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Just because a​ project's payback period is relatively long​ doesn't mean it is not profitable in the long run. Consider an investment in LED lights with a price tag of ​$225 comma 000. The estimated annual savings in electricity and routine maintenance is ​$40 comma 700 and the life of the LED lights is 15 years. Assume that the payback period of three years or less is desired by the investor. a. What is the simple payback period for the​ lights? b. What is the IRR of this​ investment? c. What do you conclude from Part ​(a) and Part ​(b)​?

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letmeanswer

Solution:

a. Since annual net revenue increase is equivalent i.e. any duration of the same cash flow), the plan payback period can be determined with the following formula:

[tex]\bold{Payback \ period = \frac{Investment \ required}{Net \ annual \ cash \ inflow}}[/tex]

[tex]\Rightarrow \frac{\$225,000}{\$40,700}[/tex]

[tex]\Rightarrow 5.5 years[/tex]

The simple payback period for the lights is 5.5years

b. See the inner Return Factor value (5.5) for the current Return Factor of 15 years for [tex]\$1[/tex] panel. After this factor has been located see the corresponding Rate of Interest, It is [tex]16\%[/tex].

c. The conclusion is both Part (a) and Part (b).

Answer:

(a)   investment in LED=$225,000

       Annual savings in electricity and routine maintenance =​$40,700

Simple Payback Period =Investment Outlay =  $225,000 =5.528 years

                                              Annual Savings       $40,700

(b)  The IRR of this​ investment=    rα+ NPVα    (rβ-rα)

                                                          (NPVα-NPVβ)

Where  IRR is Internal Rate of Return

             NPV  stand for Net Present Value

             rα=Lower discount rate chosen

            rβ= Higher discount rate chosen

           NPVα= NPV at rα

            NPVβ= NPV at  Rβ

DCF stands for Discount Factor.

Calculation of NPVα & NPVβ

Year          $              DCF@10%   PV               DCF@15%                PV

0          (225,000)        1             (225,000)          1                      (225,000)    

1-15          40,700        4.1772         170,014           8.1371             331,178.41

                                                       (54,986)                                106,178.41

rα=10% ; rβ=15% ; NPVα= (54,986); NPVβ=106,178.41

IRR=10%+ (54,986) (15%-10%)          =0.1+ (0.3412)(0.5)=0.2705=27.05%  

                   (54,986)-106,178.41

IRR=27.05%

(c) Conclusions:

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.                                              

Explanation:

Payback period means the time required to get back money spent on an investment through annual savings or cash inflow.

Internal Rate of Return (IRR) refers to the interest rate at which the net present value of all the cash flows from an investment equal zero.

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