Question

Find the discounted payback period for the following project. The discount rate is 10%

	Project X
Initial Outlay	$8,845
Year 1	$3,480
Year 2	$3,765
Year 3	$5,094
Year 4	$6,366

Round the answer to two decimal places.

Answer 1

Present Value factor

= 1 / ( 1 + r) ^ n

Where,

r = Discount rate = 10% or 0.10

So, PV Factor for year 2 will be

= 1 / ( 1.10 ^ 2)

= 1 / 1.21

= 0.826446

The following table shows the calculations :

Discounted Payback Period = A +	B
	C

Where,
A = Last period with a negative discounted cumulative cash flow;
B = Absolute value of discounted cumulative cash flow at the end of the period A; and
C = Discounted cash flow during the period after A.

Calculations	A	B	C = A x B	D = Sum C
Period	Cash Flow	PV Factor	Present Value	Cumulative
0	-8,845.00	1	-8,845.00	-8,845.00
1	3,480.00	0.909091	3,163.64	-5,681.36
2	3,765.00	0.826446	3,111.57	-2,569.79
3	5,094.00	0.751315	3,827.20	1,257.40
4	6,366.00	0.683013	4,348.06	5,605.47

So, as per above formula, discounted payback period

= 2 + | -2569.79| / 3827.19

= 2.67 Years