Question

Nowadays it is very important to reduce? one's carbon? "footprint" (how much carbon we produce in our daily? lifestyles). Minimizing the use of fossil fuels and instead resorting to renewable sources of energy? (e.g., solar? energy) are vital to a? "sustainable" lifestyle and a lower carbon footprint.? Let's consider solar panels that prewarm the water fed to a conventional home water heater. The solar panels have an installed cost of ?$3 comma 231 ?, and they reduce the? homeowner's energy bill by ?$29.5 per month. The residual value of the solar panels is negligible at the end of their 12 ?-year life. What is the annual effective IRR of this? investment? The annual effective IRR of this investment is nothing ?%. ?(Round to two decimal? places.)

Answer 1

ANSWER:

We will first find the irr of the solar panel and then the effective irr. in order to do that the pw of this will have to be equated to zero.

pw of solar panel = initial cost + monrly saving(p/a,i,n)

i =?

n = 12 years or 144 months

initial cost = 3,231

monthly saving = 29.5

pw of solar power = -3231 + 29.5(p/a,i,144)

0 =  -3231 + 29.5(p/a,i,144)

3231 = 29.5(p/a,i,144)

solving i by trial and error we get i = 0.3969% per month

so the nominal irr = 0.3969% per month

annual effective irr = ( 1 + nominal irr / number of compounding periods) ) ^ number of compounding periods -1

annual effective irr = ( 1 + 0.3969% / 12) ) ^ 12 - 1

annual effective irr = ( 1 + 0.000331) ^ 12 - 1

annual effective irr = (1.000331) ^ 12 - 1

annual effective irr = 1.003976 - 1

annual effective irr = 0.003976 or 0.3976%

so the annual effective irr = 0.3976%