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The Callaway Cattle Company is considering the construction of a new feed handling system for its feed lot in​ Abilene, Kansas. The new system will provide annual labor savings and reduced waste totaling $ 185 comma 000 while the initial investment is only ​$485 comma 000. ​ Callaway's management has used a simple payback method for evaluating new investments in the past but plans to calculate the discounted payback to analyze the investment. Where the appropriate discount rate for this type of project is 9 ​percent, what is the​ project's discounted payback​ period?

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Answer:

Payback period= 3.13 years

Explanation:

Giving the following information:

The new system will provide annual labor savings and reduced waste totaling $ 185,000 while the initial investment is only ​$485,000. ​ The appropriate discount rate for this type of project is 9 ​percent.

Year 1= (185,000/1.09) - 485,000= -315,275.23

Year 2= (185,000/1.09^2) - 315,275.23= -159,564.43

Year 3= (185,000/1.09^3) - 159,564.43= -16,710.49

Year 4= (185,000/1.09^4) - 16,710.49= 114,348.17

Payback period= 3 years + (16710.49/131,058.66)= 3.13 years

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