entire cost of heating water with​ electricity, answer the following questions.

b. What is the IRR of this investment if the solar panels have a life of 11 years?

Answer 1

initial cost = 1300

Saving per month = 33

Total month = 11*12 = 132

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

-1300 + 33*(P/A, i%,132) = 0

(P/A, i%,132) = 1300/33 = 39.393939

Using trail and error

At i = 1%, (P/A, i%,132) = 73.110751

At i = 1.5%, (P/A, i%,132) = 57.325714

At i = 2%, (P/A, i%,132) = 46.337755

At i = 2.25%, (P/A, i%,132) = 42.087986

At i = 2.5%, (P/A, i%,132) = 38.463580

Using interpolation

i = 2.25% + [(42.087986-39.393939)/(42.087986-38.463580)]*(2.5-2.25)

i = 2.25% + 0.18582

i = 2.436% per month = 2.44% (Approx)

IRR per year = 2.436*12 = 29.232% = 29.23% per year (Approx)

Using RATE function in excel

Initial cost	1300
Total no. Of months	132
Monthly savings	33
IRR Monthly	2.43%
IRR Yearly	29.18%