Question

​(Discounted payback period​) You are considering a project with the following cash​ flows:

YEAR   PROJECT
CASH FLOW
0   -40,000
1   15,000
2   15,000
3   15,000
4   15,000

If the appropriate discount rate 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

The cash flows are:
Year 0:-40000
Year 1:15000
Year 2:15000
Year 3:15000
Year 4:15000

Formula to calculate the discounted value=Cash flow/(1+discount rate)^Number of years
Given that the discount rate is 12%.

Discounted cash flows are calculated as:
Year 0:-40000/(1+12%)^0=-40000/(1.12)^0=-40000/1=-40000
Year 1:15000/(1+12%)^1=15000/(1.12)^1=15000/1.12=13392.85714
Year 2:15000/(1+12%)^2=15000/(1.12)^2=15000/1.2544=11957.90816
Year 3:15000/(1+12%)^3=15000/(1.12)^3=15000/1.404928=10676.70372
Year 4:15000/(1+12%)^4=15000/(1.12)^4=15000/1.57351936=9532.771176

Now, cumulative discounted cash flows are:
Year 0:-40000
Year 1:13392.85714-40000=-26607.14286
Year 2:11957.90816-26607.14286=-14649.2347
Year 3:10676.70372-14649.2347=-3972.53098
Year 4:9532.771176-3972.53098=5560.240196

Payback period=Full years until recovery + (Unrecovered cost at the beginning of last year)/(Cash flow during the last year)
Full years until recovery=3
Unrecovered cost at the beginning of last year=3972.53098
Cash flow during the last year=9532.771176
Payback period=3+3972.53098/9532.771176=3+0.416723627=3.416723627 or 3.42 years (Rounded up to two decimal places)

So, the discounted payback period=3.42 years