A house costs $ 1,725 to heat with its existing oil-burning boiler during the first year...

A house costs $ 1,725 to heat with its existing oil-burning boiler during the first year and this cost is expected to increase by $ 25 in each subsequent year. For an investment of $ 3,000, a natural gas furnace can be installed, and the winter heating bill is estimated to be $ 1,000 and expected to increase $ 15 each year. If the homeowner's MARR is 7% per year, what is the discounted payback period of this proposed investment (round down your answer)?

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Expert Solution

Option (C).

Annual saving = Annual cost of existing boiler - Annual cost of new furnace

Discounted Payback period (DPBP) is the time by when cumulative discounted Annual Saving becomes zero.

Year	Boiler Cost ($)	Furnace Cost ($)	Saving ($)	PV Factor @7%	Discounted Saving ($)	Cumulative Discounted Saving ($)
			(C) = (A) - (B)	(D)	(E) = (C) x (D)
0		3,000	-3,000	1.0000	-3,000	-3,000
1	1,725	1,000	725	0.9346	678	-2,322
2	1,750	1,015	735	0.8734	642	-1,680
3	1,775	1,030	745	0.8163	608	-1,072
4	1,800	1,045	755	0.7629	576	-496
5	1,825	1,060	765	0.7130	545	49
6	1,850	1,075	775	0.6663	516	566
7	1,875	1,090	785	0.6227	489	1,054
8	1,900	1,105	795	0.5820	463	1,517
9	1,925	1,120	805	0.5439	438	1,955
10	1,950	1,135	815	0.5083	414	2,369

DPBP lies between years 4 and 5.

DPBP = 4 + (Absolute value of cumulative discounted cash flow, year 4 / Discounted cash flow, year 5)

= 4 + (496 / 545)

= 4 + 0.94

= 4.94

~ 5 years

Rahul Sunny answered 1 year ago

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