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 $3,000, and they reduce the homeowner’s energy bill by $30 per month. The residual value of the solar panels is negligible at the end of their 25-year life. What is the annual effective IRR of this investment?please do it out step by step not using excel

Answer 1

Annual saving = $30 x 12 = $360

If IRR f the project be R%, then

$3,000 = $360 x P/A(R%, 25)

P/A(R%, 25) = $3,000 / $360 = 8.3333

From P/A Factor table, we find:

P/A(11%, 25) = 8.4217

P/A(12%, 25) = 7.8431

Since 8.4217 > 8.3333 > 7.8431, we get

P/A(11%, 25) > P/A(R%, 25) > P/A(12%, 25).

Therefore

11% > R > 12%.

Using interpolation,

(R - 11)% / (12 - 11)% = (8.3333 - 8.4217) / (7.8431 - 8.4217)

(R - 11)% / 1% = (-0.0884) / (-0.5786)

R - 11% = 0.15

R = 11.15%