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 $20,000. A conventional system will cost $7,000. Austin is eligible for a 30% tax credit to be applied immediately to the purchase. He estimates that he will save $1,500 per year in utility bills with the geothermal system. These cash out flows can be assumed to occur at the end of the year. The cost of capital (or interest rate) for Austin is 7%. How long will Austin have to use the system to justify the additional expense over the conventional model? (i. what is the DISCOUNTED payback period in years? Also at interest rate of 8% what is the NPV of this project
Q. 1). Solution :- Calculation of discounted payback period in years :-
Initial additional cash outflow on geothermal system = 20000 (Expense on geothermal system) - 7000 (Expense on conventional system) - 30 % of 20000 (Tax credit).
= 20000 - 7000 - 6000
= 20000 - 13000
= $ 7000.
Present value of cash inflow = 1500 / 0.07
= $ 21428.57 (approx)
Discounted pay back period = Initial additional cash outflow on geothermal system / Present value of cash inflow.
= 7000 / 21428.57
= 0.3 Years (approx).
Conclusion :- Discounted pay back period = 0.3 Years (approx).
Q. 2). Solution :- NPV of project = Present value of cash inflows - Present value of additional cash outflow.
= 1500 / 0.08 - 7000
= 18750 - 7000
= $ 11750.
Conclusion :- NPV of project = $ 11750.
Austin needs to purchase a new heating/cooling system for his home. He is thinking about having a geothermal system inst...
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