Question 1168823: Austin needs to purchase a new heating/cooling system for his home. He is thinking about having a geothermal system installed, but he wants to know how long it will take to recoup the additional cost of the system. The geothermal system will cost $20,500. A conventional system will cost $6,000. Austin is eligible for a 30% tax credit to be applied immediately to the purchase only if he chooses the geothermal system. He estimates that he will save $1,500 per year in utility bills with the geothermal system. These cash outflows can be assumed to occur at the end of the year. The cost of capital (or interest rate) for Austin is 6%. How long will Austin have to use the system to justify the additional expense over the conventional model? In other words, what is the DISCOUNTED payback period in years? Discount future cash flows before calculating payback rounded UP to a whole year. (Enter just the number without comma and round off decimals.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there's a nice little online calculator that does this for you.
that calculator can be found at https://www.calculator.net/payback-period-calculator.html
what you have to do is feed it the net cash flow.
it does the discounting for you.
it will tell you the payback period for the net cash flow and the discounted net cash flow.
it will also tell you the internal rate of return for your project.
it will handle even cash flows, such as in your problem, and uneven cash flows, which can happen more often than not.
in your problem, you have even cash flows.
what you have to do is get the difference between your project and the competing project.
the geothermal system cost is 20,500
the conventional system cost is 6,000
you get a 30% tax credit on the geothermal system.
the net cost of the geothermal system is therefore 20,500 minus 30% * 20,500 = 20,500 minus .3 * 20,500 = 14,350.
the net difference between your system cost and the competing system cost is 14,350 minus 6,000 = 8,350.
that's what you enter as the initial investment.
your savings per year are 1500.
these are the differences each year between the geothermal annual operating costs and the competing project annual operating costs.
since the competing project annual costs are 1500 more than the geothermal project annual costs, the net cash flow is positive for the geothermal project for each year of the investment period.
the investment period is how long you make your study.
it's usually a finite period that's decided before doing the analysis.
i assumed a 10 year study.
it also asks you for the percent increase / decrease in the annual costs each year.
if you don't want to consider those, than enter 0 in the percent increase / decrease field.
otherwise it will change the values of the operating costs for each year of the study and not give you what you expect.
it does show you the year by year cash flows, so you can determine if your inputs were made correctly.
my entries were:
initial investment = 8350
cash flow = 1500
percent increase / decrease = 0
number of years = 10
discount rate percent = 6
this is what the calculator did for me.
the non-discounted payback period is 5.567 years.
the discounted payback period is 6.976 years.
the internal rate of return is 12.37%
any questions, give me a shout.
theo
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