Hi, I\'m unsure of how to calculate the current value of the bond here. I\'m an

Question

Hi, I'm unsure of how to calculate the current value of the bond here. I'm an engineering econ student. This is problem 5-11 frm Engineering Economy 16th ed. by Sullivan. Thanks!!

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 $2,857, and they reduce the homeowner's energy bill by S31.5 per month. The residual value of the solar panels is negligible at the end of their 11-year life. What is the annual effective IRR of this investment? The annual effective IRR of this investment is 90 (Round to two decimal places.)

Explanation / Answer

Installed cost = $2857

Monthly instalment = $31.5

Time = 11 years = 132 months

Let, monthly interest rate = R

At IRR, Present value of all monthly instalment will be equal to initial cost.

Then,

Installed cost = $2857 = 31.5*(1-1/(1+R)^132)/R

At R = .7%

PV of all monthly instalment = $2708.064

At R = .6%

PV of all monthly instalment = $2866.441

As per the method of interpolation,

R = .6% + ((PV at .6% - 2857)/( PV at .6% - PV at .7%))*(.7% - .6%)

R = .6% + ((2866.441 - 2857)/( 2866.441-2708.064))* (.7% - .6%)

R = .606% approx.

Thus,

Effective annual IRR = (1+R)^12 – 1 = (1+.606%)^12 - 1

Effective annual IRR = 7.52% approx.

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