Question

An investment project has annual cash inflows of $3,300, $4,200, $5,400, and $4,600, and a discount rate of 15 percent.

  

What is the discounted payback period for these cash flows if the initial cost is $6,000? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Discounted payback period

years

  

What is the discounted payback period for these cash flows if the initial cost is $8,100? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Discounted payback period

years

  

What is the discounted payback period for these cash flows if the initial cost is $11,100? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Discounted payback period

years

Answer 1

Discounted PBP is the period in which initial investment is recovered after considering the time value of Money.

Year	Opening Bal	CF	PVF @15%	Disc CF	Clsoing Bal
1	$ 6,000.00	$ 3,300.00	0.8696	$ 2,869.57	$   3,130.43
2	$ 3,130.43	$ 4,200.00	0.7561	$ 3,175.80	$       -45.37
3	$      -45.37	$ 5,400.00	0.6575	$ 3,550.59	$ -3,595.96
4	$ -3,595.96	$ 4,600.00	0.5718	$ 2,630.06	$ -6,226.02

Disc PBP = Period in which least +ve CB + [ CB at that Year / Disc CF in Next Year ]

= 1 + [ 3130.43 / 3175.80 ]

= 1 + 0.99

= 1.99 Years:

Part B:

Year	Opening Bal	CF	PVF @15%	Disc CF	Clsoing Bal
1	$ 8,100.00	$ 3,300.00	0.8696	$ 2,869.57	$   5,230.43
2	$ 5,230.43	$ 4,200.00	0.7561	$ 3,175.80	$   2,054.63
3	$ 2,054.63	$ 5,400.00	0.6575	$ 3,550.59	$ -1,495.96
4	$ -1,495.96	$ 4,600.00	0.5718	$ 2,630.06	$ -4,126.02

Disc PBP = Period in which least +ve CB + [ CB at that Year / Disc CF in Next Year ]

= 2 + [ 2054.63 / 3550.59 ]

= 2 + 0.58

= 2.58 Years

Part C:

Year	Opening Bal	CF	PVF @15%	Disc CF	Clsoing Bal
1	$ 11,100.00	$ 3,300.00	0.8696	$ 2,869.57	$   8,230.43
2	$   8,230.43	$ 4,200.00	0.7561	$ 3,175.80	$   5,054.63
3	$   5,054.63	$ 5,400.00	0.6575	$ 3,550.59	$   1,504.04
4	$   1,504.04	$ 4,600.00	0.5718	$ 2,630.06	$ -1,126.02

Disc PBP = Period in which least +ve CB + [ CB at that Year / Disc CF in Next Year ]

= 3 + [ 1504.04 / 2630.06]

= 3 + 0.57

= 3.57 Years