In: Economics
A 2 ,000 square foot house in New Jersey costs $1,800 each winter to heat with its existing oil-burning furnace. For an investment of $6, 000, a natural gas furnace can be installed, and the winter heating bill is estimated to be $1 ,200. If the homeowner's MARR is 6% per year, what is the discounted payback period of this proposed investment? Choose the correct answer below. A. The discounted payback period of this proposed investment is 10 years. B. The discounted payback period of this proposed investment is 12 years. C. The discounted payback period of this proposed investment is 16 years. D. The discounted payback period of this proposed investment is 14 years.
Annual cost for heating before installation of furnace = 1800
Investment = 6000
Annual cost after installation = 1200
Annual Saving = 1800 - 1200 = 600
MARR = 6%
We need to find the present value of net cash flow and cumulative cash flow and find the yr in which cumulative cash flow turns positive
year | Net Cash Flow | Discount factor | Present value | Cumulative Cash flow |
0 | -6000 | 1.00000 | -6,000.00 | -6000.00 |
1 | 600 | 0.94340 | 566.04 | -5,433.96 |
2 | 600 | 0.89000 | 534.00 | -4,899.96 |
3 | 600 | 0.83962 | 503.77 | -4,396.19 |
4 | 600 | 0.79209 | 475.26 | -3,920.94 |
5 | 600 | 0.74726 | 448.35 | -3,472.58 |
6 | 600 | 0.70496 | 422.98 | -3,049.61 |
7 | 600 | 0.66506 | 399.03 | -2,650.57 |
8 | 600 | 0.62741 | 376.45 | -2,274.12 |
9 | 600 | 0.59190 | 355.14 | -1,918.98 |
10 | 600 | 0.55839 | 335.04 | -1,583.95 |
11 | 600 | 0.52679 | 316.07 | -1,267.88 |
12 | 600 | 0.49697 | 298.18 | -969.69 |
13 | 600 | 0.46884 | 281.30 | -688.39 |
14 | 600 | 0.44230 | 265.38 | -423.01 |
15 | 600 | 0.41727 | 250.36 | -172.65 |
16 | 600 | 0.39365 | 236.19 | 63.54 |
17 | 600 | 0.37136 | 222.82 | 286.36 |
Discounted payback period = Last period with a negative discounted cumulative cash flow + (Absolute value of discounted cumulative cash flow at the end of that period / Discounted cash flow during the next period)
= 15 + 172.65/236.19
= 15.73 yrs
Hence the discounted payback period is 16 yrs. Therefore option C is correct.