We consider replacing an existing electrical water heater...

We consider replacing an existing electrical water heater with an array of solar panels. The net installed investment.cost of the panels is $1,400 ($2,000 less a 30% tax credit from the government). Based on an energy audit, the existing water heater uses 200 kilowatt hours (kWh) of electricity per month, so at $0.12 per kWh, the cost of operating the water heater is $24 per month. Assuming the solar panels can save the entire cost of heating water with electricity, answer the following questions. What equation can you use to find the IRR of this investment if the solar panels have a life of 10 years? A) 0 = -$1,400 + $24 (P/A, i% per year, 10 years) B) 0 = -$1,400 + $24 (A/P, i% per month, 120 months) C) 0 = -$1,400 + $24 (P/A, i% per month, 120 months) D) 0 = -$1,400 + $24 (A/P, i% per year, 10 years)

Transcript

00:02 All right, so in this problem, we're looking at putting solar panels up, installing solar on our house, saving money.

00:09 So let's say that it costs 20 cents per kilowatt hour to buy power from a power company, okay? so this is what we're trying to save.

00:22 This is what it would cost us right here if we just kept staying on the grid and buying power from the power company.

00:32 So we're looking at, well, it's going to cost $100 per square foot to install these solar panels and hook them up and all that.

00:42 Each square foot is going to produce 20 kilowatt hours every year.

00:48 And the government is going to pay for 50 % of us to install these solar panels.

00:55 So let's start and figure out what the initial cost is.

00:58 And we're putting 300 square feet of solar panels up.

01:02 So it's $100 per square foot.

01:09 Let's do it this way.

01:11 We're going to install 300 square feet, okay? i'm trying to show you with the units.

01:24 So the square feet are going to be gone.

01:26 All we're going to be left with is dollars.

01:28 So this is our cost.

01:30 So our cost is 300 times 100 or 300 hundred, $30 ,000 is the total cost.

01:42 Total cost.

01:45 Now remember, the government's going to pay 50 % of that, thankfully.

01:51 Yippee.

01:51 So the government's paying 50%, government's paying half.

01:55 So our cost from us, our part, is only 50 % times $30 ,000 or $15 ,000.

02:13 This is what we got to cover.

02:18 So this is our out of pocket, the other 15 ,000 was paid for by the taxpayers, which i guess technically if you're a taxpayer, you're paying for part of that too.

02:32 Okay, whatever.

02:33 But out of our budget, we only have to write a check or conjure up $15 ,000 of our own money and then the government covers the other 15 ,000.

02:42 This is what you want to put in the first box.

02:45 Okay, now it's the second part.

02:49 It says, come up with a function or a formula to figure out the break even point.

02:56 What are we saving? how much money are we saving by using these solar panels? okay, so we have 300 square feet up on our roof.

03:14 So let me do it in a different color.

03:19 So we have 300 square feet and each one is going to produce 20 kilowatt hours per year per square foot.

03:28 So we get 20 kilowatt hours a year per square foot.

03:44 Okay, so the feet squared are going to be gone.

03:47 So when we multiply this per year, when we multiply this together, we're getting six with three zeros kilowatt hours every year per year.

04:01 That's how much by using our solar panels, our solar array is producing 6 ,000 kilowatt hours per year.

04:10 So our savings, since it costs us 20 kilowatt hours or 20 cents per kilowatt hour, our function is going to be, our formula is...

04:27 So our savings, let's do it this way.

04:32 Savings equals 6 ,000 kilowatt hours per year times 20 cents per kilowatt hour times t years.

05:04 Okay, so there's our little formula.

05:07 The kilowatt hours will reduce out, the years will reduce out, right? years reduces out, kilowatt hours reduces out.

05:15 So our savings is when you multiply this, $1 ,200 times t, that's what our savings is going to be...

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