Question

In: Economics

A family is considering installing a household solar energy system. The system has an installed cost...

A family is considering installing a household solar energy system. The system has an installed cost of $1700 and they reduce the homeowner’s energy bill by $400 per year. The residual value of the solar panels is $150 at the end of their 5-year life. What is the annual effective IRR of this investment? Assume the family has a MARR of 10%. Please use the interpolation method and only fill in the number of your calculated result in the blank, e.g., if the result is 7.537%, fill in “7.54”; also keep 2 digits after the decimal point.

Expert Solution

Installed cost = 1,700

Reduction in energy bill (Savings) = 400 per year

Residual Value (Salvage Value) = 150

Life = 5 years

What is the IRR of the investment?

Calculating IRR using Trial and Error Method.

Let the interest rate is 10%.

Calculate the PW of the investment at 10%

PW = -1,700 + 400 (P/A, 10%, 5) + 150 (P/F, 10%, 5)

PW = -1,700 + 400 (3.7908) + 150 (0.6209) = -90.545

The PW is negative. So, decrease the rate of interest to get positive PW.

Decrease the MARR to 8% and calculate the PW.

PW = -1,700 + 400 (P/A, 8%, 5) + 150 (P/F, 8%, 5)

PW = -1,700 + 400 (3.9927) + 150 (0.6806) = -0.83

The PW is still negative. So, decrease the rate of interest to get positive PW.

Decrease the MARR to 7% and calculate the PW.

PW = -1,700 + 400 (P/A, 7%, 5) + 150 (P/F,7%, 5)

PW = -1,700 + 400 (4.1002) + 150 (0.7130) = 47.03

Now, use interpolation and calculate the IRR.

IRR = 7% + [47.03 – 0 ÷ 47.03 – (-0.83)] * 1%

IRR = 7.982%

Rounding up to two decimal points

IRR = 7.98%

Rahul Sunny answered 4 days ago

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