Question

Heinlein Inc is considering investing in a project with a cost of $100k. The project is expected to produce cash flows of $50 in year 1, 80 in year 2, and 215 in year 3. If the discount rate is 0.09 what is the discounted payback period.  

Answer 1

The discounted payback period (DPP) is the amount of time that it takes (in years) for the initial cost of a project to equal to discounted value of expected cash flows, or the time it takes to break even from an investment. In order to calculate the answer, we first need to calculate the discounted value of these cashflows:

CF0 = $100k, CF1 = $50k, CF2 = $80k, CF3 = $215.

We first need to calculate the discounted values for each cashflows at time perior t=0.

Year	Cashflow	Discounted cashflow
0	($100,000)	= -100000\(1 + 0.09)^0 = -100,000
1	$50,000	= 50000\(1 + 0.09)^1 = 45,871.6
2	$80,000	= 80000\(1 + 0.09)^2 = 67,334.4
3	$215,000	= 215000\(1 + 0.09)^3 = 166,019.4

Now, first discounted cash inflow (year 1) is $45,871.56. In order to re-earn the invested amount of $100,000,  $54,128.44 more is needed. But discounted cashflow for year 2 is 67,333.4 which is higher than what we require. Hence the fraction of year to earn $54,128.44 = $54,128.44/$67,333.4 = 0.80 year

Discounted payback period = 1 year + 0.80 year = 1.80 years