Question

11-8: Payback Period Discounted payback Project K costs $40,000, its expected cash inflows are $9,000 per year for 8 years, and its WACC is 11%. What is the project's discounted payback? Round your answer to two decimal places. years

Answer 1

Year 0: -40000
Year 1:9000
Year 2:9000
Year 3:9000
Year 4:9000
Year 5:9000
Year 6:9000
Year 7:9000
Year 8:9000

Discounted net cash flows at the wacc of 11%:
Year 0: -40000
Year 1:9000/(1+11%)^1=8108.108108
Year 2:9000/(1+11%)^2=7304.601899
Year 3:9000/(1+11%)^3=6580.722432
Year 4:9000/(1+11%)^4=5928.578767
Year 5:9000/(1+11%)^5=5341.061953
Year 6:9000/(1+11%)^6=4811.767525
Year 7:9000/(1+11%)^7=4334.925698
Year 8:9000/(1+11%)^8=3905.338467

Cumulative discounted net cash flows are:
Year 0: -40000
Year 1:8108.108108-40000=-31891.89189
Year 2:7304.601899-31891.89189=-24587.28999
Year 3:6580.722432-24587.28999=-18006.56756
Year 4:5928.578767-18006.56756=-12077.98879
Year 5:5341.061953-12077.98879=-6736.926837
Year 6:4811.767525-6736.926837=-1925.159312
Year 7:4334.925698-1925.159312=2409.766386
Year 8:3905.338467

Discounted payback period=Full years until recovery +(Unrecovered cost at the beginning of last year)/(Cash flow during the last year)
=6+(1925.159312)/(4334.925698)
=6.44 years