Answer: 3.83 years
Step-by-step explanation:
The Discounted Payback period is used to determine how long it would take a project to payback the investment made in it given required return adjusted cashflows.
Year 1.
= 17,000 / ( 1 + 11.4%)
= $15,260
Year 2
= 20,000/ 1.114²
= $16,116
Year 3
= 27,000/1.114³
= $19,530
Year 4
= 30,000/1.114⁴
= $19,480
Investment Balance up to year 3
= -67,000 + 15,260 + 16,116 + 19,530
= -$16,904
The amount left is smaller than the discounted Cashflow for Year 4 so the Investment will be paid back in year 4.
= 16,904/19,480
= 0.83
0.83 of year 4 will be taken to pay off Investment.
In total;
= 3 complete years + 0.83 in 4th year
= 3.83 years.