Question

Compute the Discounted Payback statistic for Project X and recommend whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent and the maximum allowable discounted payback is 3 years.

Time:	0	1	2	3	4	5
Cash flow:	-980	380	600	520	420	270

Multiple Choice

• 2.78 years, accept

• 3.44 years, reject

• 2.44 years, accept

• 4.78 years, reject

Answer 1

Given cash flow about a project X,

Cost of capital for the project Kc = 12%

Its discounted cash flow and cumulative discounted cash flows are also calculated as below:

discounted cash flow = cash flow/(1+Kc)^year

cumulative discounted cash flow = previous year cumulative discounted cash flow + current year discounted cash flow

Year	Cash flow	Discounted Cash flow	Cumulative discounted cash flow
0	$     -980.00	$                          -980.00	$                                                   -980.00
1	$       380.00	$                            339.29	$                                                   -640.71
2	$       600.00	$                            478.32	$                                                   -162.40
3	$       520.00	$                            370.13	$                                                     207.73
4	$       420.00	$                            266.92	$                                                     474.65
5	$       270.00	$                            153.21	$                                                     627.85

Discounted Payback period of a project = year before the cumulative discounted cash flow turns positive + (discounted cumulative cash flow of period before recovery/discounted cash flow of recovery period)

So, here Payback period = 2 + 162.40/370.13 = 2.44 years

Since maximum allowable discounted payback period is 3 years and projects discounted payback period is 2.44 years, Project should be accepted.

Option C is correct.