Question

Compute the discounted payback statistic for Project D if the appropriate cost of capital is 13 percent and the maximum allowable discounted payback is four years. (Do not round intermediate calculations and round your final answer to 2 decimal places. If the project does not pay back, then enter a "0" (zero).

PROJECT D:

TIME               0                    1                     2                      3                4              5

Cash Flow    $ -11,800          $3,430             $4,340           $1,680             $0          $1,160

Discounted Payback Period =

Should this be rejected YES or NO

Answer 1

Cash flow for the Project D are

Year	0	1	2	3	4	5
Cash flow	-11800	3430	4340	1680	0	1160

For calculating the discounted payback period, one needs to first find the discounted cash flow for each of the year

Discounted cash flow for a year = Cash flow for a year / (1 + discount rate)ⁿ

where discount rate = cost of capital and n= year of cash flow

Discounted cash flow for a year 0 = -11800 / (1 + 13%)⁰ = -11800

Discounted cash flow for year 1 = 3430 / (1 + 13%)¹ = 3430 / 1.13 = 3035.3982

Discounted cash flow for year 2 = 4340 / (1 + 13%)² = 80 / 1.13² = 3398.8566

Similarly we can find the discounted cash flow for other years, we get the following values

Year	0	1	2	3	4	5
Cash flow	-11800	3430	4340	1680	0	1160
Discounted Cash flow	-11800.0000	3035.3982	3398.8566	1164.3243	0.0000	629.6015

We will now calculate the cumulative discounted cash flows

Cumulative discounted cash flow for year 0 = Discounted cash flow for 0 = -11800

Cumulative discounted cash flow for a year = Cumulative discounted cash flow for previous year + discounted cash flow for a year

Cumulative discounted cash flow for year 1 = Cumulative discounted cash flow for previous year 0 + discounted cash flow for year 1 = --11800 + 3035.3982= - 8764.6018

Cumulative discounted cash flow for year 2 = Cumulative discounted cash flow for previous year 1 + discounted cash flow for year 2 = -8764.6018 + 3398.8566= -5365.7452

In a similar way, one can find the cumulative discounted cash flow for other years, we get following table

Year	0	1	2	3	4	5
Cash flow	-11800	3430	4340	1680	0	1160
Discounted Cash flow	-11800.0000	3035.3982	3398.8566	1164.3243	0.0000	629.6015
Cumulative discounted cash flow	-11800.0000	-8764.6018	-5365.7452	-4201.4209	-4201.4209	-3571.8194

As cumulative discounted cash flows do not become positive during the lifetime of the project, hence project does not pays back its initial investment.during its life time

As given in the question if project dose not pay back, then one should enter a '0'

Hence, For answer: Discounted Payback period: 0

It is know that project does not pay back during life time of 5 years and maximum allowable discounted payback is 4 years. Therefore we observe the project is unable to recover its investment in 4 years on the basis of discounted payback. Hence project should be rejected

For Answer : Should this be rejected: Yes