Question

Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 12 percent, and that the maximum allowable payback and discounted payback statistic for the project are 2 and 3 years, respectively.

Time	0	1	2	3	4	5	6
Cash Flow	-1,150	30	570	770	770	370	770

Use the discounted payback decision rule to evaluate this project; should it be accepted or rejected?

Multiple Choice

• 2.75 years, accept

• 3.25 years, reject

• 2.67 years, accept

• 3.33 years, reject

Please show math, excel formulas preferred, thanks!

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 @12%	Disc CF	Clsoing Bal
1	$ 1,150.00	$    30.00	$      0.89	$    26.79	$ 1,123.21
2	$ 1,123.21	$ 570.00	$      0.80	$ 454.40	$    668.81
3	$    668.81	$ 770.00	$      0.71	$ 548.07	$    120.74
4	$    120.74	$ 770.00	$      0.64	$ 489.35	$ -368.61
5	$ -368.61	$ 370.00	$      0.57	$ 209.95	$ -578.55
6	$ -578.55	$ 770.00	$      0.51	$ 390.11	$ -968.66

Disc PBP = Year in which least +ve Closig Bal + [ Bal at that year / Disc CF in next year ]

= 3 + [ 120.74 / 489.35 ]

= 3 + 0.25

= 3.25 Years

As Disc PBP > Required Disc PBP, Project shall be rejected.

Option B is correct.