Question

(Discounted payback period) 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 $195,000 while the initial investment is only $490,000. 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 12 percent, what is the project's discounted payback period? The project's discounted payback period is years. (Round to two decimal places.)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

PAJ A B C D E F G 1 Discount rate 12% Year 0 1 CF P VF(12%) ($490,000.00) 1.000000 $195,000.00 0.89286 $195,000.00 0.79719 $195,000.00 0.71178 $195,000.00 0.63552 $195,000.00 0.56743 PV CF ($490,000.00) $174,107.14 $155,452.81 $138,797.15 $123,926.03 $110,648.24 Cumulative PV CF ($490,000.00) ($315,892.86) ($160,440.05) ($21,642.90)| $102,283.12 $212,931.36 5 11 12 Discounted Payback Period 3.17 years 15 2 Discount rate 8% 17 Year 0 1 Project A ($110,000.00) $31,000.00 $31,000.00 $31,000.00 $31,000.00 $31,000.00 $13,774.01 Project B ($110,000.00) $0.00 $0.00 $0.00 $0.00 $240,000.00 $53,339.97 3 5 NPV 25 Project-B is recommended as it has higher NPV

Cell reference -

A B C D E F 1 2 1 Discount rate 0.12 Year СЕ 5 6 O 1 -490000 195000 195000 195000 195000 195000 PVF(12%) =1/(1+$C$2)^B5 =1/(1+$C$2)^B6 =1/(1+$C$2^B7 =1/(1+$C$2)^B8 =1/(1+$C$2)^B9 =1/(1+$C$2)^B10 | PV CF Cumulative PV CF =C5*D5 =E5 =C6*D6 =F5+E6 1=C7*D7 =F6+E7 =C8*D8 =F7+E8 =C9*D9 =F8+E9 =C10*D10 =F9+E10 3 10 5 12 Discounted Payback Period =B8+(-F8/(F9-F8)) years 14 0.08 15 2 Discount rate 16 17 Year Project A Project B -110000 -110000 31000 31000 0 31000 lo 31000 31000 240000 =C18+NPV(C15, C19:C23) =D18+NPV(C15,D19:D23) | 24 NPV Project-B is recommended as it has higher NPV

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.