A young engineering graduate is interested in buying a solar energy system for h

Question

A young engineering graduate is interested in buying a solar energy system for her home She is investigating two particular systems shown below: Soltech $6,000 50/year 700/year 400 15 yearS Solarex Initial cost Annual maintenance cost Annual savings in heating costs Salvage value (end of life Expected life 1,000/year 500 20 years Use an analysis period of 20 years. Select the most desirable one based on a MARR of 5% using the following methods: a. Internal rate of return b. Payback period c. Benefit/cost

Explanation / Answer

Solarex Softech Initial cost 10000 6000 Annual savings 1000 700 AMC 100 50 Net annual savings 900 650 Salvage value 500 400 Life 20 15 MARR 6% 6% a. Or use linear interpolation - AT IRR ; NPV = 0 (i) Solarex Year Cash Flow PV Factors Present value 6% 7% 15% 20% 0 -10000 1 1 -10000 -10000 1 to 20 900 11.4699 10.5940 10322.9291 9534.612821 20 500 0.311804727 0.258419003 155.9023634 129.2095014 478.8314602 -336.1776776 r= NPV = 6% 478.8314602 r 0 7% -336.1776776 r-6/7-6 = (0-478.83)/(-336.18-478.83) r-6 = 0.5875 x 1 r = = 6+ 0.5875 r = 6.59% Approx (ii) Softech Year Cash Flow PV Factors Present value 7% 8% 15% 20% 0 -6000 1 1 -6000 -6000 1 to 15 650 9.1079 8.5595 5920.144103 5563.661147 15 400 0.36244602 0.315241705 144.9784079 126.096682 65.12251118 -310.2421709 r= NPV = 7% 65.12251118 r 0 8% -310.2421709 r-7/8-7 = (0-65.12)/(-310.24 - 65.12) r-7 = 0.1734 x 1 r = 7+0.1734 r = 7.17% Approx (b) Payback period - Payback period = Solarex = 10000/900 = 11.11111111 Softech = 6000/650 = 9.230769231 (c ) Profitability Index (Cost benefit) = PV of cash inflows/initial investment = Solarex Softech Initial cost 1 10000 6000 Net annual savings 2 900 650 Salvage value 3 500 400 Life 4 20 15 MARR 5 6% 6% PVAF(6%, Life) 6 11.4699 9.7122 PVIF(6%, Life) 7 0.311804727 0.417265061 PV of net annual savings 8 =(2 x 6) 10322.9291 6312.961842 Pv of Salvage value 9 =(3 x7) 155.9023634 166.9060243 Total cash inflow 10 = 8 + 9 10478.83146 6479.867866 PI = 10 by 1 1.047883146 1.079977978 Conclusion - Solarex Softech Remarks IRR 6.59% 7.17% Softech with higher IRR Payback 11.11111111 9.230769231 Softech with lower Payback Cost benefit 1.047883146 1.079977978 Softech with higher PI Softech should be selected. Please provide feedback……... thanks in advance……… :-)

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