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 10 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	-1,070	100	500	700	700	300	700

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

Multiple Choice

• 2.83 years, accept

• 2.92 years, accept

• 3.08 years, reject

• 3.09 years, reject

Answer 1

Determination of Discounted Pay back period:

Year	Cash flows	Disc @ 10%	Discounted Cash flows( Cash flow * Discounting Factor)	Cummultive Discount cash flows
1	$100	0.9091	$90.91	$90.91
2	$500	0.8264	$413.22	$ 90.91+$ 413.22= $ 504.13
3	$700	0.7513	$525.92	$ 504.13+$525.92= $ 1030.05
4	$700	0.6830	$478.11	$ 1030.05+$ 478.11= $ 1508.16
5	$300	0.6209	$186.28	$ 1508.16+$ 186.28= $ 1694.44
6	$700	0.5645	$395.13	$ 1694.44+$ 395.13= $ 2089.57

Initial Outlay = $ 1070

Pay Back Period = Years before full recovery +( Unrecovered amount at the start of the year/ Casf flow during the year)

= 3+ ( $ 1070-$ 1030.05)/ $ 478.11

= 3+ $ 39.95/$ 478.11

= 3+0.8355

= 3.083 years

Discounted pay back period is 3.083 years but the Firm cut off period is 3 years. Since the Discounted pay back period is more than the cut off period, so we should reject the Project.

Hence Option 3) 3.08 years, reject the Project is the Correct answer.

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