Question

In: Economics

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)?

3

4

5

6

7

Solutions

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 2 years ago
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