Question
In: Accounting
You bought a house two years ago and the hot water heater just died. You are...
You bought a house two years ago and the hot water heater just died. You are considering replacing it with an updated version of the same model, which would cost you $200 including installation. Your family consumes about 110 gal of hot water daily, which costs you $230 in utilities each year. The new tank comes with a 20-year guarantee, and at the end of that time, you assume it would be discarded and a new version installed, so zero salvage cost.
Alternatively, you have been researching solar powered hot water systems and found a system that would meet your family’s requirements. It includes two solar panels and a storage tank with an auxiliary heating coil for those cloudy days. Total cost for this new system is $1250 including installation. To power the backup system is estimated to cost $60/year in utilities, and every fourth year, starting in year 4, $185 of maintenance will be required. At the 20-year point, you assume technology would have improved so this system would have zero value, and a new system would be installed.
Assuming a 7% discount rate, which system would be more economical over the 20-year life? When would the two systems be equal in cost?
Please show in excel
Solutions
Expert Solution
| (a) | Solar powered hot water system is more economical because it present value is less than the other. | ||||||||
| (b) | At a cost of $ 1,529 ( 1,250 + 279 ) of solar powered hot water, two systems woule be equal in cost. | ||||||||
| Working:- | |||||||||
| Updated hot water heater | Solar Powered hot water |
| Year | Outflow | PV Factor@7% | Present Value | Year | Outflow | PV Factor@7% | Present Value | |||
| 0 | -200 | 1 | -200 | 0 | -1,250 | 1 | -1,250 | |||
| 1 | -230 | 0.93458 | -215 | 1 | -60 | 0.93458 | -56 | |||
| 2 | -230 | 0.87344 | -201 | 2 | -60 | 0.87344 | -52 | |||
| 3 | -230 | 0.81630 | -188 | 3 | -60 | 0.81630 | -49 | |||
| 4 | -230 | 0.76290 | -175 | 4 Beginning* | -185 | 0.81630 | -151 | |||
| 5 | -230 | 0.71299 | -164 | 4 | -60 | 0.76290 | -46 | |||
| 6 | -230 | 0.66634 | -153 | 5 | -60 | 0.71299 | -43 | |||
| 7 | -230 | 0.62275 | -143 | 6 | -60 | 0.66634 | -40 | |||
| 8 | -230 | 0.58201 | -134 | 7 | -60 | 0.62275 | -37 | |||
| 9 | -230 | 0.54393 | -125 | 8 Beginning | -185 | 0.62275 | -115 | |||
| 10 | -230 | 0.50835 | -117 | 8 | -60 | 0.58201 | -35 | |||
| 11 | -230 | 0.47509 | -109 | 9 | -60 | 0.54393 | -33 | |||
| 12 | -230 | 0.44401 | -102 | 10 | -60 | 0.50835 | -31 | |||
| 13 | -230 | 0.41496 | -95 | 11 | -60 | 0.47509 | -29 | |||
| 14 | -230 | 0.38782 | -89 | 12 Beginning | -185 | 0.47509 | -88 | |||
| 15 | -230 | 0.36245 | -83 | 12 | -60 | 0.44401 | -27 | |||
| 16 | -230 | 0.33873 | -78 | 13 | -60 | 0.41496 | -25 | |||
| 17 | -230 | 0.31657 | -73 | 14 | -60 | 0.38782 | -23 | |||
| 18 | -230 | 0.29586 | -68 | 15 | -60 | 0.36245 | -22 | |||
| 19 | -230 | 0.27651 | -64 | 16 Beginning | -185 | 0.36245 | -67 | |||
| 20 | -230 | 0.25842 | -59 | 16 | -60 | 0.33873 | -20 | |||
| Total | -4,800 | -2,637 | 17 | -60 | 0.31657 | -19 | ||||
| 18 | -60 | 0.29586 |
&nbs
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