Answer:
(a)   investment in LED=$225,000
        Annual savings in electricity and routine maintenance =$40,700 
<em>Simple Payback Period </em>=<u>Investment Outlay </u>=  <u>$225,000 </u> =5.528 years
                                               Annual Savings       $40,700
(b)  <em>The IRR of this investment=    </em><em><u>rα+ NPVα    (rβ-rα)</u></em>
<em>                                                           (NPVα-NPVβ)</em>
<em>Where  IRR is Internal Rate of Return</em>
<em>              NPV  stand for Net Present Value</em>
<em>              rα=Lower discount rate chosen</em>
<em>             rβ= Higher discount rate chosen</em>
<em>            NPVα= NPV at rα</em>
<em>             NPVβ= NPV at  Rβ</em>
<em> DCF stands for Discount Factor.</em>
<em>Calculation of NPVα & NPVβ</em>
<u><em>Year          $              [email protected]%   PV               [email protected]%                PV</em></u>
 0          (225,000)        1             (225,000)          1                      (225,000)    
1-15          40,700        4.1772         <u>170,014    </u>       8.1371             <u>331,178.41</u>
                                                       <em><u>  (54,986)   </u></em><u>  </u>                            <em><u>106,178.41</u></em>
<em><u /></em>
rα=10% ; rβ=15% ; NPVα= (54,986); NPVβ=106,178.41
IRR=10%+<u> (54,986) (15%-10%) </u>          =0.1+ (0.3412)(0.5)=0.2705=27.05%   
                    (54,986)-106,178.41
<em>IRR=27.05% </em>
<em>(c) Conclusions:</em>
Part (a): The payback calculated above is 5 years and 6 months. This did not meet payback period of three years or less desirable by the investor.
Part (b): IRR of 27.05% should be compared with the firm cost of capital. If firm cost of capital is lower than 27.05%, the project should be accepted otherwise, it should rejected.                                              
<em></em>
Explanation:
<em>Payback period</em> means the time required to get back money spent on an investment through annual savings or cash inflow. 
<em>Internal Rate of Return (IRR)</em> refers to the interest rate at which the net present value of all the cash flows from an investment equal zero.